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sha256:6e3384deba1be1b2903b7399c313253d73b6f11738e951e783ad02c7235dfdf9 +size 813959 diff --git a/49E1T4oBgHgl3EQf6QXo/content/tmp_files/2301.03522v1.pdf.txt b/49E1T4oBgHgl3EQf6QXo/content/tmp_files/2301.03522v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..333c12461c6b702065d1a54c7241baf8dae43b5e --- /dev/null +++ b/49E1T4oBgHgl3EQf6QXo/content/tmp_files/2301.03522v1.pdf.txt @@ -0,0 +1,515 @@ +arXiv:2301.03522v1 [gr-qc] 9 Jan 2023 +A Comment on “Traversable wormhole dynamics +on a quantum processor” +Galina Weinstein +Reichman University, The Efi Arazi School of Computer Science, Herzliya; +University of Haifa, The Department of Philosophy, Haifa, Israel. +January 10, 2023 +Abstract +There has been a lot of buzz surrounding the latest Nature paper, +”Traversable wormhole dynamics on a quantum processor”. The Nature +paper discusses an experiment in which Google’s Sycamore quantum pro- +cessor is used to simulate a sparsified version of an SYK model. It is shown +that the simplified model preserves the key gravitational characteristics of +the original SYK model and that it is sufficient to produce a traversable +wormhole behavior. The experiment does not create an actual wormhole. +Rather, the team of researchers shows an equivalence between a gravity +picture and a quantum information picture. This paper gives an account +of the experiment and addresses philosophical questions arising from the +theoretical and experimental work. +1 +Quantum chaos and scrambling +Let us begin with the quantum butterfly effect, which is essential for the under- +standing of the experiment. The butterfly effect implies scrambling [5]. Quan- +tum scrambling is the quantum analog of chaotic dynamics in classical systems. +Scrambling describes many-body dynamics which, though ultimately unitary, +scatter initially localized quantum information across all of the system’s avail- +able degrees of freedom. Black holes are the fastest scramblers in the universe +and are therefore the most chaotic bodies in the cosmos [14]; [1]. +More specifically, quantum information present in a small local area of space +spreads out, and we must search a large region to recover the information. +This is the scrambling of the quantum information while the system evolves. +Heisenberg’s operators evolve in a way that reminds the chaotic butterfly effect: +they were first local, and now they are spread over many regions in space. This +is the butterfly effect in quantum systems. +It should be stressed that when we speak about black holes, we are not +talking about black holes that form from gravitational collapse. Rather what +1 + +is meant by black holes here and thereafter is eternal black holes (two-sided +black holes) or two anti-de Sitter space (Ads) black holes. The eternal black +hole is dual to two copies of the original conformal field theory (CFT) in the +thermofield double (TFD) state. +The TFD state is an entangled pure state +between two identical copies of the quantum system (CFT): +1 +√ +Zβ +|T FDβ⟩ = eβ(HL+HR) |nn⟩L,R . +(1) +Tracing out one of the copies HL (the SYK Hamiltonian applied to the +left system) or HR (the SYK Hamiltonian applied to the right system) gives a +thermal state (with Majorana fermions). In other words, tracing out either copy +produces the thermal density matrix at inverse temperature β. The |nn⟩L,R is +the thermofield double state at an infinite temperature. +The left and right +external bulk regions of the eternal black hole are joined through a wormhole +and are thus dual to the TFD state [10]. +The models for the onset and dynamics of quantum chaos are called the +Sachdev-Ye-Kitaev (SYK) models. The SYK models lead to scrambling and +spreading of the information among the quantum many-body system. But the +SYK models possess gravity duals. +They are also a paradigm for quantum +holographic matter and the gravitational interpretation through the holographic +principle or duality (the AdS/CFT correspondence or gauge/gravity duality); +the equivalence between two descriptions of the same system: quantum gravity +in (d+1) dimensions, on the one hand, and quantum field theory in d dimensions, +on the other. +The above characteristics of the SYK Hamiltonian for N fermions have led +to realizing holographic physics in the laboratory, what is called quantum gravity +in the lab. I will further discuss quantum gravity in the lab in section 9. +An SYK model becomes extremely chaotic at the very beginning of its devel- +opment. In the SYK model, the out-of-time-order correlation (OTOC) functions +are used to diagnose quantum chaos, and measure the growth of operators in +space, unitarily evolving (in the Heisenberg interpretation of quantum mechan- +ics) as a function of time. With chaotic time evolution, the butterfly effect will +cause most of the OTOC functions in the average to decay exponentially [5]. +In the semi-classical limit (in quantum systems with many degrees of free- +dom), this scrambling of information and operator growth due to chaotic behav- +ior is exponential and is measured using the quantum Lyapunov exponent. But +unlike the classical Lyapunov exponent, there exists a bound on the quantum +Lyapunov exponent. This is additionally measured by the butterfly velocity, the +very equivalent measure of the classical chaotic butterfly effect. The quantum +Lyapunov exponent and the scrambling rate are the ones that characterize the +beginning and appearance of quantum chaos in this system [11]. +It should be noted that an interesting characteristic of the SYK model, which +is related to the quantum Lyapunov exponent and the OTOC, is that the model +exhibits maximally chaotic behavior. It means that like eternal black holes, the +SYK model is a very fast scrambler of information. There is another important +2 + +quantity called, Loschmidt echo, which is intimately tied to quantum chaos. The +echo is defined as the probability that the chaotic system would return to its +initial state. +As said above, we characterize quantum scrambling and quantum chaos by +measuring the OTOC function. However, OTOCs do not generally discriminate +between quantum scrambling and the effects of both ordinary quantum deco- +herence and experimental noise: quantum scrambling and classical noise lead +the OTOC to decay exponentially with time. It is a major problem if quantum +scrambling is indistinguishable from quantum decoherence and noise, where the +information in a system is lost to the environment [9];[15]. +Isolated systems are idealized models but unfortunately, realistic systems +are open systems and are in interaction with the environment. Suppose there +is a system of n qubits. +This system is not an isolated and closed system. +The n qubits are interacting with many interfering particles in the complex +environment. It is almost impossible to follow the dynamics of each particle, +so what we have here is a system that is many-body system, and decoherence +induced by the environment. As the system evolves, the n qubits get entangled +with the many-body system of the environment, and there are more disturbances +and perturbations and more degrees of freedom. Decoherence happens naturally +to quantum computers since like scrambling, qubits can’t be perfectly isolated +from the environment. +It was found that a quantum teleportation protocol enables one to differen- +tiate between scrambling and decoherence. Thus using teleportation one can +verify scrambling behavior even in the face of decoherence and experimental +imperfection [1];[15]. +2 +SYK models and holography +The SYK Hamiltonian is a model for quantum chaos and holography. That +is, there is correspondence between the SYK model and scrambling/quantum +chaotic behavior on the one hand, and eternal black holes, on the other. This +dual possibility led a team of researchers to the realization that they might +be able to create a model of teleportation through a traversable wormhole. +They discovered that a process called unscrambling comes after scrambling in a +wormhole. The discovery of a process of scrambling followed by unscrambling +has boosted the possibility of realizing a quantum mechanism called size wind- +ing in the lab. This process completely goes against everything we know from +classical chaos and irreversibility. The size-winding mechanism is reminiscent +of Poincare’s Recurrence Theorem of classical physics. But in the dual gravi- +tational interpretation, size-winding leads to the interesting conclusion that a +particle can pass through a wormhole (a holographic wormhole). +The protocol is the following: on the left side of the wormhole, the infor- +mation is scrambled. Since the two sides, right and left of the wormhole are +connected (coupled), the information, i.e., qubits, is unscrambled and pops up +on the right side. Two essential things enable traversability: the two sides of +3 + +the wormhole must be entangled before sending the information and the two +sides must be coupled after sending the message. +It was thought that it was possible to study the dynamics of a wormhole, +through which a qubit can pass, by simulating the SYK model of N Majorana +fermions. It was suggested that realizing the holographic SYK model on the +Google Sycamore chip might open a window to an understanding of the quantum +gravity of holographic traversable wormholes. +The SYK models of a quantum many-body system simulate the scrambling- +unscrambling method. +According to the holographic principle, systems that +are not gravitational but are entangled will exhibit properties that are identical +to quantum gravity. Hence, reasoned the team of researchers, an experiment +implementing the entanglement of qubits can be performed in the laboratory +to test theories of quantum gravity. This experiment consists of two entangled +systems of n qubits, on the right and n qubits on the left. In this protocol +obviously, the dynamics of the system are chaotic (quantum mechanically) and +is described by the SYK model. +One inserts a qubit (the message) on the left side of the system (L subsys- +tem), and it evolves in time. The qubit is entangled with one of the qubits on +the L subsystem. It means that the qubit begins to spread among the n qubits +(a small number of qubits) on the left side, and in all parts of the subsystem. +After a certain time, the qubit is entangled with the qubits of the L subsystem. +But then the qubit suddenly reappears, is unscrambled, and recoheres on the +other side, the right side (R), very far from the L side, where it was scrambled. +There is something that caused the original qubit, which entered on the +far-left side, to suddenly be focused on the far-right side at a future time, even +though it was completely mixed up on the left side. +It is bizarre from the quantum mechanical point of view, says the team of +researchers, but what makes things less weird is that it may be explained or in- +terpreted using the paradigm of quantum gravity and the holographic principle: +a traversable wormhole protocol is equivalent to the above quantum information +protocol [2]. +We start from two separated black holes, the so-called scramblers. The tele- +ported signal reappears on the right side when the two black holes are connected +by a wormhole. In the quantum system, we speak of the method of scrambling- +unscrambling. But with respect to a wormhole, the above mechanism is called +teleportation-by-size, a protocol of quantum teleportation through the worm- +hole, i.e., information transmission is dependent on operator-size growth. +So, argues the team of researchers, if we imagine that the two sides of the +system represent two sides of the eternal black holes (L and R) that are con- +nected by a wormhole, then the explanation for the phenomenon is simpler. A +teleported message is sent through an emergent wormhole: it is injected into L +and arrives at R later due to a coupling operator [2]. +4 + +3 +Perfect size winding +The above scenario requires perfect size winding. The team of researchers first +describes size-winding purely from the boundary point of view and then applies +it to the traversable wormholes (in the bulk). +In the Heisenberg picture, near the scrambling time (just before the onset of +the chaotic behavior) for the SYK model, a thermal operator P is inserted at a +negative time into the left boundary (the left side L). Recall that the growth +of the size of an operator is a basic manifestation of quantum chaos and com- +plexity of the system. The operator-size distribution is winding in the clockwise +direction. A coupling is applied between the two subsystems L and R. The +LR coupling unwinds the complex winding of the operator size distribution, it +winds the size distribution in the opposite direction, accurately reversing the +winding direction. The thermal operator P from the left side will be exactly +mapped to its right side. We obtain a counterclockwise size distribution corre- +sponding to a thermal operator P inserted on the other boundary (the right side +R) at a positive time [2]. The team of researchers stresses: ”We explicitly show +size-winding of thermal operators near the scrambling time for the SYK model, +and we conjecture that the phenomenon can also be found in other holographic +systems” [13]. +Perfect size winding provides a necessary condition for traversable wormhole +behavior. It occurs in the ground state, the state of lowest possible energy where +the temperature is zero (low temperature through the wormhole). +The team of researchers expects systems with a holographic dual to exhibit +perfect size winding [13]. In other words, the SYK model is dual to a traversable +wormhole only in the low-temperature regime, and it exhibits perfect size wind- +ing in the low-temperature limit. But this applies to large N Majorana fermions +interacting with large q other Majorana fermions (teleportation of q fermions). +The team of researchers then pondered: What is the most simplified Hamil- +tonian that preserves the gravitational physics of the original SYK model? How +many qubits do we need to simulate this Hamiltonian on a quantum device? It +was shown that N = 10 was sufficient to produce the traversable wormhole be- +havior. The team employed learning techniques to construct a sparsified version +of the SYK model. Sparsification reduces the complexity of the system. +A simplified learned Hamiltonian was constructed. Its ground state was close +to a TFD state. Techniques from machine learning (and a kind of approximation +called Trotterization) were applied to optimize the procedure. The techniques +were performed on a classical computer. The sparsification procedure reduced +the SYK model to a sparse N = 10 SYK model. ”We choose q = 4” fermions +interacting with N other fermions of the simplified version of the SYK Hamil- +tonian, ”and demonstrate gravitational physics at sufficiently small N”, where +N = 7. +Since ”The wormhole teleportation protocol also introduces a pair +of entangled qubits, i.e., a reference qubit that is entangled with the injected +qubit”, then ”the total circuit has 9 qubits”. Hence, the sparsified SYK model +was experimentally realized with N = 9 qubits [6]. +It should be mentioned that at about the same time, Leonard Susskind and +5 + +a team of researchers were working on what seems like a bigger project, a sparse +SYK model that recovers the global physics of ordinary SYK models. In par- +ticular, at low temperatures, their model exhibits a gravitational sector that is +maximally chaotic. The sparsity of the model, so writes the team, ”consider- +ably reduces the cost of quantum simulation algorithms”. This, so claims the +team, makes their sparse SYK model ”the most efficient currently known route +to simulate a holographic model of quantum gravity”. The team of researchers +add: ”On a practical level, sparse systems typically admit much more efficient +computer simulations—both classical and quantum. By significantly reducing +the resources needed to simulate black holes in holographic models of quantum +gravity, these results bring us closer to the goal of studying ’quantum gravity +in the lab’” [16]. +4 +Majorana fermions versus transmons +The sparse Hamiltonian is doubled to give left HL and right HR Hamiltonians +with N Majorana fermions on each side. Each side is a simulation of the SYK +model, the learned Hamiltonian. +The wormhole experiment was realized with superconducting qubits on the +Google Sycamore. I would like to emphasize that I am not speaking now of +claims related to quantum supremacy. The Sycamore consists of an array of +54 superconducting qubits called transmons (transmission-line shunted plasma +oscillation qubits). +The transmon is closely related to the charge qubits or +Cooper–Pair–Box (CPB) (Cooper pairs that are tunneling in a Josephson junc- +tion). The transmon fixes the weakness of the CPB and as compared to the +CPB, it greatly reduces charge noise sensitivity in the qubit [8]. +That said, the team of researchers is speaking of the Majorana SYK model +with N fermions with which they produce evidence of gravitational physics +in the sparsified SYK system: ”To encode 7 Majorana fermions on the left +system and 7 Majorana fermions on the right system, we require 7 qubits (two +fermions per qubit)” [6]. The team of researchers also writes: ”we assume that +the total number of qubits (or fermions) on each side is n, and the number +of message qubits (or fermions) that are transmitted by the state transfer or +operator transfer protocols is m” [13]. +This is problematic because it is not at all clear whether one superconducting +transmon qubit represents two Majorana fermions or rather, one transmon qubit +represents one Majorana fermion. +5 +The quantum information picture +The practical steps of the teleportation protocol (step-by-step) in the quantum +information picture (without gravity) are as follows (based on [2]): +1) Two identical copies of the quantum system are prepared: a system of 7 +qubits on the left (side L) and a system of 7 qubits on the right (side R). The +6 + +two subsystems are entangled in the TFD state; that is, we have entangled Bell +pairs shared between L and R. +2) We evolve all the qubits on the side L “backward in time” by acting with +the inverse of the time-evolution operator (exp+iHt). +3) A qubit Q (the message) is injected into L at a certain time (swapped into +side L: a SWAP gate). Now we evolve subsystem L “forward in time” using the +time-evolution operator (exp−iHt). As a result, Q is entangled with a reference +qubit P; Q is then scrambled with P and among the 7 qubits on the subsystem +L (the carrier qubits). +4) We now weakly couple side L to side R (at t = 0), applying a coupling +operator (expiµV , where V is the interaction term and µ represents the coupling +interaction). The coupling is applied suddenly: All the 7 qubits on side L are +now coupled to the 7 qubits on the side R. +5) We now evolve side R “forward in time” using the time-evolution oper- +ator (exp−iHt). Side R is subsequently measured. The qubit Q (the message) +reappears unscrambled, it arrives unscathed at R and there is no need to de- +code it (a final SWAP gate: extract qubit Q from R). The message has been +teleported while being first scrambled and then unscrambled. The teleported +qubit is highly error-protected [4]. +The team of researchers distinguishes between two mechanisms of transmis- +sion with the wormhole circuit [2]: +1) The low-temperature teleportation: If µ < 0, the qubit Q experiences a +time advance and is rescued on the side R. This is wormhole teleportation. +2) On the other hand, when µ > 0 the qubit is entangled with the qubits of +side L but is not unscrambled and its destiny is oblivion. +6 +The gravity picture +According to Occam’s razor, the simplest explanation for the above mecha- +nism is teleportation-by-size, i.e., holographic teleportation. Thus in the grav- +ity picture, a message has been teleported through a semi-classical holographic +traversable wormhole [2]. Holographically, the above coupled LR quantum sys- +tem is dual to a wormhole that connects the two sides of the eternal black hole. +The LR coupling renders the wormhole traversable; if µ < 0, the coupling oper- +ator generates a negative energy shockwave in the bulk, modifying the geometry +of the wormhole and allowing traversability. When µ > 0 the coupling generates +a positive energy shockwave and the qubit falls into the singularity. The team +of researchers writes: ”we observe increased teleportation when the interaction +introduces a negative energy shockwave rather than a positive one. The asym- +metric signature is consistent with the physical interpretation that the qubit +underwent teleportation through the wormhole” [6]. +The point is that for very low temperatures, the information does not vanish +and the original entanglement between Q and T does not get destroyed by +chaotic perturbations. +How is this possible? +Although there is scrambling +and quantum chaotic behavior, the weak coupling interaction between L and +7 + +R entangles L and R, and the qubit Q is unscrambled. This is perfect size +winding which causes teleportation around the scrambling time. In the perfect +size winding protocol of scrambling followed by unscrambling the teleported +qubit is highly error-protected [4]. I further discuss this issue in section 9. +7 +Why should we believe the gravity picture? +In the new experiment performed with the Sycamore chip, the team of re- +searchers shows that their coarse-grained SYK model preserves key properties +of the traversable wormhole physics: perfect size winding, coupling interac- +tion on either side of the wormhole that is consistent with a negative energy +shock wave, a Shapiro time delay, causal time-order of signals emerging from +the wormhole, and scrambling [6]. +Besides sending a single qubit from left to right, another qubit is inserted +from right to left. The result is time-ordered teleportation, which is interpreted +as a demonstration of gravitational teleportation. At time −t0, a qubit Q is +swapped into L. Simultaneously, a qubit R is swapped into R. At the time +t1, the team of researchers performs a measurement and compares the two pro- +cesses. +They found that the presence of R delayed the arrival of the signal traveling +left to right, and interpreted this delay observed in the learned Hamiltonian as +due to a Shapiro time delay. It is also demonstrated that in the high-temperature +regime, non-gravitational teleportation occurs, and there is no size winding [6]. +Working with collaborators from Caltech, Fermilab, and Harvard, the quan- +tum system was subjected to numerous tests to determine if it showed quantum +gravitational behavior. The above signatures were verified on classical com- +puters, so claims the team of researchers, confirming that the dynamics of the +quantum system were consistent with a quantum gravity interpretation and the +holographic principle [17]. +8 +Scientific explanation is not truth +We usually proceed from the success of an experiment to the conclusion that +our explanation is likely to be approximately true, or true. We think that if an +explanation is the best among the competing explanations of the experiment, +then it is probably true. But it should be stressed that the fit between the +simplified SYK model and the explanation in terms of an emergent wormhole +does not mean that the latter explanation is literally true. Neither does it mean +that holographic wormholes exist or that they are real. What is meant by saying +that this explanation is the simplest among the other hypotheses is mainly that, +it is the best fit for the experimental setup, and that holographic teleportation +fits the teleportation mechanism at the basis of the said experiment. +The point is that according to the ER = EPR hypothesis, the gravity picture +is equivalent to the quantum information picture, and ”The traversable worm- +8 + +hole expressed as a quantum circuit, equivalent to the gravitational picture in +the semiclassical limit of an infinite number of qubits” [6]. But although the +analogy between the experimental setup and the emergent geometry is sugges- +tive, it does not follow from the experiment that the wormhole gravitational +picture is real. We can only say that teleportation-by-size is the hypothesis +that explains the experiment best. This is so even if it explains the evidence. +”Truth” requires a step beyond the judgment that the holographic wormhole +hypothesis fits the experimental setup and the data and is better than all of its +rivals. +9 +Quantum gravity in the lab +Advocates of the ”quantum gravity in the Lab” program argue: ”The ‘quan- +tum gravity in the lab’ program does not need to wait for large error-corrected +quantum computers. Progress can be made even in the Noisy Intermediate-Scale +Quantum (NISQ) era” [13]. There is a problem with this statement. +As is well known, quantum computers are prone to many errors and the +Sycamore quantum device has a large error rate [7]. In this state of affairs, ”If, +at any point in time, a small error occurs, the chaotic dynamics will not undo +themselves, and the particle will not make it through the wormhole” [17]. +At large times, a small perturbation can destroy the correlations between the +two sides L and R of the quantum system that would otherwise exist without +the perturbation. Although the qubits of the Sycamore processor are cooled +down to cryogenic temperatures and are held in an ultra-high vacuum chamber, +the entangled qubits can decohere quickly due to interaction (entanglement) +with the environment (incoherent errors). The team of researchers writes: ”In +general, errors can include coherent errors [crosstalk errors and qubit phase] and +incoherent sources of noise; in simulations, we assume fully incoherent errors and +observe agreement with experimental data” [6]. +A team of researchers trained a quantum neural network (in a quantum +machine learning context). An appropriate ansatz can mitigate coherent errors +for only a small number of qubits (18) on the Sycamore quantum device [12]. +Proponents of the ”quantum gravity in the Lab” program show that ”with some +caveats we can use a finite fraction of the fermions” [13]. So in order to reduce +the coherent errors, ”the total circuit has 9 qubits” [6]. Recall that in practice, +only 7 qubits were used to simulate a ”wormhole-like teleportation”. The other +two qubits served as the teleported qubits [6] (see sections 3 and 5). +Using +machine learning, the team of researchers was able to make the quantum model +simple enough to preserve the key gravitational properties, so that it could be +realized with a circuit with 164 two-qubit gates [6]. A more complex model +would increase the number of gates, and consequently also the error rate. +In the Caltech press release, it is said that the team of researchers found a +quantum system, a “baby” SYK-like model, prepared to preserve the key prop- +erties of a gravitational wormhole. To achieve this, the team had to first reduce +the SYK model to a simplified form, a feat they achieved using machine learn- +9 + +ing tools on conventional computers. They employed learning techniques to find +and prepare a simple SYK-like quantum system that could be encoded in the +Sycamore quantum architecture, and that would preserve the key gravitational +property: the negative energy shockwave. The greatest achievement was sim- +plifying the microscopic description of the SYK quantum system and studying +the resulting effective model that the team found on the Sycamore quantum +processor. The team of researchers found it “curious and surprising how the +optimization on one characteristic of the model [the negative energy shockwave +or LR coupling] preserved the other characteristics” [3]. +Reducing the SYK model to a simplified form is an achievement that is to +be celebrated. But this demonstrates the amazing capabilities of conventional +computers. It is important to stress that no wormhole was created in the lab, +and moreover, no one has ever observed or found any evidence of any wormhole. +Acknowledgement +This work is supported by ERC advanced grant number 834735. +References +[1] +M. S. Blok, V. V. Ramasesh, T. Schuster, K. O’Brien, J. M. Kreikebaum, D. +Dahlen, A. Morvan, B. Yoshida, N. Y. Yao and I. Siddiqi (2021). ”Quantum +Information Scrambling in a Superconducting Qutrit Processor.” Physical +Review X 10, pp. 021010-1- 021010-21. +[2] +A. R. Brown, H. Gharibyan, S. Leichenauer, H. W. Lin, S. Nezami, G. +Salton, L. Susskind, B. Swingle and M. Walter (2019). ”Quantum Gravity +in the Lab: Teleportation by Size and Traversable Wormholes.” arXiv: +1911.06314v2 [quant-ph] +[3] +Clavin, W. (2022). ”Physicists observe wormhole dynamics using a quan- +tum computer.” Caltech. +[4] +P. Gao and D. L. Jafferis (2021). ”A traversable wormhole teleportation +protocol in the SYK model.” Journal of High Energy Physics 2021, pp. +1-43. +[5] +P. Hosur, X-L. Qi, D. A. Roberts, and B. Yoshida, (2016). ”Chaos in Quan- +tum Channels,” Journal of High Energy Physics 2016, pp. 1-48. +[6] +D. Jafferis, A. Zlokapa, J. D. Lykken, D. K. Kolchmeyer, S. I. Davis, N. +Lauk, H. Neven, and M. Spiropulu (2022). ”Traversable wormhole dynamics +on a quantum processor.” Nature 612, pp. 51–55. +[7] +G. +Kalai, +Y. +Rinott, +T. +Shoham +(2022). +”Google’s +2019 +’Quan- +tum +Supremacy’ +Claims: +Data, +Documentation, +and +Discussion.” +arXiv:2210.12753v2 [quant-ph], pp. 1-34. +10 + +[8] +J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. +Blais, M. H. Devoret, S. M. Girvin and R. J. Schoelkopf (2007). ”Charge- +insensitive qubit design derived from the Cooper pair box.” Physical Review +A 76, pp. 042319-1-042319-19. +[9] +K. A. Landsman, C. Figgatt, T. Schuster, N. M. Linke, B. Yoshida, N. Y. +Yao, and C. Monroe (2019). ”Verified quantum information scrambling.” +Nature 567, pp. 61–65. +[10] J. +Maldacena +and +X.-L. +Qi +(2018) +Eternal +traversable +wormhole, +arXiv:1804.00491v3 [hep-th], pp. 1-74. +[11] J. Maldacena, S. H. Shenker and D. Stanford, (2016). ”A Bound on Chaos.” +Journal of High Energy Physics (2016), pp. 1-16. +[12] M. Y. Niu, A. Zlokapa, M. Broughton, S. Boixo, M. Mohseni, V. Smelyan- +skyi, and H. Neven (2022). ”Entangling Quantum Generative Adversarial +Networks.”Physical Review Letters 128.220505. +[13] S. Nezami, H. W. Lin, A. R. Brown, H. Gharibyan, S. Leichenauer, G. +Salton, L. Susskind, B. Swingle and M. Walter (2022). ”Quantum Gravity +in the Lab: Teleportation by Size and Traversable Wormholes, Part II.” +arXiv: 2102.01064v1 [quant-ph] +[14] Y. Sekino and L. Susskind (2008). ”Fast scramblers.” Journal of High En- +ergy Physics 10, pp. 1-14. +[15] B. Yoshida and N. Y. Yao (2019). ”Disentangling Scrambling and Deco- +herence via Quantum Teleportation.” Physical Review X 9, pp. 011006-1- +011006-17. +[16] S. Xu, L. Susskind, Y. Su, B. Swingle (2020). ”A Sparse Model of Quantum +Holography.” arXiv:2008.02303v1 [cond-mat.str-el], pp. 1-55. +[17] Zlokapa, A. (2022). ”Making a Traversable Wormhole with a Quantum +Computer.” Google Research. +11 + diff --git a/49E1T4oBgHgl3EQf6QXo/content/tmp_files/load_file.txt b/49E1T4oBgHgl3EQf6QXo/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..6d698998ddee103439e0c02483b697320e0a930e --- /dev/null +++ b/49E1T4oBgHgl3EQf6QXo/content/tmp_files/load_file.txt @@ -0,0 +1,383 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf,len=382 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content='03522v1 [gr-qc] 9 Jan 2023 A Comment on “Traversable wormhole dynamics on a quantum processor” Galina Weinstein Reichman University, The Efi Arazi School of Computer Science, Herzliya;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' University of Haifa, The Department of Philosophy, Haifa, Israel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' January 10, 2023 Abstract There has been a lot of buzz surrounding the latest Nature paper, ”Traversable wormhole dynamics on a quantum processor”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The Nature paper discusses an experiment in which Google’s Sycamore quantum pro- cessor is used to simulate a sparsified version of an SYK model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' It is shown that the simplified model preserves the key gravitational characteristics of the original SYK model and that it is sufficient to produce a traversable wormhole behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The experiment does not create an actual wormhole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Rather, the team of researchers shows an equivalence between a gravity picture and a quantum information picture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' This paper gives an account of the experiment and addresses philosophical questions arising from the theoretical and experimental work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' 1 Quantum chaos and scrambling Let us begin with the quantum butterfly effect, which is essential for the under- standing of the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The butterfly effect implies scrambling [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Quan- tum scrambling is the quantum analog of chaotic dynamics in classical systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Scrambling describes many-body dynamics which, though ultimately unitary, scatter initially localized quantum information across all of the system’s avail- able degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Black holes are the fastest scramblers in the universe and are therefore the most chaotic bodies in the cosmos [14];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' More specifically, quantum information present in a small local area of space spreads out, and we must search a large region to recover the information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' This is the scrambling of the quantum information while the system evolves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Heisenberg’s operators evolve in a way that reminds the chaotic butterfly effect: they were first local, and now they are spread over many regions in space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' This is the butterfly effect in quantum systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' It should be stressed that when we speak about black holes, we are not talking about black holes that form from gravitational collapse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Rather what 1 is meant by black holes here and thereafter is eternal black holes (two-sided black holes) or two anti-de Sitter space (Ads) black holes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The eternal black hole is dual to two copies of the original conformal field theory (CFT) in the thermofield double (TFD) state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The TFD state is an entangled pure state between two identical copies of the quantum system (CFT): 1 √ Zβ |T FDβ⟩ = eβ(HL+HR) |nn⟩L,R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' (1) Tracing out one of the copies HL (the SYK Hamiltonian applied to the left system) or HR (the SYK Hamiltonian applied to the right system) gives a thermal state (with Majorana fermions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' In other words, tracing out either copy produces the thermal density matrix at inverse temperature β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The |nn⟩L,R is the thermofield double state at an infinite temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The left and right external bulk regions of the eternal black hole are joined through a wormhole and are thus dual to the TFD state [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The models for the onset and dynamics of quantum chaos are called the Sachdev-Ye-Kitaev (SYK) models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The SYK models lead to scrambling and spreading of the information among the quantum many-body system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' But the SYK models possess gravity duals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' They are also a paradigm for quantum holographic matter and the gravitational interpretation through the holographic principle or duality (the AdS/CFT correspondence or gauge/gravity duality);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' the equivalence between two descriptions of the same system: quantum gravity in (d+1) dimensions, on the one hand, and quantum field theory in d dimensions, on the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The above characteristics of the SYK Hamiltonian for N fermions have led to realizing holographic physics in the laboratory, what is called quantum gravity in the lab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' I will further discuss quantum gravity in the lab in section 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' An SYK model becomes extremely chaotic at the very beginning of its devel- opment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' In the SYK model, the out-of-time-order correlation (OTOC) functions are used to diagnose quantum chaos, and measure the growth of operators in space, unitarily evolving (in the Heisenberg interpretation of quantum mechan- ics) as a function of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' With chaotic time evolution, the butterfly effect will cause most of the OTOC functions in the average to decay exponentially [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' In the semi-classical limit (in quantum systems with many degrees of free- dom), this scrambling of information and operator growth due to chaotic behav- ior is exponential and is measured using the quantum Lyapunov exponent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' But unlike the classical Lyapunov exponent, there exists a bound on the quantum Lyapunov exponent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' This is additionally measured by the butterfly velocity, the very equivalent measure of the classical chaotic butterfly effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The quantum Lyapunov exponent and the scrambling rate are the ones that characterize the beginning and appearance of quantum chaos in this system [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' It should be noted that an interesting characteristic of the SYK model, which is related to the quantum Lyapunov exponent and the OTOC, is that the model exhibits maximally chaotic behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' It means that like eternal black holes, the SYK model is a very fast scrambler of information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' There is another important 2 quantity called, Loschmidt echo, which is intimately tied to quantum chaos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The echo is defined as the probability that the chaotic system would return to its initial state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' As said above, we characterize quantum scrambling and quantum chaos by measuring the OTOC function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' However, OTOCs do not generally discriminate between quantum scrambling and the effects of both ordinary quantum deco- herence and experimental noise: quantum scrambling and classical noise lead the OTOC to decay exponentially with time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' It is a major problem if quantum scrambling is indistinguishable from quantum decoherence and noise, where the information in a system is lost to the environment [9];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content='[15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Isolated systems are idealized models but unfortunately, realistic systems are open systems and are in interaction with the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Suppose there is a system of n qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' This system is not an isolated and closed system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The n qubits are interacting with many interfering particles in the complex environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' It is almost impossible to follow the dynamics of each particle, so what we have here is a system that is many-body system, and decoherence induced by the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' As the system evolves, the n qubits get entangled with the many-body system of the environment, and there are more disturbances and perturbations and more degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Decoherence happens naturally to quantum computers since like scrambling, qubits can’t be perfectly isolated from the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' It was found that a quantum teleportation protocol enables one to differen- tiate between scrambling and decoherence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Thus using teleportation one can verify scrambling behavior even in the face of decoherence and experimental imperfection [1];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content='[15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' 2 SYK models and holography The SYK Hamiltonian is a model for quantum chaos and holography.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' That is, there is correspondence between the SYK model and scrambling/quantum chaotic behavior on the one hand, and eternal black holes, on the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' This dual possibility led a team of researchers to the realization that they might be able to create a model of teleportation through a traversable wormhole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' They discovered that a process called unscrambling comes after scrambling in a wormhole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The discovery of a process of scrambling followed by unscrambling has boosted the possibility of realizing a quantum mechanism called size wind- ing in the lab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' This process completely goes against everything we know from classical chaos and irreversibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The size-winding mechanism is reminiscent of Poincare’s Recurrence Theorem of classical physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' But in the dual gravi- tational interpretation, size-winding leads to the interesting conclusion that a particle can pass through a wormhole (a holographic wormhole).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The protocol is the following: on the left side of the wormhole, the infor- mation is scrambled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Since the two sides, right and left of the wormhole are connected (coupled), the information, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=', qubits, is unscrambled and pops up on the right side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Two essential things enable traversability: the two sides of 3 the wormhole must be entangled before sending the information and the two sides must be coupled after sending the message.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' It was thought that it was possible to study the dynamics of a wormhole, through which a qubit can pass, by simulating the SYK model of N Majorana fermions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' It was suggested that realizing the holographic SYK model on the Google Sycamore chip might open a window to an understanding of the quantum gravity of holographic traversable wormholes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The SYK models of a quantum many-body system simulate the scrambling- unscrambling method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' According to the holographic principle, systems that are not gravitational but are entangled will exhibit properties that are identical to quantum gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Hence, reasoned the team of researchers, an experiment implementing the entanglement of qubits can be performed in the laboratory to test theories of quantum gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' This experiment consists of two entangled systems of n qubits, on the right and n qubits on the left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' In this protocol obviously, the dynamics of the system are chaotic (quantum mechanically) and is described by the SYK model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' One inserts a qubit (the message) on the left side of the system (L subsys- tem), and it evolves in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The qubit is entangled with one of the qubits on the L subsystem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' It means that the qubit begins to spread among the n qubits (a small number of qubits) on the left side, and in all parts of the subsystem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' After a certain time, the qubit is entangled with the qubits of the L subsystem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' But then the qubit suddenly reappears, is unscrambled, and recoheres on the other side, the right side (R), very far from the L side, where it was scrambled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' There is something that caused the original qubit, which entered on the far-left side, to suddenly be focused on the far-right side at a future time, even though it was completely mixed up on the left side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' It is bizarre from the quantum mechanical point of view, says the team of researchers, but what makes things less weird is that it may be explained or in- terpreted using the paradigm of quantum gravity and the holographic principle: a traversable wormhole protocol is equivalent to the above quantum information protocol [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' We start from two separated black holes, the so-called scramblers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The tele- ported signal reappears on the right side when the two black holes are connected by a wormhole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' In the quantum system, we speak of the method of scrambling- unscrambling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' But with respect to a wormhole, the above mechanism is called teleportation-by-size, a protocol of quantum teleportation through the worm- hole, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=', information transmission is dependent on operator-size growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' So, argues the team of researchers, if we imagine that the two sides of the system represent two sides of the eternal black holes (L and R) that are con- nected by a wormhole, then the explanation for the phenomenon is simpler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' A teleported message is sent through an emergent wormhole: it is injected into L and arrives at R later due to a coupling operator [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' 4 3 Perfect size winding The above scenario requires perfect size winding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The team of researchers first describes size-winding purely from the boundary point of view and then applies it to the traversable wormholes (in the bulk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' In the Heisenberg picture, near the scrambling time (just before the onset of the chaotic behavior) for the SYK model, a thermal operator P is inserted at a negative time into the left boundary (the left side L).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Recall that the growth of the size of an operator is a basic manifestation of quantum chaos and com- plexity of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The operator-size distribution is winding in the clockwise direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' A coupling is applied between the two subsystems L and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The LR coupling unwinds the complex winding of the operator size distribution, it winds the size distribution in the opposite direction, accurately reversing the winding direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The thermal operator P from the left side will be exactly mapped to its right side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' We obtain a counterclockwise size distribution corre- sponding to a thermal operator P inserted on the other boundary (the right side R) at a positive time [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The team of researchers stresses: ”We explicitly show size-winding of thermal operators near the scrambling time for the SYK model, and we conjecture that the phenomenon can also be found in other holographic systems” [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Perfect size winding provides a necessary condition for traversable wormhole behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' It occurs in the ground state, the state of lowest possible energy where the temperature is zero (low temperature through the wormhole).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The team of researchers expects systems with a holographic dual to exhibit perfect size winding [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' In other words, the SYK model is dual to a traversable wormhole only in the low-temperature regime, and it exhibits perfect size wind- ing in the low-temperature limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' But this applies to large N Majorana fermions interacting with large q other Majorana fermions (teleportation of q fermions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The team of researchers then pondered: What is the most simplified Hamil- tonian that preserves the gravitational physics of the original SYK model?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' How many qubits do we need to simulate this Hamiltonian on a quantum device?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' It was shown that N = 10 was sufficient to produce the traversable wormhole be- havior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The team employed learning techniques to construct a sparsified version of the SYK model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Sparsification reduces the complexity of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' A simplified learned Hamiltonian was constructed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Its ground state was close to a TFD state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Techniques from machine learning (and a kind of approximation called Trotterization) were applied to optimize the procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The techniques were performed on a classical computer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The sparsification procedure reduced the SYK model to a sparse N = 10 SYK model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' ”We choose q = 4” fermions interacting with N other fermions of the simplified version of the SYK Hamil- tonian, ”and demonstrate gravitational physics at sufficiently small N”, where N = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Since ”The wormhole teleportation protocol also introduces a pair of entangled qubits, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=', a reference qubit that is entangled with the injected qubit”, then ”the total circuit has 9 qubits”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Hence, the sparsified SYK model was experimentally realized with N = 9 qubits [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' It should be mentioned that at about the same time, Leonard Susskind and 5 a team of researchers were working on what seems like a bigger project, a sparse SYK model that recovers the global physics of ordinary SYK models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' In par- ticular, at low temperatures, their model exhibits a gravitational sector that is maximally chaotic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The sparsity of the model, so writes the team, ”consider- ably reduces the cost of quantum simulation algorithms”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' This, so claims the team, makes their sparse SYK model ”the most efficient currently known route to simulate a holographic model of quantum gravity”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The team of researchers add: ”On a practical level, sparse systems typically admit much more efficient computer simulations—both classical and quantum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' By significantly reducing the resources needed to simulate black holes in holographic models of quantum gravity, these results bring us closer to the goal of studying ’quantum gravity in the lab’” [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' 4 Majorana fermions versus transmons The sparse Hamiltonian is doubled to give left HL and right HR Hamiltonians with N Majorana fermions on each side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Each side is a simulation of the SYK model, the learned Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The wormhole experiment was realized with superconducting qubits on the Google Sycamore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' I would like to emphasize that I am not speaking now of claims related to quantum supremacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The Sycamore consists of an array of 54 superconducting qubits called transmons (transmission-line shunted plasma oscillation qubits).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The transmon is closely related to the charge qubits or Cooper–Pair–Box (CPB) (Cooper pairs that are tunneling in a Josephson junc- tion).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The transmon fixes the weakness of the CPB and as compared to the CPB, it greatly reduces charge noise sensitivity in the qubit [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' That said, the team of researchers is speaking of the Majorana SYK model with N fermions with which they produce evidence of gravitational physics in the sparsified SYK system: ”To encode 7 Majorana fermions on the left system and 7 Majorana fermions on the right system, we require 7 qubits (two fermions per qubit)” [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The team of researchers also writes: ”we assume that the total number of qubits (or fermions) on each side is n, and the number of message qubits (or fermions) that are transmitted by the state transfer or operator transfer protocols is m” [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' This is problematic because it is not at all clear whether one superconducting transmon qubit represents two Majorana fermions or rather, one transmon qubit represents one Majorana fermion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' 5 The quantum information picture The practical steps of the teleportation protocol (step-by-step) in the quantum information picture (without gravity) are as follows (based on [2]): 1) Two identical copies of the quantum system are prepared: a system of 7 qubits on the left (side L) and a system of 7 qubits on the right (side R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The 6 two subsystems are entangled in the TFD state;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' that is, we have entangled Bell pairs shared between L and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' 2) We evolve all the qubits on the side L “backward in time” by acting with the inverse of the time-evolution operator (exp+iHt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' 3) A qubit Q (the message) is injected into L at a certain time (swapped into side L: a SWAP gate).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Now we evolve subsystem L “forward in time” using the time-evolution operator (exp−iHt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' As a result, Q is entangled with a reference qubit P;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Q is then scrambled with P and among the 7 qubits on the subsystem L (the carrier qubits).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' 4) We now weakly couple side L to side R (at t = 0), applying a coupling operator (expiµV , where V is the interaction term and µ represents the coupling interaction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The coupling is applied suddenly: All the 7 qubits on side L are now coupled to the 7 qubits on the side R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' 5) We now evolve side R “forward in time” using the time-evolution oper- ator (exp−iHt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Side R is subsequently measured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The qubit Q (the message) reappears unscrambled, it arrives unscathed at R and there is no need to de- code it (a final SWAP gate: extract qubit Q from R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The message has been teleported while being first scrambled and then unscrambled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The teleported qubit is highly error-protected [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The team of researchers distinguishes between two mechanisms of transmis- sion with the wormhole circuit [2]: 1) The low-temperature teleportation: If µ < 0, the qubit Q experiences a time advance and is rescued on the side R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' This is wormhole teleportation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' 2) On the other hand, when µ > 0 the qubit is entangled with the qubits of side L but is not unscrambled and its destiny is oblivion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' 6 The gravity picture According to Occam’s razor, the simplest explanation for the above mecha- nism is teleportation-by-size, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=', holographic teleportation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Thus in the grav- ity picture, a message has been teleported through a semi-classical holographic traversable wormhole [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Holographically, the above coupled LR quantum sys- tem is dual to a wormhole that connects the two sides of the eternal black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The LR coupling renders the wormhole traversable;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' if µ < 0, the coupling oper- ator generates a negative energy shockwave in the bulk, modifying the geometry of the wormhole and allowing traversability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' When µ > 0 the coupling generates a positive energy shockwave and the qubit falls into the singularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The team of researchers writes: ”we observe increased teleportation when the interaction introduces a negative energy shockwave rather than a positive one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The asym- metric signature is consistent with the physical interpretation that the qubit underwent teleportation through the wormhole” [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The point is that for very low temperatures, the information does not vanish and the original entanglement between Q and T does not get destroyed by chaotic perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' How is this possible?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Although there is scrambling and quantum chaotic behavior, the weak coupling interaction between L and 7 R entangles L and R, and the qubit Q is unscrambled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' This is perfect size winding which causes teleportation around the scrambling time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' In the perfect size winding protocol of scrambling followed by unscrambling the teleported qubit is highly error-protected [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' I further discuss this issue in section 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' 7 Why should we believe the gravity picture?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' In the new experiment performed with the Sycamore chip, the team of re- searchers shows that their coarse-grained SYK model preserves key properties of the traversable wormhole physics: perfect size winding, coupling interac- tion on either side of the wormhole that is consistent with a negative energy shock wave, a Shapiro time delay, causal time-order of signals emerging from the wormhole, and scrambling [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Besides sending a single qubit from left to right, another qubit is inserted from right to left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The result is time-ordered teleportation, which is interpreted as a demonstration of gravitational teleportation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' At time −t0, a qubit Q is swapped into L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Simultaneously, a qubit R is swapped into R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' At the time t1, the team of researchers performs a measurement and compares the two pro- cesses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' They found that the presence of R delayed the arrival of the signal traveling left to right, and interpreted this delay observed in the learned Hamiltonian as due to a Shapiro time delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' It is also demonstrated that in the high-temperature regime, non-gravitational teleportation occurs, and there is no size winding [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Working with collaborators from Caltech, Fermilab, and Harvard, the quan- tum system was subjected to numerous tests to determine if it showed quantum gravitational behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The above signatures were verified on classical com- puters, so claims the team of researchers, confirming that the dynamics of the quantum system were consistent with a quantum gravity interpretation and the holographic principle [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' 8 Scientific explanation is not truth We usually proceed from the success of an experiment to the conclusion that our explanation is likely to be approximately true, or true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' We think that if an explanation is the best among the competing explanations of the experiment, then it is probably true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' But it should be stressed that the fit between the simplified SYK model and the explanation in terms of an emergent wormhole does not mean that the latter explanation is literally true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Neither does it mean that holographic wormholes exist or that they are real.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' What is meant by saying that this explanation is the simplest among the other hypotheses is mainly that, it is the best fit for the experimental setup, and that holographic teleportation fits the teleportation mechanism at the basis of the said experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The point is that according to the ER = EPR hypothesis, the gravity picture is equivalent to the quantum information picture, and ”The traversable worm- 8 hole expressed as a quantum circuit, equivalent to the gravitational picture in the semiclassical limit of an infinite number of qubits” [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' But although the analogy between the experimental setup and the emergent geometry is sugges- tive, it does not follow from the experiment that the wormhole gravitational picture is real.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' We can only say that teleportation-by-size is the hypothesis that explains the experiment best.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' This is so even if it explains the evidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' ”Truth” requires a step beyond the judgment that the holographic wormhole hypothesis fits the experimental setup and the data and is better than all of its rivals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' 9 Quantum gravity in the lab Advocates of the ”quantum gravity in the Lab” program argue: ”The ‘quan- tum gravity in the lab’ program does not need to wait for large error-corrected quantum computers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Progress can be made even in the Noisy Intermediate-Scale Quantum (NISQ) era” [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' There is a problem with this statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' As is well known, quantum computers are prone to many errors and the Sycamore quantum device has a large error rate [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' In this state of affairs, ”If, at any point in time, a small error occurs, the chaotic dynamics will not undo themselves, and the particle will not make it through the wormhole” [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' At large times, a small perturbation can destroy the correlations between the two sides L and R of the quantum system that would otherwise exist without the perturbation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Although the qubits of the Sycamore processor are cooled down to cryogenic temperatures and are held in an ultra-high vacuum chamber, the entangled qubits can decohere quickly due to interaction (entanglement) with the environment (incoherent errors).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The team of researchers writes: ”In general, errors can include coherent errors [crosstalk errors and qubit phase] and incoherent sources of noise;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' in simulations, we assume fully incoherent errors and observe agreement with experimental data” [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' A team of researchers trained a quantum neural network (in a quantum machine learning context).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' An appropriate ansatz can mitigate coherent errors for only a small number of qubits (18) on the Sycamore quantum device [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Proponents of the ”quantum gravity in the Lab” program show that ”with some caveats we can use a finite fraction of the fermions” [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' So in order to reduce the coherent errors, ”the total circuit has 9 qubits” [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Recall that in practice, only 7 qubits were used to simulate a ”wormhole-like teleportation”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The other two qubits served as the teleported qubits [6] (see sections 3 and 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Using machine learning, the team of researchers was able to make the quantum model simple enough to preserve the key gravitational properties, so that it could be realized with a circuit with 164 two-qubit gates [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' A more complex model would increase the number of gates, and consequently also the error rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' In the Caltech press release, it is said that the team of researchers found a quantum system, a “baby” SYK-like model, prepared to preserve the key prop- erties of a gravitational wormhole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' To achieve this, the team had to first reduce the SYK model to a simplified form, a feat they achieved using machine learn- 9 ing tools on conventional computers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' They employed learning techniques to find and prepare a simple SYK-like quantum system that could be encoded in the Sycamore quantum architecture, and that would preserve the key gravitational property: the negative energy shockwave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The greatest achievement was sim- plifying the microscopic description of the SYK quantum system and studying the resulting effective model that the team found on the Sycamore quantum processor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' The team of researchers found it “curious and surprising how the optimization on one characteristic of the model [the negative energy shockwave or LR coupling] preserved the other characteristics” [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Reducing the SYK model to a simplified form is an achievement that is to be celebrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' But this demonstrates the amazing capabilities of conventional computers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' It is important to stress that no wormhole was created in the lab, and moreover, no one has ever observed or found any evidence of any wormhole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E1T4oBgHgl3EQf6QXo/content/2301.03522v1.pdf'} +page_content=' Acknowledgement This work is supported by ERC advanced grant number 834735.' metadata={'source': 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100644 index 0000000000000000000000000000000000000000..7b3661e41b507c74ebd9cc13e98e04c651d3ca09 --- /dev/null +++ b/6dE3T4oBgHgl3EQfRAnz/content/tmp_files/2301.04418v1.pdf.txt @@ -0,0 +1,2455 @@ +MNRAS 000, 1–15 (0000) +Preprint 12 January 2023 +Compiled using MNRAS LATEX style file v3.0 +The comptonizing medium of the black-hole X-ray binary +MAXI J1535−571 through type-C quasi-periodic oscillations +Divya Rawat1⋆, Mariano M´endez2, Federico Garc´ıa2,3,4, Diego Altamirano5, Konstantinos Karpouzas2,5, +Liang Zhang5, Kevin Alabarta2,5, Tomaso M. Belloni6, Pankaj Jain7, Candela Bellavita4 +1Inter-University Center for Astronomy and Astrophysics, Ganeshkhind, Pune 411007, India +2Kapteyn Astronomical Institute, University of Groningen, PO BOX 800, Groningen NL-9700 AV, the Netherlands +3Instituto Argentino de Radioastronom´ıa (CCT La Plata, CONICET; CICPBA; UNLP), C.C.5, (1894) Villa Elisa, Buenos Aires, Argentina +4Facultad de Ciencias Astron´omicas y Geof´ısicas, Universidad Nacional de La Plata, Paseo del Bosque, B1900FWA La Plata, Argentina +5School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK +6INAF-Osservatorio Astronomico di Brera, via E. Bianchi 46, I-23807, Merate, Italy +7Department of physics, IIT Kanpur, Kanpur, Uttar Pradesh 208016, India +Accepted XXX. Received YYY; in original form ZZZ +ABSTRACT +We present a detailed spectral and temporal analysis of the black-hole candidate MAXI J1535−571 using NICER +observations in September and October 2017. We focus specifically on observations in the hard-intermediate state +when the source shows type-C quasi-periodic oscillations (QPOs). We fitted the time-averaged spectrum of the source +and the rms and phase-lag spectra of the QPO with a one-component time-dependent Comptonization model. We +found that the corona contracts from ∼ 104 to ∼ 3 × 103 km as the QPO frequency increases from ∼ 1.8 Hz to +∼ 9.0 Hz. The fits suggest that the system would consists of two coronas, a small one that dominates the time- +averaged spectrum and a larger one, possibly the jet, that dominates the rms and lag spectra of the QPO. We found +a significant break in the relation of the spectral parameters of the source and the properties of the QPO, including +its lag spectra, with QPO frequency. The change in the relations happens when the QPO frequency crosses a critical +frequency νc ≈ 3.0 Hz. Interestingly, the QPO reaches this critical frequency simultaneously as the radio emission +from the jet in this source is quenched. +Key words: accretion, accretion discs — black hole physics — X-rays: binaries — X-rays: individual: MAXI J1535−571 +1 INTRODUCTION +In the outburst, the transient black-hole X-ray binary +(BHXB) system shows substantial X-ray variability (Belloni +& Stella 2014). These systems spend long periods in qui- +escence, with sporadic outbursts lasting weeks to months, +during which the X-ray flux increases by up to three orders +of magnitude compared to the quiescent phase (Remillard +& McClintock 2006). During an outburst, transient BHXBs +initially appear in the low-hard state (LHS) and, as the +outburst progresses, move to the high-soft state (HSS) via +the hard-intermediate (HIMS) and soft-intermediate state +(SIMS) (Belloni et al. 2005, 2011, and references within). +Finally, before returning to the quiescent state, BHXBs +transition from the HSS to the LHS. In the LHS, a hard +component due to Comptonization from an electron plasma +with temperature 50 − 100 keV appears in the X-ray spec- +trum as a power law with photon index 1.5–2.0 (Gilfanov +2010). In contrast, the HSS spectrum is dominated by an +optically thick thermal component generally modelled with a +⋆ E-mail: rawatdivya838@gmail.com (DR) +multi-temperature disc blackbody, occasionally accompanied +by a soft power-law-like component with Γ ≥2 (M´endez +& van der Klis 1997; Done et al. 2007). The evolution of +the outburst of a BHXB can be best characterised in a +hardness-intensity diagram (HID), where typically systems +trace a well-defined path often shaped as a “q” (Fender et al. +2004, Belloni et al. 2005). +These systems show complex fast-time variability, which +is strongly state-dependent. This variability takes the form +of broadband noise components on top of which, in specific +states, quasi-periodic oscillations (QPOs) can be observed +(e.g. Chen et al. 1997; Takizawa et al. 1997; Psaltis et al. +1999; Nowak 2000; Casella et al. 2004, 2005; Belloni et al. +2005). The QPOs appear in the power density spectrum +(PDS; van der Klis & Jansen 1985) as relatively narrow +peaks. The QPOs have been broadly divided into three +categories, the mHz QPO with QPO frequency ranging from +few mHz to Hz (e.g., Dewangan et al. 2006, Koljonen et al. +2011, Altamirano & Strohmayer 2012, Pasham et al. 2013), +low-frequency QPOs (LFQPOs) with frequencies ranging +from just below 1 Hz up to 20 Hz (e.g., Motta et al. 2015), +© 0000 The Authors +arXiv:2301.04418v1 [astro-ph.HE] 11 Jan 2023 + +2 +Rawat et. al. +and +high-frequency +QPOs +(HFQPOs) +with +frequencies +above 100 Hz and up to ∼500 Hz (e.g., Miller et al. 2001, +Strohmayer 2001, Belloni et al. 2012, M´endez et al. 2013, +Belloni & Stella 2014). LFQPOs appear in different spectral +states and have been further classified as type A, B, and C +(Wijnands et al. 1999, Homan et al. 2001, Remillard et al. +2002, Casella et al. 2004). Among the three types, type-C +is the one that is most often observed, showing a high rms +amplitude, between 1% and 20%, and a quality factor1 +usually larger than 6.0 (Wijnands et al. 1999; Casella et al. +2004; Belloni & Stella 2014, see Ingram & Motta 2019, for a +review). +MAXI J1535−571 (hereafter MAXI J1535) is a galactic +transient, initially detected by MAXI/GSC (Negoro et al. +2017a) and SWIFT/BAT (Kennea et al. 2017, Markwardt +et al. 2017) on September 2, 2017. The X-ray variability +(Negoro et al. 2017b), optical (Scaringi & ASTR211 Stu- +dents 2017) and near-infrared (Din¸cer 2017) properties of the +source suggest that MAXI J1535 is a low-mass X-ray binary +(LMXB) source. Radio observations with the Australia +Telescope Compact Array (ATCA) show a signature of a +compact radio jet (Russell et al. 2017); this and the observed +luminosity suggest that this system harbours a black hole +(Negoro et al. 2017b). Study of radio (Chauhan et al. 2019) +and X-ray (Sridhar et al. 2019) observations suggest that the +distance to the source is 4–6 kpc, and the jet inclination angle +is constrained to ≤ 45◦ (Russell et al. 2019). X-ray spectral +studies suggest that the system harbours a near-maximally +spinning black hole (Gendreau et al. 2017, Xu et al. 2018, +Miller et al. 2018). There are some conflicting estimates of +the mass of the black hole in the system (Sreehari et al. +2019, Sridhar et al. 2019), but they are all based on fits to +the X-ray spectrum and are therefore model dependent. No +dynamical mass measurement from optical observations is +available. +A state transition study of MAXI J1535 during outburst, +from September 2017 to April 2018 (Nakahira et al. 2018) +shows that the source behaved like other BHXB systems +tracing a q-shape in the HID (Tao et al. 2018). In the LHS +and HIMS, starting from September 9-18, 2017, MAXI J1535 +showed a type-C QPO with a centroid frequency in the +0.2-3.4 Hz range (Gendreau et al. 2017, Mereminskiy et al. +2018, Stiele & Kong 2018, Huang et al. 2018, Bhargava et al. +2019). The source transitioned to the SIMS and then to +the HSS from September 19-26, 2017. The stable and weak +type A/B LFQPO appears in the SIMS (Stiele & Kong +2018, Stevens et al. 2018, Huang et al. 2018). In the HIMS +and LHS, the type-C QPO reappears from September 26 +to October 9, 2017. After the end of the main outburst +in mid-May 2018, five re-brightening events were reported +by Parikh et al. (2019). A state transition during these +re-flares was reported by C´uneo et al. (2020) using NICER +observations. +Kumar & Misra (2014) proposed a model to study the +Comptonisation medium of neutron-star X-ray binary sys- +1 Quality factor=QPO frequency/QPO width +tems, which was later extended by Karpouzas et al. (2020). +This model was originally developed for high-frequency +QPOs in accreting neutron-star systems. Still, it has been +recently extended by Bellavita et al. (2022) to LFQPOs +in BHXBs and was applied to the type-C QPO in GRS +1915+105 by Karpouzas et al. (2021) and M´endez et al. +(2022), and the type-B QPO in MAXI J1348−630 (Garc´ıa +et al. 2021; Bellavita et al. 2022). Zhang et al. (2022) has +applied the same model using Insight-HXMT observations +of the type-C QPO in MAXI J1535 up to 150 keV. The +rationale behind applying this model to type-C in BHXB +is that the fractional rms amplitude of these QPOs can be +as large as ∼ 15% up to ∼200 keV (Ma et al. 2021). At +those energies, Comptonization dominates the emission in +these systems (e.g., the disc and the reflection component +peak at, respectively, ∼1−3 keV and ∼ 20−25 keV and both +drop quickly above that), and hence Comptonization is most +likely responsible for the rms amplitude and lags of the QPO. +In this paper, we report the results of the spectro-temporal +analysis of MAXI J1535 using NICER observations. To study +the Comptonization medium of the source, we fit the rms and +phase-lag spectra of the QPO with a one-component time- +dependent Comptonization model, vkompthdk (Karpouzas +et al. 2020; Bellavita et al. 2022). In Section 2, we describe the +observations and data analysis techniques, and in Section 3 +we present the results of our analysis and the fits of the model +to the rms and lag spectra of the type-C QPO. Finally, we +discuss our findings in Section 4 and summarise our results +in Section 5. +2 OBSERVATION AND DATA ANALYSIS +We used observations of MAXI J1535 obtained in September +and October 2017 with the Neutron Star Interior Composi- +tion Explorer (NICER Gendreau et al. 2012). The observa- +tions ID’s used are 1050360101-1050360120 & 1130360101- +1130360114. NICER’s XTI (X-ray Timing Instrument Gen- +dreau et al. 2016) covers the 0.2-12.0 keV band and has an +effective area of >2000 cm2 at 1.5 keV. The energy and time +resolutions are 85 eV at 1 keV and 4 ×10−8 s (hereafter +∆tnicer), respectively. We used the nicerl22 task to process +each observation applying the standard calibration process +and screening. We used only those intervals for which the +exposure time was > 100 s after running the nicerl2 task. +For some intervals, we found that the source flux was vary- +ing significantly. To make sure we are not averaging features +of two spectrally and temporally different states, we divided +a single observation into segments with a more or less con- +stant source count rate and studied the temporal and spectral +properties of each segment independently. The details of each +observation and segment are given in Table 1. +2.1 Timing analysis +We extracted the fractional rms amplitude (root-mean +square) normalised (Belloni & Hasinger 1990) PDS for each +2 https://heasarc.gsfc.nasa.gov/docs/nicer/analysis_ +threads/nicerl2/ +MNRAS 000, 1–15 (0000) + +Comptonizing medium of MAXI J1535−571 +3 +Figure 1. Left panel: NICER light curve of MAXI J1535−571 in the 0.5-10.0 keV band. The shaded area represents the approximate time +when the radio emission was quenched (Russell et al. 2019). Right panel: Hardness intensity diagram (HID) using NICER observations. +In the HID, the line shows the general movement of the source in this diagram as the outburst progressed, with the start and end points +of the outburst at, (HR = 0.27, Intensity = 8000) and (HR = 0.22, Intensity = 8000), respectively. In both panels, each point corresponds +to 100 sec, and the colour scale panels indicate the frequency of the QPO. +Table 1. Observation log of MAXI J1535, including timing parameters. The columns are the observation number, the NICER ObsID, the +start and end time of the observation, the 0.5-10.0 keV count rate, the standard deviation of the count rate, σcount, the hardness ratio, +HR, the standard deviation of the hardness ratio, σHR, the QPO centroid frequency and the QPO fractional rms amplitude. The errors +are at 1σ. The observations with an asterisk are those for which the QPO was insignificant in the lowest energy bands. +Obs no. +ObsID +Tstart +Tstop +count rate +σcount +HR +σHR +QPO frequency +QPO Fractional +(M.J.D) +(M.J.D) +(0.5-10.0 keV) +(5−10keV) +(0.5−2.0keV) +(Hz) +rms (%) +1 +1050360105 +58008.988 +58009.126 +8140 ± 5 +48 +0.272 +0.002 +2.74 ± 0.01 +7.0 ± 0.2 +2 +1050360105 +58009.165 +58009.193 +7847 ± 4 +36 +0.280 +0.002 +2.44 ± 0.01 +6.5 ± 0.2 +3 +1050360105 +58009.229 +58009.301 +7676 ± 6 +30 +0.285 +0.004 +2.32 ± 0.01 +6.7 ± 0.2 +4 +1050360105 +58009.807 +58009.945 +7327 ± 4 +65 +0.307 +0.003 +1.83 ± 0.01 +7.3 ± 0.2 +5 +1050360106 +58010.001 +58010.525 +7364 ± 1 +138 +0.311 +0.005 +1.81 ± 0.00 +7.2 ± 0.1 +6 +1050360107 +58011.865 +58011.940 +8654 ± 7 +47 +0.299 +0.002 +2.15 ± 0.01 +6.9 ± 0.2 +7 +1050360108 +58012.187 +58012.258 +9134 ± 3 +130 +0.294 +0.006 +2.41 ± 0.01 +7.4 ± 0.2 +8 +1050360108 +58012.316 +58012.583 +9492 ± 2 +320 +0.285 +0.002 +2.77 ± 0.01 +7.3 ± 0.2 +9 +1050360109 +58013.216 +58013.222 +10088 ± 1 +4 +0.285 +0.004 +2.75 ± 0.02 +7.0 ± 0.2 +10 +1050360109 +58013.281 +58013.410 +10922 ± 4 +191 +0.275 +0.008 +3.27 ± 0.02 +7.0 ± 0.3 +11 +1050360109 +58013.481 +58013.740 +11290 ± 2 +227 +0.282 +0.005 +3.19 ± 0.03 +6.7 ± 0.3 +12 +1050360109 +58013.988 +58013.998 +10461 ± 5 +71 +0.288 +0.001 +2.72 ± 0.01 +6.7 ± 0.2 +13 +1050360110 +58014.053 +58014.063 +10744 ± 1 +5 +0.286 +0.002 +2.84 ± 0.01 +7.5 ± 0.2 +14 +1050360110 +58014.824 +58014.835 +13795 ± 1 +5 +0.269 +0.003 +4.75 ± 0.01 +5.7 ± 0.1 +15 +1050360111 +58015.276 +58015.669 +16992 ± 3 +161 +0.257 +0.005 +9.01 ± 0.04 +1.7 ± 0.1 +16 +∗1050360112 +58016.240 +58016.957 +17040 ± 9 +31 +0.256 +0.010 +7.55 ± 0.06 +2.6 ± 0.2 +17 +1050360113 +58017.011 +58017.858 +16995 ± 1 +7 +0.244 +0.017 +7.45 ± 0.03 +2.9 ± 0.1 +18 +∗1130360103 +58026.726 +58026.814 +14304 ± 2 +445 +0.235 +0.002 +7.09 ± 0.03 +2.4 ± 0.1 +19 +1130360104 +58027.755 +58027.779 +12363 ± 3 +105 +0.240 +0.002 +5.42 ± 0.01 +4.7 ± 0.1 +20 +1130360105 +58028.720 +58028.872 +12321 ± 2 +213 +0.237 +0.002 +5.73 ± 0.01 +4.5 ± 0.0 +21 +∗1130360106 +58029.749 +58029.836 +12527 ± 2 +151 +0.229 +0.002 +6.77 ± 0.02 +3.5 ± 0.1 +22 +1130360107 +58030.715 +58030.865 +10831 ± 2 +381 +0.238 +0.004 +4.57 ± 0.01 +4.6 ± 0.1 +23 +1130360108 +58031.361 +58031.894 +11163 ± 2 +370 +0.234 +0.006 +4.82 ± 0.01 +3.5 ± 0.0 +24 +1130360113 +58036.498 +58036.695 +9747 ± 10 +19 +0.206 +0.007 +5.19 ± 0.03 +3.0 ± 0.2 +25 +1130360114 +58037.032 +58037.677 +8767 ± 4 +183 +0.224 +0.004 +4.50 ± 0.01 +5.0 ± 0.1 +segment using the General High-energy Aperiodic Timing +Software (GHATS)3 version 2.1.0. The 0.2-10.0 keV data +were re-binned in time by a factor of 62500, such that the +time resolution was 0.0025 s, corresponding to a Nyquist +frequency of 200 Hz, and PDS were produced from intervals +3 http://www.brera.inaf.it/utenti/belloni/GHATS_Package/ +Home.html +of 8192 points (20.48 s). For each segment, the PDS for +the intervals were averaged. We fitted the PDS in the +frequency 100-200 Hz, where the source shows no intrinsic +variability, with a constant representing the Poisson noise, +which we then subtracted. We ended up with an averaged, +Poisson-noise subtracted PDS for each segment that we +re-binned logarithmically such that each frequency bin is +larger than the previous one by a factor exp(1/100). We +MNRAS 000, 1–15 (0000) + +• without type-C QPOs +·with type-C QPOs18000 +9 +•without type-C QPOs +·with type-C QPOs +16000 +8 +14000 +7 +[zH] +Intensity [counts s' +12000 +6 +5 +10000 +4 +8000 +3 +2 +0.18 +0.20 +0.22 +0.24 +0.26 +0.28 +0.30 +0.32 +HR [(5-10 keV)/(0.5-2 keV)4 +Rawat et. al. +Table 2. Time-averaged spectra and corona model parameters of MAXI J1535. The columns are the observation number, the hydrogen +column density, NH, the power-law photon index of nthcomp, Γ, the inner disc temperature, kTin, the seed photon temperature of +vkompthdk, kTs, the size of the corona, L, the fraction of the flux of the seed-photon source due to feedback from the corona, η, and +the amplitude of the variability of the external heating rate, δ ˙Hext. The errors are at 1σ. The observations with an asterisk are those for +which the QPO was insignificant in the lowest energy bands. +Obs no. +NH +Γ +kTin +kTs +L +η +δ ˙Hext +χ2 +ν(dof) +1022 cm−2 +(keV) +(keV) +( 103 km) +% +1 +2.19 ± 0.01 +2.43 ± 0.02 +0.68 ± 0.01 +0.35 ± 0.05 +5.1 ± 1.0 +0.62 ± 0.05 +12.2 ± 0.6 +231.4 (243) +2 +2.19 ± 0.01 +2.29 ± 0.01 +0.62 ± 0.01 +0.29 ± 0.03 +8.3 ± 1.1 +0.75 ± 0.09 +12.0 ± 0.5 +191.9 (242) +3 +2.18 ± 0.01 +2.26 ± 0.01 +0.61 ± 0.01 +0.23 ± 0.04 +8.7 ± 1.1 +0.82+0.18 +−0.38 +11.3 ± 1.1 +240.5 (243) +4 +2.17 ± 0.01 +2.12 ± 0.01 +0.55 ± 0.01 +0.14 ± 0.01 +12.6 ± 0.5 +1.00 − 0.04 +11.1 ± 0.4 +219.8 (243) +5 +2.16 ± 0.01 +2.11 ± 0.00 +0.55 ± 0.01 +0.15 ± 0.01 +13.2 ± 0.4 +1.00 − 0.45 +11.5 ± 0.3 +242.3 (243) +6 +2.15 ± 0.01 +2.18 ± 0.01 +0.60 ± 0.01 +0.24 ± 0.03 +9.1 ± 1.0 +0.79 ± 0.12 +12.2 ± 0.7 +177.9 (243) +7 +2.17 ± 0.01 +2.27 ± 0.01 +0.64 ± 0.01 +0.36 ± 0.05 +6.6 ± 1.2 +0.64 ± 0.07 +15.0 ± 0.7 +173.2 (243) +8 +2.15 ± 0.01 +2.67 ± 0.04 +0.79 ± 0.01 +0.33 ± 0.04 +5.7 ± 0.9 +0.76 ± 0.07 +11.2 ± 0.7 +234.8 (243) +9 +2.19 ± 0.01 +2.34 ± 0.02 +0.68 ± 0.01 +0.47 ± 0.07 +4.8 ± 0.9 +0.59 ± 0.05 +14.4 ± 0.9 +169.3 (243) +10 +2.21 ± 0.01 +2.48 ± 0.02 +0.74 ± 0.01 +0.39 ± 0.07 +4.4 ± 1.2 +0.55 ± 0.07 +13.5 ± 1.0 +155.1 (243) +11 +2.19 ± 0.01 +2.85 ± 0.11 +0.85 ± 0.02 +0.36 ± 0.05 +5.5 ± 1.2 +0.77 ± 0.11 +10.5 ± 0.9 +192.2 (222) +12 +2.20 ± 0.01 +2.33 ± 0.01 +0.67 ± 0.01 +0.37 ± 0.04 +6.5 ± 0.8 +0.66 ± 0.05 +13.3 ± 0.5 +152.4 (243) +13 +2.20 ± 0.01 +2.36 ± 0.01 +0.69 ± 0.01 +0.37 ± 0.04 +6.4 ± 0.8 +0.69 ± 0.06 +14.3 ± 0.5 +176.3 (243) +14 +2.23 ± 0.01 +2.61 ± 0.06 +0.98 ± 0.02 +0.43 ± 0.05 +3.8 ± 0.5 +0.73 ± 0.06 +14.1 ± 0.8 +168.4 (242) +15 +2.30 ± 0.01 +2.49 ± 0.17 +1.18 ± 0.01 +0.56 ± 0.04 +4.0 ± 0.5 +1.00 − 0.11 +17.3 ± 2.0 +195.8 (239) +16 +2.29 ± 0.01 +2.60 ± 0.14 +1.13 ± 0.02 +0.52 ± 0.07 +3.7 ± 1.0 +0.69 ± 0.18 +15.6 ± 2.4 +165.0 (236) +17 +2.29 ± 0.00 +2.40 ± 0.24 +1.19 ± 0.01 +0.39 ± 0.04 +3.4 ± 0.2 +0.88 ± 0.04 +20.6 ± 1.2 +177.0 (242) +18 +2.27 ± 0.01 +2.71 ± 0.10 +1.05 ± 0.02 +0.55 ± 0.04 +3.0 ± 0.3 +0.60 ± 0.06 +11.7 ± 0.8 +244.4 (229) +19 +2.24 ± 0.00 +2.61 ± 0.08 +0.95 ± 0.02 +0.46 ± 0.04 +3.8 ± 0.5 +0.65 ± 0.05 +14.3 ± 1.1 +203.6 (242) +20 +2.30 ± 0.01 +3.03 ± 0.02 +0.85 ± 0.01 +0.63 ± 0.02 +4.0 ± 0.2 +0.57 ± 0.03 +14.1 ± 0.4 +204.5 (240) +21 +2.31 ± 0.01 +3.38 ± 0.05 +0.92 ± 0.01 +0.76 ± 0.04 +2.7 ± 0.2 +0.44 ± 0.03 +13.5 ± 0.8 +198.2 (215) +22 +2.31 ± 0.02 +2.66 ± 0.03 +0.71 ± 0.02 +0.57 ± 0.03 +4.8 ± 0.4 +0.51 ± 0.04 +13.3 ± 0.6 +258.0 (219) +23 +2.28 ± 0.01 +3.07 ± 0.04 +0.85 ± 0.01 +0.55 ± 0.03 +4.5 ± 0.4 +0.66 ± 0.05 +9.1 ± 0.5 +223.1 (238) +24 +2.21 ± 0.00 +2.69 ± 0.08 +0.96 ± 0.02 +0.40 ± 0.05 +6.2 ± 1.5 +1.00 − 0.33 +12.8 ± 1.9 +191.4 (241) +25 +2.23 ± 0.00 +2.58 ± 0.03 +0.82 ± 0.02 +0.43 ± 0.03 +5.5 ± 0.7 +0.67 ± 0.08 +15.9 ± 0.5 +174.9 (242) +fitted all the PDS with a model consisting of up to five +Lorentzians to represent the broadband noise component +and the QPOs. Each Lorentzian has three parameters: the +centroid frequency, ν0, the full-width at half-maximum, +FWHM, and the total power, equal to the integral of the +Lorentzian function over the full frequency range. We only +included a Lorentzian in the model if its total power was at +least 3σ different from zero, given the error of this parameter. +We visually inspected the PDS from all segments and used +only those with a clear type-C QPO. +Next, we extracted PDS in 10 energy bands, 1.0–1.5, 1.5– +1.9, 1.9–2.3, 2.3–3.0, 3.0–3.5, 3.5–4.0, 4.0–5.0, 5.0–6.0, 6.0– +8.0, and 8.0–12.0 keV that we normalised to fractional rms for +each band. To extract phase/time lags, we computed FFTs +from the data in the ten energy bands and measured the lags +using the phases of the cross-spectra with the 2.0–3.0 keV +band as a reference, following the procedure of Nowak et al. +(1999b). To calculate the lags of the QPO, we averaged the +cross spectra within one full-width half-maximum around the +centroid frequency of the QPO for each segment in which we +detected a significant QPO. For 4 segments, marked with an +asterisk in Table 1, the QPO was insignificant in the lowest +energy bands. We merged some low-energy bands in those +cases and extracted the rms and lag spectra for 7 energy +bands (1.0–2.3, 2.3–3.5, 3.5–4.0, 4.0–5.0, 5.0–6.0, 6.0–8.0, and +8.0–12.0 keV). +2.2 Spectral analysis +We produced the spectra and background files using the +NICER background estimator tool 3C 50 RGv54. The +background-subtracted +spectrum +for +each +segment +was +re-binned using grppha such that each spectral bin had +at least 30 counts and the bins over-sampled the spectral +resolution of the detector by a factor 3. We used Heasoft +version 6.30 and CALDB version 20210707 to create the re- +sponse (rmf) and ancillary response (arf) files. We fitted the +time-averaged spectrum of the source in the 1.0 − 10.0 keV +band using the model tbabs*(diskbb+gauss+nthcomp) +in xspec. The Tbabs models the interstellar absorption. +We used the cross-section tables of Verner et al. (1996) +and the abundances of Wilms et al. (2000) and left the +hydrogen column density as a free parameter. The diskbb +component models the thermal emission from an optically +thick and geometrically thin accretion disc (Mitsuda et al. +1984, Makishima et al. 1986) while nthcomp (Zdziarski +et al. 1996, ˙Zycki et al. 1999) models the Comptonised +emission from the X-ray corona. We kept both the diskbb +parameters, the temperature at inner disk radius, kTin, and +the normalisation free. The nthcomp model parameters +are the power-law photon index, Γ, electron temperature, +kTe, seed photon temperature, kTbb, and normalization. +4 https://heasarc.gsfc.nasa.gov/docs/nicer/tools/nicer_ +bkg_est_tools.html +MNRAS 000, 1–15 (0000) + +Comptonizing medium of MAXI J1535−571 +5 +The seed-photon temperature kTbb was tied to kTin of +the diskbb component. We have fitted a relatively broad +iron line present in the residuals with a Gaussian, gauss +in xspec. In addition to the broad line, the spectra show +narrow residuals at ∼6.4 keV. We have added one more +gauss component to account for the narrow line (if required). +We fit the rms with the model vkompthdk*dilution5 +(Karpouzas et al. 2020; Bellavita et al. 2022) and the lag +spectra with the model vkompthdk at the QPO frequency. +vkompthdk can compute both the time-dependent and +the time-averaged spectrum. The time-dependent version of +vkompthdk is the one that fits the rms and lags. The time- +averaged version of vkompthdk is the same as nthcomp. +The parameters of vkompthdk are hence the temperature of +the seed photon source, kTs, the temperature of the corona, +kTe, the power-law index, Γ (all of them identical to kTbb, +kTe and Γ of nthcomp), plus the size of the corona, L, the +feedback fraction, η (between 0 to 1), the amplitude of the +variability of the external heating rate, δ ˙Hext, and the lag of +the model in the 2–3 keV energy band, reflag. These param- +eters can be used to compute the fraction of the corona flux, +ηint, that returns to the disc (see Karpouzas et al. 2020 for +details). The parameters L, η, δ ˙Hext, and reflag are only rel- +evant for the fits to the rms and lag spectra and do not affect +the time-averaged version of the vkompthdk. The parame- +ter reflag is an additive normalisation that allows the model +to match the data, given that the observer is free to choose +the reference energy band of the lags. We froze the electron +temperature of nthcomp and vkompthdk at kTe = 21 keV +(Sridhar et al. 2019) because the 1.0-10.0 keV energy band +is not suitable to constrain it. The dilution component is +a function of energy (E). It accounts for the fact that the +rms amplitude we observe is diluted by the emission of the +other components that we assume do not vary. The dilution +component is therefore defined as; +dilution(E) = +nthcomp(E) +diskbb(E) + gauss(E) + nthcomp(E) +(See details in Bellavita et al. (2022).) Because NH towards +the source is high, any emission below 1 keV could be at- +tributed to calibration artefacts; therefore, we have decided +to exclude data below 1.0 keV in our fits. Using HXMT data +in the 2–100 keV range, Zhang et al. (2022) reported a hydro- +gen column density, NH=5.6*1022 cm−2, that is higher than +the value we have obtained here using NICER in the 1–10 +keV range. +3 RESULTS +The left panel of Figure 1 shows the NICER light curve +of MAXI J1535 during its 2017 outburst. While the right +panel of Figure 1 shows the evolution of the source in the +HID. Here intensity is defined as the source count rate in +the 0.5–10.0 keV band, and hardness ratio (HR) is the ratio +of the source intensity in the 5.0–10.0 keV and 0.5–2.0 keV +bands. The colour scale shown at the right of both Figures +represents the QPO frequency range 1.8–9.0 Hz, with red +5 https://github.com/candebellavita/vkompth +being the lowest and navy blue being the highest end of the +QPO frequency range. The source’s X-ray count rate and +HR and their respective standard deviation values for each +segment are given in Table 1. +3.1 Spectral fits +From the fits to the time-averaged spectrum, the rms and +phase-lag spectra of the QPO for each segment, we find that +during the first two days of our observations, the inner disc +temperature, kTin, and the photon index, Γ, of the Comp- +tonised component first drop (Figure 2) as the source moves +to the right in the HID (Figure 1 right panel), from hardness +ratio ∼ 0.27 to hardness ratio ∼ 0.31. Between MJD 58010 +and MJD 58012, the source intensity increases, and the spec- +trum softens again. The source starts to move up and to the +left in the HID, and kTin and Γ increase very quickly for +about five days. At the end of this period, the source reaches +the highest intensity in our observations. The accretion disc +is the hottest, kTin ≈ 1.1 − 1.2 keV, and the Comptonised +component is described with Γ ≈ 2.7 − 2.8. At this point, the +source enters the HSS and the PDS show no QPOs. When +the source transitions back to the SIMS and the HIMS, at +around MJD 58025, kTin and Γ are approximately correlated +with the X-ray flux (see Figures 1 and 2). We give each seg- +ment’s spectral parameters and goodness of fit in Table 2. In +a few segments the reduced χ2 is less than 1 (last column of +Table 2). The low χ2 values come from the fit to the steady- +state spectra (SSS). We provide the χ2 and the number of +channels for the fits to the individual spectra and the total +χ2 and the number of degree of freedom in Table A.1. Un- +less otherwise specified, the errors represent the 1σ confidence +(68%) interval for the corresponding parameter. +3.2 Power Density Spectra +Following Belloni et al. (2002), we fit the PDS with a +0-centred Lorentzian to represent the broadband noise +component and three separate Lorentzians to fit the narrow +QPO, its harmonic component, and the high-frequency +noise. The features in the PDS have a frequency in the +ratio of 1:2, and we, therefore, identify the strongest peak +as the fundamental and the other as the second harmonic. +The PDS also shows a low-frequency noise component when +the strongest QPO peak was at a frequency above 4.0 Hz +(Figure 3). Therefore, we used an additional Lorentzian to +fit the low-frequency noise component whenever required. +We have studied the QPO fractional rms amplitude in the +0.5–10.0 keV energy band as a function of QPO frequency +(left panel of Figure 4) and confirmed that the QPO we +have identified as fundamental followed a similar relation to +the one found for GRS 1915+105 (Zhang et al. 2020). The +type-C QPO appears in the LHS and HIMS as a narrow +peak with high rms amplitude in the PDS. The properties +of the observed broadband noise and the QPO justify the +identification of the QPO as type-C (Casella et al. 2004). +We fitted the PDS for three different energy bands (0.5–2.0 +KeV, 2.0–4.0 keV, 4.0–10.0 keV) when the type-C QPO was +at 1.8 Hz, 4.5 Hz, and 7.0 Hz. We show the fitted PDS and +their respective frequency lag spectra in Figure 3. The lag +MNRAS 000, 1–15 (0000) + +6 +Rawat et. al. +Figure 2. The evolution of Γ of the corona (left panel) and kTin of the disc (right panel) of MAXI J1535−571. The values of Γ and kTin +are obtained from the fits to the time-averaged spectra, the rms and phase-lag spectra of the QPO. +and rms values at the QPO frequency are given in Appendix +Table A.2. When the QPO frequency is higher than 7.0 +Hz, the QPO fractional rms amplitude decreases, and the +harmonic component becomes insignificant. +The evolution of the QPO centroid frequency is shown in +the right panel of Figure 4. The QPO frequency first decreases +from 2.7 to 1.8 Hz and then increases to its maximum value of +9.0 Hz. After that, the QPO frequency varies in the 4.5 − 7.5 +Hz range. The QPO frequency and fractional rms amplitude +in the 0.5 − 10.0 keV band for each observation are given in +Table 1. We have plotted Γ and kTin as a function of QPO +frequency as shown in Figure 5. We found that both Γ and +kTin increase with QPO frequency. +To extract the rms spectrum, we fit the PDS in 10 energy +bands, fixing the QPO centroid frequency and FWHM to the +best-fitting values in the 2.0–10.0 keV PDS. The rms and +phase lag spectra when the QPO frequency was 1.8 Hz, 4.5 +Hz, and 7.0 Hz are shown in the top and bottom panels of Ap- +pendix Figure A1. While the fractional rms amplitude of the +QPO increases with photon energy for all QPO frequencies, +the rms spectrum steepens as the QPO frequency increases +from 1.8 Hz to 7.0 Hz (see upper panels in Appendix Fig- +ure A1). The change of the slope of the rms spectrum of the +QPO is driven by a factor ∼ 3 drop of the rms amplitude at +the lowest energies when the QPO is at low frequencies. In +contrast, the rms amplitude at the highest energies remains +more or less constant as the QPO frequency changes by a +factor of ∼ 4. Although, in general, the low-energy photons +at the QPO frequency lag behind the high-energy photons for +all QPO frequencies, the lag spectrum of the QPO changes +with QPO frequency. When the QPO frequency is between +1.8 Hz and 2.4 Hz, the lag spectrum shows a minimum at ∼ 4 +keV, with the photons at low and high energies lagging the +4–5 keV photons by 0.1 − 0.3 rad. As the QPO frequency in- +creases, the minimum of the lag spectrum of the QPO moves +to higher energies, with the minimum reaching ∼ 9 − 10 keV +at the highest QPO frequency, and the low-energy photons +lag the high-energy ones by up to ∼ 0.8 rad. The rms and +phase-lag spectra of the QPO in MAXI J1535 in these obser- +vations with NICER are consistent with the pattern observed +for the type-C QPO by Rawat et al. (2019) in GRS 1915+105 +and Garg et al. (2022) in MAXI J1535 with AstroSat, over +the common energy range of both instruments. +3.3 One component time-dependent Comptonization model +To understand the changes observed in the rms and lag spec- +tra of the QPO (see Section 3.2), we fitted the rms and +lag spectra of the QPO at each QPO frequency with the +vkompthdk model. During the fits we linked kTe and Γ of +nthcomp to kTe and Γ of vkompthdk. We first linked kTs +of vkompthdk to kTin of diskbb, and we found large resid- +uals in the fits of the phase-lag spectra (Figure 6) because +vkompthdk fails to reproduce the minimum of the lags. We +subsequently let kTin and kTs vary independently, and the +fits improve significantly (Figure 6). The simultaneous fitted +time-averaged spectra, rms spectra and lag spectra when the +QPO frequency was ∼1.8 Hz and the residuals of the best- +fitting model are shown in Figure 7 (The peak in the residuals +of the time-averaged spectra at 1.84 keV corresponds to the +absorption edge features of silicon.). We show a similar plot +for the QPO frequencies 4.5 Hz and 7.0 Hz (for which we +show a PDS in Figure 3) in the Appendix Figures A2 and +A3. We discuss the implication of letting kTin and kTs free +in Section 4.3. The best-fitting parameters and χ2 of the fits +are given in Table 2. +We plotted the model parameters as a function of QPO fre- +quency in Figure 8. The size of the corona decreases from +∼ 104 km (which corresponds to 670 Rg for a 10 M⊙ black +hole ) to ∼ 3×103 km (201 Rg) while the temperature of the +seed photon source, kTs, increases from ∼ 0.1 keV to ∼ 0.4 +keV as the QPO frequency increases from 1.8 Hz to ∼3.0 Hz. +At QPO frequencies ≥3.0 Hz, the size of the corona and the +temperature of the seed photon source remain more or less +constant at respectively ∼ 3 − 6 × 103 km and 0.5 keV. The +error bars on η are large, and it is hard to follow any trend if +present, although η appears to decrease from ∼0.8 to ∼0.6 as +the QPO frequency increases as shown in Appendix Figure +A4. The best-fitting values of η imply that ηint is in the range +of 10−25%. Comparing the trends in Figures 5 and 8, it is +apparent that there is a sudden change of the properties of +the source when the QPO frequency is below and above ∼ 3.0 +Hz. The change of behaviour of all the quantities appears to +occur at the same QPO frequency, which we call critical fre- +MNRAS 000, 1–15 (0000) + +Comptonizing medium of MAXI J1535−571 +7 +0.0010 +0.0100 +P(f)*f +QPO= 1.824 ± 0.004 Hz +0.5-2.0 keV +0.0010 +0.0100 +QPO= 1.820 ± 0.004 Hz +2.0-4.0 keV +0.0010 +0.0100 +0.1000 +QPO= 1.824 ± 0.004 Hz +4.0-10.0 keV +0.1 +1.0 +10.0 +frequency (Hz) +− 0.2 +0.0 +0.2 +Phase lag (rad) +0.1 +1.0 +10.0 +frequenc (Hz) +− 0.2 +0.0 +0.2 +0.1 +1.0 +10.0 +frequenc (Hz) +− 0.2 +0.0 +0.2 +0.0010 +0.0100 +P(f)*f +QPO= 4.43 ± 0.03 Hz +0.5-2.0 keV +0.0010 +0.0100 +QPO= 4.48 ± 0.02 Hz +2.0-4.0 keV +0.0010 +0.0100 +QPO= 4.51 ± 0.02 Hz +4.0-10.0 keV +0.1 +1.0 +10.0 +frequency (Hz) +− 0.25 +0.00 +0.25 +Phase lag (rad) +0.1 +1.0 +10.0 +freq ency (Hz) +− 0.25 +0.00 +0.25 +0.1 +1.0 +10.0 +freq ency (Hz) +− 0.25 +0.00 +0.25 +0.0000 +0.0001 +0.0010 +0.0100 +P(f)*f +QPO= 6.9 ± 0.1 Hz +0.5-2.0 keV +0.0000 +0.0001 +0.0010 +0.0100 +QPO= 7.06 ± 0.04 Hz +2.0-4.0 keV +0.0000 +0.0001 +0.0010 +0.0100 +QPO= 7.13 ± 0.03 Hz +4.0-10.0 keV +0.1 +1.0 +10.0 +frequency (Hz) +− 0.25 +0.00 +0.25 +Phase lag ( ad) +0.1 +1.0 +10.0 +f equency (Hz) +− 0.25 +0.00 +0.25 +0.1 +1.0 +10.0 +f equency (Hz) +− 0.25 +0.00 +0.25 +Figure 3. The top panels show the power density spectra (power multiplied by frequency) of MAXI J1535−571 for three QPO frequencies, +1.8 Hz, 4.5 Hz, and 7.0 Hz, and three different energy bands. The PDS is fitted with three to five Lorentzians. The bottom panels show +the frequency phase-lag spectra. The reference energy band is 0.5-10.0 keV here. The vertical dashed lines indicate the ranges over which +the QPO fundamental lags we measured (ν ± FWHM/2). +MNRAS 000, 1–15 (0000) + +8 +Rawat et. al. +2 +3 +4 +5 +6 +7 +8 +9 +QPO frequency (Hz) +2 +3 +4 +5 +6 +7 +QPO fractional rm (0.5-10.0 keV) +10 +15 +20 +25 +30 +35 +time (days since MJD=58000) +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +QPO frequency (Hz) +Figure 4. Left panel: QPO fractional rms amplitude in the 0.5–10.0 keV energy band as a function of QPO frequency for MAXI J1535−571. +Right panel: Evolution of the QPO frequency of MAXI 1535-571. The shaded area represents the radio jet quenching interval (Russell +et al. 2019). +2 +3 +4 +5 +6 +7 +8 +9 +QPO frequency (Hz) +2.0 +2.2 +2.4 +2.6 +2.8 +3.0 +3.2 +3.4 +3.6 +Γ +2 +3 +4 +5 +6 +7 +8 +9 +QPO frequency (Hz) +0.5 +0.6 +0.7 +0.8 +0.9 +1.0 +1.1 +1.2 +kTin (keV) +Figure 5. The dependence of Γ (left panel) and kTin (right panel) upon QPO frequency in MAXI J1535−571. The values of Γ and kTin +are obtained from the fits to the time-averaged spectra, the rms and phase-lag spectra of the QPO. +quency, νc. +To estimate the critical frequency, we assume that the break +in the relation of the disc and corona model parameters, and +time lags as a function of QPO frequency, happens at the +same QPO frequency, i.e., νc. In Figure 8 we show fits with a +power-law (red) and broken power-law (blue) to the relation +of L, kTs, time lag, kTin with QPO frequency. The parame- +ters of the broken power law are the power-law indices α1 and +α2 below and above the break frequency νc and a normalisa- +tion parameter. We have calculated the F-test probability for +the fits with a power law and a broken power-law and found +that the probability ranges from (0.2−1)×10−4, which indi- +cates that a broken power-law in general fits the data better +than a power law. (To account for the dispersion of the data +points around the model was larger than the statistical errors, +we have added a systematic of 6%.) The break for each indi- +vidual fit is in the range 2.7–2.8 Hz, and the break appears +to be at the same QPO frequency in all cases. Since there is +a hint of a break in the relationship of the time lags and kTin +with QPO frequency, we fitted all the four relations (L, kTs, +time lag, kTin) together with a broken power law model as +shown in Figure 8, with the critical frequency tied. We got +Table 3. Broken power-law best-fitting parameters to the relations +of L, kTs, time lags of the QPO and kTin vs. QPO frequency +shown in Figure 8. The parameters α1 and α2 are the power-law +indices for νQP O ≤ νc and νQP O > νc, respectively. +Parameter +α1 +α2 +bknpower norm +L (km) +1.8 ± 0.4 +0.5 ± 0.2 +(3.8 ± 1.3) × 104 +kTs (keV) +-2.2 ± 0.5 +-0.3 ± 0.2 +0.04 ± 0.01 +kTin (keV) +-0.6 ± 0.2 +-0.4 ± 0.1 +0.7 ± 0.1 +time lag (m sec) +0.6 ± 0.4 +1.2 ± 0.2 +0.007 ± 0.002 +Note: The best-fitting parameters values shown above are for the +joint fits of all the parameter vs. QPO frequency plot with νc tied. +νc = 3.0±0.4 Hz. If we let νc vary separately for each fit, the +χ2 changes from 141.84 (dof=88) to 133.38 (dof=85) with an +F-test probability of ∼ 0.15. This confirms that the best fit +does not improve significantly if we let νc free. We conclude +that the break is consistent with being at the same frequency +in all relations plotted in Figures 5 and 8. The details of the +best-fitting parameters are given in Table 3. +MNRAS 000, 1–15 (0000) + +Comptonizing medium of MAXI J1535−571 +9 +0.0 +0.1 +0.2 +0.3 + Phase lag (rad) +kTin and kTs free +kTs=kTin +1.0 +10.0 +Energy (keV) +−5 +0 +5 +(data-model)/error +Figure 6. The phase-lag spectra of the QPO of MAXI J1535−571 +fitted with the vkompthdk model keeping kTin and kTs tied to +each other (red), and free (black). The bottom panel shows the +respective residuals of the fits. The data corresponds to obs ID +1050360105 with QPO frequency∼1.8 Hz +4 DISCUSSION +We have analysed NICER observations of MAXI J1535−571 +during the initial phase of the outburst in September and +October 2017. The rms and lag spectrum of the type-C +QPO, the spectral parameters deduced from fits to the +time-averaged energy spectra of the source (the temperature +of the accretion disc, kTin), and the parameters from fits +to the rms and lag spectra of the QPO (the size of the +corona, L, the temperature of the source that provides the +seed photons that inverse-Compton scatter in the corona, +kTs, all change in a similar manner as the frequency of the +type-C QPO increases from 1.8 Hz to 9 Hz. While some of +these quantities increase (kTin, kTs, phase lags) and others +decrease (rms amplitude of the QPO, L ) with increasing +QPO frequency, we find that all these quantities show a sig- +nificant break in the relation at a QPO frequency νc ∼ 3.0 Hz. +At low QPO frequencies, the lag spectrum of the type-C +QPO in MAXI J1535 increases at low and high energies +and is minimum at ∼ 4 keV. This is similar to what is +observed for the type-B QPO in the black hole candidate +MAXI J1348−630 (Belloni et al. 2020, Garc´ıa et al. 2021). In +the case of MAXI J1348−630, Belloni et al. (2020) proposed +that the fact that photons at energies below ∼ 3 keV lag +behind photons at ∼ 3 keV is due to down scattering of +the photons emitted by the disc in the corona, that they +assume is the jet. To reach these conclusions, instead of a +black body-like seed spectrum, Belloni et al. (2020) assumed +a simplified seed-source spectrum that is flat between 2 and +3 keV and does not emit at other energies. Such a spectrum, +however, neglects the dilution of the lags caused by black +body photons emitted below 2 keV that escape without +being up-/down-scattered in the corona. If one considers +a more realistic (a black body or a disc) seed spectrum of +equivalent temperature, the lags turn out to be flat below +∼ 2 − 3 keV, different from what is observed (Kylafis et al. +2021). On the other hand, using the model of Karpouzas +et al. (2020), Garc´ıa et al. (2021) showed that the shape +of the lag spectrum (and the rms spectrum as well) of +MAXI J1348−630 can be explained by corona photons that +impinge back onto the accretion disc and emerge later and at +energies below those of the photons that were up-scattered in +the corona. This feedback loop between the corona and the +disc is the reason for the positive lags between the photons +with energies below ∼ 2 − 3 keV and those with energies of +∼ 2 − 3 keV. At the same time, inverse Compton scattering +in the corona explains that photons with energies above +∼ 2 − 3 keV lag behind the 2 − 3 keV photons. Our fits to +the rms and lag spectra of the QPO in MAXI J1535 here +show the same. +4.1 Connection of critical frequency with radio jet quenching +Using AstroSat, and swift observation of the period MJD +58008 − 58013 and 58004 − 58017, Mereminskiy et al. (2018) +and Bhargava et al. (2019) found a tight correlation between +the QPO frequency and the power-law index that models +the hard component in the energy spectrum. Using nicer +observation of the period MJD 58008.99 − 58037.68, we, on +the other hand, found a significant break in the spectral and +corona parameters as a function of QPO frequency. The rms +and lag spectra of the QPO below and above νc are also +significantly different. The break in the relation between the +QPO lags and QPO frequency at νc ∼3.0 Hz in MAXI J1535 +is similar to the break found by Zhang et al. (2020) in GRS +1915+105 when the QPO frequency is ∼2 Hz, and to the +one in GX 339-4 (Zhang et al. 2017) at a QPO frequency of +∼1.7 Hz. +Interestingly, the frequency of the QPO in MAXI J1535 +crosses the value of 3.0 Hz on September 17 2017 (MJD +58013; see Figure 4 and Table 1). This date coincides +with the time at which the radio emission from the jet +in this source is quenched (Russell et al. 2019), which we +marked by the shaded area in Figure 4. Indeed, the radio +emission of the jet in MAXI J1535 quenches in the period +MJD 58013.60 − 58014.18; after that, in the period MJD +58014.18 − 58015.37 (Table 1 Russell et al. 2019) the source +makes a transition from the hard intermediate to the soft +intermediate state. A similar behaviour has been observed +by M´endez et al. (2022) for GRS 1915+105, i.e., a low radio +emission at or above a QPO frequency of ∼2.0 Hz, and +increased radio emission below that QPO frequency, the +QPO frequency at which Zhang et al. (2020) found that the +lags of the QPO change from soft to hard. +4.2 Size of the corona +From fits to the rms and lag spectra of the QPO with +the vkompthdk, here we find that the size of the corona +decreases very rapidly from ∼ 104 km to ∼ 4000 − 5000 km +MNRAS 000, 1–15 (0000) + +10 +Rawat et. al. +1 +10 +100 +counts s−1 keV−1 +0.1 +0.05 +Fractional rms +1 +10 +2 +5 +−0.2 +0 +0.2 +Phase lags (rad) +Energy (keV) +−2 +0 +2 +(data−model)/error +−2 +−1 +0 +1 +2 +(data−model)/error +1 +10 +2 +5 +−1 +0 +1 +(data−model)/error +Energy (keV) +Figure 7. Fits of the vkompthdk model to the data of MAXI J1535—571. From top to bottom, the left panel shows the time-averaged +spectrum of the source fitted with the model tbabs*(diskbb+gauss+nthcomp), the rms spectrum of the QPO fitted with the model +vkompthdk*dilution, and the phase-lag spectrum of the QPO fitted with the model vkompthdk when the QPO frequency was at ∼1.8 +Hz. The right panels show the respective residuals of the best-fitting model to the data. The 2.0–3.0 keV band is the reference band for +the phase lag spectra. +when the QPO frequency increases from ∼ 1.8 Hz to ∼ 3.2 +Hz; from that point on the corona size remains more or less +constant or decreases slightly from ∼ 4000 − 5000 km down +to ∼ 3000 km as the QPO frequency increases from ∼ 3.2 Hz +up to ∼ 9 Hz. Figure 4 shows that the QPO frequency does +not increase monotonically during these observations. In +contrast, from Figures 4 and 8, it is apparent that the size of +the corona first increases from ∼ 2000 km to ∼ 104 km, and +it then decreases back to ∼ 3000 km (first 10 points in the +right panel of Figure 4). At this time, coincident with the +time that the radio emission from the jet is quenched (Russell +et al. 2019), the size of the corona continues decreasing but +at a lower rate than before. Assuming that MAXI J1535 +harbours a 10-solar mass black hole, the maximum and mini- +mum size of the corona are, respectively, ∼ 670 and ∼ 201 Rg. +At low QPO frequency, the trends of the corona size and +feedback fraction as a function of QPO frequency reported +in this work are similar to those in Zhang et al. (2022), and +both in their work and ours the relation between the size +of the corona and the frequency of the QPO shows a break +at νQP O ≈ 3 − 4 Hz. The difference between their and our +corona sizes in the common range of QPO frequency comes +from the coverage down to lower energies with NICER in our +case than in Zhang et al. (2022) with HXMT: The magnitude +of the lags of the QPO increases as energy decreases, and the +size of the corona in the vkompth model is driven by the +magnitude of the lags. Since we go to lower QPO frequencies +than Zhang et al. (2022), we find that the size of the corona +continues increasing as the QPO frequency decreases below +∼ 2 Hz, where they do not have data. At QPO frequencies +above ∼ 4 Hz Zhang et al. (2022) find an increase of the +corona size, whereas here we find that the size continues +decreasing with QPO frequency, albeit at a slower rate than +below ∼ 3 − 4 Hz. We note that Zhang et al. (2022) did not +include the effect of dilution of the non-variable components +MNRAS 000, 1–15 (0000) + +Comptonizing medium of MAXI J1535−571 +11 +2 +3 +4 +6 +9 +QPO frequency (H ) +104 +3 × 103 +4 × 103 +6 × 103 +L (km) +broken power-law +power-law +2 +3 +4 +6 +9 +QPO frequency (Hz) +10−1 +100 +2 10−1 +3 10−1 +4 10−1 +6 10−1 +kTs (keV) +broken power-law +power-law +2 +3 +4 +6 +9 +QPO freq ency (Hz) +10−3 +6 × 10−4 +2 × 10−3 +3 × 10−3 +4 × 10−3 +time lag (secs) +broken power-law +power-law +2 +3 +4 +6 +9 +QPO frequency (Hz) +100 +6 10−1 +kTin (keV) +broken power-law +power-law +Figure 8. Dependence of L, kTs, time lags of the QPO and kTin upon QPO frequency in MAXI J1535 −571. The red and blue dotted +lines show the best-fitting power law and a broken power-law to the data. The best-fitting parameters for each relation are given in Table +3. The time lags are between photons in the 1.0–12.0 keV and 2.0–6.0 keV bands at the QPO frequency. The vertical dotted dashed line +represents the best-fitting break frequency, νc = 3.0 Hz. +the rms amplitude of the QPO in their model, and that +dilution is more important at high QPO frequency, where +the contribution of the accretion disc to the total emission +increases. +Our result is similar to previous findings in other BHXBs +(e.g. Kara et al. 2019, Karpouzas et al. 2021). In contrast to +Kara et al. (2019) where a change of the vertical size of the +corona is proposed to explain the shorter reverberation lags +for MAXI J1820+070, De Marco et al. (2021) infer a change +in the inner accretion disc radius leading to smaller coronal +size than reported in this work. Using the JED-SAD model +for the same source, Marino et al. (2021) reported that the +size of the jet emitting region, which plays the corona role +in their model, of 30-60 Rg. Axelsson & Veledina (2021) +showed that the variability of the iron line feature could +not be explained using the lamp-post geometry assumed +by Kara et al. (2019) and, instead, a truncated inner hot +flow geometry is required. Using a spectral-timing model +based on propagating fluctuations and incorporating the +reverberation from the variable Comptonisation components, +Kawamura et al. (2022) further supported a truncated inner +hot flow geometry. However, we note that the mass accretion +rate propagation fluctuation mechanism used by Kawamura +et al. (2022) can only explain the hard lags, and a separate +mechanism is required to explain to soft lags in MAXI +J1820+070 and in the QPO of MAXI J1535−571 and other +sources. +The trend of the size of the corona vs QPO frequency is +similar in MAXI J1535−571 and GRS 1915+105 (see Figure +8, and the supplementary Figure 4 in M´endez et al. 2022 +and figure 5 in Garc´ıa et al. 2022). Using a reverberation +model for the lags of the broadband noise component in the +power spectrum, Wang et al. (2021) found a corona that +is ≳300 Rg in the hard to soft state transition of MAXI +J1820+070. Similarly, using polarimetry measurements with +PoGO+, Chauvin et al. (2018) found that the corona in +Cyg X-1 is ≳100 Rg, while they exclude a corona of ∼6 Rg +obtained from the lamp post model. The sizes reported in +this work are consistent with the values published by Kylafis +& Reig (2019), Kylafis et al. (2021), Reig & Kylafis (2021), +who used Monte Carlo simulations of Comptonization in +a jet. The Comptonization model used in this work has +some simplifications; for instance, the corona is spherically +symmetric with constant temperature and optical depth. +MNRAS 000, 1–15 (0000) + +12 +Rawat et. al. +This was discussed in Karpouzas et al. (2021), and Garc´ıa +et al. (2021) and, as explained in M´endez et al. (2022), since +the actual geometry of the corona is likely different, the +values given by the model should be considered as a char- +acteristic size of the corona rather than the actual radius of +a spherical corona (see M´endez et al. 2022; Garc´ıa et al. 2022). +The size of the corona that we infer from our model is +larger than the values obtained from fits to the energy spec- +tra of black-hole systems with models that consider reflection +off the accretion disc from a corona that is assumed to be a +lamppost emitter (e.g., Vincent et al. 2016). These spectral +fits yield corona sizes of 1−20 Rg (Fabian et al. 2012). Using +the average soft lags over a broad frequency range in the +power spectrum and light travel-time arguments, Wang et al. +(2022) found that corona sizes in a dozen black-hole systems +in the hard-intermediate state, during the transition from +the low-hard to the soft-intermediate state, are comparable, +within a factor of a few, to the ones we infer here (see also +Wang et al. 2021). Suppose the assumption that the lags of +the broadband noise reflect the light travel time from the +corona to the disc is correct. In that case, the corona sizes in +Wang et al. (2022) are, in fact, lower limits for two reasons: +(i) Wang et al. (2022) estimate the corona sizes based on +the average time lag over a broad frequency range, whereas +the magnitudes of the soft lags are larger than the average +over a large range of QPO frequencies (see, for instance, +their Fig. 3, panel h). (ii) Wang et al. (2022) measured the +lags between the bands 0.5 − 1 and 2 − 5 keV. Suppose the +lags are minimum at around ∼ 2 keV and increase both at +energies below and above that (see their Fig. 3, panel g). In +that case, the magnitude of the time lags between photons +at ∼ 2 and ∼ 0.5 keV, and hence the light travel distance +from the corona to the disc will be larger than what they +report. Notice, however, that in Kara et al. 2019, Wang +et al. 2021 and Wang et al. 2022, the authors estimate the +characteristic height of the lamppost corona above the disc. +Notice that it is not straightforward to infer sizes from +simple light travel-time arguments applied to the time +lags of the broadband noise components because: (i) The +broadband noise component in the power spectrum of +accreting black-hole and neutron-star systems is, in fact, +the combination of multiple Lorentzians (e.g., Psaltis et al. +1999, Nowak 2000). Since the properties of these Lorentzians +are correlated with each other (e.g., frequency-frequency +correlations in Psaltis et al. 1999) and with the source +spectral parameters (e.g., Vignarca et al. 2003; Mereminskiy +et al. 2018; Agrawal 2006 and references therein), therefore, +most likely, these Lorentzians are not just an empirical +description of the power spectrum, but each of them rep- +resents a relatively well-defined, over a limited frequency +range, variability component of the physical properties of +the accretion flow. Suppose this decomposition is correct (as +suggested by the works cited above). In that case, a more +logical and accurate way is to compute the phase lag that +results from the combined cross spectra of these Lorentzians +in the Fourier real and imaginary space. The phase-lag +calculated like that can be different from computed from the +average of the cross-spectrum over a broad frequency range +(as has been done in many works before, see, e.g. Nowak +et al. 1999a; Reig et al. 2000; Altamirano & M´endez 2015; +Wang et al. 2022). If the lags calculated from the Lorentzian +decomposition, as suggested above, were due to light travel +time, the magnitude of time lags (see, for instance, Fig. 6) +imply large corona sizes. So even combining the lags of the +Lorentzians in Fourier space will lead to big corona sizes. +ii) It needs to be clarified how to convert time lags into +distances using simple light travel-time arguments because +the lags depend strongly upon Fourier frequency (e.g., Fig. +3 panel h of Wang et al. 2022). Therefore, there is no single +Fourier frequency at which the time lag would represent the +correct light travel time that should be used to infer the +corona size. (We note that models like RELTRANS, Ingram +et al. (2019) calculate the full variability self consistently +instead of using simple light travel-time arguments.) +Given the typical magnitudes of the lags of the QPO (this +paper; Karpouzas et al. 2020; Garc´ıa et al. 2021; Karpouzas +et al. 2021; Bellavita et al. 2022) or of the broadband noise +component (Wang et al. 2022; but see above for the caveats +of these measurements) in these systems, any variability +model that interprets the observed lags as delays of photons +travelling through a medium around a compact object would +necessarily yield large corona sizes since time lags of a few +hundredths to a few tenths of seconds translate into light +travel distances of a few thousand to a few 10,000 km. +While propagation of accretion-rate fluctuations (Ar´evalo & +Uttley 2006) would yield smaller sizes of the comptonizing +region because, in this case, the viscous time scale is at play, +propagation of accretion-rate fluctuations only account for +hard lags. In contrast, the broadband noise component and +the QPOs often show soft lags. +Our results are not necessarily inconsistent with the QPO +frequency being due to Lense-Thirring Precession (LTP, +Stella & Vietri 1998; but see Mastichiadis et al. 2022). For +instance, Ingram et al. (2016) fitted the energy spectra of +the BHXRB H1743−322 over the cycle of a ∼4–5 QPO +and concluded that the results are consistent with LTP of +an inner hot torus in this source. However, as explained by +Ingram et al. (2016), their data could be reproduced equally +well if the torus was fixed and it was the disc the one that +processed at the Lense–Thirring precession frequency. Their +choice of one geometry over the other was based on the fact +that the rms spectrum of the QPO is hard, and hence the +emission at the QPO frequency could not come from the disc. +In the model of Karpouzas et al. (2020), the rms spectrum of +the QPO is a consequence of inverse-Compton scattering of +soft disc photons in the corona (the torus in the scenario of +Ingram et al. 2016), such that the high rms amplitude values +of the QPO at high energies may reflect the variability of the +soft disc emission at the Lense–Thirring precession frequency +that is inverse-Compton scattered in the corona. This, plus +the feedback from the corona to the disc, naturally explain +the variability of the iron line discussed by Ingram et al. +(2016) and the rms spectrum of the QPO. The LTP model +and the reverberation model for the lags of the QPO in GRS +1915+105 (Nathan et al. 2022) also yield a large corona +(unless one considers an extra lag due to thermalisation; +see Nathan et al. 2022). Therefore, the LTP model needs to +explain how a large corona, which should necessarily extend +beyond the disc’s inner truncation radius, can precess as +a solid body. However, whether the QPO frequency is due +to LTP is a matter of debate that needs to be addressed +MNRAS 000, 1–15 (0000) + +Comptonizing medium of MAXI J1535−571 +13 +by general relativistic magneto-hydrodynamic (GRMHD) +simulations, which is beyond the scope of this paper. +4.3 A Dual Corona +When we tied the inner-disc temperature of the time- +averaged spectra, kTin, to the seed-photon temperature of +the vkompthdk model, kTs, our fits could not reproduce +the shape of the lag spectrum. Letting these two parameters +free yields a significant improvement in the fit statistics +(see Section 3.3 and Figure 6). We speculate that this +difference between the seed photon temperature of nthcomp +and vkompthdk is due to a more complex structure of +the comptonizing region than that described by a uniform +corona. Sridhar et al. (2019), Bhargava et al. (2019) & Garg +et al. (2022) used AstroSat observations of MAXI J1535 that +coincide with the first few days of the NICER observations +reported in this work. They modelled the combined SXT and +LAXPC spectra and reported a lower inner disc temperature +(kTin=0.20–0.35 keV) than we found in this work. It should +be noted that Bhargava et al. (2019) and Garg et al. (2022) +modelled the spectra in the 1-30 keV energy range. Also, the +source is highly absorbed, and the spectrum drops at low +energies, so the reported inner disc temperature may not +be accurate. Sreehari et al. (2019) used the same AstroSat +observation and modelled the broadband spectra in the +0.3-80.0 keV band and reported electron temperatures with +nthcomp in the range 21-63 keV. Using the same AstroSat +observation, Sridhar et al. (2019) reported an electron +temperature of ∼21 keV. As the 0.8-10.0 keV spectra of +NICER could not constrain the electron temperature, we +chose to fix it to the values reported by Sreehari et al. +(2019) and Sridhar et al. (2019). The electron temperature +(∼90–108 keV) reported by Garg et al. 2022 is higher than +the value (∼21 keV) we have used in this work. It should be +noted that in Garg et al. (2022), they are fixed the optical +depth of the corona, which together with Γ gives kTe. +Using a dual-component comptonization model for type- +B QPOs, Garc´ıa et al. (2021) and Peirano et al. (2022) ar- +gued that the comptonizing medium of the BHXB sources, +MAXI J1348−630 and GX 339−4 consist of two coronas. A +relatively small corona of ∼300 km, close to the black hole +dominates the time-averaged spectra, and a large corona of +∼18000 km, possibly the jet, dominates the lag spectrum +(Peirano et al. 2022). Their best-fitting results yield a lower +seed photon temperature of the large corona compared to the +small corona, with the seed photon temperature of the small +corona linked to kTbb of nthcomp. Peirano et al. (2022) pro- +posed that this difference is due to the fact that the seed pho- +tons for the small corona come from the inner, hotter parts, +of the disc whereas the seed photons for the large corona +come from the outer, cooler parts, of the disc. A similar +dual-corona geometry could explain the difference between +kTin of the diskbb (linked to kTbb of nthcomp) and kTs of +vkompthdk in our fits. Since we find that kTbb > kTs, also in +MAX J1535−571 the small corona would dominate the emis- +sion of the time-averaged spectra, whereas the big corona +would dominate the lags. We found that the rms spectra do +not change much between the two fits (kTs=kTin or kTs free), +so we conclude that the rms amplitude is not affected much +by the size of the corona. The fraction of the corona flux that +returns to the disc is ηint 10–25 % in all the cases. This and +the large corona size further indicate that the large corona is +the jet. +5 SUMMARY AND CONCLUSIONS +We +have +analysed +all +NICER +observation +of +MAXI +J1535−571 taken on September and October 2017. We fit +the energy spectra of the source and the rms and lag spectra +of the type-C QPO in this source with the one-component +time dependent Comptonization model vkompthdk. Below +we summarize our results: +• The size of the corona of MAXI J1535−571 decreases +from 104 km when the QPO frequency is ≥2 Hz to ∼3000 +km when the QPO frequency is ∼9.0 Hz. +• The behaviour of all the spectral parameters and the rms +and lag spectra of the QPO changes above and below a critical +QPO frequency, νc =3.0±0.4 Hz. Interestingly, the time at +which this critical frequency happens coincide with the period +when the radio jet emission quenches for this source. +• Comparing our results with those in previous work, the +data are consistent with a dual corona: a small corona lying +close to the black hole and a larger one, possibly the jet. +ACKNOWLEDGEMENTS +This research is part of a project proposed for the COSPAR +PCB fellowship program. We would like to thank the ref- +eree for constructive comments that helped improve this +paper. DR would like to thank COSPAR, ISRO and Pro- +fessor Diego Altamirano for jointly funding the academic +visit to the University of Southampton. MM, FG and KK +acknowledge support from the research programme Athena +with project number 184.034.002, which is (partly) financed +by the Dutch Research Council (NWO). FG acknowledges +support from PIP 0102 and PIP 0113 (CONICET). FG is a +CONICET researcher. This work received financial support +from PICT-2017-2865 (ANPCyT). KA acknowledges support +from a UGC-UKIERI Phase 3 Thematic Partnership (UGC- +UKIERI-2017-18-006; PI: P. Gandhi). TMB acknowledges fi- +nancial contribution from PRIN INAF 2019 n.15. CB is a +fellow of Consejo Interuniversitario Nacional (CIN). +DATA AVAILABILITY +The NICER XTI observations used in this work are available +at NICER Archive6. +REFERENCES +Agrawal P. C., 2006, Advances in Space Research, 38, 2989 +Altamirano D., M´endez M., 2015, MNRAS, 449, 4027 +Altamirano D., Strohmayer T., 2012, ApJ, 754, L23 +Ar´evalo P., Uttley P., 2006, MNRAS, 367, 801 +6 https://heasarc.gsfc.nasa.gov/docs/nicer/nicer_archive. +html +MNRAS 000, 1–15 (0000) + +14 +Rawat et. al. +Axelsson M., Veledina A., 2021, MNRAS, 507, 2744 +Bellavita C., Garc´ıa F., M´endez M., Karpouzas K., 2022, MNRAS, +515, 2099 +Belloni T., Hasinger G., 1990, A&A, 230, 103 +Belloni T. M., Stella L., 2014, Space Sci. 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The columns are the observation number, the chi-square of the fit to the steady-state spectrum (χ2 +SSS), rms spectrum (χ2 +rms), +lag spectrum (χ2 +lag) with, in each case, the number of channels in each spectrum and the total reduced chi-square of the combined fit with +degree of freedom. +Obs no. +χ2 +SSS (channel) +χ2 +rms (channel) +χ2 +lag (channel) +χ2 +total (dof) +1 +206.9 (238) +15.5 (10) +9.0 (10) +231.4 (243) +2 +176.5 (237) +7.8 (10) +7.6 (10) +191.9 (242) +3 +219.5 (238) +7.7 (10) +13.3 (10) +240.5 (243) +4 +205.6 (238) +4.7 (10) +9.4 (10) +219.8 (243) +5 +206.8 (238) +13.8 (10) +21.8 (10) +242.3 (243) +6 +167.9 (238) +5.1 (10) +4.8 (10) +177.9 (243) +7 +165.9 (238) +5.0 (10) +2.4 (10) +173.2 (243) +8 +227.7 (238) +4.8 (10) +2.3 (10) +234.8 (243) +9 +157.1 (238) +5.0 (10) +7.2 (10) +169.3 (243) +10 +146.1 (238) +4.7 (10) +4.3 (10) +155.1 (243) +11 +176.4 (217) +13.0 (10) +2.7 (10) +192.2 (222) +12 +129.3 (238) +10.6 (10) +12.5 (10) +152.4 (243) +13 +157.3 (238) +7.3 (10) +11.8 (10) +176.3 (243) +14 +147.0 (238) +17.7 (10) +3.8 (10) +168.4 (242) +15 +183.9 (235) +9.3 (10) +2.7 (10) +195.8 (239) +16 +146.9 (238) +13.3 (7) +4.8 (7) +165.0 (236) +17 +142.4 (238) +23.0 (10) +11.6 (10) +177.0 (242) +18 +240.5 (231) +3.0 (7) +0.9 (7) +244.4 (229) +19 +184.0 (238) +10.5 (10) +9.1 (10) +203.6 (242) +20 +185.3 (235) +3.7 (10) +15.5 (10) +204.5 (240) +21 +181.6 (216) +11.6 (7) +5.1 (7) +198.2 (215) +22 +211.3 (214) +23.1 (10) +23.6 (10) +258.0 (219) +23 +183.8 (232) +26.2 (10) +13.1 (11) +223.1 (238) +24 +184.1 (238) +5.0 (10) +2.3 (9) +191.4 (241) +25 +159.6 (238) +5.2 (10) +10.1 (10) +174.9 (242) +Note: Notice that some parameters are linked in the combined fits and therefore we cannot give the number of degrees of freedom for +each individual fit. So, channel numbers for individual spectra are given here. +Figure A1. The top and bottom panels show respectively the fractional rms and phase-lag spectra of the type-C QPO in MAXI J1535−571 +fitted with vkompthdk model. The 2.0–3.0 keV band is the reference band for the phase lag spectra. +MNRAS 000, 1–15 (0000) + +Comptonizing medium of MAXI J1535−571 +17 +Table A.2. The columns are the observation number, QPO frequency, QPO fractional rms amplitude and time lags at the QPO frequency +of MAXI J1535−571. Here rms1 and lag1 are in the 0.5–2.0 keV band, rms2 and lag2 are in the 2.0–4.0 keV band, and rms3 and lag3 are +in the 4.0–10.0 keV band. The reference band for lags is 0.5–10.0 keV. +Obs no. +QPO frequency +QPO fractional +lag1 +QPO fractional +lag2 +QPO fractional +lag3 +(Hz) +rms1 (%) +(msec) +rms2 (%) +(msec) +rms3 (%) +(msec) +1 +2.74 ± 0.01 +5.2 ± 0.1 +10.2 ± 1.0 +7.3 ± 0.2 +−1.49 ± 0.38 +9.4 ± 0.3 +−6.4 ± 0.7 +2 +2.44 ± 0.01 +5.0 ± 0.2 +12.5 ± 0.9 +6.7 ± 0.2 +−2.22 ± 0.41 +8.7 ± 0.3 +−7.1 ± 0.7 +3 +2.32 ± 0.01 +5.5 ± 0.2 +12.7 ± 1.2 +6.8 ± 0.3 +−3.20 ± 0.54 +8.8 ± 0.4 +−6.0 ± 1.1 +4 +1.83 ± 0.01 +5.8 ± 0.1 +12.5 ± 0.8 +7.4 ± 0.2 +−4.63 ± 0.38 +8.7 ± 0.3 +−2.7 ± 0.7 +5 +1.81 ± 0.00 +5.8 ± 0.1 +12.1 ± 0.5 +7.4 ± 0.1 +−4.20 ± 0.22 +9.2 ± 0.1 +−3.2 ± 0.4 +6 +2.15 ± 0.01 +5.6 ± 0.2 +14.0 ± 0.9 +7.1 ± 0.2 +−3.24 ± 0.39 +8.6 ± 0.3 +−7.1 ± 0.7 +7 +2.41 ± 0.01 +5.8 ± 0.2 +13.3 ± 1.2 +7.7 ± 0.3 +−1.59 ± 0.47 +9.8 ± 0.4 +−9.4 ± 0.9 +8 +2.77 ± 0.01 +5.5 ± 0.2 +12.6 ± 1.1 +7.6 ± 0.2 +−2.05 ± 0.42 +9.5 ± 0.4 +−6.9 ± 0.9 +9 +2.75 ± 0.02 +5.3 ± 0.2 +12.3 ± 1.3 +7.2 ± 0.2 +−1.35 ± 0.57 +10.0 ± 0.4 +−8.4 ± 1.1 +10 +3.27 ± 0.02 +4.9 ± 0.2 +9.1 ± 1.5 +7.1 ± 0.3 +−1.44 ± 0.54 +10.6 ± 0.4 +−5.5 ± 1.0 +11 +3.19 ± 0.03 +5.3 ± 0.3 +12.6 ± 1.7 +7.0 ± 0.3 +−1.42 ± 0.65 +10.5 ± 0.5 +−7.1 ± 1.1 +12 +2.72 ± 0.01 +4.7 ± 0.2 +13.7 ± 0.9 +6.9 ± 0.2 +−1.79 ± 0.33 +9.3 ± 0.3 +−8.1 ± 0.6 +13 +2.84 ± 0.01 +5.4 ± 0.2 +13.1 ± 0.9 +7.6 ± 0.2 +−2.10 ± 0.32 +10.4 ± 0.3 +−6.7 ± 0.6 +14 +4.75 ± 0.01 +3.2 ± 0.3 +9.3 ± 0.8 +5.6 ± 0.1 +0.23 ± 0.24 +9.7 ± 0.2 +−6.2 ± 0.4 +15 +9.01 ± 0.04 +−− +4.4 ± 0.4 +1.5 ± 0.1 +0.07 ± 0.15 +3.7 ± 0.1 +−3.2 ± 0.2 +16 +7.54 ± 0.05 +1.4 ± 0.4 +6.4 ± 0.6 +2.2 ± 0.3 +0.50 ± 0.26 +6.0 ± 0.2 +−4.7 ± 0.3 +17 +7.54 ± 0.06 +1.3 ± 0.2 +5.3 ± 0.5 +2.8 ± 0.1 +0.20 ± 0.14 +5.9 ± 0.2 +−3.9 ± 0.2 +18 +7.09 ± 0.03 +1.1 ± 0.1 +4.8 ± 0.4 +2.2 ± 0.1 +0.01 ± 0.12 +5.3 ± 0.1 +−3.6 ± 0.2 +19 +5.42 ± 0.01 +2.7 ± 0.1 +7.9 ± 0.5 +4.6 ± 0.1 +−0.21 ± 0.17 +9.3 ± 0.2 +−4.6 ± 0.2 +20 +5.73 ± 0.01 +2.6 ± 0.1 +8.3 ± 0.2 +4.4 ± 0.1 +−0.40 ± 0.08 +9.1 ± 0.1 +−4.3 ± 0.1 +21 +6.77 ± 0.02 +1.9 ± 0.1 +6.4 ± 0.3 +3.3 ± 0.1 +−0.24 ± 0.10 +7.6 ± 0.1 +−3.7 ± 0.1 +22 +4.57 ± 0.01 +2.8 ± 0.1 +10.8 ± 0.4 +4.6 ± 0.1 +−0.91 ± 0.13 +8.2 ± 0.2 +−5.6 ± 0.2 +23 +4.82 ± 0.01 +2.0 ± 0.1 +9.5 ± 0.5 +4.0 ± 0.0 +−0.39 ± 0.13 +6.3 ± 0.1 +−5.3 ± 0.2 +24 +5.19 ± 0.03 +2.0 ± 0.2 +7.7 ± 1.7 +2.9 ± 0.2 +−0.23 ± 0.51 +7.2 ± 0.3 +−4.6 ± 0.8 +25 +4.50 ± 0.01 +3.1 ± 0.1 +9.1 ± 0.6 +5.2 ± 0.1 +−0.69 ± 0.22 +9.2 ± 0.2 +−5.1 ± 0.4 +MNRAS 000, 1–15 (0000) + +18 +Rawat et. al. +0.1 +1 +10 +100 +1000 +104 +counts s−1 keV−1 +0.1 +0.02 +0.05 +Fractional rms +1 +10 +2 +5 +0 +0.5 +Phase lags (rad) +Energy (keV) +−2 +0 +2 +(data−model)/error +−2 +−1 +0 +1 +2 +(data−model)/error +1 +10 +2 +5 +−2 +0 +2 +(data−model)/error +Energy (keV) +Figure A2. The same plot as shown in Figure 7 at ∼4.5 Hz QPO frequency in MAXI J1535−571. +MNRAS 000, 1–15 (0000) + +Comptonizing medium of MAXI J1535−571 +19 +0.1 +1 +10 +100 +1000 +104 +counts s−1 keV−1 +0.01 +0.1 +0.02 +0.05 +Fractional rms +1 +10 +2 +5 +−0.2 +0 +0.2 +0.4 +Phase lags (rad) +Energy (keV) +−2 +0 +2 +(data−model)/error +−2 +−1 +0 +1 +2 +(data−model)/error +1 +10 +2 +5 +−1 +0 +1 +(data−model)/error +Energy (keV) +Figure A3. The same plot as shown in Figure 7 at ∼7.0 Hz QPO frequency in MAXI J1535−571. +2 +3 +4 +5 +6 +7 +8 +9 +QPO frequency (Hz) +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +1.0 +η +Figure A4. Dependence of the η upon QPO frequency in MAXI J1535−571. The values of η are obtained from the fits to the time-averaged +spectra, the rms and phase-lag spectra of the QPO. +MNRAS 000, 1–15 (0000) + diff --git a/6dE3T4oBgHgl3EQfRAnz/content/tmp_files/load_file.txt b/6dE3T4oBgHgl3EQfRAnz/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..8bcca8af5eec405f8f13d6c820945d4814dd442a --- /dev/null +++ b/6dE3T4oBgHgl3EQfRAnz/content/tmp_files/load_file.txt @@ -0,0 +1,2613 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf,len=2612 +page_content='MNRAS 000, 1–15 (0000) Preprint 12 January 2023 Compiled using MNRAS LATEX style file v3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 The comptonizing medium of the black-hole X-ray binary MAXI J1535−571 through type-C quasi-periodic oscillations Divya Rawat1⋆, Mariano M´endez2, Federico Garc´ıa2,3,4, Diego Altamirano5, Konstantinos Karpouzas2,5, Liang Zhang5, Kevin Alabarta2,5, Tomaso M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Belloni6, Pankaj Jain7, Candela Bellavita4 1Inter-University Center for Astronomy and Astrophysics, Ganeshkhind, Pune 411007, India 2Kapteyn Astronomical Institute, University of Groningen, PO BOX 800, Groningen NL-9700 AV, the Netherlands 3Instituto Argentino de Radioastronom´ıa (CCT La Plata, CONICET;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' CICPBA;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' UNLP), C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5, (1894) Villa Elisa, Buenos Aires, Argentina 4Facultad de Ciencias Astron´omicas y Geof´ısicas, Universidad Nacional de La Plata, Paseo del Bosque, B1900FWA La Plata, Argentina 5School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK 6INAF-Osservatorio Astronomico di Brera, via E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Bianchi 46, I-23807, Merate, Italy 7Department of physics, IIT Kanpur, Kanpur, Uttar Pradesh 208016, India Accepted XXX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Received YYY;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' in original form ZZZ ABSTRACT We present a detailed spectral and temporal analysis of the black-hole candidate MAXI J1535−571 using NICER observations in September and October 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We focus specifically on observations in the hard-intermediate state when the source shows type-C quasi-periodic oscillations (QPOs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We fitted the time-averaged spectrum of the source and the rms and phase-lag spectra of the QPO with a one-component time-dependent Comptonization model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We found that the corona contracts from ∼ 104 to ∼ 3 × 103 km as the QPO frequency increases from ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 Hz to ∼ 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The fits suggest that the system would consists of two coronas, a small one that dominates the time- averaged spectrum and a larger one, possibly the jet, that dominates the rms and lag spectra of the QPO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We found a significant break in the relation of the spectral parameters of the source and the properties of the QPO, including its lag spectra, with QPO frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The change in the relations happens when the QPO frequency crosses a critical frequency νc ≈ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Interestingly, the QPO reaches this critical frequency simultaneously as the radio emission from the jet in this source is quenched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Key words: accretion, accretion discs — black hole physics — X-rays: binaries — X-rays: individual: MAXI J1535−571 1 INTRODUCTION In the outburst, the transient black-hole X-ray binary (BHXB) system shows substantial X-ray variability (Belloni & Stella 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' These systems spend long periods in qui- escence, with sporadic outbursts lasting weeks to months, during which the X-ray flux increases by up to three orders of magnitude compared to the quiescent phase (Remillard & McClintock 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' During an outburst, transient BHXBs initially appear in the low-hard state (LHS) and, as the outburst progresses, move to the high-soft state (HSS) via the hard-intermediate (HIMS) and soft-intermediate state (SIMS) (Belloni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2005, 2011, and references within).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Finally, before returning to the quiescent state, BHXBs transition from the HSS to the LHS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' In the LHS, a hard component due to Comptonization from an electron plasma with temperature 50 − 100 keV appears in the X-ray spec- trum as a power law with photon index 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 (Gilfanov 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' In contrast, the HSS spectrum is dominated by an optically thick thermal component generally modelled with a ⋆ E-mail: rawatdivya838@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='com (DR) multi-temperature disc blackbody, occasionally accompanied by a soft power-law-like component with Γ ≥2 (M´endez & van der Klis 1997;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Done et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The evolution of the outburst of a BHXB can be best characterised in a hardness-intensity diagram (HID), where typically systems trace a well-defined path often shaped as a “q” (Fender et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2004, Belloni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' These systems show complex fast-time variability, which is strongly state-dependent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' This variability takes the form of broadband noise components on top of which, in specific states, quasi-periodic oscillations (QPOs) can be observed (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 1997;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Takizawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 1997;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Psaltis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Nowak 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Casella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2004, 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Belloni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The QPOs appear in the power density spectrum (PDS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' van der Klis & Jansen 1985) as relatively narrow peaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The QPOs have been broadly divided into three categories, the mHz QPO with QPO frequency ranging from few mHz to Hz (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=', Dewangan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2006, Koljonen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2011, Altamirano & Strohmayer 2012, Pasham et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2013), low-frequency QPOs (LFQPOs) with frequencies ranging from just below 1 Hz up to 20 Hz (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=', Motta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2015), © 0000 The Authors arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='04418v1 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='HE] 11 Jan 2023 2 Rawat et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' and high-frequency QPOs (HFQPOs) with frequencies above 100 Hz and up to ∼500 Hz (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=', Miller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2001, Strohmayer 2001, Belloni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2012, M´endez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2013, Belloni & Stella 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' LFQPOs appear in different spectral states and have been further classified as type A, B, and C (Wijnands et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 1999, Homan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2001, Remillard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2002, Casella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Among the three types, type-C is the one that is most often observed, showing a high rms amplitude, between 1% and 20%, and a quality factor1 usually larger than 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 (Wijnands et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Casella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Belloni & Stella 2014, see Ingram & Motta 2019, for a review).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' MAXI J1535−571 (hereafter MAXI J1535) is a galactic transient, initially detected by MAXI/GSC (Negoro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2017a) and SWIFT/BAT (Kennea et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2017, Markwardt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2017) on September 2, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The X-ray variability (Negoro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2017b), optical (Scaringi & ASTR211 Stu- dents 2017) and near-infrared (Din¸cer 2017) properties of the source suggest that MAXI J1535 is a low-mass X-ray binary (LMXB) source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Radio observations with the Australia Telescope Compact Array (ATCA) show a signature of a compact radio jet (Russell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' this and the observed luminosity suggest that this system harbours a black hole (Negoro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2017b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Study of radio (Chauhan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2019) and X-ray (Sridhar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2019) observations suggest that the distance to the source is 4–6 kpc, and the jet inclination angle is constrained to ≤ 45◦ (Russell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' X-ray spectral studies suggest that the system harbours a near-maximally spinning black hole (Gendreau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2017, Xu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2018, Miller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' There are some conflicting estimates of the mass of the black hole in the system (Sreehari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2019, Sridhar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2019), but they are all based on fits to the X-ray spectrum and are therefore model dependent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' No dynamical mass measurement from optical observations is available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' A state transition study of MAXI J1535 during outburst, from September 2017 to April 2018 (Nakahira et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2018) shows that the source behaved like other BHXB systems tracing a q-shape in the HID (Tao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' In the LHS and HIMS, starting from September 9-18, 2017, MAXI J1535 showed a type-C QPO with a centroid frequency in the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 Hz range (Gendreau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2017, Mereminskiy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2018, Stiele & Kong 2018, Huang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2018, Bhargava et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The source transitioned to the SIMS and then to the HSS from September 19-26, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The stable and weak type A/B LFQPO appears in the SIMS (Stiele & Kong 2018, Stevens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2018, Huang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' In the HIMS and LHS, the type-C QPO reappears from September 26 to October 9, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' After the end of the main outburst in mid-May 2018, five re-brightening events were reported by Parikh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' A state transition during these re-flares was reported by C´uneo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2020) using NICER observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Kumar & Misra (2014) proposed a model to study the Comptonisation medium of neutron-star X-ray binary sys- 1 Quality factor=QPO frequency/QPO width tems, which was later extended by Karpouzas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' This model was originally developed for high-frequency QPOs in accreting neutron-star systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Still, it has been recently extended by Bellavita et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022) to LFQPOs in BHXBs and was applied to the type-C QPO in GRS 1915+105 by Karpouzas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2021) and M´endez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022), and the type-B QPO in MAXI J1348−630 (Garc´ıa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Bellavita et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022) has applied the same model using Insight-HXMT observations of the type-C QPO in MAXI J1535 up to 150 keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The rationale behind applying this model to type-C in BHXB is that the fractional rms amplitude of these QPOs can be as large as ∼ 15% up to ∼200 keV (Ma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' At those energies, Comptonization dominates the emission in these systems (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=', the disc and the reflection component peak at, respectively, ∼1−3 keV and ∼ 20−25 keV and both drop quickly above that), and hence Comptonization is most likely responsible for the rms amplitude and lags of the QPO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' In this paper, we report the results of the spectro-temporal analysis of MAXI J1535 using NICER observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' To study the Comptonization medium of the source, we fit the rms and phase-lag spectra of the QPO with a one-component time- dependent Comptonization model, vkompthdk (Karpouzas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Bellavita et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' In Section 2, we describe the observations and data analysis techniques, and in Section 3 we present the results of our analysis and the fits of the model to the rms and lag spectra of the type-C QPO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Finally, we discuss our findings in Section 4 and summarise our results in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2 OBSERVATION AND DATA ANALYSIS We used observations of MAXI J1535 obtained in September and October 2017 with the Neutron Star Interior Composi- tion Explorer (NICER Gendreau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The observa- tions ID’s used are 1050360101-1050360120 & 1130360101- 1130360114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' NICER’s XTI (X-ray Timing Instrument Gen- dreau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2016) covers the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2-12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV band and has an effective area of >2000 cm2 at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The energy and time resolutions are 85 eV at 1 keV and 4 ×10−8 s (hereafter ∆tnicer), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We used the nicerl22 task to process each observation applying the standard calibration process and screening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We used only those intervals for which the exposure time was > 100 s after running the nicerl2 task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' For some intervals, we found that the source flux was vary- ing significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' To make sure we are not averaging features of two spectrally and temporally different states, we divided a single observation into segments with a more or less con- stant source count rate and studied the temporal and spectral properties of each segment independently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The details of each observation and segment are given in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 Timing analysis We extracted the fractional rms amplitude (root-mean square) normalised (Belloni & Hasinger 1990) PDS for each 2 https://heasarc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='gsfc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='nasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='gov/docs/nicer/analysis_ threads/nicerl2/ MNRAS 000, 1–15 (0000) Comptonizing medium of MAXI J1535−571 3 Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Left panel: NICER light curve of MAXI J1535−571 in the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The shaded area represents the approximate time when the radio emission was quenched (Russell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Right panel: Hardness intensity diagram (HID) using NICER observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' In the HID, the line shows the general movement of the source in this diagram as the outburst progressed, with the start and end points of the outburst at, (HR = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='27, Intensity = 8000) and (HR = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='22, Intensity = 8000), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' In both panels, each point corresponds to 100 sec, and the colour scale panels indicate the frequency of the QPO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Observation log of MAXI J1535, including timing parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The columns are the observation number, the NICER ObsID, the start and end time of the observation, the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV count rate, the standard deviation of the count rate, σcount, the hardness ratio, HR, the standard deviation of the hardness ratio, σHR, the QPO centroid frequency and the QPO fractional rms amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The errors are at 1σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The observations with an asterisk are those for which the QPO was insignificant in the lowest energy bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Obs no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' ObsID Tstart Tstop count rate σcount HR σHR QPO frequency QPO Fractional (M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='D) (M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='D) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV) (5−10keV) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0keV) (Hz) rms (%) 1 1050360105 58008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='988 58009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='126 8140 ± 5 48 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='272 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='002 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='74 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 2 1050360105 58009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='165 58009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='193 7847 ± 4 36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='280 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='002 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='44 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 3 1050360105 58009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='229 58009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='301 7676 ± 6 30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='285 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='004 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='32 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='7 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 4 1050360105 58009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='807 58009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='945 7327 ± 4 65 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='307 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='003 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='83 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 5 1050360106 58010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='001 58010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='525 7364 ± 1 138 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='311 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='005 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='81 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='00 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 6 1050360107 58011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} 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+page_content='2 7 1050360108 58012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='187 58012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='258 9134 ± 3 130 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='294 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='006 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='41 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 8 1050360108 58012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='316 58012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='583 9492 ± 2 320 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='285 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='002 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='77 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 9 1050360109 58013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='216 58013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='222 10088 ± 1 4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='285 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='361 58031.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='894 11163 ± 2 370 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='234 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='006 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='82 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 24 1130360113 58036.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='498 58036.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='695 9747 ± 10 19 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='206 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='007 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='19 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 25 1130360114 58037.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='032 58037.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='677 8767 ± 4 183 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='224 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='004 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='50 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 segment using the General High-energy Aperiodic Timing Software (GHATS)3 version 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV data were re-binned in time by a factor of 62500, such that the time resolution was 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0025 s, corresponding to a Nyquist frequency of 200 Hz, and PDS were produced from intervals 3 http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='brera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='inaf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='it/utenti/belloni/GHATS_Package/ Home.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='html of 8192 points (20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='48 s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' For each segment, the PDS for the intervals were averaged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We fitted the PDS in the frequency 100-200 Hz, where the source shows no intrinsic variability, with a constant representing the Poisson noise, which we then subtracted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We ended up with an averaged, Poisson-noise subtracted PDS for each segment that we re-binned logarithmically such that each frequency bin is larger than the previous one by a factor exp(1/100).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=" We MNRAS 000, 1–15 (0000) without type-C QPOs with type-C QPOs18000 9 without type-C QPOs with type-C QPOs 16000 8 14000 7 [zH] Intensity [counts s' 12000 6 5 10000 4 8000 3 2 0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='22 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='24 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='26 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='28 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='32 HR [(5-10 keV)/(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5-2 keV)4 Rawat et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Time-averaged spectra and corona model parameters of MAXI J1535.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The columns are the observation number, the hydrogen column density, NH, the power-law photon index of nthcomp, Γ, the inner disc temperature, kTin, the seed photon temperature of vkompthdk, kTs, the size of the corona, L, the fraction of the flux of the seed-photon source due to feedback from the corona, η, and the amplitude of the variability of the external heating rate, δ ˙Hext.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The errors are at 1σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The observations with an asterisk are those for which the QPO was insignificant in the lowest energy bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Obs no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' NH Γ kTin kTs L η δ ˙Hext χ2 ν(dof) 1022 cm−2 (keV) (keV) ( 103 km) % 1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='19 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='43 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='68 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='35 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='05 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='62 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='05 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 231.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 (243) 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='19 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='29 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='62 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='29 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='03 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='75 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='09 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 191.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 223.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 (238) 24 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='21 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='00 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='69 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='96 ± 0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='9 191.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 (241) 25 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='23 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='00 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='58 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='82 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='43 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='03 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='67 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='08 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='9 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 174.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='9 (242) fitted all the PDS with a model consisting of up to five Lorentzians to represent the broadband noise component and the QPOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Each Lorentzian has three parameters: the centroid frequency, ν0, the full-width at half-maximum, FWHM, and the total power, equal to the integral of the Lorentzian function over the full frequency range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We only included a Lorentzian in the model if its total power was at least 3σ different from zero, given the error of this parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We visually inspected the PDS from all segments and used only those with a clear type-C QPO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Next, we extracted PDS in 10 energy bands, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5– 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='9, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='9–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3–3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0–3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0–5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0– 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0, and 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0–12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV that we normalised to fractional rms for each band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' To extract phase/time lags, we computed FFTs from the data in the ten energy bands and measured the lags using the phases of the cross-spectra with the 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0–3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV band as a reference, following the procedure of Nowak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (1999b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' To calculate the lags of the QPO, we averaged the cross spectra within one full-width half-maximum around the centroid frequency of the QPO for each segment in which we detected a significant QPO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' For 4 segments, marked with an asterisk in Table 1, the QPO was insignificant in the lowest energy bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We merged some low-energy bands in those cases and extracted the rms and lag spectra for 7 energy bands (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3–3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0–5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0–8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0, and 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0–12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 Spectral analysis We produced the spectra and background files using the NICER background estimator tool 3C 50 RGv54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The background-subtracted spectrum for each segment was re-binned using grppha such that each spectral bin had at least 30 counts and the bins over-sampled the spectral resolution of the detector by a factor 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We used Heasoft version 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='30 and CALDB version 20210707 to create the re- sponse (rmf) and ancillary response (arf) files.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We fitted the time-averaged spectrum of the source in the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 − 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV band using the model tbabs*(diskbb+gauss+nthcomp) in xspec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The Tbabs models the interstellar absorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We used the cross-section tables of Verner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (1996) and the abundances of Wilms et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2000) and left the hydrogen column density as a free parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The diskbb component models the thermal emission from an optically thick and geometrically thin accretion disc (Mitsuda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 1984, Makishima et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 1986) while nthcomp (Zdziarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 1996, ˙Zycki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 1999) models the Comptonised emission from the X-ray corona.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We kept both the diskbb parameters, the temperature at inner disk radius, kTin, and the normalisation free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The nthcomp model parameters are the power-law photon index, Γ, electron temperature, kTe, seed photon temperature, kTbb, and normalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 4 https://heasarc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='gsfc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='nasa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='gov/docs/nicer/tools/nicer_ bkg_est_tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='html MNRAS 000, 1–15 (0000) Comptonizing medium of MAXI J1535−571 5 The seed-photon temperature kTbb was tied to kTin of the diskbb component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We have fitted a relatively broad iron line present in the residuals with a Gaussian, gauss in xspec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' In addition to the broad line, the spectra show narrow residuals at ∼6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We have added one more gauss component to account for the narrow line (if required).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We fit the rms with the model vkompthdk*dilution5 (Karpouzas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Bellavita et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2022) and the lag spectra with the model vkompthdk at the QPO frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' vkompthdk can compute both the time-dependent and the time-averaged spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The time-dependent version of vkompthdk is the one that fits the rms and lags.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The time- averaged version of vkompthdk is the same as nthcomp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The parameters of vkompthdk are hence the temperature of the seed photon source, kTs, the temperature of the corona, kTe, the power-law index, Γ (all of them identical to kTbb, kTe and Γ of nthcomp), plus the size of the corona, L, the feedback fraction, η (between 0 to 1), the amplitude of the variability of the external heating rate, δ ˙Hext, and the lag of the model in the 2–3 keV energy band, reflag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' These param- eters can be used to compute the fraction of the corona flux, ηint, that returns to the disc (see Karpouzas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2020 for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The parameters L, η, δ ˙Hext, and reflag are only rel- evant for the fits to the rms and lag spectra and do not affect the time-averaged version of the vkompthdk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The parame- ter reflag is an additive normalisation that allows the model to match the data, given that the observer is free to choose the reference energy band of the lags.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We froze the electron temperature of nthcomp and vkompthdk at kTe = 21 keV (Sridhar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2019) because the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV energy band is not suitable to constrain it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The dilution component is a function of energy (E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' It accounts for the fact that the rms amplitude we observe is diluted by the emission of the other components that we assume do not vary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The dilution component is therefore defined as;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' dilution(E) = nthcomp(E) diskbb(E) + gauss(E) + nthcomp(E) (See details in Bellavita et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=') Because NH towards the source is high, any emission below 1 keV could be at- tributed to calibration artefacts;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' therefore, we have decided to exclude data below 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV in our fits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Using HXMT data in the 2–100 keV range, Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022) reported a hydro- gen column density, NH=5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6*1022 cm−2, that is higher than the value we have obtained here using NICER in the 1–10 keV range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 3 RESULTS The left panel of Figure 1 shows the NICER light curve of MAXI J1535 during its 2017 outburst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' While the right panel of Figure 1 shows the evolution of the source in the HID.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Here intensity is defined as the source count rate in the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5–10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV band, and hardness ratio (HR) is the ratio of the source intensity in the 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0–10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The colour scale shown at the right of both Figures represents the QPO frequency range 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8–9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Hz, with red 5 https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='com/candebellavita/vkompth being the lowest and navy blue being the highest end of the QPO frequency range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The source’s X-ray count rate and HR and their respective standard deviation values for each segment are given in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 Spectral fits From the fits to the time-averaged spectrum, the rms and phase-lag spectra of the QPO for each segment, we find that during the first two days of our observations, the inner disc temperature, kTin, and the photon index, Γ, of the Comp- tonised component first drop (Figure 2) as the source moves to the right in the HID (Figure 1 right panel), from hardness ratio ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='27 to hardness ratio ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Between MJD 58010 and MJD 58012, the source intensity increases, and the spec- trum softens again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The source starts to move up and to the left in the HID, and kTin and Γ increase very quickly for about five days.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' At the end of this period, the source reaches the highest intensity in our observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The accretion disc is the hottest, kTin ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 keV, and the Comptonised component is described with Γ ≈ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='7 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' At this point, the source enters the HSS and the PDS show no QPOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' When the source transitions back to the SIMS and the HIMS, at around MJD 58025, kTin and Γ are approximately correlated with the X-ray flux (see Figures 1 and 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We give each seg- ment’s spectral parameters and goodness of fit in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' In a few segments the reduced χ2 is less than 1 (last column of Table 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The low χ2 values come from the fit to the steady- state spectra (SSS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We provide the χ2 and the number of channels for the fits to the individual spectra and the total χ2 and the number of degree of freedom in Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Un- less otherwise specified, the errors represent the 1σ confidence (68%) interval for the corresponding parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 Power Density Spectra Following Belloni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2002), we fit the PDS with a 0-centred Lorentzian to represent the broadband noise component and three separate Lorentzians to fit the narrow QPO, its harmonic component, and the high-frequency noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The features in the PDS have a frequency in the ratio of 1:2, and we, therefore, identify the strongest peak as the fundamental and the other as the second harmonic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The PDS also shows a low-frequency noise component when the strongest QPO peak was at a frequency above 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Hz (Figure 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Therefore, we used an additional Lorentzian to fit the low-frequency noise component whenever required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We have studied the QPO fractional rms amplitude in the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5–10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV energy band as a function of QPO frequency (left panel of Figure 4) and confirmed that the QPO we have identified as fundamental followed a similar relation to the one found for GRS 1915+105 (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The type-C QPO appears in the LHS and HIMS as a narrow peak with high rms amplitude in the PDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The properties of the observed broadband noise and the QPO justify the identification of the QPO as type-C (Casella et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We fitted the PDS for three different energy bands (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 KeV, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0–10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV) when the type-C QPO was at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 Hz, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 Hz, and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We show the fitted PDS and their respective frequency lag spectra in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The lag MNRAS 000, 1–15 (0000) 6 Rawat et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The evolution of Γ of the corona (left panel) and kTin of the disc (right panel) of MAXI J1535−571.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The values of Γ and kTin are obtained from the fits to the time-averaged spectra, the rms and phase-lag spectra of the QPO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' and rms values at the QPO frequency are given in Appendix Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' When the QPO frequency is higher than 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Hz, the QPO fractional rms amplitude decreases, and the harmonic component becomes insignificant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The evolution of the QPO centroid frequency is shown in the right panel of Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The QPO frequency first decreases from 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='7 to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 Hz and then increases to its maximum value of 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' After that, the QPO frequency varies in the 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 − 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 Hz range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The QPO frequency and fractional rms amplitude in the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 − 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV band for each observation are given in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We have plotted Γ and kTin as a function of QPO frequency as shown in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We found that both Γ and kTin increase with QPO frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' To extract the rms spectrum, we fit the PDS in 10 energy bands, fixing the QPO centroid frequency and FWHM to the best-fitting values in the 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0–10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV PDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The rms and phase lag spectra when the QPO frequency was 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 Hz, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 Hz, and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Hz are shown in the top and bottom panels of Ap- pendix Figure A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' While the fractional rms amplitude of the QPO increases with photon energy for all QPO frequencies, the rms spectrum steepens as the QPO frequency increases from 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 Hz to 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Hz (see upper panels in Appendix Fig- ure A1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The change of the slope of the rms spectrum of the QPO is driven by a factor ∼ 3 drop of the rms amplitude at the lowest energies when the QPO is at low frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' In contrast, the rms amplitude at the highest energies remains more or less constant as the QPO frequency changes by a factor of ∼ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Although, in general, the low-energy photons at the QPO frequency lag behind the high-energy photons for all QPO frequencies, the lag spectrum of the QPO changes with QPO frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' When the QPO frequency is between 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 Hz and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 Hz, the lag spectrum shows a minimum at ∼ 4 keV, with the photons at low and high energies lagging the 4–5 keV photons by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 rad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' As the QPO frequency in- creases, the minimum of the lag spectrum of the QPO moves to higher energies, with the minimum reaching ∼ 9 − 10 keV at the highest QPO frequency, and the low-energy photons lag the high-energy ones by up to ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 rad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The rms and phase-lag spectra of the QPO in MAXI J1535 in these obser- vations with NICER are consistent with the pattern observed for the type-C QPO by Rawat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2019) in GRS 1915+105 and Garg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022) in MAXI J1535 with AstroSat, over the common energy range of both instruments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 One component time-dependent Comptonization model To understand the changes observed in the rms and lag spec- tra of the QPO (see Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2), we fitted the rms and lag spectra of the QPO at each QPO frequency with the vkompthdk model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' During the fits we linked kTe and Γ of nthcomp to kTe and Γ of vkompthdk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We first linked kTs of vkompthdk to kTin of diskbb, and we found large resid- uals in the fits of the phase-lag spectra (Figure 6) because vkompthdk fails to reproduce the minimum of the lags.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We subsequently let kTin and kTs vary independently, and the fits improve significantly (Figure 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The simultaneous fitted time-averaged spectra, rms spectra and lag spectra when the QPO frequency was ∼1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 Hz and the residuals of the best- fitting model are shown in Figure 7 (The peak in the residuals of the time-averaged spectra at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='84 keV corresponds to the absorption edge features of silicon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We show a similar plot for the QPO frequencies 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 Hz and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Hz (for which we show a PDS in Figure 3) in the Appendix Figures A2 and A3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We discuss the implication of letting kTin and kTs free in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The best-fitting parameters and χ2 of the fits are given in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We plotted the model parameters as a function of QPO fre- quency in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The size of the corona decreases from ∼ 104 km (which corresponds to 670 Rg for a 10 M⊙ black hole ) to ∼ 3×103 km (201 Rg) while the temperature of the seed photon source, kTs, increases from ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 keV to ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 keV as the QPO frequency increases from 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 Hz to ∼3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' At QPO frequencies ≥3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Hz, the size of the corona and the temperature of the seed photon source remain more or less constant at respectively ∼ 3 − 6 × 103 km and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The error bars on η are large, and it is hard to follow any trend if present, although η appears to decrease from ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 to ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 as the QPO frequency increases as shown in Appendix Figure A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The best-fitting values of η imply that ηint is in the range of 10−25%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Comparing the trends in Figures 5 and 8, it is apparent that there is a sudden change of the properties of the source when the QPO frequency is below and above ∼ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The change of behaviour of all the quantities appears to occur at the same QPO frequency, which we call critical fre- MNRAS 000, 1–15 (0000) Comptonizing medium of MAXI J1535−571 7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0010 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0100 P(f)*f QPO= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='824 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='004 Hz 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0010 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0100 QPO= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='820 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='004 Hz 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0010 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0100 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1000 QPO= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='824 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='004 Hz 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 frequency (Hz) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 Phase lag (rad) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 frequenc (Hz) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 frequenc (Hz) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0010 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0100 P(f)*f QPO= 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='43 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='03 Hz 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0010 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0100 QPO= 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='48 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='02 Hz 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0010 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0100 QPO= 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='51 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='02 Hz 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 frequency (Hz) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='25 Phase lag (rad) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 freq ency (Hz) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 freq ency (Hz) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0010 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0100 P(f)*f QPO= 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='9 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 Hz 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0010 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0100 QPO= 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='06 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='04 Hz 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0010 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0100 QPO= 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='13 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='03 Hz 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 frequency (Hz) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='25 Phase lag ( ad) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 f equency (Hz) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 f equency (Hz) − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='25 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The top panels show the power density spectra (power multiplied by frequency) of MAXI J1535−571 for three QPO frequencies, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 Hz, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 Hz, and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Hz, and three different energy bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The PDS is fitted with three to five Lorentzians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The bottom panels show the frequency phase-lag spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The reference energy band is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The vertical dashed lines indicate the ranges over which the QPO fundamental lags we measured (ν ± FWHM/2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' MNRAS 000, 1–15 (0000) 8 Rawat et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2 3 4 5 6 7 8 9 QPO frequency (Hz) 2 3 4 5 6 7 QPO fractional rm (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV) 10 15 20 25 30 35 time (days since MJD=58000) 1 2 3 4 5 6 7 8 9 10 QPO frequency (Hz) Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Left panel: QPO fractional rms amplitude in the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5–10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV energy band as a function of QPO frequency for MAXI J1535−571.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Right panel: Evolution of the QPO frequency of MAXI 1535-571.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The shaded area represents the radio jet quenching interval (Russell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2 3 4 5 6 7 8 9 QPO frequency (Hz) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 Γ 2 3 4 5 6 7 8 9 QPO frequency (Hz) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 kTin (keV) Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The dependence of Γ (left panel) and kTin (right panel) upon QPO frequency in MAXI J1535−571.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The values of Γ and kTin are obtained from the fits to the time-averaged spectra, the rms and phase-lag spectra of the QPO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' quency, νc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' To estimate the critical frequency, we assume that the break in the relation of the disc and corona model parameters, and time lags as a function of QPO frequency, happens at the same QPO frequency, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=', νc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' In Figure 8 we show fits with a power-law (red) and broken power-law (blue) to the relation of L, kTs, time lag, kTin with QPO frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The parame- ters of the broken power law are the power-law indices α1 and α2 below and above the break frequency νc and a normalisa- tion parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We have calculated the F-test probability for the fits with a power law and a broken power-law and found that the probability ranges from (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2−1)×10−4, which indi- cates that a broken power-law in general fits the data better than a power law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (To account for the dispersion of the data points around the model was larger than the statistical errors, we have added a systematic of 6%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=') The break for each indi- vidual fit is in the range 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='7–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 Hz, and the break appears to be at the same QPO frequency in all cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Since there is a hint of a break in the relationship of the time lags and kTin with QPO frequency, we fitted all the four relations (L, kTs, time lag, kTin) together with a broken power law model as shown in Figure 8, with the critical frequency tied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We got Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Broken power-law best-fitting parameters to the relations of L, kTs, time lags of the QPO and kTin vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' QPO frequency shown in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The parameters α1 and α2 are the power-law indices for νQP O ≤ νc and νQP O > νc, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Parameter α1 α2 bknpower norm L (km) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3) × 104 kTs (keV) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='04 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 kTin (keV) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='7 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 time lag (m sec) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='007 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='002 Note: The best-fitting parameters values shown above are for the joint fits of all the parameter vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' QPO frequency plot with νc tied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' νc = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' If we let νc vary separately for each fit, the χ2 changes from 141.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='84 (dof=88) to 133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='38 (dof=85) with an F-test probability of ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' This confirms that the best fit does not improve significantly if we let νc free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We conclude that the break is consistent with being at the same frequency in all relations plotted in Figures 5 and 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The details of the best-fitting parameters are given in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' MNRAS 000, 1–15 (0000) Comptonizing medium of MAXI J1535−571 9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 Phase lag (rad) kTin and kTs free kTs=kTin 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Energy (keV) −5 0 5 (data-model)/error Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The phase-lag spectra of the QPO of MAXI J1535−571 fitted with the vkompthdk model keeping kTin and kTs tied to each other (red), and free (black).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The bottom panel shows the respective residuals of the fits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The data corresponds to obs ID 1050360105 with QPO frequency∼1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 Hz 4 DISCUSSION We have analysed NICER observations of MAXI J1535−571 during the initial phase of the outburst in September and October 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The rms and lag spectrum of the type-C QPO, the spectral parameters deduced from fits to the time-averaged energy spectra of the source (the temperature of the accretion disc, kTin), and the parameters from fits to the rms and lag spectra of the QPO (the size of the corona, L, the temperature of the source that provides the seed photons that inverse-Compton scatter in the corona, kTs, all change in a similar manner as the frequency of the type-C QPO increases from 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 Hz to 9 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' While some of these quantities increase (kTin, kTs, phase lags) and others decrease (rms amplitude of the QPO, L ) with increasing QPO frequency, we find that all these quantities show a sig- nificant break in the relation at a QPO frequency νc ∼ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' At low QPO frequencies, the lag spectrum of the type-C QPO in MAXI J1535 increases at low and high energies and is minimum at ∼ 4 keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' This is similar to what is observed for the type-B QPO in the black hole candidate MAXI J1348−630 (Belloni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2020, Garc´ıa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' In the case of MAXI J1348−630, Belloni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2020) proposed that the fact that photons at energies below ∼ 3 keV lag behind photons at ∼ 3 keV is due to down scattering of the photons emitted by the disc in the corona, that they assume is the jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' To reach these conclusions, instead of a black body-like seed spectrum, Belloni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2020) assumed a simplified seed-source spectrum that is flat between 2 and 3 keV and does not emit at other energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Such a spectrum, however, neglects the dilution of the lags caused by black body photons emitted below 2 keV that escape without being up-/down-scattered in the corona.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' If one considers a more realistic (a black body or a disc) seed spectrum of equivalent temperature, the lags turn out to be flat below ∼ 2 − 3 keV, different from what is observed (Kylafis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' On the other hand, using the model of Karpouzas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2020), Garc´ıa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2021) showed that the shape of the lag spectrum (and the rms spectrum as well) of MAXI J1348−630 can be explained by corona photons that impinge back onto the accretion disc and emerge later and at energies below those of the photons that were up-scattered in the corona.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' This feedback loop between the corona and the disc is the reason for the positive lags between the photons with energies below ∼ 2 − 3 keV and those with energies of ∼ 2 − 3 keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' At the same time, inverse Compton scattering in the corona explains that photons with energies above ∼ 2 − 3 keV lag behind the 2 − 3 keV photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Our fits to the rms and lag spectra of the QPO in MAXI J1535 here show the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 Connection of critical frequency with radio jet quenching Using AstroSat, and swift observation of the period MJD 58008 − 58013 and 58004 − 58017, Mereminskiy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2018) and Bhargava et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2019) found a tight correlation between the QPO frequency and the power-law index that models the hard component in the energy spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Using nicer observation of the period MJD 58008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='99 − 58037.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='68, we, on the other hand, found a significant break in the spectral and corona parameters as a function of QPO frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The rms and lag spectra of the QPO below and above νc are also significantly different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The break in the relation between the QPO lags and QPO frequency at νc ∼3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Hz in MAXI J1535 is similar to the break found by Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2020) in GRS 1915+105 when the QPO frequency is ∼2 Hz, and to the one in GX 339-4 (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2017) at a QPO frequency of ∼1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='7 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Interestingly, the frequency of the QPO in MAXI J1535 crosses the value of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Hz on September 17 2017 (MJD 58013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' see Figure 4 and Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' This date coincides with the time at which the radio emission from the jet in this source is quenched (Russell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2019), which we marked by the shaded area in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Indeed, the radio emission of the jet in MAXI J1535 quenches in the period MJD 58013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='60 − 58014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='18;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' after that, in the period MJD 58014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='18 − 58015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='37 (Table 1 Russell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2019) the source makes a transition from the hard intermediate to the soft intermediate state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' A similar behaviour has been observed by M´endez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022) for GRS 1915+105, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=', a low radio emission at or above a QPO frequency of ∼2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Hz, and increased radio emission below that QPO frequency, the QPO frequency at which Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2020) found that the lags of the QPO change from soft to hard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 Size of the corona From fits to the rms and lag spectra of the QPO with the vkompthdk, here we find that the size of the corona decreases very rapidly from ∼ 104 km to ∼ 4000 − 5000 km MNRAS 000, 1–15 (0000) 10 Rawat et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 1 10 100 counts s−1 keV−1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='05 Fractional rms 1 10 2 5 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 Phase lags (rad) Energy (keV) −2 0 2 (data−model)/error −2 −1 0 1 2 (data−model)/error 1 10 2 5 −1 0 1 (data−model)/error Energy (keV) Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Fits of the vkompthdk model to the data of MAXI J1535—571.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' From top to bottom, the left panel shows the time-averaged spectrum of the source fitted with the model tbabs*(diskbb+gauss+nthcomp), the rms spectrum of the QPO fitted with the model vkompthdk*dilution, and the phase-lag spectrum of the QPO fitted with the model vkompthdk when the QPO frequency was at ∼1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The right panels show the respective residuals of the best-fitting model to the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0–3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV band is the reference band for the phase lag spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' when the QPO frequency increases from ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 Hz to ∼ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 Hz;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' from that point on the corona size remains more or less constant or decreases slightly from ∼ 4000 − 5000 km down to ∼ 3000 km as the QPO frequency increases from ∼ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 Hz up to ∼ 9 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Figure 4 shows that the QPO frequency does not increase monotonically during these observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' In contrast, from Figures 4 and 8, it is apparent that the size of the corona first increases from ∼ 2000 km to ∼ 104 km, and it then decreases back to ∼ 3000 km (first 10 points in the right panel of Figure 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' At this time, coincident with the time that the radio emission from the jet is quenched (Russell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2019), the size of the corona continues decreasing but at a lower rate than before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Assuming that MAXI J1535 harbours a 10-solar mass black hole, the maximum and mini- mum size of the corona are, respectively, ∼ 670 and ∼ 201 Rg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' At low QPO frequency, the trends of the corona size and feedback fraction as a function of QPO frequency reported in this work are similar to those in Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022), and both in their work and ours the relation between the size of the corona and the frequency of the QPO shows a break at νQP O ≈ 3 − 4 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The difference between their and our corona sizes in the common range of QPO frequency comes from the coverage down to lower energies with NICER in our case than in Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022) with HXMT: The magnitude of the lags of the QPO increases as energy decreases, and the size of the corona in the vkompth model is driven by the magnitude of the lags.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Since we go to lower QPO frequencies than Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022), we find that the size of the corona continues increasing as the QPO frequency decreases below ∼ 2 Hz, where they do not have data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' At QPO frequencies above ∼ 4 Hz Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022) find an increase of the corona size, whereas here we find that the size continues decreasing with QPO frequency, albeit at a slower rate than below ∼ 3 − 4 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We note that Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022) did not include the effect of dilution of the non-variable components MNRAS 000,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 1–15 (0000) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='Comptonizing medium of MAXI J1535−571 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='11 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='9 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='QPO frequency (H ) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='104 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 × 103 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 × 103 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 × 103 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='L (km) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='broken power-law ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='power-law ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='9 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='QPO frequency (Hz) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='10−1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='10−1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='10−1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='10−1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='10−1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='kTs (keV) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='broken power-law ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='power-law ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='9 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='QPO freq ency (Hz) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='10−3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 × 10−4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 × 10−3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 × 10−3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 × 10−3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='time lag (secs) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='broken power-law ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='power-law ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='9 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='QPO frequency (Hz) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='10−1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='kTin (keV) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='broken power-law ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='power-law ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Dependence of L, kTs, time lags of the QPO and kTin upon QPO frequency in MAXI J1535 −571.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The red and blue dotted lines show the best-fitting power law and a broken power-law to the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The best-fitting parameters for each relation are given in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The time lags are between photons in the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0–12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV bands at the QPO frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The vertical dotted dashed line represents the best-fitting break frequency, νc = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' the rms amplitude of the QPO in their model, and that dilution is more important at high QPO frequency, where the contribution of the accretion disc to the total emission increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Our result is similar to previous findings in other BHXBs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Kara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2019, Karpouzas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' In contrast to Kara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2019) where a change of the vertical size of the corona is proposed to explain the shorter reverberation lags for MAXI J1820+070, De Marco et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2021) infer a change in the inner accretion disc radius leading to smaller coronal size than reported in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Using the JED-SAD model for the same source, Marino et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2021) reported that the size of the jet emitting region, which plays the corona role in their model, of 30-60 Rg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Axelsson & Veledina (2021) showed that the variability of the iron line feature could not be explained using the lamp-post geometry assumed by Kara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2019) and, instead, a truncated inner hot flow geometry is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Using a spectral-timing model based on propagating fluctuations and incorporating the reverberation from the variable Comptonisation components, Kawamura et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022) further supported a truncated inner hot flow geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' However, we note that the mass accretion rate propagation fluctuation mechanism used by Kawamura et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022) can only explain the hard lags, and a separate mechanism is required to explain to soft lags in MAXI J1820+070 and in the QPO of MAXI J1535−571 and other sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The trend of the size of the corona vs QPO frequency is similar in MAXI J1535−571 and GRS 1915+105 (see Figure 8, and the supplementary Figure 4 in M´endez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2022 and figure 5 in Garc´ıa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Using a reverberation model for the lags of the broadband noise component in the power spectrum, Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2021) found a corona that is ≳300 Rg in the hard to soft state transition of MAXI J1820+070.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Similarly, using polarimetry measurements with PoGO+, Chauvin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2018) found that the corona in Cyg X-1 is ≳100 Rg, while they exclude a corona of ∼6 Rg obtained from the lamp post model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The sizes reported in this work are consistent with the values published by Kylafis & Reig (2019), Kylafis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2021), Reig & Kylafis (2021), who used Monte Carlo simulations of Comptonization in a jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The Comptonization model used in this work has some simplifications;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' for instance, the corona is spherically symmetric with constant temperature and optical depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' MNRAS 000, 1–15 (0000) 12 Rawat et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' This was discussed in Karpouzas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2021), and Garc´ıa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2021) and, as explained in M´endez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022), since the actual geometry of the corona is likely different, the values given by the model should be considered as a char- acteristic size of the corona rather than the actual radius of a spherical corona (see M´endez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Garc´ıa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The size of the corona that we infer from our model is larger than the values obtained from fits to the energy spec- tra of black-hole systems with models that consider reflection off the accretion disc from a corona that is assumed to be a lamppost emitter (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=', Vincent et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' These spectral fits yield corona sizes of 1−20 Rg (Fabian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Using the average soft lags over a broad frequency range in the power spectrum and light travel-time arguments, Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022) found that corona sizes in a dozen black-hole systems in the hard-intermediate state, during the transition from the low-hard to the soft-intermediate state, are comparable, within a factor of a few, to the ones we infer here (see also Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Suppose the assumption that the lags of the broadband noise reflect the light travel time from the corona to the disc is correct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' In that case, the corona sizes in Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022) are, in fact, lower limits for two reasons: (i) Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022) estimate the corona sizes based on the average time lag over a broad frequency range, whereas the magnitudes of the soft lags are larger than the average over a large range of QPO frequencies (see, for instance, their Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 3, panel h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (ii) Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022) measured the lags between the bands 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 − 1 and 2 − 5 keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Suppose the lags are minimum at around ∼ 2 keV and increase both at energies below and above that (see their Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 3, panel g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' In that case, the magnitude of the time lags between photons at ∼ 2 and ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 keV, and hence the light travel distance from the corona to the disc will be larger than what they report.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Notice, however, that in Kara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2019, Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2021 and Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2022, the authors estimate the characteristic height of the lamppost corona above the disc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Notice that it is not straightforward to infer sizes from simple light travel-time arguments applied to the time lags of the broadband noise components because: (i) The broadband noise component in the power spectrum of accreting black-hole and neutron-star systems is, in fact, the combination of multiple Lorentzians (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=', Psaltis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 1999, Nowak 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Since the properties of these Lorentzians are correlated with each other (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=', frequency-frequency correlations in Psaltis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 1999) and with the source spectral parameters (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=', Vignarca et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Mereminskiy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Agrawal 2006 and references therein), therefore, most likely, these Lorentzians are not just an empirical description of the power spectrum, but each of them rep- resents a relatively well-defined, over a limited frequency range, variability component of the physical properties of the accretion flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Suppose this decomposition is correct (as suggested by the works cited above).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' In that case, a more logical and accurate way is to compute the phase lag that results from the combined cross spectra of these Lorentzians in the Fourier real and imaginary space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The phase-lag calculated like that can be different from computed from the average of the cross-spectrum over a broad frequency range (as has been done in many works before, see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Nowak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 1999a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Reig et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Altamirano & M´endez 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' If the lags calculated from the Lorentzian decomposition, as suggested above, were due to light travel time, the magnitude of time lags (see, for instance, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 6) imply large corona sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' So even combining the lags of the Lorentzians in Fourier space will lead to big corona sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' ii) It needs to be clarified how to convert time lags into distances using simple light travel-time arguments because the lags depend strongly upon Fourier frequency (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=', Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 3 panel h of Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Therefore, there is no single Fourier frequency at which the time lag would represent the correct light travel time that should be used to infer the corona size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (We note that models like RELTRANS, Ingram et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2019) calculate the full variability self consistently instead of using simple light travel-time arguments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=') Given the typical magnitudes of the lags of the QPO (this paper;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Karpouzas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Garc´ıa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Karpouzas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Bellavita et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2022) or of the broadband noise component (Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' but see above for the caveats of these measurements) in these systems, any variability model that interprets the observed lags as delays of photons travelling through a medium around a compact object would necessarily yield large corona sizes since time lags of a few hundredths to a few tenths of seconds translate into light travel distances of a few thousand to a few 10,000 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' While propagation of accretion-rate fluctuations (Ar´evalo & Uttley 2006) would yield smaller sizes of the comptonizing region because, in this case, the viscous time scale is at play, propagation of accretion-rate fluctuations only account for hard lags.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' In contrast, the broadband noise component and the QPOs often show soft lags.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Our results are not necessarily inconsistent with the QPO frequency being due to Lense-Thirring Precession (LTP, Stella & Vietri 1998;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' but see Mastichiadis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' For instance, Ingram et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2016) fitted the energy spectra of the BHXRB H1743−322 over the cycle of a ∼4–5 QPO and concluded that the results are consistent with LTP of an inner hot torus in this source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' However, as explained by Ingram et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2016), their data could be reproduced equally well if the torus was fixed and it was the disc the one that processed at the Lense–Thirring precession frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Their choice of one geometry over the other was based on the fact that the rms spectrum of the QPO is hard, and hence the emission at the QPO frequency could not come from the disc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' In the model of Karpouzas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2020), the rms spectrum of the QPO is a consequence of inverse-Compton scattering of soft disc photons in the corona (the torus in the scenario of Ingram et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2016), such that the high rms amplitude values of the QPO at high energies may reflect the variability of the soft disc emission at the Lense–Thirring precession frequency that is inverse-Compton scattered in the corona.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' This, plus the feedback from the corona to the disc, naturally explain the variability of the iron line discussed by Ingram et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2016) and the rms spectrum of the QPO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The LTP model and the reverberation model for the lags of the QPO in GRS 1915+105 (Nathan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2022) also yield a large corona (unless one considers an extra lag due to thermalisation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' see Nathan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Therefore, the LTP model needs to explain how a large corona, which should necessarily extend beyond the disc’s inner truncation radius, can precess as a solid body.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' However, whether the QPO frequency is due to LTP is a matter of debate that needs to be addressed MNRAS 000, 1–15 (0000) Comptonizing medium of MAXI J1535−571 13 by general relativistic magneto-hydrodynamic (GRMHD) simulations, which is beyond the scope of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 A Dual Corona When we tied the inner-disc temperature of the time- averaged spectra, kTin, to the seed-photon temperature of the vkompthdk model, kTs, our fits could not reproduce the shape of the lag spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Letting these two parameters free yields a significant improvement in the fit statistics (see Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 and Figure 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We speculate that this difference between the seed photon temperature of nthcomp and vkompthdk is due to a more complex structure of the comptonizing region than that described by a uniform corona.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Sridhar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2019), Bhargava et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2019) & Garg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022) used AstroSat observations of MAXI J1535 that coincide with the first few days of the NICER observations reported in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' They modelled the combined SXT and LAXPC spectra and reported a lower inner disc temperature (kTin=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='20–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='35 keV) than we found in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' It should be noted that Bhargava et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2019) and Garg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022) modelled the spectra in the 1-30 keV energy range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Also, the source is highly absorbed, and the spectrum drops at low energies, so the reported inner disc temperature may not be accurate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Sreehari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2019) used the same AstroSat observation and modelled the broadband spectra in the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3-80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV band and reported electron temperatures with nthcomp in the range 21-63 keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Using the same AstroSat observation, Sridhar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2019) reported an electron temperature of ∼21 keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' As the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV spectra of NICER could not constrain the electron temperature, we chose to fix it to the values reported by Sreehari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2019) and Sridhar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The electron temperature (∼90–108 keV) reported by Garg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2022 is higher than the value (∼21 keV) we have used in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' It should be noted that in Garg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022), they are fixed the optical depth of the corona, which together with Γ gives kTe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Using a dual-component comptonization model for type- B QPOs, Garc´ıa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2021) and Peirano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022) ar- gued that the comptonizing medium of the BHXB sources, MAXI J1348−630 and GX 339−4 consist of two coronas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' A relatively small corona of ∼300 km, close to the black hole dominates the time-averaged spectra, and a large corona of ∼18000 km, possibly the jet, dominates the lag spectrum (Peirano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Their best-fitting results yield a lower seed photon temperature of the large corona compared to the small corona, with the seed photon temperature of the small corona linked to kTbb of nthcomp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Peirano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' (2022) pro- posed that this difference is due to the fact that the seed pho- tons for the small corona come from the inner, hotter parts, of the disc whereas the seed photons for the large corona come from the outer, cooler parts, of the disc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' A similar dual-corona geometry could explain the difference between kTin of the diskbb (linked to kTbb of nthcomp) and kTs of vkompthdk in our fits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Since we find that kTbb > kTs, also in MAX J1535−571 the small corona would dominate the emis- sion of the time-averaged spectra, whereas the big corona would dominate the lags.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We found that the rms spectra do not change much between the two fits (kTs=kTin or kTs free), so we conclude that the rms amplitude is not affected much by the size of the corona.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The fraction of the corona flux that returns to the disc is ηint 10–25 % in all the cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' This and the large corona size further indicate that the large corona is the jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 5 SUMMARY AND CONCLUSIONS We have analysed all NICER observation of MAXI J1535−571 taken on September and October 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We fit the energy spectra of the source and the rms and lag spectra of the type-C QPO in this source with the one-component time dependent Comptonization model vkompthdk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Below we summarize our results: The size of the corona of MAXI J1535−571 decreases from 104 km when the QPO frequency is ≥2 Hz to ∼3000 km when the QPO frequency is ∼9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The behaviour of all the spectral parameters and the rms and lag spectra of the QPO changes above and below a critical QPO frequency, νc =3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Interestingly, the time at which this critical frequency happens coincide with the period when the radio jet emission quenches for this source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Comparing our results with those in previous work, the data are consistent with a dual corona: a small corona lying close to the black hole and a larger one, possibly the jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' ACKNOWLEDGEMENTS This research is part of a project proposed for the COSPAR PCB fellowship program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' We would like to thank the ref- eree for constructive comments that helped improve this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' DR would like to thank COSPAR, ISRO and Pro- fessor Diego Altamirano for jointly funding the academic visit to the University of Southampton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' MM, FG and KK acknowledge support from the research programme Athena with project number 184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='034.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='002, which is (partly) financed by the Dutch Research Council (NWO).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' FG acknowledges support from PIP 0102 and PIP 0113 (CONICET).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' FG is a CONICET researcher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' This work received financial support from PICT-2017-2865 (ANPCyT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' KA acknowledges support from a UGC-UKIERI Phase 3 Thematic Partnership (UGC- UKIERI-2017-18-006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' PI: P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Gandhi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' TMB acknowledges fi- nancial contribution from PRIN INAF 2019 n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' CB is a fellow of Consejo Interuniversitario Nacional (CIN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' DATA AVAILABILITY The NICER XTI observations used in this work are available at NICER Archive6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' REFERENCES Agrawal P.' metadata={'source': 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Nature, 313, 768 APPENDIX A: MNRAS 000, 1–15 (0000) 16 Rawat et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The columns are the observation number, the chi-square of the fit to the steady-state spectrum (χ2 SSS), rms spectrum (χ2 rms), lag spectrum (χ2 lag) with, in each case, the number of channels in each spectrum and the total reduced chi-square of the combined fit with degree of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Obs no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' χ2 SSS (channel) χ2 rms (channel) χ2 lag (channel) χ2 total (dof) 1 206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='9 (238) 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 (10) 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 (10) 231.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 (243) 2 176.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 (243) 4 205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 (238) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='7 (10) 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 (10) 219.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 (243) 5 206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 (238) 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 (229) 19 184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 (238) 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 (10) 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 (10) 203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 (242) 20 185.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 (235) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 (238) 24 184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 (238) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 (10) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 (9) 191.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 (241) 25 159.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 (238) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 (10) 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 (10) 174.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='9 (242) Note: Notice that some parameters are linked in the combined fits and therefore we cannot give the number of degrees of freedom for each individual fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' So, channel numbers for individual spectra are given here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Figure A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The top and bottom panels show respectively the fractional rms and phase-lag spectra of the type-C QPO in MAXI J1535−571 fitted with vkompthdk model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0–3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV band is the reference band for the phase lag spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' MNRAS 000, 1–15 (0000) Comptonizing medium of MAXI J1535−571 17 Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The columns are the observation number, QPO frequency, QPO fractional rms amplitude and time lags at the QPO frequency of MAXI J1535−571.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Here rms1 and lag1 are in the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV band, rms2 and lag2 are in the 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV band, and rms3 and lag3 are in the 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0–10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The reference band for lags is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5–10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Obs no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' QPO frequency QPO fractional lag1 QPO fractional lag2 QPO fractional lag3 (Hz) rms1 (%) (msec) rms2 (%) (msec) rms3 (%) (msec) 1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='74 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='49 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='38 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='7 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='44 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='9 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='7 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='22 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='41 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='7 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='7 3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='32 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='7 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='20 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='54 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 −6.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='42 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='7 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='9 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 ± 0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='73 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='40 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='08 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 21 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='77 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='02 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='9 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='24 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='10 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='7 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 22 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='57 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='91 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='13 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 −5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 23 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='82 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='39 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='13 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 −5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 24 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='19 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='03 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='7 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='7 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='9 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='23 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='51 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='3 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 25 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='50 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='69 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='22 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 −5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 MNRAS 000, 1–15 (0000) 18 Rawat et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 1 10 100 1000 104 counts s−1 keV−1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='05 Fractional rms 1 10 2 5 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 Phase lags (rad) Energy (keV) −2 0 2 (data−model)/error −2 −1 0 1 2 (data−model)/error 1 10 2 5 −2 0 2 (data−model)/error Energy (keV) Figure A2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The same plot as shown in Figure 7 at ∼4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 Hz QPO frequency in MAXI J1535−571.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' MNRAS 000, 1–15 (0000) Comptonizing medium of MAXI J1535−571 19 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 1 10 100 1000 104 counts s−1 keV−1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='05 Fractional rms 1 10 2 5 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 Phase lags (rad) Energy (keV) −2 0 2 (data−model)/error −2 −1 0 1 2 (data−model)/error 1 10 2 5 −1 0 1 (data−model)/error Energy (keV) Figure A3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The same plot as shown in Figure 7 at ∼7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 Hz QPO frequency in MAXI J1535−571.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' 2 3 4 5 6 7 8 9 QPO frequency (Hz) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content='0 η Figure A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' Dependence of the η upon QPO frequency in MAXI J1535−571.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' The values of η are obtained from the fits to the time-averaged spectra, the rms and phase-lag spectra of the QPO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} +page_content=' MNRAS 000, 1–15 (0000)' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/6dE3T4oBgHgl3EQfRAnz/content/2301.04418v1.pdf'} diff --git a/7dE2T4oBgHgl3EQf7gj3/content/2301.04211v1.pdf b/7dE2T4oBgHgl3EQf7gj3/content/2301.04211v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d9e58f008fb8d597e6d4aa68bbfed3203b3f7e28 --- /dev/null +++ b/7dE2T4oBgHgl3EQf7gj3/content/2301.04211v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f374a1fcc81edc96ccb03793fac8a0ceb9e21441f02e5fd441d61ac7dfadf209 +size 629639 diff --git a/7dE2T4oBgHgl3EQf7gj3/vector_store/index.faiss b/7dE2T4oBgHgl3EQf7gj3/vector_store/index.faiss new file mode 100644 index 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b/89AzT4oBgHgl3EQfFPox/content/tmp_files/2301.01006v1.pdf.txt @@ -0,0 +1,1086 @@ +POLICY PRE-TRAINING FOR AUTONOMOUS DRIVING +VIA SELF-SUPERVISED GEOMETRIC MODELING +Penghao Wu1,2∗ Li Chen1 Hongyang Li1,3† Xiaosong Jia1,3∗ Junchi Yan1,3 Yu Qiao1 +1OpenDriveLab, Shanghai AI Laboratory +2UC San Diego +3Shanghai Jiao Tong University +ABSTRACT +Witnessing the impressive achievements of pre-training techniques on large-scale +data in the field of computer vision and natural language processing, we won- +der whether this idea could be adapted in a grab-and-go spirit, and mitigate the +sample inefficiency problem for visuomotor driving. Given the highly dynamic +and variant nature of the input, the visuomotor driving task inherently lacks view +and translation invariance, and the visual input contains massive irrelevant in- +formation for decision making, resulting in predominant pre-training approaches +from general vision less suitable for the autonomous driving task. To this end, +we propose PPGeo (Policy Pre-training via Geometric modeling), an intuitive +and straightforward fully self-supervised framework curated for the policy pre- +training in visuomotor driving. We aim at learning policy representations as a +powerful abstraction by modeling 3D geometric scenes on large-scale unlabeled +and uncalibrated YouTube driving videos. The proposed PPGeo is performed in +two stages to support effective self-supervised training. In the first stage, the +geometric modeling framework generates pose and depth predictions simulta- +neously, with two consecutive frames as input. In the second stage, the visual +encoder learns driving policy representation by predicting the future ego-motion +and optimizing with the photometric error based on current visual observation +only. As such, the pre-trained visual encoder is equipped with rich driving pol- +icy related representations and thereby competent for multiple visuomotor driv- +ing tasks. As a side product, the pre-trained geometric modeling networks could +bring further improvement to the depth and odometry estimation tasks. Extensive +experiments covering a wide span of challenging scenarios have demonstrated +the superiority of our proposed approach, where improvements range from 2% +to even over 100% with very limited data. Code and models will be available at +https://github.com/OpenDriveLab/PPGeo. +1 +INTRODUCTION +Policy learning refers to the learning process of an autonomous agent acquiring the decision-making +policy to perform a certain task in a particular environment. Visuomotor policy learning (Mnih et al., +2015; Levine et al., 2016; Hessel et al., 2018; Laskin et al., 2020; Toromanoff et al., 2020) takes as +input raw sensor observations and predicts the action, simultaneously cooperating and training the +perception and control modules in an end-to-end fashion. For visuomotor policy models, learning +tabula rasa is difficult, where it usually requires a prohibitively large corpus of labeled data or en- +vironment interactions to achieve satisfactory performance (Espeholt et al., 2018; Wijmans et al., +2019; Yarats et al., 2020). +To mitigate the sample efficiency caveat in visuomotor policy learning, pre-training the visual per- +ception network in advance is a promising solution. Recent studies (Shah & Kumar, 2021; Parisi +et al., 2022; Xiao et al., 2022; Radosavovic et al., 2022; Shah et al., 2022) have demonstrated that +applying popular visual pre-training approaches, including ImageNet (Deng et al., 2009) classifica- +tion, contrastive learning (He et al., 2020; Chen et al., 2020c), masked image modeling (MIM) (He +et al., 2022; Xie et al., 2022), and language-vision pre-training (Radford et al., 2021), could guar- +antee superior representation for robotic policy learning tasks, e.g., dexterous manipulation, motor +∗Work done during internship at Shanghai AI Laboratory. +†Corresponding author. Email to: lihongyang@pjlab.org.cn +1 +arXiv:2301.01006v1 [cs.CV] 3 Jan 2023 + +Figure 1: Uniqueness of visuomotor driving policy learning. The planned trajectory is shown as red +points. (a) static obstacles and background buildings (objects in yellow rectangles) are irrelevant to +the driving decision; (b) the traffic signal in the visual input (marked with the green box) is extremely +difficult to recognize and yet deterministic for control outputs; (c) the pre-trained visual encoder has +to be robust to different light and weather conditions. Photo credit from (Caesar et al., 2020). +control skills and visual navigation. However, for one crucial and challenging visuomotor task in +particular, namely end-to-end autonomous driving1, the aforementioned predominant pre-training +methods may not be the optimal choice (Yamada et al., 2022; Zhang et al., 2022b). +In this paper, we aim to investigate why ever-victorious pre-training approaches for general computer +vision tasks and robotic control tasks are prone to fail in case of end-to-end autonomous driving. +For conventional pre-training methods in general vision tasks, e.g., classification, segmentation and +detection, they usually adopt a wide range of data augmentations to achieve translation and view +invariance (Zhang et al., 2016; Wu et al., 2018). For robotic control tasks, the input sequence is +generally of small resolution; the environment setting is simple and concentrated on objects (Parisi +et al., 2022; Radosavovic et al., 2022). We argue that the visuomotor driving investigated in this +paper, is sensitive to geometric relationships and usually comprises complex scenarios. +As described in Fig. 1(a), the input data often carry irrelevant information, such as background +buildings, far-away moving vehicles, nearby static obstacles, etc., which are deemed as noises for +the decision making task. To obtain a good driving policy, we argue that the desirable model should +only concentrate on particular parts/patterns of the visual input. That is, taking heed of direct or +deterministic relation to the decision making, e.g., traffic signals in Fig. 1(b). However, concurrent +pre-training approaches fail to fulfill such a requirement. There comes a natural and necessary +demand to formulate a pre-training scheme curated for end-to-end autonomous driving. We attempt +to pre-train a visual encoder with a massive amount of driving data crawled freely from the web, +such that given limited labeled data, downstream applications could generalize well and quickly +adapt to various driving environments as depicted in Fig. 1(c). +The pivotal question is how to introduce driving-decision awareness into the pre-training process +to help the visual encoder concentrate on crucial visual cues for driving policy. One may resort +to directly predicting ego-motion based on single frame sensor input, constraining the network on +learning policy-related features. Previous literature tackles the supervision problem with pseudo +labeling training on either an open dataset (Zhang et al., 2022b) or the target domain data (Zhang +et al., 2022a). However, pseudo labeling approaches suffer from noisy predictions from poorly +calibrated models - this is true especially when there exists distinct domain gap such as geographical +locations and traffic complexities (Rizve et al., 2020). +To address the bottleneck aforementioned, we propose PPGeo (Policy Pre-training via Geometric +modeling), a fully self-supervised driving policy pre-training framework to learn from unlabeled +and uncalibrated driving videos. It models the 3D geometric scene by jointly predicting ego-motion, +depth, and camera intrinsics. Since directly learning ego-motion based on single frame input along +with depth and intrinsics training from scratch is too difficult, it is necessary to separate the visual en- +coder pre-training from depth and intrinsics learning in two stages. In the first stage, the ego-motion +is predicted based on consecutive frames as does in conventional depth estimation frameworks (Go- +dard et al., 2017; 2019). In the second stage, the future ego-motion is estimated based on the single +frame by a visual encoder, and could be optimized with the depth and camera intrinsics network +well-learned in the first stage. As such, the visual encoder is capable of inferring future ego-motion +based on current input alone. The pre-trained visual encoder could be well adopted for downstream +driving tasks since it captures driving policy related information. As a side product, the depth and +1We use end-to-end autonomous driving and visuomotor autonomous driving interchangeably in this paper. +2 + +Irrelevant Object +Deterministic Signal +Light/Weather Variation +(a) +(b) +(c)𝐼𝑡+1 +𝐼𝑡 +PoseNet +DepthNet +Visual Encoder +(Our Focus) +Depth 𝐷𝑡 +(a) Self-supervised Visuomotor Policy Pre-training +(b) Downstream Tasks +Intrinsic K +Ego Motion T +Photometric +Reconstruction +Ego Motion T +Photometric +Reconstruction +𝐼𝑡 +a.1 Stage One +a.2 Stage Two +- Single frame input +- Since a car is ahead +- We need to STOP +- Consecutive frames input +- Since frames barely change +- We need to STOP +frozen +Visual Encoder +(Fine-tuned) +Policy Learning +Visual Input +Figure 2: Overview of PPGeo. (a) We focus on pre-training an effective visual encoder to encode +driving policy related information by predicting ego-motion based on single frame input (a.2 Stage +Two). As achieving such a goal without labels is non-trivial, the visual encoder is obtained with the +aid of a preceding procedure (a.1 Stage One) with temporal inputs and two sub-networks (pose and +depth). In this illustrative example, the ego-vehicle needs to take action of STOP. The ego-motion +in (a.1) is inferred by judging two consecutive frames barely change; whilst the ego-motion in (a.2) +is predicted based on single visual input - focusing on driving policy related information. As such, +the visual encoder could be fine-tuned and applied to a wide span of downstream tasks in (b). +pose networks could be utilized as new initial weights for depth and odometry estimation tasks, +bringing in an additional performance gain. To sum up, our key contributions are three-fold: +• We propose a pre-training paradigm curated for various visuomotor driving tasks. To the best of +our knowledge, this is the first attempt to achieve a fully self-supervised framework without any +need of pseudo-labels2, leveraging the effect of pre-training by large-scale data to the full extent. +• We devise a visual encoder capable of predicting ego-motion based on single visual input, being +able to extract feature representations closely related to driving policy. Such a design of visual +encoder is flexible to extend to various downstream applications. +• We demonstrate the superiority of our approach on a set of end-to-end driving scenarios, covering +different types and difficulty levels. The performance in terms of various metrics is improved from +2% to even over 100% in challenging cases with very limited data. +2 +METHODOLOGY +2.1 +OVERVIEW +The visuomotor policy learning for autonomous driving targets generating a policy π, such that it +makes driving decisions, e.g., control actions or planned trajectory, from visual observation x. Our +goal is to pre-train a visual encoder φ(x), which maps the raw image input to a compact repre- +sentation containing important information for driving decision making. The representation is then +utilized by the policy π(φ(x)) to perform driving tasks. As shown in Fig. 2, our pre-training method +pre-trains the visual encoder on unlabeled driving videos via two stages in a self-supervised manner. +2.2 +TWO-STAGE SELF-SUPERVISED TRAINING +Stage One: Self-supervised Geometric Modeling. During the first stage, given a target image It +and source images It′ in a sequence, we jointly estimate the depth of the target image, the intrinsics +of the camera, and the 6-DoF ego-motion between these two frames. Given the estimations, we are +able to model the 3D geometry of the scene, and reconstruct the target image by projecting pixels in +2Pseudo-labels here mean using another model trained on additional labeled data to create “artificial” labels +for the unlabeled dataset. +3 + +the source images. Formally, the pixel-wise correspondence between It and It′ is calculated as: +pt′ = KTt→t′Dt(pt)K−1pt, +(1) +where pt and pt′ are the homogeneous coordinates of the pixel in It and It′ respectively, K is the +predicted camera intrinsic matrix, and Dt(pt) represents the predicted depth value at pixel pi in +It. With this relationship, the target image It′→t could be reconstructed with pixels in It′, and be +optimized by the photometric reconstruction error. Following Godard et al. (2019), we choose two +images adjacent to the current frame as the source images, i.e., t′ ∈ {t − 1, t + 1}. +The DepthNet consists of a common encoder-decoder structure (Godard et al., 2019) and estimates +the depth map of the input image. Two images are stacked together and fed into the encoder of +the PoseNet, whose bottleneck feature is then utilized to predict the camera intrinsics and the ego- +motion via two separate MLP-based heads. For camera intrinsics estimation, optical center (cx, cy) +and focal lengths fx, fy are regressed similarly as in Gordon et al. (2019); Chanduri et al. (2021). +Stage Two: Visuomotor Policy Pre-training. After the first stage of training, the DepthNet and +PoseNet are well trained and fitted to the driving video data. Then, in the second stage, we replace +the PoseNet for ego-motion estimation with the visual encoder φ(x) prepared for downstream driv- +ing policy learning tasks. Now the visual encoder only takes a single frame image as input and +predicts ego-motion between the current frame and subsequent frame. +Specifically, the visual encoder estimates the ego-motion Tt→t+1 based on It alone and Tt→t−1 +based on It−1 followed by an inverse operation, respectively. The visual encoder is optimized +by the photometric reconstruction error similar to the first stage, aside from a modification where +the DepthNet and the intrinsics estimation are frozen and not backpropagated. This is empirically +observed towards better performance. By doing so, the visual encoder is enforced to learn the actual +driving policy, since the ego-motion between two consecutive frames is straightforwardly related to +the driving decision or action taken at the current timestamp. +One might argue that the PoseNet trained in the first stage could provide pseudo motion labels, with +which the visual encoder could be directly supervised. However, the ego-motion predicted from +the PoseNet is too sparse compared with the geometric projection approach. In our pipeline, every +pixel provides supervision for the visual encoder so that inaccurate depth estimation in some pixels +could be mitigated by the accurate ones, i.e., it constructs a “global” optimization. In contrast, direct +supervision from the PoseNet would be greatly affected by the undesirable prediction inaccuracy +and noise results. This is especially true for diverse uncalibrated online videos (Zhang et al., 2022a). +Thus far, the backbone of visual encoder φ(x) has gained knowledge about the driving policy from +the diverse driving videos. It can then be applied to downstream visuomotor autonomous driving +tasks as the initial weights. Besides, the DepthNet and PoseNet trained on this large corpus of +uncalibrated video data could also be utilized in depth and odometry estimation tasks. +2.3 +LOSS FUNCTION +Following Godard et al. (2019), the loss function is comprised of the photometric loss and the +smoothness loss. The photometric error is comprised of an ℓ1 term and an SSIM (structural similarity +index measure) term (Wang et al., 2004): +ℓpe = α +2 (1 − SSIM(It, It′→t)) + (1 − α)ℓ1(It, It′→t), +(2) +where we set α = 0.85 following the practice (Godard et al., 2017; 2019). The smooth loss is: +ℓs = |∂xd∗ +t |e−|∂xIt| + |∂yd∗ +t |e−|∂yIt|, +(3) +where d∗ +t is the mean-normalized inverse depth map. We also adopt the minimum reprojection loss +and auto-masking scheme (Godard et al., 2019) to improve self-supervised depth estimation. +3 +EXPERIMENTS +All pre-training experiments are conducted on the hours-long unlabeled YouTube driving +videos (Zhang et al., 2022b). It covers different driving conditions e.g., geographical locations and +weather. We sample 0.8 million frames in total at 1 Hz for training. For the first stage in PPGeo +4 + +pipeline, we train the model for 30 epochs by Adam (Kingma & Ba, 2015) optimizer with a learning +rate of 10−4 which drops to 10−5 after 25 epochs. For the second stage, the encoder is trained for 20 +epochs using the AdamW (Loshchilov & Hutter, 2017) optimizer. A cyclic learning rate scheduler +is applied with the learning rate ranging from 10−6 to 10−4. The batch size for both stages is 128. +We use data augmentations including ColorJitter, RamdomGrayScale, and GaussianBlur. +3.1 +DESCRIPTION ON COMPARED BASELINES +We use ResNet-34 (He et al., 2016) as the encoder and load different pre-trained weights for the +initialization of downstream tasks. We compare PPGeo with pre-training methods including: +Random. We use the default Kaiming initialization (He et al., 2015) for convolution layers and +constant initialization for batchnorms. +ImageNet. We use the model weight provided by Torchvision (Marcel & Rodriguez, 2010), which +is pre-trained with the classification task on ImageNet (Deng et al., 2009). +MIM. The model is pre-trained with the masked image modeling method on the YouTube driving +video, which tries to reconstruct images with random masked-out patches. SimMIM (Xie et al., +2022) is adopted as it is suitable for convolutional networks. +MoCo. We pre-train the model using MoCo-v2 (Chen et al., 2020c) on the YouTube driving videos. +We exclude RandomResizedCrop and RandomHorizontalFlip augmentations as they are not suitable +for the driving task. +ACO. Following Zhang et al. (2022b), it is pre-trained using action-conditioned contrastive learning +on the YouTube driving videos. ACO trains an inverse dynamic model to generate pseudo steer +labels for driving videos, based on which steer-based discrimination is added on top of MoCo-v2. +SelfD. SelfD (Zhang et al., 2022a) is not a pre-training method strictly since it needs to train the +whole policy model on the driving video for each task, while other pre-training methods aforemen- +tioned provide a general pre-training visual model for all tasks. We still include it for comparison +due to its close relationship to our target. Specifically, we follow Zhang et al. (2022a) to train the +model for each task with the following pipeline: training on the task data → training on the YouTube +data with pseudo-label → fine-tuning on the task data. +3.2 +DESCRIPTION ON DOWNSTREAM AUTONOMOUS DRIVING TASKS +We carry out experiments under (1) three imitation learning based closed-loop driving tasks in +CARLA (Dosovitskiy et al., 2017), (2) one reinforcement learning based driving task in CARLA, +and (3) an open-loop planning task on real-world autonomous driving dataset nuScenes (Caesar +et al., 2020), to fully validate the effectiveness of PPGeo. We briefly describe each task below. +Navigation. +It corresponds to the goal-conditioned navigation task in the CoRL2017 bench- +mark (Dosovitskiy et al., 2017). The agent is trained in Town01 and tested in Town02 with unseen +weather, and there are no other traffic participants. We use different sizes of training data (from +4K to 40K) following Zhang et al. (2022b) to evaluate the generalization ability of pre-trained vi- +sual encoders when labeled data is limited and conduct the closed-loop evaluation. The evaluation +metric is success rate, denoting the portion of 50 pre-defined routes finished without any collision. +And traffic lights are ignored here. CILRS (Codevilla et al., 2019), a classic image based end-to-end +autonomous driving model, is adopted for training and evaluation. +Navigation Dynamic. This is the navigation dynamic task in the CoRL2017 benchmark (Dosovit- +skiy et al., 2017). The setting differentiates from Navigation that there are other dynamic objects +such as randomly generated vehicles, which substantially increases the difficulty of driving safety. +Leaderboard Town05-long. This challenging and realistic benchmark corresponds to the Leader- +Board benchmark (CARLA, 2022). We collect 40K training data in Town01, 03, 04, 06 and eval- +uate on 10 routes in the unseen Town05 (Prakash et al., 2021). Due to the challenging scenarios +in this task, we evaluate different pre-training approaches with the state-of-the-art image-based au- +tonomous driving model TCP (Wu et al., 2022). The major metrics of this task are Driving Score, +Route Completion, and Infraction Score (all the higher the better). Route Completion denotes the +portion of the route completed by the agent. Infraction Score is the number of infractions made +5 + +Table 1: The Successful Rate results of the closed-loop Navigation task (mean by 3 random trials). +Pre-train Method +Navigation - # of training samples +10% (4K) +20% (8K) +40% (16K) +100% (40K) +Random +0.0 ± 0.0 +9.6 ± 5.2 +15.3 ± 4.5 +73.3 ± 2.3 +ImageNet +24.7± 2.0 +42.0 ± 2.0 +69.3 ± 6.4 +87.3 ± 4.6 +MIM +4.7 ± 1.2 +8.0 ± 0.0 +31.3 ± 2.3 +57.3 ± 3.1 +MoCo +7.7 ± 2.1 +39.3 ± 9.2 +48.7 ± 4.2 +69.3 ± 1.2 +ACO +24.0 ± 2.0 +44.0 ± 1.2 +71.3 ± 1.2 +92.0 ± 3.5 +SelfD +12.0± 0.0 +32.0 ± 0.0 +50.7 ± 2.3 +62.7 ± 1.2 +PPGeo (ours) +42.0 ± 2.0 +73.3 ± 6.1 +91.3 ± 1.2 +96.7 ± 1.2 +along the route including pedstrain collisions, vehicle collisions, red light infractions, etc. And the +main metric Driving Score is the product of Route Completion and Infraction Score. +Reinforcement Learning. Proximal Policy Optimization (PPO) (Schulman et al., 2017) is used +to train the CILRS (Codevilla et al., 2019) model initialized with different pre-trained weights in +CARLA Town01 environment. The reward shaping details follow Roach (Zhang et al., 2021). We +also conduct experiments to freeze the pre-trained visual encoder during training to further study the +effectiveness of the pre-trained feature representations. +nuScenes Planning. This task involves trajectory planning in real-world dataset nuScenes (Caesar +et al., 2020). Given the current visual input, the model plans a 3-second trajectory (0.5 Hz), and the +planned trajectory is compared with the ground truth log. We also calculate the collision rate, where +a collision is defined as overlaps with future vehicles and pedestrians based on planned waypoints. +The metric of this tasks includes (1) the L2 distance between predicted trajectory and ground truth +trajectory, and (2) the collision rate. Metrics are measured at different time lengths from 1s to 3s. +The planning model used here is comprised of a visual encoder and a GRU-based planner to predict +each waypoint auto-regressively. We use the official train-val split for training and evaluation. +3.3 +NUMERIC COMPARISON ON DOWNSTREAM TASKS +For imitation learning based closed-loop driving tasks, the evaluation results are shown in Table 1- +3. We present the plot between episode return and environment steps of each method in Fig. 3 for +the reinforcement learning experiments. The open-loop nuScenes planning results are provided in +Table 4. We could observe that PPGeo outperforms other baselines by a large margin in all tasks. +Note that the model is tested under a different number of fine-tuning samples from 10% (4K) to full +40K in the Navigation and Navigation Dynamic tasks. In the case of the particularly small size of +training samples, PPGeo still demonstrates competitive performance and has a larger improvement +gap of over 100%. This validates the generalization ability of the pre-trained visual encoder, which +is important when adapting to a new environment with very limited labeled data. In the more chal- +lenging and real-world style Leaderboard Town05-long task in Table 3, the model pre-trained with +our method achieves the highest driving score and infraction score. PPGeo well handles cases where +the agent needs to stop, leading to much fewer vehicle collisions and red light infractions. +Since ACO considers steering angles only during pre-training, its performance degrades on more +challenging scenarios where brake and throttles are also important. SelfD performs slightly better +than ACO in complex cases while it significantly degenerates when the task data is limited, as +affected by the unsatisfying pseudo labeling model. ImageNet pre-training also shows competitive +performance, which might credit to its ability of finding salient objects in the scene when the input +contains little irrelevant information (see examples in Sec. 3.5). +3.4 +DEPTH AND ODOMETRY ESTIMATION +In this part, we explore whether the large-scale training on uncalibrated data could benefit the depth +and odometry estimation models as well and validate the effectiveness of first-stage training. Specif- +ically, we employ the DepthNet and PoseNet trained after the first stage as initial weights for Mon- +odepthv2 (Godard et al., 2019), and conduct experiments on KITTI (Geiger et al., 2012). Results +in Table 5 indicate that pre-training on large-scale driving videos could bring performance improve- +6 + +Table 2: The Successful Rate results of the closed-loop Navigation Dynamic (mean by 3 random +trials). +Pre-train Method +Navigation Dynamic - # of training samples +10% (4K) +20% (8K) +40% (16K) +100% (40K) +Random +0.0 ± 0.0 +2.0 ± 0.0 +10.0 ± 0.0 +32.0 ± 8.0 +ImageNet +10.7± 1.2 +28.7 ± 5.0 +64.7 ± 2.3 +72.7 ± 1.2 +MIM +7.3 ± 1.2 +10.3 ± 2.5 +14.7 ± 3.1 +58.7 ± 1.2 +MoCo +4.7 ± 1.2 +12.0 ± 4.0 +28.0 ± 5.3 +66.7 ± 2.3 +ACO +8.0 ± 1.2 +12.0 ± 0.0 +22.0 ± 2.0 +47.3 ± 5.0 +SelfD +8.0 ± 0.0 +29.3 ± 1.2 +38.0 ± 1.6 +59.3 ± 6.4 +PPGeo (ours) +23.3 ± 1.2 +34.0 ± 5.3 +71.3 ± 1.2 +84.0 ± 5.3 +Table 3: Closed-loop Leaderboard Town05-long task results. Besides three main metrics, infraction +details are also reported (all the lower the better). Evaluation repeats 3 times with the mean reported. +Pre-train +Method +Driving +Score +Infraction +Score +Route +Completion +Collisions +pedestrian +Collisions +vehicle +Collisions +layout +Off-road +violations +Agent +blocked +Red light +violations +Random +33.50±1.67 +0.65±0.02 +60.49±2.93 +0.09±0.07 +1.16±0.40 +0.00±0.00 +0.44±0.13 +0.97±0.09 +0.53±0.12 +ImageNet +41.29±3.20 +0.77±0.03 +57.52±4.87 +0.00±0.00 +0.71±0.20 +0.11±0.15 +0.15±0.01 +1.01±0.16 +0.29±0.10 +MIM +36.39±0.21 +0.72±0.04 +61.75±2.26 +0.14±0.11 +0.91±0.12 +0.04±0.07 +0.18±0.17 +0.87±0.03 +0.14±0.11 +MoCo +32.10±2.04 +0.65±0.02 +64.09±4.01 +0.13±0.11 +0.79±0.16 +0.00±0.00 +0.49±0.07 +0.81±0.15 +0.45±0.13 +ACO +33.05±3.05 +0.67±0.06 +59.52±3.21 +0.00±0.00 +0.69±0.28 +0.05±0.07 +0.54±0.05 +0.94±0.08 +0.73±0.10 +SelfD +38.76±3.02 +0.65±0.03 +68.72±7.36 +0.17±0.07 +0.84±0.18 +0.00±0.00 +0.32±0.03 +0.75±0.15 +0.12±0.08 +PPGeo +47.44±5.63 +0.79±0.08 +65.05±5.11 +0.04±0.05 +0.54±0.29 +0.00±0.00 +0.16±0.11 +0.76±0.10 +0.04±0.05 +100 +200 +300 +400 +500 +600 +700 +800 +Steps (K) +100 +0 +100 +200 +300 +400 +500 +Episode Return +Visual Encoder Fine-tuning +ImageNet +MoCo +ACO +PPGeo +100 +200 +300 +400 +500 +600 +700 +800 +Steps (K) +100 +200 +300 +400 +Episode Return +Visual Encoder Frozen +ImageNet +MoCo +ACO +PPGeo +Figure 3: Learning curves of the RL agents using PPGeo and three other best pre-training baselines. +Left: the pre-trained visual encoder is jointly fine-tuned during RL training; Right: the visual en- +coder is frozen during RL training. The episode return is the mean with standard deviation in shade +across three runs with different random seeds. +Table 4: Open-loop nuScenes planning results. We evaluate the ℓ2 distance between model predic- +tions and the ground truth trajectory and collision rate in horizons from 1 second to 3 seconds. +Pre-train Method +L2 (m) ↓ +Collision Rate (%) ↓ +1s +2s +3s +1s +2s +3s +Random +1.621 +2.722 +3.851 +0.550 +1.779 +3.375 +ImagNet +1.331 +2.202 +3.086 +0.315 +0.550 +1.366 +MIM +1.412 +2.357 +3.331 +0.297 +0.622 +1.507 +MoCo +1.528 +2.545 +3.585 +0.560 +1.235 +2.390 +ACO +1.496 +2.496 +3.519 +0.446 +1.178 +2.223 +SelfD +1.419 +2.359 +3.316 +0.353 +0.923 +2.044 +PPGeo (ours) +1.302 +2.154 +3.018 +0.270 +0.425 +0.941 +7 + +Table 5: Improvement from our pre-training method on depth and odometry estimation tasks. +Pre-train +Method +Depth Estimation +Odometry Estimation +abs rel ↓ +sq rel ↓ +rmse ↓ +rmse log ↓ +a1 ↑ +a2 ↑ +a3 ↑ +Sequence 09 ↓ +Sequence 10 ↓ +ImageNet +0.118 +0.902 +4.873 +0.196 +0.871 +0.958 +0.981 +0.017±0.010 +0.015±0.010 +PPGeo +0.114 +0.805 +4.599 +0.186 +0.874 +0.962 +0.984 +0.016±0.009 +0.013±0.009 +Ours +ACO +ImageNet +MoCo +Origin +Figure 4: Eigen-Cam (Muhammad & Yeasin, 2020) activation maps of the learned representation +from different pre-training methods on the driving video data. +Table 6: Ablative study on key designs of PPGeo on the Navigation task. +# +Experiment +Navigation - # of training samples +10% (4K) +20% (8K) +40% (16K) +100% (40K) +1 +Single stage +24.2 ± 2.0 +53.3 ± 1.2 +79.3 ± 4.2 +92.7 ± 2.3 +2 +No frozen in 2nd stage +32.7 ± 1.2 +58.0 ± 2.0 +86.0 ± 2.1 +92.0 ± 2.0 +3 +PoseNet direct supervision +18.0 ± 2.0 +52.0 ± 2.0 +76.7 ± 1.2 +90.0 ± 0.0 +4 +PPGeo +42.0 ± 2.0 +73.3 ± 6.1 +91.3 ± 1.2 +96.7 ± 1.2 +ment to both depth and odometry estimation tasks, which is an additional harvest of our pre-training +framework. We refer readers to Godard et al. (2019) for details about the metrics of these tasks. +3.5 +VISUALIZATION RESULTS +Here we provide heatmaps of the feature representations learned by different pre-training methods +using Eigen-Cam (Muhammad & Yeasin, 2020) to show the attended regions in Fig. 4. In many +cases (Row 1&2), our model mainly concentrates on the lane in front of the ego vehicle, which is +highly related to driving. And our model PPGeo well captures the specific cues causing the brake +action including front vehicles (Row 3&4) and traffic lights (Row 5). We also observe that the model +pre-trained with ImageNet classification tends to capture salient objects in the image. This is helpful +when the salient objects are straightforwardly related to the driving decision (Row 4); but it may +focus on wrong objects when the input contains other irrelevant information (Row 2&3). +3.6 +ABLATIVE STUDY +We conduct ablative study as to different designs of PPGeo on the Navigation task in Table 6. Train- +ing the visual encoder and DepthNet in a single stage simultaneously (Row 1) leads to an inferior +performance, indicating that it is quite challenging for the visual encoder to learn the correct ego- +motion if depth estimation is also trained from scratch. Moreover, jointly optimizing the DepthNet +in the second stage (Row 2, not frozen) degrades the depth estimation quality and harms the per- +formance. In Row 3, we observe that utilizing the PoseNet obtained in the first stage to provide +8 + +pseudo label supervision directly leads to inferior results, since an inaccurate pseudo label impairs +the learning process to great extent. +4 +RELATED WORK +Pre-training for NLP and General Vision. Pre-training or representation learning has proved to be +an essential key to the success of artificial intelligence. In the field of Natural Language Processing +(NLP), with the powerful capability of Transformer (Vaswani et al., 2017), pre-training on large- +scale datasets with large models then fine-tuning on downstream tasks has become the dominant +paradigm (Kenton & Toutanova, 2019; Brown et al., 2020). As for the field of Computer Vision, +training specific downstream tasks with the supervised pre-trained weights of visual encoder via +ImageNet classification task is widely adopted. Recently, unsupervised and self-supervised learn- +ing methods such as contrastive learning (He et al., 2020; Chen et al., 2020c;b) and masked im- +age modeling (Bao et al., 2021; He et al., 2022; Xie et al., 2022; Peng et al., 2022) have gained +impressive improvement over ImageNet pre-training on various vision benchmarks. Very recent +vision-language co-training approaches (Radford et al., 2021; Wang et al., 2022) demonstrate their +extraordinary potential in the domain of multi-modal learning and applications. Yet, these generic +representation learning methods adopt various data augmentation techniques to achieve translation +and view invariance, while visuomotor driving sets in a highly dynamic environment. In this work, +we show that the ever-victorious pre-training methods may not be the optimal choice, and introduce +a curated paradigm for visuomotor driving policy learning. +Pre-training for Visuomotor Applications. Learning a control policy directly from raw visual +input is challenging since the model needs to reason about visual pixels and dynamic behaviors +simultaneously. Moreover, training visuomotor models from scratch usually requires tons of labeled +data or environment interactions. To this end, recently, Shah & Kumar (2021) shows that feature +representations from ResNet (He et al., 2016) pre-trained on ImageNet classification is helpful for +RL-based dexterous manipulation tasks. Parisi et al. (2022) conducts extensive experiments on +applying “off-the-shelf” pre-trained vision models in diverse control domains and validates their +benefits to train control policies. CLIP (Radford et al., 2021) is also adopted in some embodied +AI and robot navigation problems (Shah et al., 2022). Besides borrowing pre-trained weights for +visuomotor tasks, researchers in robotics now desire a paradigm learning policy representations +from raw data directly. Xiao et al. (2022); Radosavovic et al. (2022); Seo et al. (2022); Gupta et al. +(2022) inherit the MIM spirit to realize visual pre-training for control tasks. Yang & Nachum (2021) +investigates unsupervised representation learning objectives from D4RL environments (Fu et al., +2020), and Yamada et al. (2022) further adopts task-induced approaches to learn from prior tasks. +However, compared with visuomotor driving, the visual inputs of such control tasks are less diverse +which usually concentrate on objects and are much more compact. +To our best knowledge, ACO (Zhang et al., 2022b) is the only pre-training method customized +for autonomous driving. By first training an inverse dynamic model on nuScenes (Caesar et al., +2020), they get pseudo steer labels of the driving videos and then construct the steer-conditioned +discrimination for contrastive learning following MoCo. However, ACO ignores other crucial driv- +ing factors such as throttle and brakes, and its performance is largely limited by the inverse dynamic +model. SelfD (Zhang et al., 2022a) is not strictly designed for pre-training while it also makes +use of vast amounts of videos to learn driving policies via semi-supervised learning. It acquires the +pseudo labeling knowledge from the target domain. These two methods both depend on the accuracy +of pseudo labeling. In contrast, we realize fully self-supervised learning through dense geometric +reconstruction, evading the possible adverse effect. +Policy Learning for Autonomous Driving. Visuomotor autonomous driving learns a driving pol- +icy directly from sensor inputs in an end-to-end manner (Codevilla et al., 2018; 2019; Liang et al., +2018; Chen et al., 2020a; Prakash et al., 2021; Chen et al., 2021; Wu et al., 2022; Shao et al., 2022). +In essence, the inherent difficulty of the urban-style autonomous driving tasks makes such meth- +ods data-hungry. Interfuser (Shao et al., 2022), the current top-1 method on the CARLA Leader- +board (CARLA, 2022), requires 3 million labeled data samples for imitation learning (behavior +cloning specifically). RL-based model MaRLn (Toromanoff et al., 2020) needs 20 million environ- +ment steps of interaction. The sample efficiency problem greatly impedes the real-world application +of such approaches. In this work, we propose a self-supervised pre-training pipeline to learn driving +9 + +policy related representations on unlabeled driving videos, and pave the way for these visuomotor +autonomous driving models to further achieve satisfying performance. +5 +CONCLUSION AND DISCUSSION +In this work, we have proposed a fully self-supervised visuomotor driving policy pre-training +paradigm PPGeo by modeling the 3D geometry of large-scale unlabeled driving videos. Taking +a direct approach to infer the ego-motion and benefiting from the two-stage pre-training pipeline, +we enable the visual encoder to learn driving policies based on single visual input. 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In ICCV, 2021. 6 +13 + +POLICY PRE-TRAINING FOR AUTONOMOUS DRIVING +VIA SELF-SUPERVISED GEOMETRIC MODELING +Supplementary Materials +In this Supplementary document, we first provide detailed network structures in Sec. A. More de- +scription and visual illustrations of the downstream tasks are discussed in Sec. B. Last, we discuss +limitations and common failure cases in Sec. C. +A +NETWORK DETAILS +For all experiments, the backbone of the visual encoder is ResNet-34 (He et al., 2016), and the +detailed structure of it is provided in Table 7. For DepthNet and PoseNet, we follow the same model +structure as Godard et al. (2019) with a two-layer MLP focal length head and a two-layer MLP +optical center head added to the bottleneck of the PoseNet to predict the intrinsic matrix. Please +refer to Godard et al. (2019) for model details. +For the Navigation, Navigation Dynamic, and Reinforcement Learning tasks, we use CILRS (Codev- +illa et al., 2019) and the model details are provided in Table 8. For the Leaderboard Town05-long +task, TCP (Wu et al., 2022) is chosen as our agent, and we refer readers to Wu et al. (2022) for model +details. For the nuScenes Planning, the trajectory planning model structure is shown in Table 9. +Table 7: Detailed structure of the visual encoder. +Layer Type +Channels +Stride +Kernel Size +Activation Function +Image Encoder +ResNet-34 +Measurement Encoder +Conv +256 +1 +1 +ReLU +Conv +256 +3 +1 +ReLU +Conv +256 +3 +1 +ReLU +Conv +6 +1 +1 +ReLU +Average Pooling +Table 8: Detailed structure of the CILRS model. +Layer Type +Dims in +Dims out +Activation Function +Image Encoder +ResNet-34 +512 +Speed Encoder +FC +1 +256 +ReLU +FC +256 +512 +- +Speed Pred Head +FC +512 +256 +ReLU +FC +256 +256 +ReLU +FC +256 +256 +ReLU +Control Pred Head +FC +512 +256 +ReLU +FC +256 +256 +ReLU +FC +256 +3 +Sigmoid +14 + +Table 9: Detailed structure of the trajectory planning model. +Image Encoder +ResNet-34 +Bottleneck +Layer Type +Dims in +Dims out +Activation Function +FC +512 +256 +ReLU +FC +256 +256 +- +Decoder +Layer Type +Hidden dim +Input Dim +Output Dim +GRU +256 +2 +2 +B +DOWNSTREAM TASKS DETAILS +For Navigation and Navigation Dynamic, training data is collected in Town01, and the closed-loop +testing is conducted in Town02. The maps of Town01 and Town02 are shown in Fig. 5. The agent +needs to follow a series of sparse waypoints to navigate from the start point to the end point and +avoid collisions. The difference between Navigation and Navigation Dynamic is that there are other +dynamic vehicles and pedestrians in the town. Examples are provided in Fig. 6. +The Leaderboard-Town05-long task is more close to real-world urban driving, with different chal- +lenging scenarios added to the route. The map of Town05 is shown in Fig. 5. +Town 01 +Town 02 +Town 05 +Figure 5: Maps of Town01, Town02, and Town05. +Navigation +Navigation Dynamic +Figure 6: Examples of the front view image for Navigation and Navigation Dynamic tasks. +15 + +C +LIMITATIONS +In this part, we analyze some failure cases and limitations of our method. Since the visual encoder +need to predict the future motion based on a single front-view image, there might be some factors +that directly influence the driving decision not shown in the image (e.g., vehicles behind the ego +vehicle, factors related to the driver, navigation information). Some of such cases are provided +in Fig. 7. In these cases, the visual encoder does not get enough information to make the correct +prediction. These samples during training may hamper the learning process. After training, one +may use the difference between the prediction from PoseNet and that from visual encoder to filter +out these samples, and re-train the visual encoder. +𝐼𝑡 +𝐼𝑡+1 +Figure 7: Failure cases where the driving decision/future motion can not be inferred from It. For the +cases in Row 1 and Row 2, by comparing It and It+1, we know that the ego vehicle stops. However, +there is no clear clue in It indicating it should stop. For the case in Row 3, the ego vehicle is turning +left, while we could hardly tell the turning direction from It alone. +16 + diff --git a/89AzT4oBgHgl3EQfFPox/content/tmp_files/load_file.txt b/89AzT4oBgHgl3EQfFPox/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..108dc844a455e540e871daf037ecf82f2732188b --- /dev/null +++ b/89AzT4oBgHgl3EQfFPox/content/tmp_files/load_file.txt @@ -0,0 +1,995 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf,len=994 +page_content='POLICY PRE-TRAINING FOR AUTONOMOUS DRIVING VIA SELF-SUPERVISED GEOMETRIC MODELING Penghao Wu1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2∗ Li Chen1 Hongyang Li1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3† Xiaosong Jia1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3∗ Junchi Yan1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 Yu Qiao1 1OpenDriveLab,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Shanghai AI Laboratory 2UC San Diego 3Shanghai Jiao Tong University ABSTRACT Witnessing the impressive achievements of pre-training techniques on large-scale data in the field of computer vision and natural language processing,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' we won- der whether this idea could be adapted in a grab-and-go spirit,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' and mitigate the sample inefficiency problem for visuomotor driving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Given the highly dynamic and variant nature of the input, the visuomotor driving task inherently lacks view and translation invariance, and the visual input contains massive irrelevant in- formation for decision making, resulting in predominant pre-training approaches from general vision less suitable for the autonomous driving task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' To this end, we propose PPGeo (Policy Pre-training via Geometric modeling), an intuitive and straightforward fully self-supervised framework curated for the policy pre- training in visuomotor driving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We aim at learning policy representations as a powerful abstraction by modeling 3D geometric scenes on large-scale unlabeled and uncalibrated YouTube driving videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The proposed PPGeo is performed in two stages to support effective self-supervised training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In the first stage, the geometric modeling framework generates pose and depth predictions simulta- neously, with two consecutive frames as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In the second stage, the visual encoder learns driving policy representation by predicting the future ego-motion and optimizing with the photometric error based on current visual observation only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' As such, the pre-trained visual encoder is equipped with rich driving pol- icy related representations and thereby competent for multiple visuomotor driv- ing tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' As a side product, the pre-trained geometric modeling networks could bring further improvement to the depth and odometry estimation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Extensive experiments covering a wide span of challenging scenarios have demonstrated the superiority of our proposed approach, where improvements range from 2% to even over 100% with very limited data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Code and models will be available at https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='com/OpenDriveLab/PPGeo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 1 INTRODUCTION Policy learning refers to the learning process of an autonomous agent acquiring the decision-making policy to perform a certain task in a particular environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Visuomotor policy learning (Mnih et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Levine et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Hessel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Laskin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Toromanoff et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2020) takes as input raw sensor observations and predicts the action, simultaneously cooperating and training the perception and control modules in an end-to-end fashion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' For visuomotor policy models, learning tabula rasa is difficult, where it usually requires a prohibitively large corpus of labeled data or en- vironment interactions to achieve satisfactory performance (Espeholt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Wijmans et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Yarats et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' To mitigate the sample efficiency caveat in visuomotor policy learning, pre-training the visual per- ception network in advance is a promising solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Recent studies (Shah & Kumar, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Parisi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Xiao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Radosavovic et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Shah et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022) have demonstrated that applying popular visual pre-training approaches, including ImageNet (Deng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2009) classifica- tion, contrastive learning (He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2020c), masked image modeling (MIM) (He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Xie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022), and language-vision pre-training (Radford et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2021), could guar- antee superior representation for robotic policy learning tasks, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', dexterous manipulation, motor ∗Work done during internship at Shanghai AI Laboratory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' †Corresponding author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Email to: lihongyang@pjlab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='org.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='cn 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='01006v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='CV] 3 Jan 2023 Figure 1: Uniqueness of visuomotor driving policy learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The planned trajectory is shown as red points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' (a) static obstacles and background buildings (objects in yellow rectangles) are irrelevant to the driving decision;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' (b) the traffic signal in the visual input (marked with the green box) is extremely difficult to recognize and yet deterministic for control outputs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' (c) the pre-trained visual encoder has to be robust to different light and weather conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Photo credit from (Caesar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' control skills and visual navigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' However, for one crucial and challenging visuomotor task in particular, namely end-to-end autonomous driving1, the aforementioned predominant pre-training methods may not be the optimal choice (Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In this paper, we aim to investigate why ever-victorious pre-training approaches for general computer vision tasks and robotic control tasks are prone to fail in case of end-to-end autonomous driving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' For conventional pre-training methods in general vision tasks, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', classification, segmentation and detection, they usually adopt a wide range of data augmentations to achieve translation and view invariance (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' For robotic control tasks, the input sequence is generally of small resolution;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' the environment setting is simple and concentrated on objects (Parisi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Radosavovic et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We argue that the visuomotor driving investigated in this paper, is sensitive to geometric relationships and usually comprises complex scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' As described in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 1(a), the input data often carry irrelevant information, such as background buildings, far-away moving vehicles, nearby static obstacles, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', which are deemed as noises for the decision making task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' To obtain a good driving policy, we argue that the desirable model should only concentrate on particular parts/patterns of the visual input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' That is, taking heed of direct or deterministic relation to the decision making, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', traffic signals in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 1(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' However, concurrent pre-training approaches fail to fulfill such a requirement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' There comes a natural and necessary demand to formulate a pre-training scheme curated for end-to-end autonomous driving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We attempt to pre-train a visual encoder with a massive amount of driving data crawled freely from the web, such that given limited labeled data, downstream applications could generalize well and quickly adapt to various driving environments as depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 1(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The pivotal question is how to introduce driving-decision awareness into the pre-training process to help the visual encoder concentrate on crucial visual cues for driving policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' One may resort to directly predicting ego-motion based on single frame sensor input, constraining the network on learning policy-related features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Previous literature tackles the supervision problem with pseudo labeling training on either an open dataset (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022b) or the target domain data (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' However, pseudo labeling approaches suffer from noisy predictions from poorly calibrated models - this is true especially when there exists distinct domain gap such as geographical locations and traffic complexities (Rizve et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' To address the bottleneck aforementioned, we propose PPGeo (Policy Pre-training via Geometric modeling), a fully self-supervised driving policy pre-training framework to learn from unlabeled and uncalibrated driving videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' It models the 3D geometric scene by jointly predicting ego-motion, depth, and camera intrinsics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Since directly learning ego-motion based on single frame input along with depth and intrinsics training from scratch is too difficult, it is necessary to separate the visual en- coder pre-training from depth and intrinsics learning in two stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In the first stage, the ego-motion is predicted based on consecutive frames as does in conventional depth estimation frameworks (Go- dard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In the second stage, the future ego-motion is estimated based on the single frame by a visual encoder, and could be optimized with the depth and camera intrinsics network well-learned in the first stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' As such, the visual encoder is capable of inferring future ego-motion based on current input alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The pre-trained visual encoder could be well adopted for downstream driving tasks since it captures driving policy related information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' As a side product, the depth and 1We use end-to-end autonomous driving and visuomotor autonomous driving interchangeably in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 2 Irrelevant Object Deterministic Signal Light/Weather Variation (a) (b) (c)𝐼𝑡+1 𝐼𝑡 PoseNet DepthNet Visual Encoder (Our Focus) Depth 𝐷𝑡 (a) Self-supervised Visuomotor Policy Pre-training (b) Downstream Tasks Intrinsic K Ego Motion T Photometric Reconstruction Ego Motion T Photometric Reconstruction 𝐼𝑡 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='1 Stage One a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 Stage Two Single frame input Since a car is ahead We need to STOP Consecutive frames input Since frames barely change We need to STOP frozen Visual Encoder (Fine-tuned) Policy Learning Visual Input Figure 2: Overview of PPGeo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' (a) We focus on pre-training an effective visual encoder to encode driving policy related information by predicting ego-motion based on single frame input (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 Stage Two).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' As achieving such a goal without labels is non-trivial, the visual encoder is obtained with the aid of a preceding procedure (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='1 Stage One) with temporal inputs and two sub-networks (pose and depth).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In this illustrative example, the ego-vehicle needs to take action of STOP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The ego-motion in (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='1) is inferred by judging two consecutive frames barely change;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' whilst the ego-motion in (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2) is predicted based on single visual input - focusing on driving policy related information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' As such, the visual encoder could be fine-tuned and applied to a wide span of downstream tasks in (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' pose networks could be utilized as new initial weights for depth and odometry estimation tasks, bringing in an additional performance gain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' To sum up, our key contributions are three-fold: We propose a pre-training paradigm curated for various visuomotor driving tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' To the best of our knowledge, this is the first attempt to achieve a fully self-supervised framework without any need of pseudo-labels2, leveraging the effect of pre-training by large-scale data to the full extent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We devise a visual encoder capable of predicting ego-motion based on single visual input, being able to extract feature representations closely related to driving policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Such a design of visual encoder is flexible to extend to various downstream applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We demonstrate the superiority of our approach on a set of end-to-end driving scenarios, covering different types and difficulty levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The performance in terms of various metrics is improved from 2% to even over 100% in challenging cases with very limited data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 2 METHODOLOGY 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='1 OVERVIEW The visuomotor policy learning for autonomous driving targets generating a policy π, such that it makes driving decisions, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', control actions or planned trajectory, from visual observation x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Our goal is to pre-train a visual encoder φ(x), which maps the raw image input to a compact repre- sentation containing important information for driving decision making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The representation is then utilized by the policy π(φ(x)) to perform driving tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 2, our pre-training method pre-trains the visual encoder on unlabeled driving videos via two stages in a self-supervised manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 TWO-STAGE SELF-SUPERVISED TRAINING Stage One: Self-supervised Geometric Modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' During the first stage, given a target image It and source images It′ in a sequence, we jointly estimate the depth of the target image, the intrinsics of the camera, and the 6-DoF ego-motion between these two frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Given the estimations, we are able to model the 3D geometry of the scene, and reconstruct the target image by projecting pixels in 2Pseudo-labels here mean using another model trained on additional labeled data to create “artificial” labels for the unlabeled dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 3 the source images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Formally, the pixel-wise correspondence between It and It′ is calculated as: pt′ = KTt→t′Dt(pt)K−1pt, (1) where pt and pt′ are the homogeneous coordinates of the pixel in It and It′ respectively, K is the predicted camera intrinsic matrix, and Dt(pt) represents the predicted depth value at pixel pi in It.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' With this relationship, the target image It′→t could be reconstructed with pixels in It′, and be optimized by the photometric reconstruction error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Following Godard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' (2019), we choose two images adjacent to the current frame as the source images, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', t′ ∈ {t − 1, t + 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The DepthNet consists of a common encoder-decoder structure (Godard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2019) and estimates the depth map of the input image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Two images are stacked together and fed into the encoder of the PoseNet, whose bottleneck feature is then utilized to predict the camera intrinsics and the ego- motion via two separate MLP-based heads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' For camera intrinsics estimation, optical center (cx, cy) and focal lengths fx, fy are regressed similarly as in Gordon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Chanduri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Stage Two: Visuomotor Policy Pre-training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' After the first stage of training, the DepthNet and PoseNet are well trained and fitted to the driving video data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Then, in the second stage, we replace the PoseNet for ego-motion estimation with the visual encoder φ(x) prepared for downstream driv- ing policy learning tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Now the visual encoder only takes a single frame image as input and predicts ego-motion between the current frame and subsequent frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Specifically, the visual encoder estimates the ego-motion Tt→t+1 based on It alone and Tt→t−1 based on It−1 followed by an inverse operation, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The visual encoder is optimized by the photometric reconstruction error similar to the first stage, aside from a modification where the DepthNet and the intrinsics estimation are frozen and not backpropagated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' This is empirically observed towards better performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' By doing so, the visual encoder is enforced to learn the actual driving policy, since the ego-motion between two consecutive frames is straightforwardly related to the driving decision or action taken at the current timestamp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' One might argue that the PoseNet trained in the first stage could provide pseudo motion labels, with which the visual encoder could be directly supervised.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' However, the ego-motion predicted from the PoseNet is too sparse compared with the geometric projection approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In our pipeline, every pixel provides supervision for the visual encoder so that inaccurate depth estimation in some pixels could be mitigated by the accurate ones, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', it constructs a “global” optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In contrast, direct supervision from the PoseNet would be greatly affected by the undesirable prediction inaccuracy and noise results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' This is especially true for diverse uncalibrated online videos (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Thus far, the backbone of visual encoder φ(x) has gained knowledge about the driving policy from the diverse driving videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' It can then be applied to downstream visuomotor autonomous driving tasks as the initial weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Besides, the DepthNet and PoseNet trained on this large corpus of uncalibrated video data could also be utilized in depth and odometry estimation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 LOSS FUNCTION Following Godard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' (2019), the loss function is comprised of the photometric loss and the smoothness loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The photometric error is comprised of an ℓ1 term and an SSIM (structural similarity index measure) term (Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2004): ℓpe = α 2 (1 − SSIM(It, It′→t)) + (1 − α)ℓ1(It, It′→t), (2) where we set α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='85 following the practice (Godard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The smooth loss is: ℓs = |∂xd∗ t |e−|∂xIt| + |∂yd∗ t |e−|∂yIt|, (3) where d∗ t is the mean-normalized inverse depth map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We also adopt the minimum reprojection loss and auto-masking scheme (Godard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2019) to improve self-supervised depth estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 3 EXPERIMENTS All pre-training experiments are conducted on the hours-long unlabeled YouTube driving videos (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' It covers different driving conditions e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', geographical locations and weather.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We sample 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='8 million frames in total at 1 Hz for training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' For the first stage in PPGeo 4 pipeline, we train the model for 30 epochs by Adam (Kingma & Ba, 2015) optimizer with a learning rate of 10−4 which drops to 10−5 after 25 epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' For the second stage, the encoder is trained for 20 epochs using the AdamW (Loshchilov & Hutter, 2017) optimizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' A cyclic learning rate scheduler is applied with the learning rate ranging from 10−6 to 10−4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The batch size for both stages is 128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We use data augmentations including ColorJitter, RamdomGrayScale, and GaussianBlur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='1 DESCRIPTION ON COMPARED BASELINES We use ResNet-34 (He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2016) as the encoder and load different pre-trained weights for the initialization of downstream tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We compare PPGeo with pre-training methods including: Random.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We use the default Kaiming initialization (He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2015) for convolution layers and constant initialization for batchnorms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' ImageNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We use the model weight provided by Torchvision (Marcel & Rodriguez, 2010), which is pre-trained with the classification task on ImageNet (Deng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' MIM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The model is pre-trained with the masked image modeling method on the YouTube driving video, which tries to reconstruct images with random masked-out patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' SimMIM (Xie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022) is adopted as it is suitable for convolutional networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' MoCo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We pre-train the model using MoCo-v2 (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2020c) on the YouTube driving videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We exclude RandomResizedCrop and RandomHorizontalFlip augmentations as they are not suitable for the driving task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' ACO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Following Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' (2022b), it is pre-trained using action-conditioned contrastive learning on the YouTube driving videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' ACO trains an inverse dynamic model to generate pseudo steer labels for driving videos, based on which steer-based discrimination is added on top of MoCo-v2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' SelfD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' SelfD (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022a) is not a pre-training method strictly since it needs to train the whole policy model on the driving video for each task, while other pre-training methods aforemen- tioned provide a general pre-training visual model for all tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We still include it for comparison due to its close relationship to our target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Specifically, we follow Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' (2022a) to train the model for each task with the following pipeline: training on the task data → training on the YouTube data with pseudo-label → fine-tuning on the task data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 DESCRIPTION ON DOWNSTREAM AUTONOMOUS DRIVING TASKS We carry out experiments under (1) three imitation learning based closed-loop driving tasks in CARLA (Dosovitskiy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2017), (2) one reinforcement learning based driving task in CARLA, and (3) an open-loop planning task on real-world autonomous driving dataset nuScenes (Caesar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2020), to fully validate the effectiveness of PPGeo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We briefly describe each task below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Navigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' It corresponds to the goal-conditioned navigation task in the CoRL2017 bench- mark (Dosovitskiy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The agent is trained in Town01 and tested in Town02 with unseen weather, and there are no other traffic participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We use different sizes of training data (from 4K to 40K) following Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' (2022b) to evaluate the generalization ability of pre-trained vi- sual encoders when labeled data is limited and conduct the closed-loop evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The evaluation metric is success rate, denoting the portion of 50 pre-defined routes finished without any collision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' And traffic lights are ignored here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' CILRS (Codevilla et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2019), a classic image based end-to-end autonomous driving model, is adopted for training and evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Navigation Dynamic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' This is the navigation dynamic task in the CoRL2017 benchmark (Dosovit- skiy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The setting differentiates from Navigation that there are other dynamic objects such as randomly generated vehicles, which substantially increases the difficulty of driving safety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Leaderboard Town05-long.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' This challenging and realistic benchmark corresponds to the Leader- Board benchmark (CARLA, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We collect 40K training data in Town01, 03, 04, 06 and eval- uate on 10 routes in the unseen Town05 (Prakash et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Due to the challenging scenarios in this task, we evaluate different pre-training approaches with the state-of-the-art image-based au- tonomous driving model TCP (Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The major metrics of this task are Driving Score, Route Completion, and Infraction Score (all the higher the better).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Route Completion denotes the portion of the route completed by the agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Infraction Score is the number of infractions made 5 Table 1: The Successful Rate results of the closed-loop Navigation task (mean by 3 random trials).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Pre-train Method Navigation - # of training samples 10% (4K) 20% (8K) 40% (16K) 100% (40K) Random 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='6 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='5 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ImageNet 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='7± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='4 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='6 MIM 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='7 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='1 MoCo 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='7 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='1 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='7 ± 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 ACO 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='5 SelfD 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='7 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='7 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 PPGeo (ours) 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='1 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='7 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 along the route including pedstrain collisions, vehicle collisions, red light infractions, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' And the main metric Driving Score is the product of Route Completion and Infraction Score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Reinforcement Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Proximal Policy Optimization (PPO) (Schulman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2017) is used to train the CILRS (Codevilla et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2019) model initialized with different pre-trained weights in CARLA Town01 environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The reward shaping details follow Roach (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We also conduct experiments to freeze the pre-trained visual encoder during training to further study the effectiveness of the pre-trained feature representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' nuScenes Planning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' This task involves trajectory planning in real-world dataset nuScenes (Caesar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Given the current visual input, the model plans a 3-second trajectory (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='5 Hz), and the planned trajectory is compared with the ground truth log.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We also calculate the collision rate, where a collision is defined as overlaps with future vehicles and pedestrians based on planned waypoints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The metric of this tasks includes (1) the L2 distance between predicted trajectory and ground truth trajectory, and (2) the collision rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Metrics are measured at different time lengths from 1s to 3s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The planning model used here is comprised of a visual encoder and a GRU-based planner to predict each waypoint auto-regressively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We use the official train-val split for training and evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 NUMERIC COMPARISON ON DOWNSTREAM TASKS For imitation learning based closed-loop driving tasks, the evaluation results are shown in Table 1- 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We present the plot between episode return and environment steps of each method in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 3 for the reinforcement learning experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The open-loop nuScenes planning results are provided in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We could observe that PPGeo outperforms other baselines by a large margin in all tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Note that the model is tested under a different number of fine-tuning samples from 10% (4K) to full 40K in the Navigation and Navigation Dynamic tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In the case of the particularly small size of training samples, PPGeo still demonstrates competitive performance and has a larger improvement gap of over 100%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' This validates the generalization ability of the pre-trained visual encoder, which is important when adapting to a new environment with very limited labeled data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In the more chal- lenging and real-world style Leaderboard Town05-long task in Table 3, the model pre-trained with our method achieves the highest driving score and infraction score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' PPGeo well handles cases where the agent needs to stop, leading to much fewer vehicle collisions and red light infractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Since ACO considers steering angles only during pre-training, its performance degrades on more challenging scenarios where brake and throttles are also important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' SelfD performs slightly better than ACO in complex cases while it significantly degenerates when the task data is limited, as affected by the unsatisfying pseudo labeling model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' ImageNet pre-training also shows competitive performance, which might credit to its ability of finding salient objects in the scene when the input contains little irrelevant information (see examples in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='4 DEPTH AND ODOMETRY ESTIMATION In this part, we explore whether the large-scale training on uncalibrated data could benefit the depth and odometry estimation models as well and validate the effectiveness of first-stage training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Specif- ically, we employ the DepthNet and PoseNet trained after the first stage as initial weights for Mon- odepthv2 (Godard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2019), and conduct experiments on KITTI (Geiger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Results in Table 5 indicate that pre-training on large-scale driving videos could bring performance improve- 6 Table 2: The Successful Rate results of the closed-loop Navigation Dynamic (mean by 3 random trials).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Pre-train Method Navigation Dynamic - # of training samples 10% (4K) 20% (8K) 40% (16K) 100% (40K) Random 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ImageNet 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='7± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='7 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='7 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='7 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 MIM 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='5 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='7 ± 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='1 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='7 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 MoCo 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='7 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='7 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ACO 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 SelfD 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='6 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='4 PPGeo (ours) 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 Table 3: Closed-loop Leaderboard Town05-long task results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Besides three main metrics, infraction details are also reported (all the lower the better).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Evaluation repeats 3 times with the mean reported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Pre-train Method Driving Score Infraction Score Route Completion Collisions pedestrian Collisions vehicle Collisions layout Off-road violations Agent blocked Red light violations Random 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='50±1.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='12±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='08 PPGeo 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='44±5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='63 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='79±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='08 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='05±5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='11 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='04±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='54±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='29 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='00±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='16±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='11 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='76±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='04±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='05 100 200 300 400 500 600 700 800 Steps (K) 100 0 100 200 300 400 500 Episode Return Visual Encoder Fine-tuning ImageNet MoCo ACO PPGeo 100 200 300 400 500 600 700 800 Steps (K) 100 200 300 400 Episode Return Visual Encoder Frozen ImageNet MoCo ACO PPGeo Figure 3: Learning curves of the RL agents using PPGeo and three other best pre-training baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Left: the pre-trained visual encoder is jointly fine-tuned during RL training;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Right: the visual en- coder is frozen during RL training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The episode return is the mean with standard deviation in shade across three runs with different random seeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Table 4: Open-loop nuScenes planning results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We evaluate the ℓ2 distance between model predic- tions and the ground truth trajectory and collision rate in horizons from 1 second to 3 seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Pre-train Method L2 (m) ↓ Collision Rate (%) ↓ 1s 2s 3s 1s 2s 3s Random 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='621 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='722 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='851 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='550 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='779 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='375 ImagNet 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='331 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='202 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='086 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='315 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='550 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='366 MIM 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='412 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='357 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='331 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='297 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='622 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='507 MoCo 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='528 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='545 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='585 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='560 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='235 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='390 ACO 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='496 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='496 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='519 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='446 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='178 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='223 SelfD 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='419 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='359 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='316 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='353 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='923 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='044 PPGeo (ours) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='302 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='154 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='018 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='270 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='425 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='941 7 Table 5: Improvement from our pre-training method on depth and odometry estimation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Pre-train Method Depth Estimation Odometry Estimation abs rel ↓ sq rel ↓ rmse ↓ rmse log ↓ a1 ↑ a2 ↑ a3 ↑ Sequence 09 ↓ Sequence 10 ↓ ImageNet 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='118 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='902 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='873 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='196 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='871 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='958 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='981 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='017±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='010 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='015±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='010 PPGeo 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='114 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='805 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='599 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='186 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='874 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='962 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='984 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='016±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='009 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='013±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='009 Ours ACO ImageNet MoCo Origin Figure 4: Eigen-Cam (Muhammad & Yeasin, 2020) activation maps of the learned representation from different pre-training methods on the driving video data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Table 6: Ablative study on key designs of PPGeo on the Navigation task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' # Experiment Navigation - # of training samples 10% (4K) 20% (8K) 40% (16K) 100% (40K) 1 Single stage 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='7 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 2 No frozen in 2nd stage 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='7 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='1 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 3 PoseNet direct supervision 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='7 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 4 PPGeo 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='0 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='1 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='3 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='7 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='2 ment to both depth and odometry estimation tasks, which is an additional harvest of our pre-training framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We refer readers to Godard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' (2019) for details about the metrics of these tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='5 VISUALIZATION RESULTS Here we provide heatmaps of the feature representations learned by different pre-training methods using Eigen-Cam (Muhammad & Yeasin, 2020) to show the attended regions in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In many cases (Row 1&2), our model mainly concentrates on the lane in front of the ego vehicle, which is highly related to driving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' And our model PPGeo well captures the specific cues causing the brake action including front vehicles (Row 3&4) and traffic lights (Row 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' We also observe that the model pre-trained with ImageNet classification tends to capture salient objects in the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' This is helpful when the salient objects are straightforwardly related to the driving decision (Row 4);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' but it may focus on wrong objects when the input contains other irrelevant information (Row 2&3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='6 ABLATIVE STUDY We conduct ablative study as to different designs of PPGeo on the Navigation task in Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Train- ing the visual encoder and DepthNet in a single stage simultaneously (Row 1) leads to an inferior performance, indicating that it is quite challenging for the visual encoder to learn the correct ego- motion if depth estimation is also trained from scratch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Moreover, jointly optimizing the DepthNet in the second stage (Row 2, not frozen) degrades the depth estimation quality and harms the per- formance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In Row 3, we observe that utilizing the PoseNet obtained in the first stage to provide 8 pseudo label supervision directly leads to inferior results, since an inaccurate pseudo label impairs the learning process to great extent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 4 RELATED WORK Pre-training for NLP and General Vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Pre-training or representation learning has proved to be an essential key to the success of artificial intelligence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In the field of Natural Language Processing (NLP), with the powerful capability of Transformer (Vaswani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2017), pre-training on large- scale datasets with large models then fine-tuning on downstream tasks has become the dominant paradigm (Kenton & Toutanova, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Brown et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' As for the field of Computer Vision, training specific downstream tasks with the supervised pre-trained weights of visual encoder via ImageNet classification task is widely adopted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Recently, unsupervised and self-supervised learn- ing methods such as contrastive learning (He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2020c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='b) and masked im- age modeling (Bao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Xie et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Peng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022) have gained impressive improvement over ImageNet pre-training on various vision benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Very recent vision-language co-training approaches (Radford et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022) demonstrate their extraordinary potential in the domain of multi-modal learning and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Yet, these generic representation learning methods adopt various data augmentation techniques to achieve translation and view invariance, while visuomotor driving sets in a highly dynamic environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In this work, we show that the ever-victorious pre-training methods may not be the optimal choice, and introduce a curated paradigm for visuomotor driving policy learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Pre-training for Visuomotor Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Learning a control policy directly from raw visual input is challenging since the model needs to reason about visual pixels and dynamic behaviors simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Moreover, training visuomotor models from scratch usually requires tons of labeled data or environment interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' To this end, recently, Shah & Kumar (2021) shows that feature representations from ResNet (He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2016) pre-trained on ImageNet classification is helpful for RL-based dexterous manipulation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Parisi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' (2022) conducts extensive experiments on applying “off-the-shelf” pre-trained vision models in diverse control domains and validates their benefits to train control policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' CLIP (Radford et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2021) is also adopted in some embodied AI and robot navigation problems (Shah et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Besides borrowing pre-trained weights for visuomotor tasks, researchers in robotics now desire a paradigm learning policy representations from raw data directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Xiao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' (2022);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Radosavovic et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' (2022);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Seo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' (2022);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Gupta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' (2022) inherit the MIM spirit to realize visual pre-training for control tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Yang & Nachum (2021) investigates unsupervised representation learning objectives from D4RL environments (Fu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2020), and Yamada et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' (2022) further adopts task-induced approaches to learn from prior tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' However, compared with visuomotor driving, the visual inputs of such control tasks are less diverse which usually concentrate on objects and are much more compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' To our best knowledge, ACO (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022b) is the only pre-training method customized for autonomous driving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' By first training an inverse dynamic model on nuScenes (Caesar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2020), they get pseudo steer labels of the driving videos and then construct the steer-conditioned discrimination for contrastive learning following MoCo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' However, ACO ignores other crucial driv- ing factors such as throttle and brakes, and its performance is largely limited by the inverse dynamic model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' SelfD (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022a) is not strictly designed for pre-training while it also makes use of vast amounts of videos to learn driving policies via semi-supervised learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' It acquires the pseudo labeling knowledge from the target domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' These two methods both depend on the accuracy of pseudo labeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In contrast, we realize fully self-supervised learning through dense geometric reconstruction, evading the possible adverse effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Policy Learning for Autonomous Driving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Visuomotor autonomous driving learns a driving pol- icy directly from sensor inputs in an end-to-end manner (Codevilla et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2020a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Prakash et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Shao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In essence, the inherent difficulty of the urban-style autonomous driving tasks makes such meth- ods data-hungry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Interfuser (Shao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022), the current top-1 method on the CARLA Leader- board (CARLA, 2022), requires 3 million labeled data samples for imitation learning (behavior cloning specifically).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' RL-based model MaRLn (Toromanoff et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2020) needs 20 million environ- ment steps of interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The sample efficiency problem greatly impedes the real-world application of such approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In this work, we propose a self-supervised pre-training pipeline to learn driving 9 policy related representations on unlabeled driving videos, and pave the way for these visuomotor autonomous driving models to further achieve satisfying performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 5 CONCLUSION AND DISCUSSION In this work, we have proposed a fully self-supervised visuomotor driving policy pre-training paradigm PPGeo by modeling the 3D geometry of large-scale unlabeled driving videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Taking a direct approach to infer the ego-motion and benefiting from the two-stage pre-training pipeline, we enable the visual encoder to learn driving policies based on single visual input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Our method out- performs the peer pre-training approaches by a large margin on a series of visuomotor driving tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' For its limitation, our method currently only considers the ego-motion for a single time step, and a future direction is to devise the framework to perform multi-step motion prediction which contains more information about driving decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' REFERENCES Hangbo Bao, Li Dong, Songhao Piao, and Furu Wei.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Task-induced representation learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In ICLR, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 2, 9 12 Mengjiao Yang and Ofir Nachum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Representation matters: offline pretraining for sequential decision making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In ICML, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 9 Denis Yarats, Ilya Kostrikov, and Rob Fergus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Image augmentation is all you need: Regularizing deep reinforcement learning from pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In ICLR, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 1 Jimuyang Zhang, Ruizhao Zhu, and Eshed Ohn-Bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Selfd: Self-learning large-scale driving policies from the web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In CVPR, 2022a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 2, 4, 5, 9 Qihang Zhang, Zhenghao Peng, and Bolei Zhou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Learning to drive by watching youtube videos: Action-conditioned contrastive policy pretraining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In ECCV, 2022b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 2, 4, 5, 9 Richard Zhang, Phillip Isola, and Alexei A Efros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Colorful image colorization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In ECCV, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 2 Zhejun Zhang, Alexander Liniger, Dengxin Dai, Fisher Yu, and Luc Van Gool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' End-to-end urban driving by imitating a reinforcement learning coach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In ICCV, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 6 13 POLICY PRE-TRAINING FOR AUTONOMOUS DRIVING VIA SELF-SUPERVISED GEOMETRIC MODELING Supplementary Materials In this Supplementary document, we first provide detailed network structures in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' More de- scription and visual illustrations of the downstream tasks are discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Last, we discuss limitations and common failure cases in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' A NETWORK DETAILS For all experiments, the backbone of the visual encoder is ResNet-34 (He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2016), and the detailed structure of it is provided in Table 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' For DepthNet and PoseNet, we follow the same model structure as Godard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' (2019) with a two-layer MLP focal length head and a two-layer MLP optical center head added to the bottleneck of the PoseNet to predict the intrinsic matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Please refer to Godard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' (2019) for model details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' For the Navigation, Navigation Dynamic, and Reinforcement Learning tasks, we use CILRS (Codev- illa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2019) and the model details are provided in Table 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' For the Leaderboard Town05-long task, TCP (Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', 2022) is chosen as our agent, and we refer readers to Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' (2022) for model details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' For the nuScenes Planning, the trajectory planning model structure is shown in Table 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Table 7: Detailed structure of the visual encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Layer Type Channels Stride Kernel Size Activation Function Image Encoder ResNet-34 Measurement Encoder Conv 256 1 1 ReLU Conv 256 3 1 ReLU Conv 256 3 1 ReLU Conv 6 1 1 ReLU Average Pooling Table 8: Detailed structure of the CILRS model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Layer Type Dims in Dims out Activation Function Image Encoder ResNet-34 512 Speed Encoder FC 1 256 ReLU FC 256 512 Speed Pred Head FC 512 256 ReLU FC 256 256 ReLU FC 256 256 ReLU Control Pred Head FC 512 256 ReLU FC 256 256 ReLU FC 256 3 Sigmoid 14 Table 9: Detailed structure of the trajectory planning model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Image Encoder ResNet-34 Bottleneck Layer Type Dims in Dims out Activation Function FC 512 256 ReLU FC 256 256 Decoder Layer Type Hidden dim Input Dim Output Dim GRU 256 2 2 B DOWNSTREAM TASKS DETAILS For Navigation and Navigation Dynamic, training data is collected in Town01, and the closed-loop testing is conducted in Town02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The maps of Town01 and Town02 are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The agent needs to follow a series of sparse waypoints to navigate from the start point to the end point and avoid collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The difference between Navigation and Navigation Dynamic is that there are other dynamic vehicles and pedestrians in the town.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Examples are provided in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The Leaderboard-Town05-long task is more close to real-world urban driving, with different chal- lenging scenarios added to the route.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' The map of Town05 is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Town 01 Town 02 Town 05 Figure 5: Maps of Town01, Town02, and Town05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Navigation Navigation Dynamic Figure 6: Examples of the front view image for Navigation and Navigation Dynamic tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 15 C LIMITATIONS In this part, we analyze some failure cases and limitations of our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Since the visual encoder need to predict the future motion based on a single front-view image, there might be some factors that directly influence the driving decision not shown in the image (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=', vehicles behind the ego vehicle, factors related to the driver, navigation information).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' Some of such cases are provided in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' In these cases, the visual encoder does not get enough information to make the correct prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' These samples during training may hamper the learning process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' After training, one may use the difference between the prediction from PoseNet and that from visual encoder to filter out these samples, and re-train the visual encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 𝐼𝑡 𝐼𝑡+1 Figure 7: Failure cases where the driving decision/future motion can not be inferred from It.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' For the cases in Row 1 and Row 2, by comparing It and It+1, we know that the ego vehicle stops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' However, there is no clear clue in It indicating it should stop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' For the case in Row 3, the ego vehicle is turning left, while we could hardly tell the turning direction from It alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} +page_content=' 16' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AzT4oBgHgl3EQfFPox/content/2301.01006v1.pdf'} diff --git a/8dFAT4oBgHgl3EQfpB03/content/tmp_files/2301.08637v1.pdf.txt b/8dFAT4oBgHgl3EQfpB03/content/tmp_files/2301.08637v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..f1f4086a873a53320ccb618e3d4dcf3a55b391c2 --- /dev/null +++ b/8dFAT4oBgHgl3EQfpB03/content/tmp_files/2301.08637v1.pdf.txt @@ -0,0 +1,2871 @@ +ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN +OPERATOR +FRIEDRICH PHILIPP, MANUEL SCHALLER, KARL WORTHMANN, SEBASTIAN PEITZ, AND FELIKS N ¨USKE +ABSTRACT. We consider the data-driven approximation of the Koopman operator for stochastic differen- +tial equations on reproducing kernel Hilbert spaces (RKHS). Our focus is on the estimation error if the +data are collected from long-term ergodic simulations. We derive both an exact expression for the variance +of the kernel cross-covariance operator, measured in the Hilbert-Schmidt norm, and probabilistic bounds +for the finite-data estimation error. Moreover, we derive a bound on the prediction error of observables in +the RKHS using a finite Mercer series expansion. Further, assuming Koopman-invariance of the RKHS, +we provide bounds on the full approximation error. Numerical experiments using the Ornstein-Uhlenbeck +process illustrate our results. +1. INTRODUCTION +The Koopman operator [23] has become an essential tool in the modeling process of complex dy- +namical systems based on simulation or measurement data. The philosophy of the Koopman approach +is that for a (usually non-linear) dynamical system on a finite-dimensional space, the time-evolution of +expectation values of observable functions satisfies a linear differential equation. Hence, after “lifting” +the dynamical system into an infinite-dimensional function space of observables, linear methods become +available for its analysis. The second step is then to notice that traditional Galerkin approximations of the +Koopman operator can be consistently estimated from simulation or measurement data, establishing the +fundamental connection between the Koopman approach and modern data science. Koopman methods +have found widespread application in system identification [4], control [24, 42, 25, 17, 49], sensor place- +ment [31], molecular dynamics [50, 44, 35, 36, 18, 56], and many other fields. We refer to [19, 33, 5] for +comprehensive reviews of the state of the art. +The fundamental numerical method for the Koopman approach is Extended Dynamic Mode Decom- +position (EDMD) [54], which allows to learn a Galerkin approximation of the Koopman operator from +finite (simulation or measurement) data on a subspace spanned by a finite set of observables, often called +dictionary. An appropriate choice of said dictionary is a challenging problem. In light of this issue, +representations of the Koopman operator on large approximation spaces have been considered in recent +years, including deep neural networks [29, 32], tensor product spaces [21, 37], and reproducing kernel +Hilbert spaces (RKHS) [55, 11, 20]. In the work [20] it was shown that by means of the integral operator +associated to an RKHS, it is possible to construct a type of Galerkin approximation of the Koopman +operator. The central object are (cross-)covariance operators, which can be estimated from data, using +only evaluations of the feature map. Due to the relative simplicity of the resulting numerical algorithms +on the one hand, and the rich approximation properties of reproducing kernels on the other hand, kernel +methods have emerged as a promising candidate to overcome the fundamental problem of dictionary +selection. +A key question is the quantification of the estimation error for (compressed1) Koopman operators. For +finite dictionaries and independent, identically distributed (i.i.d.) samples, error estimates were provided +in [26, 38], see also [58] for the ODE case and [49] for an extension to control-affine systems. The +1A compression of a linear operator T to a subspace M is given by PT|M, where P denotes a projection onto M. +1 +arXiv:2301.08637v1 [math.DS] 20 Jan 2023 + +2 +F. PHILIPP, M. SCHALLER, K. WORTHMANN, S. PEITZ, AND F. N ¨USKE +estimation error for cross-covariance operators on kernel spaces was considered in [34], where general +concentration inequalities were employed. The data were also allowed to be correlated, and mixing +coefficients were used to account for the lack of independence. In this article, we take a different route +and follow the approach of our previous paper [38], where we, in addition, also derived error estimates +for the Koopman generator and operator for finite dictionaries and data collected from long-term, ergodic +trajectories. This setting is relevant in many areas of science, where sampling i.i.d. from an unknown +stationary distribution is practically infeasible, e.g., in fluid or molecular dynamics. The centerpiece of +our results was an exact expression for the variance of the finite-data estimator, which can be bounded +by an asymptotic variance. The asymptotic variance by itself is a highly interesting dynamical quantity, +which can also be described in terms of Poisson equations for the generator [27, Section 3]. +We consider the Koopman semigroup (Kt)t≥0 generated by a stochastic differential equation on the +space L2 +µ, where µ is a probability measure which is invariant w.r.t. the associated Markov process. We +study the action of Kt on observables in an RKHS H which is densely and compactly embedded in L2 +µ. If +this action is considered through the “lens” of the kernel integral operator E : L2 +µ → H (see Section 2.2), +we arrive at a family of operators Ct +H = EKtE∗ (cf. Figure 1). The action of Ct +H : H → H is that of a +cross-covariance operator: +Ct +Hψ = +� +(Ktψ)(x)k(x, ·) dµ(x), +ψ ∈ H, +where k(·, ·) is the kernel generating the RKHS H. These operators possess canonical empirical estima- +tors based on finite simulation data, which only require evaluations of the feature map. +L2 +µ +L2 +µ +H +H +Kt +E +E∗ +Ct +H +FIGURE 1. Diagram illustrating the different operators involved +Our contribution, illustrated in Figure 2, is two-fold. In our first main result, Theorem 3.1, we provide +an exact formula for the Hilbert-Schmidt variance of the canonical empirical estimator �Cm,t +H +of the cross- +covariance operator Ct +H, for m data points sampled from a long ergodic simulation. This result extends +the findings in [38] to the kernel setting and no longer depends on the dictionary size (which would +be infinite, at any rate). Due to the infinite-dimensional setting, additional assumptions are required, +in particular, a spectral decomposition of the Koopman generator. Our result allows for probabilistic +estimates for the error ∥ �Cm,t +H +− Ct +H∥HS, see Proposition 3.4. +As a second main result, we propose an empirical estimator for the restriction of the Koopman op- +erator Kt to H, truncated to finitely many terms of its estimated Mercer series expansion, and prove a +probabilistic bound for the resulting estimation error in Theorem 4.1, measured in the operator norm +for bounded linear maps from H to L2 +µ. This result can be seen as a bound on the prediction error for +the RKHS-based Koopman operator due to the use of finite data. In the situation where the RKHS is +invariant under the Koopman operator we are able to complement the preceding error analysis with a +bound on the full approximation error in Theorem 4.5. +Finally, we illustrate our results for a one-dimensional Ornstein-Uhlenbeck (OU) process. For this +simple test case, all quantities appearing in our error estimates are known analytically and can be well +approximated numerically. Therefore, we are able to provide a detailed comparison between the error +bound obtained from our results and the actual errors observed for finite data. Our experiments show that + +ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR +3 +our bounds for the estimation error of the cross-covariance operator are accurate, and that the corrections +we introduced to account for the inter-dependence of the data are indeed required. Concerning the +prediction error, we find our theoretical bounds still far too conservative, which reflects the problem of +accounting for the effect of inverting the mass matrix in traditional EDMD. This finding indicates that +additional research is required on this end. +Full Koopman +Approximation Error +Projection error +Theorem 4.5 +Variance representation +of empirical estimator +Theorem 3.1 +Estimation error +Theorem 4.1 +i.i.d. sampling +Ergodic sampling +Cross-covariance bound +Proposition 3.4 +∥Ct +ℍ − +̂ +C m,t +ℍ ∥HS +∥Kt +N − +̂ +K m,t +N ∥ℍ→L2μ(X) +∥Kt − +̂ +K m,t +N ∥ℍ→L2μ(X) +∥Kt − Kt +N∥ℍ→L2μ(X) +FIGURE 2. Illustration of main results +The paper is structured as follows: the setting is introduced in Section 2. The result concerning the +variance of the empirical cross-covariance operator, Theorem 3.1, is presented and proved in Section 3, +while our bound for the prediction error is part of Theorem 4.1 in Section 4. Numerical experiments are +shown in Section 5, conclusions are drawn in Section 6. +2. PRELIMINARIES +In this section, we provide the required background on stochastic differential equations (Section 2.1), +reproducing kernel Hilbert spaces (Section 2.2), Koopman operators (Section 2.3), and their representa- +tions on an RKHS (Section 2.4). +2.1. Stochastic differential equations. Let X ⊂ Rd and let a stochastic differential equation (SDE) +with drift vector field b : X → Rd and diffusion matrix field σ : X → Rd×d be given, i.e., +dXt = b(Xt) dt + σ(Xt) dWt, +(2.1) +where Wt is d-dimensional Brownian motion. We assume that both b and σ are Lipschitz-continuous and +that (1 + ∥ · ∥2)−1[∥b∥2 + ∥σ∥F ] is bounded on X. Then [39, Theorem 5.2.1] guarantees the existence +of a unique solution (Xt)t≥0 to (2.1). +The solution (Xt)t≥0 constitutes a continuous-time Markov process whose transition kernel will be +denoted by ρt : X ×BX → R, where BX denotes the Borel σ-algebra on X. Then ρt(x, ·) is a probability +measure for all x ∈ X, and for each A ∈ BX we have that ρt(·, A) is a representative of the conditional +probability for A containing Xt given X0 = · , i.e., +ρt(x, A) = P(Xt ∈ A|X0 = x) +for µ-a.e. x ∈ X. +Throughout, we will assume the existence of an invariant (Borel) probability measure µ for the Markov +process (Xt)t≥0, i.e., we have +� +ρt(x, A) dµ(x) = µ(A) +(2.2) +for all t ≥ 0. +In addition to being invariant, we will often assume that µ is ergodic, meaning that for any t > 0 +every ρt-invariant set A (that is, ρt(x, A) = 1 for all x ∈ A) satisfies µ(A) ∈ {0, 1}. In this case, the +Birkhoff ergodic theorem [15, Theorem 9.6] (see also (D.1)) and its generalizations apply, and allow us +to calculate expectations w.r.t. µ using long-time averages over simulation data. +We let ∥ · ∥p denote the Lp +µ(X)-norm, 1 ≤ p < ∞. In the particular case p = 2, scalar product and +norm on the Hilbert space L2 +µ(X) will be denoted by ⟨· , ·⟩µ and ∥ · ∥µ, respectively. + +4 +F. PHILIPP, M. SCHALLER, K. WORTHMANN, S. PEITZ, AND F. N ¨USKE +2.2. Reproducing kernel Hilbert spaces. In what follows, let k : X × X → R be a continuous and +symmetric positive definite kernel, that is, we have k(x, y) = k(y, x) for all x, y ∈ X and +m +� +i,j=1 +k(xi, xj)cicj ≥ 0 +for all choices of x1, . . . , xm ∈ X and c1, . . . , cm ∈ R. It is well known that k generates a so-called +reproducing kernel Hilbert space (RKHS) [1, 6, 40] (H, ⟨· , ·⟩) of continuous functions, such that for +ψ ∈ H the reproducing property +ψ(x) = ⟨ψ, Φ(x)⟩, +x ∈ X, +(2.3) +holds, where Φ : X → H denotes the so-called feature map corresponding to the kernel k, i.e., +Φ(x) = k(x, ·), +x ∈ X. +In the sequel, we shall denote the norm on H by ∥ · ∥ and the kernel diagonal by ϕ: +ϕ(x) = k(x, x), +x ∈ X. +Then for x ∈ X we have +∥Φ(x)∥2 = ⟨Φ(x), Φ(x)⟩ = ⟨k(x, ·), k(x, ·)⟩ = k(x, x) = ϕ(x). +We shall frequently make use of the following estimate: +|k(x, y)| = |⟨Φ(x), Φ(y)⟩| ≤ ∥Φ(x)∥∥Φ(y)∥ = +� +ϕ(x)ϕ(y). +In particular, it shows that k is bounded if and only if its diagonal ϕ is bounded. +By Lp +µ(X), p ∈ [1, ∞), we denote the space of all functions (not equivalence classes) on X with a +finite p-norm ∥ · ∥p. Henceforth, we shall impose the following +Compatibility Assumptions: +(A1) ϕ ∈ L2 +µ(X). +(A2) If ψ ∈ L2 +µ(X) such that +� � +k(x, y)ψ(x)ψ(y) dµ(x) dµ(y) = 0, then ψ = 0. +(A3) If ψ ∈ H such that ψ(x) = 0 for µ-a.e. x ∈ X, then ψ(x) = 0 for all x ∈ X. +Many of the statements in this subsection can also be found in [52, Chapter 4]. However, as we aim +to present the contents in a self-contained way, we provide the proofs in Appendix A. +The following lemma explains the meaning of the compatibility assumptions (A1) and (A2). +Lemma 2.1. Under the assumption that ϕ ∈ L1 +µ(X) (in particular, under assumption (A1)), we have +that H ⊂ L2 +µ(X) with +∥ψ∥µ ≤ +� +∥ϕ∥1 · ∥ψ∥, +ψ ∈ H, +(2.4) +and assumption (A2) is equivalent to the density of H in L2 +µ(X). +We have meticulously distinguished between functions and equivalence classes as there might be +distinct functions φ, ψ ∈ H, which are equal µ-almost everywhere2, i.e., φ = ψ in L2 +µ(X). The com- +patibility assumption (A3) prohibits this situation so that H can in fact be seen as a subspace of L2 +µ(X), +which is then densely and continuously embedded. +2For example, if µ = δa and φ(a) = ψ(a) + +ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR +5 +Remark 2.2. (a) Condition (A1) implies k ∈ L4 +µ⊗µ(X × X), where µ ⊗ µ is the product measure on +X × X. +(b) The density of H in L2 +µ(X) is strongly related to the term universality in the literature, see [53]. +(c) Condition (A3) holds if supp µ = X, cf. [52, Exercise 4.6]. +It immediately follows from +� +|ψ(x)|∥Φ(x)∥ dµ(x) ≤ ∥ψ∥µ∥ϕ∥1/2 +1 +, +(2.5) +for ψ ∈ L2 +µ(X) that the linear operator E : L2 +µ(X) → H, defined by +Eψ := +� +ψ(x)Φ(x) dµ(x), +ψ ∈ L2 +µ(X), +is well defined (as a Bochner integral in H) and bounded with operator norm not larger than ∥ϕ∥1/2 +1 +. +Remark 2.3. The so-called kernel mean embedding Ek, mapping probability measures ν on X to the +RKHS H, is defined by Ekν = +� +Φ(x) dν(x), see, e.g., [51]. Hence, we have Eψ = Ekν with dν = ψ dµ. +Note that the operator E is not an embedding in strict mathematical terms. The terminology embedding +rather applies to its adjoint E∗. Indeed, the operator E enjoys the simple but important property: +⟨Eψ, η⟩ = +� +ψ(x)⟨Φ(x), η⟩ dµ(x) = +� +ψ(x)η(x) dµ(x) = ⟨ψ, η⟩µ +(2.6) +for ψ ∈ L2 +µ(X) and η ∈ H. This implies that the adjoint operator E∗ : H → L2 +µ(X) is the inclusion +operator from H into L2 +µ(X), i.e., +E∗η = η, +η ∈ H. +(2.7) +We shall further define the covariance operator3 +CH := EE∗ ∈ L(H). +Recall that a linear operator T ∈ L(H) on a Hilbert space H is trace class if for some (and hence for +each) orthonormal basis (ej)j∈N of H we have that �∞ +j=1⟨(T ∗T)1/2ei, ei⟩ < ∞. A linear operator +S ∈ L(H, K) between Hilbert spaces H and K is said to be Hilbert-Schmidt [12, Chapter III.9] if S∗S is +trace class, i.e., ∥S∥2 +HS := �∞ +j=1 ∥Sei∥2 < ∞ for some (and hence for each) orthonormal basis (ej)j∈N. +Lemma 2.4. Let the Compatibility Assumptions (A1)–(A3) be satisfied. Then the following hold. +(a) The operator E is an injective Hilbert-Schmidt operator with +∥E∥2 +HS = ∥ϕ∥1. +(b) The space H is densely and compactly embedded in L2 +µ(X). +(c) The operator CH is an injective non-negative selfadjoint trace class operator. +The next theorem is due to Mercer and can be found in, e.g., [45]. It shows the existence of a particular +orthonormal basis (ej)∞ +j=1 of L2 +µ(X) composed of eigenfunctions of E∗E, which we shall henceforth call +the Mercer basis corresponding to the kernel k. Again for the sake of self-containedness, we give a short +proof in Appendix A. +3In what follows, by L(H, K) we denote the set of all bounded (i.e., continuous) linear operators between Hilbert spaces H +and K. As usual, we also set L(H) := L(H, H). + +6 +F. PHILIPP, M. SCHALLER, K. WORTHMANN, S. PEITZ, AND F. N ¨USKE +Theorem 2.5 (Mercer’s Theorem). There exists an orthonormal basis (ej)∞ +j=1 of L2 +µ(X) consisting of +eigenfunctions of E∗E with corresponding eigenvalues λj > 0 such that �∞ +j=1 λj = ∥ϕ∥1 < ∞. Fur- +thermore, (fj)∞ +j=1 with fj = +� +λjej constitutes an orthonormal basis of H consisting of eigenfunctions +of CH with corresponding eigenvalues λj. Moreover, for all x, y ∈ X, +k(x, y) = +� +j +fj(x)fj(y) = +� +j +λjej(x)ej(y), +the series converges absolutely. +2.3. The Koopman semigroup. The Koopman semigroup (Kt)t≥0 associated with the SDE (2.1) is +defined by +(Ktψ)(x) = E[ψ(Xt)|X0 = x] = +� +ψ(y) ρt(x, dy), +for ψ ∈ B(X), the set of all bounded Borel-measurable functions on X, and ρt(x, dy) = dρt(x, ·)(y). It +is easy to see that the invariance of µ is equivalent to the identity +� +Ktψ dµ = +� +ψ dµ +(2.8) +for all t ≥ 0 and ψ ∈ B(X) (which easily extends to functions ψ ∈ L1 +µ(X), see Proposition 2.7). +Remark 2.6. Note that in the case σ = 0 the SDE (2.1) reduces to the deterministic ODE ˙x = b(x). +Then (2.8) implies +� +|ψ(φ(t, x))|2 dµ(x) = +� +|ψ(x)|2 dµ(x) for all t ≥ 0 and all ψ ∈ B(X), where +φ(·, x) is the solution of the initial value problem ˙y = b(y), y(0) = x. Hence, the composition operator +Kt : ψ �→ ψ ◦ φ(t, ·) is unitary in L2 +µ(X). However, we shall require below (see Theorem 3.1) that Kt +has its spectrum in the interior of the unit circle. Therefore, we assume throughout that σ ̸= 0. +The proofs of the following two propositions can be found in Appendix A. +Proposition 2.7. For each p ∈ [1, ∞] and t ≥ 0, Kt extends uniquely to a bounded operator from +Lp +µ(X) to itself with operator norm ∥Kt∥Lp +µ→Lp +µ ≤ 1. +By Cb(X) we denote the set of all bounded continuous functions on X. As the measure µ is finite, we +have Cb(X) ⊂ B(X) ⊂ Lp +µ(X) for all p ∈ [1, ∞]. In fact, Cb(X) is dense in each Lp +µ(X), p ∈ [1, ∞), +see [48, Theorem 3.14]. +Proposition 2.8. (Kt)t≥0 is a C0-semigroup of contractions in Lp +µ(X) for each p ∈ [1, ∞). +The infinitesimal generator of the C0-semigroup (Kt)t≥0 is the (in general unbounded) operator in +L2 +µ(X), defined by +Lψ = L2 +µ- lim +t→0 +Ktψ − ψ +t +, +(2.9) +whose domain dom L is the set of all ψ ∈ L2 +µ(X) for which the above limit exists. By Proposition 2.8 +and the Lumer-Phillips theorem (see [28]), the operator L is densely defined, closed4, dissipative (i.e., +Re⟨Lψ, ψ⟩µ ≤ 0 for all ψ ∈ dom L), and its spectrum is contained in the closed left half-plane. +Lemma 2.9. The constant function 1 is contained in dom L and L1 = 0. Moreover, if M := span{1} ⊂ +L2 +µ(X), then both M and M⊥ are invariant under L and all Kt, t ≥ 0. +4Recall that a linear operator T, defined on a subspace dom T of a Hilbert space H, which maps to a Hilbert space K, is +closed if its graph is closed in H × K. + +ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR +7 +Proof. It is easy to see that Kt1 = 1 for each t ≥ 0 and hence 1 ∈ dom L with L1 = 0. Hence KtM ⊂ +M for all t ≥ 0 and LM ⊂ M. Now, if ψ ⊥ 1, then ⟨Ktψ, 1⟩µ = +� +Ktψ dµ = +� +ψ dµ = ⟨ψ, 1⟩µ = 0, +which shows that also KtM⊥ ⊂ M⊥. The relation LM⊥ ⊂ M⊥ follows from (2.9). +□ +2.4. Representation of Koopman Operators on the RKHS. Using the integral operator E, it is possi- +ble to represent the Koopman operator with the aid of a linear operator on H, which is based on kernel +evaluations. This construction mimics the well-known kernel trick used frequently in machine learning. +To begin with, for any x, y ∈ X define the rank-one operator Cxy : H → H by +Cxyψ := ⟨ψ, Φ(y)⟩Φ(x) = ψ(y)Φ(x). +For t ≥ 0 and ψ ∈ H we further define the cross-covariance operator Ct +H : H → H by +Ct +Hψ := +� � +Cxyψ ρt(x, dy) dµ(x) = +� +(Ktψ)(x)Φ(x) dµ(x) = EKtψ = EKtE∗ψ. +Thus, we have +Ct +H = EKtE∗. +(2.10) +In other words, the cross-covariance operator Ct +H represents the action of the Koopman semigroup +through the lens of the RKHS integral operator E (see [20] for details). Being the product of the two +Hilbert-Schmidt operators EKt and E∗, the operator Ct +H is trace class for all t ≥ 0 (cf. [16, p. 521]). +Note that due to ρ0(x, · ) = δx, for t = 0 this reduces to the already introduced covariance operator +� � +Cxy ρ0(x, dy) dµ(x) = +� +Cxx dµ(x) = EE∗ = CH. +The identity (2.10) shows that for all η, ψ ∈ H we have +⟨η, Ct +Hψ⟩ = ⟨η, Ktψ⟩µ, +(2.11) +which shows that the role of Ct +H is analogous to that of the stiffness matrix in a traditional finite- +dimensional approximation of the Koopman operator. In this analogy, the covariance operator CH plays +the role of the mass matrix. +2.5. Empirical estimators. Next, we introduce empirical estimators for Ct +H based on finite data (xk, yk), +k = 1, . . . , m. We consider two sampling scenarios for fixed t > 0: +(1) The xk are drawn i.i.d. from µ, and each yk ∼ µ is obtained from the conditional distribution +ρt(xk, ·), i.e., yk|(xk = x) ∼ ρt(x, ·) for µ-a.e. x ∈ X. For example, yk can be obtained by +simulating the SDE (2.1) starting from xk until time t. +(2) µ is ergodic and both xk and yk are obtained from a single (usually long-term) simulation of the +dynamics Xt at discrete integration time step ∆t > 0, using a sliding-window estimator, i.e., +x0 = X0 ∼ µ, +xk = Xk∆t, +and +yk = Xk∆t+t. +Moreover, we assume that there exists a Riesz basis (ψj)∞ +j=0 of L2 +µ(X) consisting of eigenfunc- +tions of the generator L with corresponding eigenvalues µj satisfying �∞ +j=0 e2(Re µj)∆t < ∞. +Remark 2.10. It easily follows from the discussion in Appendix B that the last assumption on the +generator L and on the decay of its eigenvalues µj is equivalent to the similarity of L to an (unbounded) +normal operator N such that eN∆t ∈ L(L2 +µ(X)) is Hilbert-Schmidt. If the assumption holds with +ψj = Sej, where (ej) is an orthonormal basis of L2 +µ(X), the operator N is given by N = � +j µj⟨ · , ej⟩ej +with dom N = {ψ : (µj⟨ψ, ej⟩) ∈ ℓ2} and L = SNS−1. The condition �∞ +j=0 e2(Re µj)∆t < ∞ then +obviously means that the eigenvalues of eN∆t form an ℓ2 sequence. + +8 +F. PHILIPP, M. SCHALLER, K. WORTHMANN, S. PEITZ, AND F. N ¨USKE +Recall that the joint distribution of two random variables X and Y is given by +dPX,Y (x, y) = dPY |X=x(y) · dPX(x). +Set X = xk and Y = yk. Then, in both cases (1) and (2), we have PX = µ and +PY |X=x(B) = P(yk ∈ B|xk = x) = P(Xt ∈ B|X0 = x) = ρt(x, B). +In other words, for the joint distribution µ0,t of xk and yk we have +dµ0,t(x, y) = dρt(x, ·)(y) · dµ(x) = ρt(x, dy) · dµ(x). +More explicitly, +µ0,t(A × B) = +� +A +ρt(x, B) dµ(x). +Now, since +Ct +H = +� � +Cxy ρt(x, dy) dµ(x) = +� +Cxy dµ0,t(x, y) = E +� +Cxk,yk +� +, +for the empirical estimator for Ct +H we choose the expression +�Cm,t +H += 1 +m +m−1 +� +k=0 +Cxk,yk. +(2.12) +3. VARIANCE OF THE EMPIRICAL ESTIMATOR +In case (1), the law of large numbers [3, Theorem 2.4] and, in case (2), ergodicity [2] ensures the +expected behavior +lim +m→∞ ∥ �Cm,t +H +− Ct +H∥HS = 0 +a.s. +However, this is a purely qualitative result, and nothing is known a priori on the rate of this convergence. +The main result of this section, Theorem 3.1, contains an exact expression for the Hilbert-Schmidt vari- +ance of the empirical estimator �Cm,t +H +based on m data points, which then yields probabilistic estimates +for the expression ∥ �Cm,t +H +− Ct +H∥HS, see Proposition 3.4. Here, our focus is on the estimation from a +single ergodic trajectory, i.e., case (2) above. While the broader line of reasoning partially resembles that +of our previous paper [38], we require additional steps due to the infinite-dimensional setting introduced +by the RKHS. +In Theorem 3.1 and its proof, we will be concerned with evolving kernels kt : X × X → R, defined +by +kt(x, x′) := +� � +k(y, y′) ρt(x, dy) ρt(x′, dy′). +We have +kt(x, x′) = +� � +⟨Φ(y), Φ(y′)⟩ ρt(x, dy) ρt(x′, dy′) = +�� +Φ(y) ρt(x, dy), +� +Φ(y′) ρt(x′, dy′) +� +. +The integrals in the last expression are well defined as limits in H for µ-a.e. x, x′ ∈ X as +� � +∥Φ(y)∥ ρt(x, dy) dµ(x) = +� � � +ϕ(y) ρt(x, dy) dµ(x) = +� � +ϕ(x) dµ(x) ≤ ∥ϕ∥1/2 +1 +, +see (2.8). This shows that kt is well defined ((µ ⊗ µ)-a.e.) and that it is a positive definite kernel on its +domain. Moreover, k0 = k and +|kt(x, x′)| ≤ +� � +ϕ(y′) +� � +ϕ(y) ρt(x, dy) ρt(x′, dy′) = (Kt√ϕ)(x) · (Kt√ϕ)(x′). + +ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR +9 +In particular, kt ∈ L2 +µ⊗µ(X 2) with ∥kt∥L2 +µ⊗µ ≤ ∥ϕ∥1. By Φt we denote the corresponding feature map, +i.e., +Φt(x) = kt(x, ·). +Note that not necessarily Φt(x) ∈ H. Finally, we define +Φt,x := Φ(x)Φt(x). +We are now in the position to formulate our first main result. +Theorem 3.1. Setting zk = (xk, yk), k = 1, . . . , m, the Hilbert-Schmidt variance of the empirical +estimator can be written as +E +� +∥ �Cm,t +H +− Ct +H∥2 +HS +� += 1 +m +� +E0(t) + 2 +m−1 +� +k=1 +m−k +m +· E +� +⟨Czk − Ct +H, Cz0 − Ct +H⟩HS +� +� +, +(3.1) +where +E0(t) := E +� +∥Cz0 − Ct +H∥2 +HS +� += ⟨Ktϕ, ϕ⟩µ − ⟨k, kt⟩L2 +µ⊗µ. +In case (1), E +� +∥ �Cm,t +H +− Ct +H∥2 +HS +� += 1 +mE0(t), whereas in case (2) we have +E +� +∥ �Cm,t +H +− Ct +H∥2 +HS +� += 1 +m +� +�E0(t) + 2 +∞ +� +j=1 +dj,tqj +1 − qj +� +1 − 1 +m · +1 − qm +j +1 − qj +�� +� , +(3.2) +with +qj = eµj∆t, +dj,t = ⟨cj,t, ψj⟩µ, +and +cj,t(x) = ⟨Φt,x, �ψj⟩µ. +Before proving Theorem 3.1 in Subsection 3.1 below, let us comment on its statements and draw some +conclusions. +Remark 3.2. (a) Note that, by ergodicity of the invariant measure µ, the generator L has no eigenvalues +on the imaginary axis, except the simple zero eigenvalue (see Proposition D.1 in the Appendix). In +contrast, if we drop the ergodicity assumption, we have +E +� +∥ �Cm,t +H +− Ct +H∥2 +HS +� += 1 +m +� +�E0(t) + 2 +∞ +� +j=ν0 +dj,tqj +1 − qj +� +1 − 1 +m · +1 − qm +j +1 − qj +�� +� + m − 1 +m +ν0−1 +� +j=1 +dj,t, +where ν0 = #{j : µj ∈ 2πi +∆t Z} is the number of eigenvalues of L of the form 2kπi +∆t , k ∈ Z, counting +multiplicities. Obviously, the last term does not decay to zero as m → ∞ if �ν0−1 +j=1 dj,t ̸= 0. +(b) The definition of cj,t requires Φt,x to be in L2 +µ(X) for µ-a.e. x ∈ X. This will in fact be proved in +Lemma 3.6 below. +In the following, we let +σ2 +m := E0(t) + 2 +∞ +� +j=1 +dj,tqj +1 − qj +� +1 − 1 +m · +1 − qm +j +1 − qj +� +and +σ2 +∞ := E0(t) + 2 +∞ +� +j=1 +dj,tqj +1 − qj +. +Then +E +� +∥ �Cm,t +H +− Ct +H∥2 +HS +� += σ2 +m +m +and σ2 +m → σ2 +∞ as m → ∞. Both infinite series converge absolutely as (qj) ∈ ℓ2 by assumption, and +(dj,t) ∈ ℓ2 as shown in the proof of Theorem 3.1. We can therefore interpret σ2 +∞ as asymptotic variance +of the estimator ˆCm,t +H , similar to our previous results in [38, Lemma 6]. +An upper bound on the variance can be obtained as follows: + +10 +F. PHILIPP, M. SCHALLER, K. WORTHMANN, S. PEITZ, AND F. N ¨USKE +Corollary 3.3. In case (2), for all m ∈ N we have +σ2 +m ≤ ⟨Ktϕ, ϕ⟩µ +� +1 + 4B +Aδq +∥q∥ℓ2 +� +, +(3.3) +where A and B denote the lower and upper Riesz bounds of (ψj), respectively, +q = (qj)∞ +j=1 , +and +δq = inf +j≥1 |1 − qj| > 0. +Proof. First of all, by Lemma 3.6, +E0(t) = ⟨Ktϕ, ϕ⟩µ − ⟨k, kt⟩L2 +µ⊗µ ≤ ⟨Ktϕ, ϕ⟩µ. +We have |1 − qj| ≥ δq and |qj| ≤ 1 for all j ≥ 1 and hence +1 +|1 − qj| · +����1 − 1 +m · +1 − qm +j +1 − qj +���� ≤ 1 +δq +� +1 + 1 +m +m−1 +� +k=0 +|qj|k +� +≤ 2 +δq +. +This and (3.7) imply (3.3). +□ +Proposition 3.4. We have the following probabilistic bound on the estimation error: +P +� +∥Ct +H − �Cm,t +H ∥HS > ε +� +≤ +� +� +� +� +� +� +� +� +� +� +� +� +� +σ2 +m +mε2 , +in case (2), +(3.4) +E0(t) +mε2 , +in case (1), +(3.5) +2 e +− +mε2 +8∥k∥2∞ , +in case (1) with bounded kernel. +(3.6) +In particular, the above also holds upon replacing the left-hand side by P +� +∥EKtψ − �Cm,t +H ψ∥ > ε +� +for +ψ ∈ H, ∥ψ∥ = 1. +Proof. The inequalities (3.4) and (3.5) are an immediate consequence of Markov’s inequality, applied to +the random variable ∥Ct +H − �Cm,t +H ∥2 +HS. The inequality (3.6) follows from Ct +H − �Cm,t +H += 1 +m +�m−1 +k=0 (Ct +H − +Czk), Hoeffding’s inequality for Hilbert space-valued random variables [43, Theorem 3.5] (see also [30, +Theorem A.5.2]), and (cf. Lemma 3.6 below) +∥Ct +H − Cxy∥HS ≤ ∥Ct +H∥HS + ∥Cxy∥HS = +� +⟨k, kt⟩L2 +µ⊗µ + +� +ϕ(x)ϕ(y) ≤ 2∥k∥∞, +since also ∥kt∥∞ ≤ ∥k∥∞. The estimate +∥EKtψ − �Cm,t +H ψ∥ = ∥EKtE∗ψ − �Cm,t +H ψ∥ = ∥(Ct +H − �Cm,t +H )ψ∥ ≤ ∥Ct +H − �Cm,t +H ∥HS +finally yields the last claim. +□ +Remark 3.5. Under additional assumptions (boundedness of the kernel, mixing, etc.), other concen- +tration inequalities than Markov’s, such as, e.g., [3, Theorem 2.12] (α-mixing) or [46, Th´eor`eme 3.1] +(β-mixing), might lead to better estimates than (3.4). +3.1. Proof of Theorem 3.1. +Lemma 3.6. Let t ≥ 0. Then Φt,x ∈ L2 +µ(X) for µ-a.e. x ∈ X with +∥Φt,x∥2 +µ ≤ ϕ(x)(Ktϕ)(x) · ⟨Ktϕ, ϕ⟩µ. +Moreover, for every t ≥ 0 we have +∥Cxy∥2 +HS = ϕ(x)ϕ(y) +and +∥Ct +H∥2 +HS = ⟨k, kt⟩L2 +µ⊗µ = +� � +Φt,x(y) dµ(y) dµ(x). + +ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR +11 +Proof. We estimate +|Φt,x(x′)|2 = |k(x, x′)kt(x, x′)|2 ≤ ϕ(x)ϕ(x′)(Kt√ϕ)2(x) · (Kt√ϕ)2(x′) +≤ ϕ(x)(Ktϕ)(x) · ϕ(x′)(Ktϕ)(x′), +where we have applied Jensen’s inequality to (Kt√ϕ)(x). This proves the first inequality. Next, if +(fj) ⊂ H denotes the Mercer basis corresponding to k, then +⟨Cxy, Cx′y′⟩HS = +� +i +⟨Cxyfi, Cx′y′fi⟩ = +� +i +fi(y)fi(y′)k(x, x′) = k(x, x′)k(y, y′) +This proves ∥Cxy∥2 +HS = ϕ(x)ϕ(y). Moreover, it yields +∥Ct +H∥2 +HS = +���� +� +Cxy dµ0,t(x, y) +���� +2 +HS += +� � +k(x, x′)k(y, y′) dµ0,t(x, y) dµ0,t(x′, y′) += +� � +k(x, x′) +�� � +k(y, y′) ρt(x, dy) ρt(x′, dy′) +� +dµ(x′) dµ(x) = ⟨k, kt⟩L2 +µ⊗µ, +as claimed. +□ +Proof of Theorem 3.1. First of all, we have +E +� +∥ �Cm,t +H +− Ct +H∥2 +HS +� += E +���� 1 +m +m−1 +� +k=0 +(Czk − Ct +H) +��� +2 +HS +� += E +� 1 +m2 +m−1 +� +k,ℓ=0 +� +Czk − Ct +H, Czℓ − Ct +H +� +HS +� += E +� +1 +m2 +m−1 +� +k=0 +∥Czk − Ct +H∥2 +HS + 2 +m2 +m−1 +� +k=0 +m−1 +� +ℓ=k+1 +� +Czk − Ct +H, Czℓ − Ct +H +� +HS +� += 1 +mE +� +∥Cz0 − Ct +H∥2 +HS +� ++ 2 +m2 +m−1 +� +k=1 +(m − k)E +� +⟨Czk − Ct +H, Cz0 − Ct +H⟩HS +� +. +where we exploited that E[⟨Czk − Ct +H, Czℓ − Ct +H⟩HS] only depends on the difference ℓ − k. +Let us compute the first term. Since E[Cz0] = Ct +H and thus E[⟨Cz0, Ct +H⟩HS] = ∥Ct +H∥2 +HS, +E +� +∥Cz0 − Ct +H∥2 +HS +� += E +� +∥Cz0∥2 +HS +� +− ∥Ct +H∥2 +HS. +For ψ ∈ H we have +∥Cz0ψ∥2 = ∥ψ(y0)Φ(x0)∥2 = ψ(y0)2ϕ(x0). +Using the Mercer basis (fi) ⊂ H corresponding to k in H (cf. Theorem 2.5), we obtain +E +� +∥Cz0∥2 +HS +� += E +� � +i +∥Cz0fi∥2� += E +� � +i +fi(y0)2ϕ(x0) +� += E[ϕ(x0)ϕ(y0)]. +Note that the latter equals (ϕ(x) = k(x, x) by definition) +E[ϕ(x0)ϕ(y0)] = +� +ϕ(x) +� +ϕ(y) ρt(x, dy) dµ(x) = +� +ϕ(x)(Ktϕ)(x) dµ(x) = ⟨Ktϕ, ϕ⟩µ. +We obtain +E +� +∥Cz0 − Ct +H∥2 +HS +� += E[ϕ(x0)ϕ(y0)] − ⟨k, kt⟩L2 +µ⊗µ = ⟨Ktϕ, ϕ⟩µ − ⟨k, kt⟩L2 +µ⊗µ = E0(t) +and thus (3.1). +Case (1). In this case, zk and zℓ are independent for k ̸= ℓ, so that +E +� +⟨Czk − Ct +H, Czℓ − Ct +H⟩HS +� += 0. + +12 +F. PHILIPP, M. SCHALLER, K. WORTHMANN, S. PEITZ, AND F. N ¨USKE +Hence, the statement of the theorem for case (1) follows. +Case (2). Here, the cross terms do not vanish. In fact, +E +� +⟨Czk − Ct +H, Cz0 − Ct +H⟩HS +� += E[⟨Czk, Cz0⟩HS] − ∥Ct +H∥2 +HS = E +� � +i +⟨Czkfi, Cz0fi⟩ +� +− ∥Ct +H∥2 +HS += E +�� � +i +fi(yk)fi(y0) +� +k(xk, x0) +� +− ∥Ct +H∥2 +HS += E +� +k(yk, y0)k(xk, x0) +� +− ∥Ct +H∥2 +HS. +Now, +E +� +k(yk, y0)k(xk, x0) +� += +� � � � +k(y′, y)k(x′, x) ρt(x′, dy′) ρk∆t(x, dx′) ρt(x, dy) dµ(x) += +� � +k(x, x′) +�� � +k(y, y′) ρt(x, dy) ρt(x′, dy′) +� +ρk∆t(x, dx′) dµ(x) += +� � +k(x, x′)kt(x, x′) ρk∆t(x, dx′) dµ(x) += +� �� +[Φ(x)Φt(x)](x′) ρk∆t(x, dx′) +� +dµ(x) += +� +[Kk∆tΦt,x](x) dµ(x). +Hence, +E +� +⟨Czk − Ct +H, Cz0 − Ct +H⟩HS +� += +� +(Kk∆tΦt,x)(x) dµ(x) − ⟨k, kt⟩L2 +µ⊗µ. +Let us now exploit the assumptions on the spectral properties of the generator L in case (2). For µ-a.e. +x ∈ X, we have +Φt,x = +∞ +� +j=0 +cj,t(x)ψj, +the series converging in L2 +µ(X). Therefore, +KsΦt,x = +∞ +� +j=0 +cj,t(x)Ksψj = +∞ +� +j=0 +cj,t(x)eµjsψj, +and thus (for k ≥ 1) +� � +Kk∆tΦt,x +� +(x) dµ(x) = +� +∞ +� +j=0 +cj,t(x)eµjk∆tψj(x) dµ(x) = +∞ +� +j=0 +dj,t · eµjk∆t = +∞ +� +j=0 +dj,t · qk +j . +This series converges absolutely for each t ≥ 0 due to our assumption that � +j |qj|2 < ∞ and since for +each j ∈ N0 we have by Lemma 3.6 that +∞ +� +j=0 +|dj,t|2 ≤ B2 +∞ +� +j=0 +∥cj,t∥2 +µ = B2 +� +∞ +� +j=0 +|⟨Φt,x, �ψj⟩µ|2 dµ(x) +≤ B2 +A2 +� +∥Φt,x∥2 +µ dµ(x) ≤ B2 +A2 ⟨Ktϕ, ϕ⟩2 +µ, +(3.7) +where A and B are the Riesz bounds of (ψj). + +ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR +13 +Without loss of generality, we may assume that µ0 = 0 with ψ0 = 1 and µ1, . . . , µν0−1 ∈ 2πi +∆t Z, +and ψk ∈ 1⊥ for k ≥ 1, see Lemma 2.9. The duality relations then imply �ψ0 = 1. Now, c0,t(x) = +⟨Φt,x, 1⟩µ = +� +k(x, y)kt(x, y) dµ(y) and hence +d0,t = ⟨c0,t, 1⟩µ = +� +c0,t(x) dµ(x) = +� � +k(x, y)kt(x, y) dµ(y) dµ(x) = ⟨k, kt⟩L2 +µ⊗µ. +(3.8) +This implies +E +� +⟨Czk − Ct +H, Cz0 − Ct +H⟩HS +� += +∞ +� +j=0 +dj,t · qk +j − ⟨k, kt⟩L2 +µ⊗µ = +∞ +� +j=1 +dj,t · qk +j +and therefore +E +� +∥ �Cm,t +H +− Ct +H∥2 +HS +� += 1 +mE0(t) + 2 +m +∞ +� +j=1 +dj,t +m−1 +� +k=1 +(1 − k +m)qk +j += 1 +m +� +�E0(t) + 2 +ν0−1 +� +j=1 +dj,t +m−1 +� +k=1 +(1 − k +m)qk +j + 2 +∞ +� +j=ν0 +dj,t +m−1 +� +k=1 +(1 − k +m)qk +j +� +� . +The identity +m−1 +� +k=1 +� +1 − k +m +� +qk = +� +q +1−q +� +1 − 1 +m · 1−qm +1−q +� +if q ̸= 1 +m−1 +2 +if q = 1 +finally yields (3.2). +□ +4. BOUND ON THE KOOPMAN PREDICTION ERROR +The kernel cross-covariance operator Ct +H can also be used to approximate the predictive capabilities +of the Koopman operator, for observables in H. Approximating the full Koopman operator involves +the inverse of the co-variance operator, which becomes an unbounded operator on a dense domain of +definition in the infinite-dimensional RKHS case. Moreover, its empirical estimator �Cm +H is finite-rank and +thus not even injective. While Fukumizu et al. tackle this problem in [10] by means of a regularization +procedure, we choose to use pseudo-inverses instead (cf. Remark 4.2). We truncate the action of the +Koopman operator using N terms of the Mercer series expansion and derive a bound for the prediction +error for fixed truncation parameter N. While we use similar ideas as presented in [11], we heavily +rely on our new results on the cross-covariance operator, cf. Section 3. Afterwards, we deal with the +case of Koopman-invariance of the RKHS [22]. Here, we establish an estimate for the truncation error, +which then yields a bound on the deviation from the full Koopman operator. We emphasize that this +error bound is extremely useful in comparison to its prior counterparts based on the assumption that the +space spanned by a finite number of so-called observables (dictionary) is invariant under the Koopman +operator. The latter essentially requires to employ only Koopman eigenfunctions as observables, see, +e.g., [25, 14]. +Let (ej) be the Mercer orthonormal basis of L2 +µ(X) corresponding to the kernel k and let λj = ∥Eej∥µ +as well as fj := +� +λjej (cf. Theorem 2.5). We arrange the Mercer eigenvalues in a non-increasing way, +i.e., +λ1 ≥ λ2 ≥ . . . . +Let ψ ∈ H. Then +Ktψ = +∞ +� +j=1 +⟨Ktψ, ej⟩µej = +∞ +� +j=1 +⟨Ct +Hψ, ej⟩ej = +N +� +j=1 +⟨Ct +Hψ, ej⟩ej + +∞ +� +j=N+1 +⟨Ct +Hψ, ej⟩ej. +(4.1) + +14 +F. PHILIPP, M. SCHALLER, K. WORTHMANN, S. PEITZ, AND F. N ¨USKE +4.1. Estimation error. In the next theorem, we estimate the probabilistic error between the first sum- +mand +Kt +Nψ = +N +� +j=1 +⟨Ct +Hψ, ej⟩ej, +ψ ∈ H, +and its empirical estimator, which is of the form �N +j=1⟨ �Cm,t +H ψ, �ej⟩�ej with approximations �ej of the ej. +Theorem 4.1. Assume that the eigenvalues λj of CH are simple, i.e., λj+1 > λj for all j. Fix an +arbitrary N ∈ N and let +δN = +min +j=1,...,N +λj − λj+1 +2 +. +(4.2) +Further, let ε ∈ (0, δN) and δ ∈ (0, 1) be arbitrary and fix some5 m ≥ max{N, 2σ2 +m +ε2δ }. Let now +�λ1 ≥ . . . ≥ �λm denote the largest m eigenvalues of �Cm +H in descending order and let �e1, . . . , �em be +corresponding eigenfunctions, respectively, such that ∥�ej∥ = �λ−1/2 +j +for j = 1, . . . , m. If we define +�Km,t +N ψ = +N +� +j=1 +⟨ �Cm,t +H ψ, �ej⟩�ej, +ψ ∈ H, +(4.3) +then, with probability at least 1 − δ, we have that +∥Kt +N − �Km,t +N ∥H→L2µ(X) ≤ +� +1 +√λN ++ N + 1 +δNλN +(1 + ∥ϕ∥1)∥ϕ∥1/2 +1 +� +ε. +(4.4) +All of the above statements equally apply to case (1) upon replacing σm by E0(t). +Remark 4.2. (a) If we set �fj = �λ1/2 +j +· �ej, then +�Cm +H = +m +� +j=1 +�λj⟨ · , �fj⟩ �fj, +and thus +N +� +j=1 +⟨ · , �ej⟩�ej = +N +� +j=1 +1 +�λj +⟨ · , �fj⟩ �fj = ( �Cm +H )† �QN, +where �QN = �N +j=1⟨ · , �fj⟩ �fj is the orthogonal projector onto the span of the first N eigenfunctions of +�Cm +H in H. Therefore, +�Km,t +N ψ = +m +� +j=1 +⟨ �Cm,t +H ψ, �ej⟩�ej = ( �Cm +H )† �QN �Cm,t +H ψ. +In particular, for N = m we have �Km,t +N += ( �Cm +H )† �Cm,t +H , which surely is one of the first canonical choices +for an empirical estimator of Kt. +(b) The functions �ej have unit length in the empirical L2 +µ-norm: +1 +m +m +� +k=1 +�ej(xk)�ej(xk) = +� +�Cm +H �ej, �ej +� += 1. +Therefore, projecting onto the first N empirical Mercer features is the whitening transformation com- +monly used in traditional EDMD [19]. +5By Corollary 3.3, an amount of at least m ≥ max +� +N , +2∥ϕ∥2 +µ +ε2δ +� +1 + +4B +Aδq ∥q∥ℓ2 +�� +data points suffices. + +ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR +15 +Proof of Theorem 4.1. By Proposition 3.4, both events ∥Ct +H − �Cm,t +H ∥HS ≤ ε and ∥CH − �Cm +H ∥HS ≤ ε +occur with probability at least 1 − δ/2, respectively. Hence, they occur simultaneously with probability +at least 1 − δ. +In the remainder of this proof we assume that both events occur. Then all the statements deduced in +the following hold with probability at least 1 − δ. +Let us define the intermediate approximation +�Km,t +N ψ = +N +� +j=1 +⟨ �Cm,t +H ψ, ej⟩ej, +ψ ∈ H. +Let ψ ∈ H be arbitrary. Setting C := Ct +H − �Cm,t +H , we have +∥Kt +Nψ − �Km,t +N ψ∥2 +µ = +����� +N +� +j=1 +� +Cψ, ej +� +ej +����� +2 +µ += +N +� +j=1 +��� +Cψ, ej +���2 = +N +� +j=1 +��� +ψ, C∗ej +���2 +≤ ∥ψ∥2 +N +� +j=1 +∥C∗ej∥2 ≤ ∥ψ∥2 +N +� +j=1 +1 +λj +∥C∗fj∥2 ≤ ∥ψ∥2 +λN +N +� +j=1 +∥C∗fj∥2 +≤ ∥ψ∥2 +λN +∞ +� +j=1 +∥C∗fj∥2 = ∥ψ∥2 +λN +· ∥Ct +H − �Cm,t +H ∥2 +HS, +and thus, +∥Kt +Nψ − �Km,t +N ψ∥µ ≤ ∥ψ∥ +√λN +· ε. +Next, we aim at estimating the remaining error +�Km,t +N ψ − �Km,t +N ψ = +N +� +j=1 +⟨ �Cm,t +H ψ, ej⟩ej − +N +� +j=1 +⟨ �Cm,t +H ψ, �ej⟩�ej += +N +� +j=1 +λ−1 +j ⟨ �Cm,t +H ψ, fj⟩fj − +N +� +j=1 +�λ−1 +j ⟨ �Cm,t +H ψ, �fj⟩ �fj += +N +� +j=1 +λ−1 +j ⟨f, fj⟩fj − +N +� +j=1 +�λ−1 +j ⟨f, �fj⟩ �fj += +N +� +j=1 +� +λ−1 +j Pjf − �λ−1 +j +�Pjf +� += +N +� +j=1 +λ−1 +j (Pj − �Pj)f + +N +� +j=1 +(λ−1 +j +− �λ−1 +j ) �Pjf, +where f = �Cm,t +H ψ, +Pjf = ⟨f, fj⟩fj +and +�Pjf = ⟨f, �fj⟩ �fj. +By (2.4), it suffices to estimate the above error in the ∥ · ∥-norm. By Theorem C.3, the first summand can +be estimated as +��� +N +� +j=1 +λ−1 +j (Pj − �Pj)f +��� ≤ +N +� +j=1 +1 +λj +∥Pj − �Pj∥∥f∥ ≤ N · ∥CH − �Cm +H ∥ +λNδN +∥f∥ ≤ +N +λNδN +∥f∥ε. + +16 +F. PHILIPP, M. SCHALLER, K. WORTHMANN, S. PEITZ, AND F. N ¨USKE +For the second summand we have +��� +N +� +j=1 +(λ−1 +j +− �λ−1 +j ) �Pjf +��� +2 += +N +� +j=1 +|λ−1 +j +− �λ−1 +j |2∥ �Pjf∥2 = +N +� +j=1 +|λj − �λj|2 +λ2 +j�λ2 +j +∥ �Pjf∥2. +Now, note that ϵ < δN by assumption and therefore ∥CH − �Cm +H ∥HS ≤ δN ≤ λN−λN+1 +2 +≤ λN +2 . For +j = 1, . . . , N, according to Theorem C.1 this implies +�λj ≥ λj − |λj − �λj| ≥ λj − ∥CH − �Cm +H ∥HS ≥ λj − λN +2 +≥ λj +2 . +Hence, +��� +N +� +j=1 +(λ−1 +j +− �λ−1 +j ) �Pjf +��� +2 +≤ 4 +N +� +j=1 +|λj − �λj|2 +λ4 +j +∥ �Pjf∥2 ≤ 4∥CH − �Cm +H ∥2 +HS +λ4 +N +∥ �QNf∥2, +and thus, +��� +N +� +j=1 +(λ−1 +j +− �λ−1 +j ) �Pjf +��� ≤ +2 +λ2 +N +∥f∥ε ≤ +1 +λNδN +∥f∥ε. +From +∥ �Cm,t +H ∥ ≤ ∥ �Cm,t +H +− Ct +H∥ + ∥Ct +H∥ ≤ ∥ �Cm,t +H +− Ct +H∥HS + ∥EKtE∗∥ ≤ ε + ∥ϕ∥1 +we conclude +�� �Km,t +N ψ − �Km,t +N ψ +�� ≤ N + 1 +λNδN +∥ �Cm,t +H ψ∥ε ≤ N + 1 +λNδN +(ε + ∥ϕ∥1)∥ψ∥ε. +All together, we obtain (recall (2.4)) +∥Kt +Nψ − �Km,t +N ψ∥µ ≤ ∥Kt +Nψ − �Km,t +N ψ∥µ + ∥ϕ∥1/2 +1 +∥ �Km,t +N ψ − �Km,t +N ψ∥ +≤ ∥ψ∥ +√λN +· ε + N + 1 +λNδN +(ε + ∥ϕ∥1)∥ϕ∥1/2 +1 +∥ψ∥ε += +� +1 +√λN ++ N + 1 +δNλN +(1 + ∥ϕ∥1)∥ϕ∥1/2 +1 +� +ε · ∥ψ∥, +which implies (4.4). +□ +4.2. Projection error in case of Koopman-invariance of the RKHS. In the preceeding section, we +have seen that the empirical operator �Km,t +N +can be written as ( �Cm +H )† �Cm,t +H +if m = N. In the limit m → ∞, +we would arrive at the operator C−1 +H Ct +H, which is not even well-defined for all ψ ∈ H, in general. +However, if the RKHS is invariant under Kt, the above operator limit is well-defined as a bounded +operator on H. In this situation we are able to extend Theorem 4.1 to an estimate on the full error made +by our empirical estimator. +We start by defining the operator +Kt +H := C−1 +H Ct +H +on its natural domain +dom Kt +H := {ψ ∈ H : Ct +Hψ ∈ ran CH}. +(4.5) +We consider Kt +H as an operator from H into itself (with domain of definition in H). +Lemma 4.3. We have +dom Kt +H = {ψ ∈ H : Ktψ ∈ H}, +(4.6) +and Kt +H is closed. + +ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR +17 +Proof. Note that Ct +Hψ ∈ ran CH if and only if EKtψ = CHφ for some φ ∈ H. Since CHφ = Eφ and +ker E = {0}, the latter is equivalent to Ktψ = φ ∈ H, which proves the representation of the domain. +As to the closedness of Kt +H, let (ψn) ⊂ dom Kt +H and φ ∈ H such that ψn → ψ in H and Kt +Hψn → φ in +H as n → ∞. The latter implies Ct +Hψn → CHφ, while the first implies Ct +Hψn → Ct +Hψ in H as n → ∞, +from which we conclude that Ct +Hψ = CHφ, i.e., ψ ∈ dom Kt +H and Kt +Hψ = φ. +□ +If the Koopman operator leaves the RKHS H invariant (i.e., KtH ⊂ H), Kt +H is defined on all of H. +Moreover, since the canonical inclusion map E∗ : H → L2(µ) is injective, it possesses an unbounded +inverse on its range H, and therefore: +C−1 +H Ct +Hφ = C−1 +H EKtE∗φ = (EE∗)−1EE∗(E∗)−1KtE∗φ = (E∗)−1KtE∗φ. +(4.7) +Remarkably, invariance of H under the Koopman operator implies that the left-hand side not only repro- +duces the Koopman operator on H, but actually defines a bounded operation. +Parts of the next proposition can be found in [22, Theorem 5.3] and [8, Theorem 1]. +Proposition 4.4. For t > 0, the following statements are equivalent: +(i) KtH ⊂ H. +(ii) Kt +H ∈ L(H). +(iii) ran Ct +H ⊂ ran CH. +Proof. With regard to the two representations (4.5) and (4.6) of the domain, it is immediate that both (i) +and (iii) are equivalent to dom Kt +H = H. The equivalence of the latter to (ii) follows from the closed +graph theorem. +□ +Note that if one of (i)–(iii) holds, then Kt +H = Kt|H. +Theorem 4.5. In addition to the assumptions in Theorem 4.1, assume that H is invariant under the +Koopman operator Kt. For fixed N ∈ N, let δN be as in (4.2), choose ε, δ, and m as in Theorem 4.1 +and define the empirical estimator �Km,t +N +as in (4.3). Then, with probability at least 1 − δ we have that +∥Kt − �Km,t +N ∥H→L2µ(X) ≤ +� +λN+1 ∥Kt +H∥ + +� +1 +√λN ++ N + 1 +δNλN +(1 + ∥ϕ∥1)∥ϕ∥1/2 +1 +� +ε. +(4.8) +Proof. First of all, Theorem 4.1 implies that +∥Kt − �Km,t +N ∥H→L2µ(X) ≤ ∥Kt − Kt +N∥H→L2µ(X) + ∥Kt +N − �Km,t +N ∥H→L2µ(X) +≤ ∥Kt − Kt +N∥H→L2µ(X) + +� +1 +√λN ++ N + 1 +δNλN +(1 + ∥ϕ∥1)∥ϕ∥1/2 +1 +� +ε. +Now, for ψ ∈ H, +∥Ktψ − Kt +Nψ∥2 +µ = +����� +∞ +� +j=N+1 +⟨Ct +Hψ, ej⟩ej +����� +2 +µ += +∞ +� +j=N+1 +|⟨Ct +Hψ, ej⟩|2 = +∞ +� +j=N+1 +1 +λj +|⟨Ct +Hψ, fj⟩|2 += +∞ +� +j=N+1 +1 +λj +|⟨Kt +Hψ, CHfj⟩|2 = +∞ +� +j=N+1 +λj|⟨Kt +Hψ, fj⟩|2 ≤ λN+1∥Kt +Hψ∥2, +which proves the theorem. +□ +We have just proved that the projection error ∥Ktψ − Kt +Nψ∥µ decays at least as fast as the square +roots of the eigenvalues of CH. Recall that (λj)j∈N ∈ ℓ1(N), since CH is trace class with �∞ +j=1 λj = +Tr(CH) = ∥E∗∥2 +HS = ∥ϕ∥1, see Lemma 2.4(c). + +18 +F. PHILIPP, M. SCHALLER, K. WORTHMANN, S. PEITZ, AND F. N ¨USKE +5. ILLUSTRATION WITH THE ORNSTEIN-UHLENBECK PROCESS +For the numerical illustration of our results, we consider the Ornstein-Uhlenbeck (OU) process on +X = R, which is given by the SDE +dXt = −αXt dt + dWt, +where α > 0 is a positive parameter. +5.1. Analytical Results. Since all relevant properties of the OU process are available in analytical form, +we can exactly calculate all of the terms appearing in our theoretical error bounds. Moreover, we can +also compute the exact estimation and prediction errors for finite data in closed form. Let us begin by +recapping the analytical results required for our analysis, which can be found in [41]. +The invariant measure µ, and the density of the stochastic transition kernel ρt, are given by +dµ(x) = +�α +π e−αx2 dx +and +dρt(x, y) = +� α +πv2 +t +exp +� +− α +v2 +t +(y − e−αtx)2� +dx dy, +with v2 +t = (1 − e−2αt)/2α. The Koopman operators Kt are self-adjoint in L2 +µ(R), their eigenvalues and +corresponding eigenfunctions are given by +qj = e−αjt +and +ψj(x) = +1 +� +2jαjj! +Hj( +√ +2αx), +j ∈ N0, +where Hj are the physicist’s Hermite polynomials. +We consider the Gaussian radial basis function (RBF) kernel with bandwidth σ > 0, i.e., +k(x, y) = exp +� +−(x − y)2 +σ2 +� +. +Let us quickly verify that this choice of the kernel satisfies the compatibility assumptions (A1)–(A3). +Indeed, (A1) is trivial as k(x, x) = 1 and (A3) follows easily from the continuity of the functions in H. +To see that H is dense in L2 +µ(R) (i.e., (A2)), let ψ ∈ L2 +µ(R) be such that ⟨ψ, Φ(y)⟩µ = 0 for all y ∈ R. +The latter means that φ∗ϕσ = 0, where φ(x) = ψ(x)e−αx2 and ϕσ(x) = e−x2/σ2. We apply the Fourier +transform and obtain �φ · � +ϕσ = 0. Noting that the Fourier transform of a Gaussian is again a Gaussian, +we get �φ = 0 and thus ψ = 0. +The Mercer eigenvalues and features with respect to the invariant measure µ of the OU process, i.e., +the eigenvalues and eigenfunctions of the integral operator E∗E in L2 +µ(R), are also available in analytical +form [9]. They are given by +λi = +� α +C1 +� +1 +σ2C1 +�i +and +ϕi(x) = γie−ζ2x2Hi +�√αηx +� +, +i ∈ N0, +using the following constants: +η = +� +1 + +4 +ασ2 +�1/4 +, +γi = +� +η +2iΓ(i + 1) +�1/2 +, +ζ2 = α +2 (η2 − 1), +C1 = α + ζ2 + σ−2. +With these results, we can compute the variance of the empirical estimator for Ct +H as described in The- +orem 3.1. The eigenvalues qj were already given above. The coefficients dj,t can be calculated using +Mercer’s theorem as +dj,t = +� � +k(x, x′)k(y, y′)ψj(x)ψj(x′) dµ0,t(x, y) dµ0,t(x′, y′) + +ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR +19 += +� +k,ℓ +λkλℓ +�� +ϕk(x)ϕℓ(y)ψj(x) dµ0,t(x, y) +�2 +. +The series needs to be truncated at a finite number of terms and the integrals can be calculated by numer- +ical integration. As d0,t = ⟨k, kt⟩L2 +µ⊗µ = ∥Ct +H∥2 +HS (cf. (3.8)), and hence +∥Ct +H∥2 +HS = +� +k,ℓ +λkλℓ +�� +ϕk(x)ϕℓ(y) dµ0,t(x, y) +�2 +, +(5.1) +the Hilbert-Schmidt norm of the cross-covariance operator Ct +H can be computed similarly. Since, for the +Gaussian RBF kernel, we have ϕ(x) = k(x, x) = 1 for all x, we therefore find +E0(t) = +� +Ktϕ, ϕ +� +µ − ∥Ct +H∥2 +HS = 1 − ∥Ct +H∥2 +HS, +completing the list of terms required by Theorem 3.1. In addition, we notice that upon replacing ei- +ther one or two of the integrals in (5.1) by finite-data averages, we can also calculate ∥ ˆCm,t +H ∥2 +HS and +⟨Ct +H, ˆCm,t +H ⟩HS. Therefore, the estimation error for finite data {(xk, yk)}m +k=1 can be obtained by simply +expanding the inner product +∥Ct +H − ˆCm,t +H ∥2 +HS = ∥Ct +H∥2 +HS + ∥ ˆCm,t +H ∥2 +HS − 2⟨ ˆCm,t +H , Ct +H⟩HS, +allowing us to precisely compare the estimation error to the error bounds obtained in Theorem 3.1. +Besides the estimation error for Ct +H, we are also interested in the prediction error, which is bounded +according to Theorem 4.1. We will compare these bounds to the actual error ∥(Kt +N − ˆKm,t +N )φ∥L2µ(X), for +a specific observable φ ∈ H and a fixed number of N Mercer features. For the OU process, it is again +beneficial to consider Gaussian observables φ: +φ(x) = +1 +� +2πσ2 +0 +exp +� +−(x − m0)2 +2σ2 +0 +� +. +Application of the Koopman operator leads to yet another, unnormalized Gaussian observable, which is +given by +Ktφ(x) = +1 +� +2πσ2 +t +exp +� +−(m0 − e−αtx)2 +2σ2 +t +� +, +σ2 +t = σ2 +0 + v2 +t . +The inner products of Ktφ with the Mercer eigenfunctions ϕi can be evaluated by numerical integration, +providing full access to the truncated observable Kt +Nφ. On the other hand, the empirical approximation +ˆKm,t +N φ can be computed directly based on the data. We note that +ˆKm,t +N φ = +N +� +j=1 +� +ˆCm,t +H φ, ˆej +� +ˆej = 1 +m +m +� +k=1 +φ(yk) +N +� +j=1 +⟨Φ(xk), ˆej⟩ ˆej = 1 +m +m +� +k=1 +φ(yk) +N +� +j=1 +ˆej(xk)ˆej. +The functions ˆej can be obtained from the eigenvalue decomposition of the standard kernel Gramian +matrix +1 +mKX := 1 +m [k(xk, xl)]m +k,l=1 , +as the latter is the matrix representation of the empirical covariance operator ˆCm +H on the subspace +span{Φ(xk)}m +k=1. If 1 +mKX = V ΛV ⊤ is the spectral decomposition of the Gramian, then +ˆej = +1 +m1/2ˆλj +m +� +l=1 +VljΦ(xl) + +20 +F. PHILIPP, M. SCHALLER, K. WORTHMANN, S. PEITZ, AND F. N ¨USKE +are the correctly normalized eigenfunctions according to Theorem 4.1. Plugging this into the above, we +find +ˆKm,t +N φ(x) = 1 +m +m +� +k=1 +φ(yk) +N +� +j=1 +1 +m1/2ˆλj +m +� +l=1 +Vljk(xl, xk) +1 +m1/2ˆλj +m +� +r=1 +Vrjk(xr, x) += 1 +mφ(Y )⊤ 1 +mKX +� +VNΛ−2 +N V ⊤ +N +� +KX,x += 1 +mφ(Y )⊤VNΛ−1 +N V ⊤ +N KX,x, +where φ(Y ) = [φ(yk)]m +k=1, KX,x = [k(xk, x)]m +k=1, VN = V [IN 0m−N]⊤, ΛN = diag(�λj)N +j=1. +5.2. Numerical Results. For the actual numerical experiments, we set α = 1, choose the elementary +integration time step as ∆t = 10−2, and set the lag time to t = 0.05. We compute the exact variance +E[∥Ct +H− ˆCm,t +H ∥2 +HS] by the expression given in Theorem 3.1, and also the coarser estimate for the variance +given in Corollary 3.3. We test three different kernel bandwidths, σ ∈ {0.05, 0.1, 0.5}. All Mercer series +are truncated after the first 10 terms for σ ∈ {0.1, 0.5}, and 20 terms for σ = 0.05, while Koopman +eigenfunction expansions are truncated after 15 terms. +In the first set of experiments, we use Chebyshev’s inequality to compute the maximal estimation +error ∥Ct +H − ˆCm,t +H ∥HS that can be guaranteed with confidence 1 − δ = 0.9, for a range of data sizes +m between m = 20 and m = 50.000. As a comparison, we generate 200 independent simulations of +length m + +t +∆t , corresponding to the sliding-window estimator with m data points, for each data size. +We then compute the resulting estimation error using the expressions given in the previous section. We +extract the 1 − δ-percentile of the estimation error for all trajectories, i.e., the maximal error that is not +exceeded by 100 ∗ (1 − δ) percent of the trajectories. In addition, we also use Chebyshev’s inequality +with the i.i.d. variance 1 +mE0(t) to predict the estimation error. The comparison of these results for all +data sizes m and the different kernel bandwidths is shown in Figure 3. We observe that the bound from +Theorem 3.1 is quite accurate, over-estimating the actual error by about a factor three, and captures the +detailed qualitative dependence of the estimation error on m. The coarser bound from Corollary 3.3, +however, appears to discard too much information, it over-estimates the error by one to two orders of +magnitude, and also does not capture the initial slope for small m. Finally, we note that for the larger +kernel bandwidths, the i.i.d. variance is indeed too small, leading to an under-estimation of the error. +This observation confirms that it is indeed necessary to take the effect of the correlation between data +points into account. +In a second set of experiments, we test the performance of our theoretical bounds concerning the +prediction of expectations for individual observables, obtained in Theorem 4.1. For the same three +Gaussian RBF kernels as in the first set of experiments, we consider the observable φ = ϕ0, i.e., the first +Mercer feature, and choose N = 10 in the Mercer series expansion Kt +Nφ and its empirical approximation +ˆKm,t +N φ. Note that φ is a different observable depending on the bandwidth. Again, we set 1 − δ = 0.9, +and use the bound from Theorem 4.1 to bound the L2 +µ-error between Kt +Nφ and ˆKm,t +N φ. As a comparison, +we compute the actual L2 +µ-error by numerical integration, using the fact that we can evaluate Kt +Nφ and +ˆKm,t +N φ based on the discussion above. We repeat this procedure 15 times and provide average errors +and standard deviations. The results for all three kernels are shown in Figure 4, and we find that our +theoretical bounds are much too pessimistic in all cases. This finding highlights our previous observation +that bounding the prediction error outside the RKHS still requires more in-depth research. + +ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR +21 +102 +103 +104 +m +10 +2 +10 +1 +100 +101 +(m) +Error for Ct , t = 0.05, += 0.050 +T 3.1 +C 3.3 +i.i.d. +Data +102 +103 +104 +m +10 +2 +10 +1 +100 +101 +(m) +Error for Ct , t = 0.05, += 0.100 +T 3.1 +C 3.3 +i.i.d. +Data +102 +103 +104 +m +10 +2 +10 +1 +100 +101 +(m) +Error for Ct , t = 0.05, += 0.500 +T 3.1 +C 3.3 +i.i.d. +Data +FIGURE 3. Probabilistic error estimates for Ct +H associated to the OU process, at lag time +t = 0.05, and the Gaussian RBF kernel with different bandwidths σ ∈ {0.05, 0.1, 0.05} +(corresponding to left, center and right panels). The blue and green curves show the es- +timated error using the fine and coarse bounds from Theorem 4.1 and Corollary 3.3, re- +spectively, while the purple curves represent the bound obtained from the i.i.d.-variance +1 +mE0(t). The red curve shows the 0.9-percentile of the estimation error based on 200 +independent simulations. +102 +103 +m +10 +1 +101 +103 +105 +107 +Prediction Error t = 0.05, += 0.050 +Prediction N = 10 +Data Bound N = 10 +102 +103 +m +10 +1 +101 +103 +105 +107 +Prediction Error t = 0.05, += 0.100 +Prediction N = 10 +Data Bound N = 10 +102 +103 +m +10 +1 +101 +103 +105 +107 +Prediction Error t = 0.05, += 0.500 +Prediction N = 10 +Data Bound N = 10 +FIGURE 4. Comparison of the theoretical bound on the prediction error ∥Kt +Nφ − +ˆKm,t +N φ∥µ, if φ is chosen as the first Mercer feature ϕ0, using N = 10 in the Mercer +series representation. The predicted error is shown in blue, error bars for the actual error +obtained from 15 independent data sets are shown in red. Different panels correspond +to the same kernel bandwidths as in Figure 3 above. +6. CONCLUSIONS +We have analyzed the finite-data estimation error for data-driven approximations of the Koopman +operator on reproducing kernel Hilbert spaces. More specifically, we have provided an exact expression +for the variance of empirical estimators for the cross-covariance operator, if a sliding-window estimator +is applied to a long ergodic trajectory of the dynamical system. This setting is relevant for many complex +systems, such as molecular dynamics simulations. Our results present a significant improvement over +the state of the art, since they concern a setting where the notorious problem of dictionary selection +can be circumvented, and therefore no longer depend on the dictionary size. We have also extended +the concept of asymptotic variance to an infinite-dimensional approximation space for the Koopman +operator. 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Zuazua, A quantitative analysis of Koopman operator methods for system identification and predictions, +Comptes Rendus. M´ecanique, Online first (2023), 1–31. + +24 +F. PHILIPP, M. SCHALLER, K. WORTHMANN, S. PEITZ, AND F. N ¨USKE +APPENDIX A. PROOFS +Proof of Lemma 2.1. Let ψ ∈ H. Then (2.4) follows from +� +|ψ(x)|2 dµ(x) = +� +|⟨ψ, Φ(x)⟩|2 dµ(x) ≤ ∥ψ∥2 +� +ϕ(x) dµ(x) = ∥ψ∥2∥ϕ∥1. +Assume that (A2) holds and that ψ ∈ L2 +µ(X) is such that ⟨ψ, Φ(x)⟩µ = 0 for all x ∈ X. Then +0 = +� +⟨ψ, Φ(x)⟩µψ(x) dµ(x) = +� � +k(x, y)ψ(x)ψ(y) dµ(x) dµ(y). +Hence, ψ = 0 by (A2). Conversely, assume that H is dense in L2 +µ(X). Let ψ ∈ L2 +µ(X) such that +� � +k(x, y)ψ(x)ψ(y) dµ(x) dµ(y) = 0. +Since the integrand equals ⟨ψ(x)Φ(x), ψ(y)Φ(y)⟩ and the +integral +� +ψ(x)Φ(x) dµ(x) exists by (2.5), we obtain +� +ψ(x)Φ(x) dµ(x) = 0H. +This implies that +⟨ψ, Φ(y)⟩µ = +� +ψ(x)k(x, y) dµ(x) = 0 for each y ∈ X. Hence, ⟨ψ, φ⟩µ = 0 for each φ ∈ H := +span{Φ(x) : x ∈ X}. Now, let φ ∈ H. Then there exists a sequence (φn) ⊂ H such that ∥φn − φ∥ → 0 +as n → ∞. Therefore, +|⟨ψ, φ⟩µ| = |⟨ψ, φ − φn⟩µ| ≤ ∥ψ∥µ∥φ − φn∥µ ≤ ∥ψ∥µ +� +∥ϕ∥1∥φ − φn∥. +Hence, ⟨ψ, φ⟩µ = 0, and the density of H in L2 +µ(X) implies ψ = 0. +□ +Proof of Lemma 2.4. (a) For ψ ∈ L2 +µ(X) we have +∥Eψ∥2 = +� � +ψ(x)ψ(y)⟨Φ(x), Φ(y)⟩ dµ(x) dµ(y) = +� � +k(x, y)ψ(x)ψ(y) dµ(x) dµ(y). +Hence, the injectivity of E follows from (A2). If (ei) is an orthonormal basis of H, then +� +i +∥E∗ei∥2 +µ = +� +i +∥ei∥2 +µ = +� +i +� +|ei(x)|2 dµ(x) = +� +i +� +|⟨Φ(x), ei⟩|2 dµ(x) = +� +∥Φ(x)∥2 dµ(x). +The claim is now a consequence of ∥Φ(x)∥2 = ϕ(x). +(b) By Lemma 2.1, H is dense in L2 +µ(X). Moreover, E∗ is compact by (a) and Schauder’s theorem +[47, Theorem 4.19]. +(c) This follows from (a) and ker CH = ker EE∗ = ker E∗ = {0} by (A3). +□ +Proof of Theorem 2.5. By Lemma 2.4, the operator E∗E ∈ B(L2 +µ(X)) is a positive self-adjoint trace- +class operator. Hence, by the well known spectral theory of compact operators (see, e.g., [12]) there +exists an orthonormal basis (ej)∞ +j=1 of L2 +µ(X) consisting of eigenfunctions of E∗E corresponding to a +summable sequence (λj)∞ +j=1 of strictly positive eigenvalues. Since E∗ψ = ψ for ψ ∈ H, we have +Eej = λjej and thus ej ∈ H for all j and CHej = EE∗ej = Eej = λjej. Moreover, ⟨fi, fj⟩ = +� +λj/λi⟨Eei, ej⟩ = +� +λj/λi⟨ei, ej⟩µ = δij by (2.6) so that the fj indeed form an orthonormal system in +H. The completeness of (fj) in H follows from the injectivity of E. Finally, �∞ +j=1 λj = Tr CH = ∥ϕ∥1 +and +k(x, y) = ⟨Φ(x), Φ(y)⟩ = +� +j +⟨Φ(x), fj⟩⟨fj, Φ(y)⟩ = +� +j +fj(x)fj(y), +which completes the proof. +□ +Proof of Proposition 2.7. Let ψ ∈ B(X). For p = ∞ we have |(Ktψ)(x)| = |Ex[ψ(Xt)]| ≤ Ex[|ψ(Xt)|] ≤ +∥ψ∥∞. If p < ∞, by Jensen’s inequality, for every convex φ : R → R we have φ ◦ Ktψ ≤ Kt(φ ◦ ψ) +and thus |Ktψ|p ≤ Kt|ψ|p, which, by invariance of µ, leads to +∥Ktψ∥p +p = +� +|Ktψ|p dµ ≤ +� +Kt|ψ|p dµ = +� +|ψ|p dµ = ∥ψ∥p +p. + +ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR +25 +The claim now follows by density of B(X) in Lp +µ(X). +□ +Proof of Proposition 2.8. Let ψ ∈ Cb(X) and fix x ∈ X. Denote the stochastic solution process of the +SDE (2.1) with initial value x by Xx +t . Since Xx +t (ω) is continuous in t for P-a.e. ω ∈ Ω (see [39, Theorem +5.2.1]), ψ(Xx +t (ω)) → ψ(Xx +0 (ω)) = ψ(x) as t → 0 for P-a.e. ω ∈ Ω. Hence, by dominated convergence, +Ktψ(x) = E[ψ(Xx +t )] = +� +ψ(Xx +t (ω)) dP(ω) → ψ(x) +as t → 0. It now follows from Proposition 2.7 and, again, dominated convergence that ∥Ktψ −ψ∥p → 0 +as t → 0. If ψ ∈ Lp +µ(X) and ε > 0, there exists η ∈ Cb(X) such that ∥ψ − η∥p < ε/3. Choose δ > 0 +such that ∥Ktη − η∥p < ε/3 for t < δ. Then +∥Ktψ − ψ∥p ≤ ∥Kt(ψ − η)∥p + ∥Ktη − η∥p + ∥η − ψ∥p < ε +for t < δ, which proves the claim. +□ +APPENDIX B. RIESZ BASES +Recall that a Riesz basis [7] of a Hilbert space H is a sequence (ψj) ⊂ H satisfying span{ψj} = H +and for which there exist A, B > 0 such that for all c ∈ ℓ2, +A∥c∥2 ≤ +��� +� +j +cjψj +��� +H ≤ B∥c∥2. +The constant A (B, resp.) is called a lower (upper, resp.) Riesz bound of the basis. Also recall that to +every Riesz basis (ψj) there exists a dual Riesz basis ( �ψj) such that ⟨ψj, �ψk⟩H = δjk. If (ψj) has the +bounds A and B, then ( �ψj) has bounds 1/B and 1/A. Every element f of H admits a representation +f = � +j⟨f, �ψj⟩Hψj = � +j⟨f, ψj⟩H �ψj and +A2∥f∥2 +H ≤ +� +j +|⟨f, ψj⟩|2 ≤ B2∥f∥2 +H +and +B−2∥f∥2 +H ≤ +� +j +|⟨f, �ψj⟩|2 ≤ A−2∥f∥2 +H. +It can furthermore be easily seen that a sequence (ψj) ⊂ H is a Riesz basis of H if and only if there +exists a boundedly invertible linear operator S ∈ L(H) and an orthonormal basis (ej) of H such that +ψj = Sej for all j. Then �ψj = (S−1)∗ej for all j, B = ∥S∥, and A = ∥S−1∥−1. +APPENDIX C. SOME FACTS FROM SPECTRAL THEORY +In this section, let H be a Hilbert space. If P is an orthogonal projection in H, we set P ⊥ = I − P. +For v ∈ H, ∥v∥ = 1, denote by Pv the rank-one orthogonal projection onto span{v}. +We say that a linear operator on H is non-negative if it is self-adjoint and its spectrum is contained +in [0, ∞). For a non-negative compact operator T on H we denote by λ1(T) ≥ λ2(T) ≥ . . . the +eigenvalues of T in descending order (counting multiplicities). We set λj(T) = 0 if j > rank(T). +Moreover, if T has only simple eigenvalues6, we let Pj(T) denote the orthogonal projection onto the +eigenspace ker(T − λj(T)) and Qn(T) = �n +j=1 Pj(T) the spectral projection corresponding to the n +largest eigenvalues of T. +Theorem C.1 ([12, Cor. II.2.3]). If T and �T are two non-negative compact operators on H, then for all +j ∈ N, +|λj(T) − λj( �T)| ≤ ∥T − �T∥. +6i.e., dim ker(T − λ) = 1 for each eigenvalue λ of T + +26 +F. PHILIPP, M. SCHALLER, K. WORTHMANN, S. PEITZ, AND F. N ¨USKE +Lemma C.2. For v, w ∈ H with ∥v∥ = ∥w∥ = 1 we have +∥Pv − Pw∥ = ∥P ⊥ +w Pv∥ = +� +1 − |⟨v, w⟩|2. +(C.1) +Proof. First of all, the second equation in (C.1) is clear, since +∥P ⊥ +w Pvf∥2 = ∥⟨f, v⟩P ⊥ +w v∥2 = |⟨f, v⟩|2(1 − ∥Pwv∥2) = |⟨f, v⟩|2(1 − |⟨v, w⟩|2). +Second, if Pv,w denotes the orthogonal projection onto Hv,w := span{v, w}, we have +∥Pv − Pw∥ = ∥(Pv − Pw)Pv,w∥ = ∥(Pv − Pw)|Hv,w∥ = +sup +x∈Hv,w, ∥x∥=1 +∥(Pv − Pw)x∥, +which is a two-dimensional problem in Hv,w. Now, if x ∈ Hv,w, ∥x∥ = 1, we write x = av + bw and +obtain a2 + 2abγ + b2 = 1, where γ = ⟨v, w⟩. Moreover, ⟨x, v⟩ = a + bγ, ⟨x, w⟩ = aγ + b and so +∥(Pv − Pw)x∥2 = ∥⟨x, v⟩v − ⟨x, w⟩w∥2 = ∥(a + bγ)v − (aγ + b)w∥2 += (a + bγ)2 − 2(a + bγ)(aγ + b)γ + (aγ + b)2 += a2 + 2abγ + b2γ2 − 2γ(a2γ + abγ2 + ab + b2γ) + a2γ2 + 2abγ + b2 += (1 − γ2)a2 + 2abγ − 2abγ3 + b2(1 − γ2) += (1 − γ2)(a2 + b2 + 2abγ) += 1 − |⟨v, w⟩|2. +Hence, the objective function is constant on {x ∈ Hv,w : ∥x∥ = 1} and (C.1) is proved. +□ +The next theorem is a variant of the Davis-Kahan sin(Θ) theorem (cf. [57]). +Theorem C.3. Let T and �T be non-negative Hilbert-Schmidt operators on H, let n ∈ N, assume that +the largest n + 1 eigenvalues of T are simple, and set +δ = +min +j=1,...,n +λj(T) − λj+1(T) +2 +. +If ∥T − �T∥HS < δ, then for j = 1, . . . , n we have +∥Pj(T) − Pj( �T)∥ ≤ ∥T − �T∥ +δ +. +Proof. For j ∈ N put λj = λj(T), Pj = Pj(T), �λj = λj( �T), and �Pj = Pj( �T). By Theorem C.1, we +have |λj − �λj| ≤ ∥T − �T∥HS < δ for all j, hence �λj is contained in the interval Ij = (λj − δ, λj + δ) +for j = 1, . . . , n + 1. By assumption, sup Ij+1 ≤ inf Ij for j = 1, . . . , n. In particular, the intervals +I1, . . . , In+1 are pairwise disjoint. +Now, let j ∈ {1, . . . , n}. Then for k ∈ N \ {j} we have |�λk − λj| > δ. Therefore, we have +dist(λj, σ( �T)\{�λj}) ≥ δ and thus, for f ∈ �P ⊥ +j H, +∥( �T − λj)f∥ ≥ dist +� +λj, σ( �T| �P ⊥ +j H) +� +∥f∥ = dist(λj, σ( �T)\{�λj})∥f∥ ≥ δ∥f∥. +As TPj = λjPj and �P ⊥ +j �T = �T �P ⊥ +j , we obtain +∥T − �T∥ ≥ ∥ �P ⊥ +j ( �T − T)Pj∥ = ∥ �P ⊥ +j �TPj − �P ⊥ +j TPj∥ = ∥( �T − λj) �P ⊥ +j Pj∥ ≥ δ∥ �P ⊥ +j Pj∥. +The claim now follows from Lemma C.2. +□ + +ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR +27 +APPENDIX D. ERGODICITY AND THE GENERATOR +In this section, we prove the following proposition on the spectral properties of the generator L under +the ergodicity assumption. +Proposition D.1. Assume that the invariant measure µ is ergodic. Then ker L = span{1} and ker(L − +iωI) = {0} for ω ∈ R\{0}. +Proof. First of all, it is worth mentioning that Lψ = 0 implies Ktψ = ψ for all t ≥ 0 and that Lψ = iωψ, +ω ∈ R \ {0}, implies K2π/ωψ = ψ. Therefore, it suffices to show that Ktψ = ψ for some t > 0 and +ψ ∈ L2 +µ(X) is only possible for constant ψ. For this, we consider the Markov process (Xnt)∞ +n=0. For +convenience, we assume w.l.o.g. that t = 1 holds. By invariance of µ, the process (Xn)∞ +n=0 is stationary, +i.e., (Xn)∞ +n=0 and (Xn+1)∞ +n=0 are equally distributed as X N0-valued random variables. According to +[15, Lemma 9.2] there exist X-valued random variables X−k, k ∈ N, such that X := (Xn)n∈Z is also +stationary. By Pµ denote the law of the X Z-valued random variable X. +On S := X Z define the left shift T : S → S by T(xn)n∈Z := (xn+1)n∈Z. Stationarity of X means +that also TX ∼ Pµ. +A set A ∈ BZ +X := � +k∈Z BX is called shift-invariant if T −1A = A. It is easy to see that the set of +shift-invariant sets forms a sub-σ-algebra I of BZ +X . Now, by [13, Corollary 5.11] and the ergodicity of +µ we have Pµ(A) ∈ {0, 1} for any A ∈ I. Now, Birkhoff’s Ergodic Theorem [15, Theorem 9.6] states +that +lim +n→∞ +1 +n +n−1 +� +k=0 +f(T kX) = E +� +f(X)|X−1I +� +(D.1) +almost surely and in L1(Ω) for any f ∈ L1(S). Given ψ ∈ L1 +µ(X), let us apply this theorem to the +function f = ψ ◦ π0, where the projection π0 : S → X is defined by π0(xn)n∈Z = x0. First of all, +� +|f| dPµ = +� +|ψ(x0)| dPµ((xn)n∈Z) = +� +|ψ(x)| dµ(x) < ∞ +as Pµ ◦ π−1 +0 += µ. Hence, we have f ∈ L1(S). Furthermore, we compute f(T kX) = ψ(π0(T kX)) = +ψ(Xk). For A ∈ I we have P(X−1A) = Pµ(A) ∈ {0, 1}. Thus, we obtain +lim +n→∞ +1 +n +n−1 +� +k=0 +ψ(Xk) = E[f(X)] = +� +f dPµ = +� +ψ ◦ π0 dPµ = +� +ψ dµ +almost surely and in L1(Ω). +Therefore, if ψ ∈ L2 +µ(X) such that Ktψ = ψ, then Kktψ = ψ for all k ∈ N0, hence for µ-a.e. x ∈ X +we have +ψ(x) = 1 +n +n−1 +� +k=0 +ψ(x) = 1 +n +n−1 +� +k=0 +Kktψ(x) = 1 +n +n−1 +� +k=0 +E[ψ(Xkt)|X0 = x] += E +� +1 +n +n−1 +� +k=0 +ψ(Xkt) +����� X0 = x +� +n→∞ +−→ +� +ψ dµ. +Thus, ψ must indeed be (µ-essentially) constant. +□ + +28 +F. PHILIPP, M. SCHALLER, K. WORTHMANN, S. PEITZ, AND F. N ¨USKE +AUTHOR AFFILIATIONS +F. Philipp TECHNISCHE UNIVERSIT ¨AT ILMENAU, INSTITUTE FOR MATHEMATICS, WEIMARER STRASSE 25, D-98693 +ILMENAU, GERMANY +Email address: friedrich.philipp@tu-ilmenau.de +M. Schaller TECHNISCHE UNIVERSIT ¨AT ILMENAU, INSTITUTE FOR MATHEMATICS, WEIMARER STRASSE 25, D- +98693 ILMENAU, GERMANY +Email address: manuel.schaller@tu-ilmenau.de +K. Worthmann TECHNISCHE UNIVERSIT ¨AT ILMENAU, INSTITUTE FOR MATHEMATICS, WEIMARER STRASSE 25, +D-98693 ILMENAU, GERMANY +Email address: karl.worthmann@tu-ilmenau.de +S. Peitz PADERBORN UNIVERSITY, DEPARTMENT OF COMPUTER SCIENCE, DATA SCIENCE FOR ENGINEERING, GER- +MANY +Email address: sebastian.peitz@upb.de +F. N¨uske MAX PLANCK INSTITUTE FOR DYNAMICS OF COMPLEX TECHNICAL SYSTEMS, MAGDEBURG, GERMANY +Email address: nueske@mpi-magdeburg.mpg.de + diff --git a/8dFAT4oBgHgl3EQfpB03/content/tmp_files/load_file.txt b/8dFAT4oBgHgl3EQfpB03/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..2fcd3555ce344001193753b7bf2d5c5113bec98e --- /dev/null +++ b/8dFAT4oBgHgl3EQfpB03/content/tmp_files/load_file.txt @@ -0,0 +1,1386 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf,len=1385 +page_content='ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR FRIEDRICH PHILIPP, MANUEL SCHALLER, KARL WORTHMANN, SEBASTIAN PEITZ, AND FELIKS N ¨USKE ABSTRACT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We consider the data-driven approximation of the Koopman operator for stochastic differen- tial equations on reproducing kernel Hilbert spaces (RKHS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Our focus is on the estimation error if the data are collected from long-term ergodic simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We derive both an exact expression for the variance of the kernel cross-covariance operator, measured in the Hilbert-Schmidt norm, and probabilistic bounds for the finite-data estimation error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Moreover, we derive a bound on the prediction error of observables in the RKHS using a finite Mercer series expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Further, assuming Koopman-invariance of the RKHS, we provide bounds on the full approximation error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Numerical experiments using the Ornstein-Uhlenbeck process illustrate our results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' INTRODUCTION The Koopman operator [23] has become an essential tool in the modeling process of complex dy- namical systems based on simulation or measurement data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The philosophy of the Koopman approach is that for a (usually non-linear) dynamical system on a finite-dimensional space, the time-evolution of expectation values of observable functions satisfies a linear differential equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Hence, after “lifting” the dynamical system into an infinite-dimensional function space of observables, linear methods become available for its analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The second step is then to notice that traditional Galerkin approximations of the Koopman operator can be consistently estimated from simulation or measurement data, establishing the fundamental connection between the Koopman approach and modern data science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Koopman methods have found widespread application in system identification [4], control [24, 42, 25, 17, 49], sensor place- ment [31], molecular dynamics [50, 44, 35, 36, 18, 56], and many other fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We refer to [19, 33, 5] for comprehensive reviews of the state of the art.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The fundamental numerical method for the Koopman approach is Extended Dynamic Mode Decom- position (EDMD) [54], which allows to learn a Galerkin approximation of the Koopman operator from finite (simulation or measurement) data on a subspace spanned by a finite set of observables, often called dictionary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' An appropriate choice of said dictionary is a challenging problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In light of this issue, representations of the Koopman operator on large approximation spaces have been considered in recent years, including deep neural networks [29, 32], tensor product spaces [21, 37], and reproducing kernel Hilbert spaces (RKHS) [55, 11, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In the work [20] it was shown that by means of the integral operator associated to an RKHS, it is possible to construct a type of Galerkin approximation of the Koopman operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The central object are (cross-)covariance operators, which can be estimated from data, using only evaluations of the feature map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Due to the relative simplicity of the resulting numerical algorithms on the one hand, and the rich approximation properties of reproducing kernels on the other hand, kernel methods have emerged as a promising candidate to overcome the fundamental problem of dictionary selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' A key question is the quantification of the estimation error for (compressed1) Koopman operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' For finite dictionaries and independent, identically distributed (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=') samples, error estimates were provided in [26, 38], see also [58] for the ODE case and [49] for an extension to control-affine systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The 1A compression of a linear operator T to a subspace M is given by PT|M, where P denotes a projection onto M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='08637v1 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='DS] 20 Jan 2023 2 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PHILIPP, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' SCHALLER, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' WORTHMANN, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PEITZ, AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' N ¨USKE estimation error for cross-covariance operators on kernel spaces was considered in [34], where general concentration inequalities were employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The data were also allowed to be correlated, and mixing coefficients were used to account for the lack of independence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In this article, we take a different route and follow the approach of our previous paper [38], where we, in addition, also derived error estimates for the Koopman generator and operator for finite dictionaries and data collected from long-term, ergodic trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' This setting is relevant in many areas of science, where sampling i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' from an unknown stationary distribution is practically infeasible, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', in fluid or molecular dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The centerpiece of our results was an exact expression for the variance of the finite-data estimator, which can be bounded by an asymptotic variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The asymptotic variance by itself is a highly interesting dynamical quantity, which can also be described in terms of Poisson equations for the generator [27, Section 3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We consider the Koopman semigroup (Kt)t≥0 generated by a stochastic differential equation on the space L2 µ, where µ is a probability measure which is invariant w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' the associated Markov process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We study the action of Kt on observables in an RKHS H which is densely and compactly embedded in L2 µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' If this action is considered through the “lens” of the kernel integral operator E : L2 µ → H (see Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='2), we arrive at a family of operators Ct H = EKtE∗ (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The action of Ct H : H → H is that of a cross-covariance operator: Ct Hψ = � (Ktψ)(x)k(x, ·) dµ(x), ψ ∈ H, where k(·, ·) is the kernel generating the RKHS H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' These operators possess canonical empirical estima- tors based on finite simulation data, which only require evaluations of the feature map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' L2 µ L2 µ H H Kt E E∗ Ct H FIGURE 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Diagram illustrating the different operators involved Our contribution, illustrated in Figure 2, is two-fold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In our first main result, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1, we provide an exact formula for the Hilbert-Schmidt variance of the canonical empirical estimator �Cm,t H of the cross- covariance operator Ct H, for m data points sampled from a long ergodic simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' This result extends the findings in [38] to the kernel setting and no longer depends on the dictionary size (which would be infinite, at any rate).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Due to the infinite-dimensional setting, additional assumptions are required, in particular, a spectral decomposition of the Koopman generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Our result allows for probabilistic estimates for the error ∥ �Cm,t H − Ct H∥HS, see Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' As a second main result, we propose an empirical estimator for the restriction of the Koopman op- erator Kt to H, truncated to finitely many terms of its estimated Mercer series expansion, and prove a probabilistic bound for the resulting estimation error in Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1, measured in the operator norm for bounded linear maps from H to L2 µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' This result can be seen as a bound on the prediction error for the RKHS-based Koopman operator due to the use of finite data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In the situation where the RKHS is invariant under the Koopman operator we are able to complement the preceding error analysis with a bound on the full approximation error in Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Finally, we illustrate our results for a one-dimensional Ornstein-Uhlenbeck (OU) process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' For this simple test case, all quantities appearing in our error estimates are known analytically and can be well approximated numerically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Therefore, we are able to provide a detailed comparison between the error bound obtained from our results and the actual errors observed for finite data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Our experiments show that ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR 3 our bounds for the estimation error of the cross-covariance operator are accurate, and that the corrections we introduced to account for the inter-dependence of the data are indeed required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Concerning the prediction error, we find our theoretical bounds still far too conservative, which reflects the problem of accounting for the effect of inverting the mass matrix in traditional EDMD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' This finding indicates that additional research is required on this end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Full Koopman Approximation Error Projection error Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='5 Variance representation of empirical estimator Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1 Estimation error Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1 i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' sampling Ergodic sampling Cross-covariance bound Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4 ∥Ct ℍ − ̂ C m,t ℍ ∥HS ∥Kt N − ̂ K m,t N ∥ℍ→L2μ(X) ∥Kt − ̂ K m,t N ∥ℍ→L2μ(X) ∥Kt − Kt N∥ℍ→L2μ(X) FIGURE 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Illustration of main results The paper is structured as follows: the setting is introduced in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The result concerning the variance of the empirical cross-covariance operator, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1, is presented and proved in Section 3, while our bound for the prediction error is part of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1 in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Numerical experiments are shown in Section 5, conclusions are drawn in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PRELIMINARIES In this section, we provide the required background on stochastic differential equations (Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1), reproducing kernel Hilbert spaces (Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='2), Koopman operators (Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='3), and their representa- tions on an RKHS (Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Stochastic differential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Let X ⊂ Rd and let a stochastic differential equation (SDE) with drift vector field b : X → Rd and diffusion matrix field σ : X → Rd×d be given, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', dXt = b(Xt) dt + σ(Xt) dWt, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1) where Wt is d-dimensional Brownian motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We assume that both b and σ are Lipschitz-continuous and that (1 + ∥ · ∥2)−1[∥b∥2 + ∥σ∥F ] is bounded on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Then [39, Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1] guarantees the existence of a unique solution (Xt)t≥0 to (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The solution (Xt)t≥0 constitutes a continuous-time Markov process whose transition kernel will be denoted by ρt : X ×BX → R, where BX denotes the Borel σ-algebra on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Then ρt(x, ·) is a probability measure for all x ∈ X, and for each A ∈ BX we have that ρt(·, A) is a representative of the conditional probability for A containing Xt given X0 = · , i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', ρt(x, A) = P(Xt ∈ A|X0 = x) for µ-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' x ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Throughout, we will assume the existence of an invariant (Borel) probability measure µ for the Markov process (Xt)t≥0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', we have � ρt(x, A) dµ(x) = µ(A) (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='2) for all t ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In addition to being invariant, we will often assume that µ is ergodic, meaning that for any t > 0 every ρt-invariant set A (that is, ρt(x, A) = 1 for all x ∈ A) satisfies µ(A) ∈ {0, 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In this case, the Birkhoff ergodic theorem [15, Theorem 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='6] (see also (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1)) and its generalizations apply, and allow us to calculate expectations w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' µ using long-time averages over simulation data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We let ∥ · ∥p denote the Lp µ(X)-norm, 1 ≤ p < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In the particular case p = 2, scalar product and norm on the Hilbert space L2 µ(X) will be denoted by ⟨· , ·⟩µ and ∥ · ∥µ, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 4 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PHILIPP, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' SCHALLER, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' WORTHMANN, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PEITZ, AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' N ¨USKE 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Reproducing kernel Hilbert spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In what follows, let k : X × X → R be a continuous and symmetric positive definite kernel, that is, we have k(x, y) = k(y, x) for all x, y ∈ X and m � i,j=1 k(xi, xj)cicj ≥ 0 for all choices of x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' , xm ∈ X and c1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' , cm ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' It is well known that k generates a so-called reproducing kernel Hilbert space (RKHS) [1, 6, 40] (H, ⟨· , ·⟩) of continuous functions, such that for ψ ∈ H the reproducing property ψ(x) = ⟨ψ, Φ(x)⟩, x ∈ X, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='3) holds, where Φ : X → H denotes the so-called feature map corresponding to the kernel k, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', Φ(x) = k(x, ·), x ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In the sequel, we shall denote the norm on H by ∥ · ∥ and the kernel diagonal by ϕ: ϕ(x) = k(x, x), x ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Then for x ∈ X we have ∥Φ(x)∥2 = ⟨Φ(x), Φ(x)⟩ = ⟨k(x, ·), k(x, ·)⟩ = k(x, x) = ϕ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We shall frequently make use of the following estimate: |k(x, y)| = |⟨Φ(x), Φ(y)⟩| ≤ ∥Φ(x)∥∥Φ(y)∥ = � ϕ(x)ϕ(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In particular, it shows that k is bounded if and only if its diagonal ϕ is bounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' By Lp µ(X), p ∈ [1, ∞), we denote the space of all functions (not equivalence classes) on X with a finite p-norm ∥ · ∥p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Henceforth, we shall impose the following Compatibility Assumptions: (A1) ϕ ∈ L2 µ(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (A2) If ψ ∈ L2 µ(X) such that � � k(x, y)ψ(x)ψ(y) dµ(x) dµ(y) = 0, then ψ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (A3) If ψ ∈ H such that ψ(x) = 0 for µ-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' x ∈ X, then ψ(x) = 0 for all x ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Many of the statements in this subsection can also be found in [52, Chapter 4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' However, as we aim to present the contents in a self-contained way, we provide the proofs in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The following lemma explains the meaning of the compatibility assumptions (A1) and (A2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Under the assumption that ϕ ∈ L1 µ(X) (in particular, under assumption (A1)), we have that H ⊂ L2 µ(X) with ∥ψ∥µ ≤ � ∥ϕ∥1 · ∥ψ∥, ψ ∈ H, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4) and assumption (A2) is equivalent to the density of H in L2 µ(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We have meticulously distinguished between functions and equivalence classes as there might be distinct functions φ, ψ ∈ H, which are equal µ-almost everywhere2, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', φ = ψ in L2 µ(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The com- patibility assumption (A3) prohibits this situation so that H can in fact be seen as a subspace of L2 µ(X), which is then densely and continuously embedded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 2For example, if µ = δa and φ(a) = ψ(a) ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR 5 Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (a) Condition (A1) implies k ∈ L4 µ⊗µ(X × X), where µ ⊗ µ is the product measure on X × X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (b) The density of H in L2 µ(X) is strongly related to the term universality in the literature, see [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (c) Condition (A3) holds if supp µ = X, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' [52, Exercise 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' It immediately follows from � |ψ(x)|∥Φ(x)∥ dµ(x) ≤ ∥ψ∥µ∥ϕ∥1/2 1 , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='5) for ψ ∈ L2 µ(X) that the linear operator E : L2 µ(X) → H, defined by Eψ := � ψ(x)Φ(x) dµ(x), ψ ∈ L2 µ(X), is well defined (as a Bochner integral in H) and bounded with operator norm not larger than ∥ϕ∥1/2 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The so-called kernel mean embedding Ek, mapping probability measures ν on X to the RKHS H, is defined by Ekν = � Φ(x) dν(x), see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Hence, we have Eψ = Ekν with dν = ψ dµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Note that the operator E is not an embedding in strict mathematical terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The terminology embedding rather applies to its adjoint E∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Indeed, the operator E enjoys the simple but important property: ⟨Eψ, η⟩ = � ψ(x)⟨Φ(x), η⟩ dµ(x) = � ψ(x)η(x) dµ(x) = ⟨ψ, η⟩µ (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='6) for ψ ∈ L2 µ(X) and η ∈ H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' This implies that the adjoint operator E∗ : H → L2 µ(X) is the inclusion operator from H into L2 µ(X), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', E∗η = η, η ∈ H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='7) We shall further define the covariance operator3 CH := EE∗ ∈ L(H).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Recall that a linear operator T ∈ L(H) on a Hilbert space H is trace class if for some (and hence for each) orthonormal basis (ej)j∈N of H we have that �∞ j=1⟨(T ∗T)1/2ei, ei⟩ < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' A linear operator S ∈ L(H, K) between Hilbert spaces H and K is said to be Hilbert-Schmidt [12, Chapter III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='9] if S∗S is trace class, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', ∥S∥2 HS := �∞ j=1 ∥Sei∥2 < ∞ for some (and hence for each) orthonormal basis (ej)j∈N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Let the Compatibility Assumptions (A1)–(A3) be satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Then the following hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (a) The operator E is an injective Hilbert-Schmidt operator with ∥E∥2 HS = ∥ϕ∥1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (b) The space H is densely and compactly embedded in L2 µ(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (c) The operator CH is an injective non-negative selfadjoint trace class operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The next theorem is due to Mercer and can be found in, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' It shows the existence of a particular orthonormal basis (ej)∞ j=1 of L2 µ(X) composed of eigenfunctions of E∗E, which we shall henceforth call the Mercer basis corresponding to the kernel k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Again for the sake of self-containedness, we give a short proof in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 3In what follows, by L(H, K) we denote the set of all bounded (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', continuous) linear operators between Hilbert spaces H and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' As usual, we also set L(H) := L(H, H).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 6 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PHILIPP, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' SCHALLER, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' WORTHMANN, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PEITZ, AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' N ¨USKE Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='5 (Mercer’s Theorem).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' There exists an orthonormal basis (ej)∞ j=1 of L2 µ(X) consisting of eigenfunctions of E∗E with corresponding eigenvalues λj > 0 such that �∞ j=1 λj = ∥ϕ∥1 < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Fur- thermore, (fj)∞ j=1 with fj = � λjej constitutes an orthonormal basis of H consisting of eigenfunctions of CH with corresponding eigenvalues λj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Moreover, for all x, y ∈ X, k(x, y) = � j fj(x)fj(y) = � j λjej(x)ej(y), the series converges absolutely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The Koopman semigroup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The Koopman semigroup (Kt)t≥0 associated with the SDE (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1) is defined by (Ktψ)(x) = E[ψ(Xt)|X0 = x] = � ψ(y) ρt(x, dy), for ψ ∈ B(X), the set of all bounded Borel-measurable functions on X, and ρt(x, dy) = dρt(x, ·)(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' It is easy to see that the invariance of µ is equivalent to the identity � Ktψ dµ = � ψ dµ (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='8) for all t ≥ 0 and ψ ∈ B(X) (which easily extends to functions ψ ∈ L1 µ(X), see Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Note that in the case σ = 0 the SDE (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1) reduces to the deterministic ODE ˙x = b(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Then (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='8) implies � |ψ(φ(t, x))|2 dµ(x) = � |ψ(x)|2 dµ(x) for all t ≥ 0 and all ψ ∈ B(X), where φ(·, x) is the solution of the initial value problem ˙y = b(y), y(0) = x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Hence, the composition operator Kt : ψ �→ ψ ◦ φ(t, ·) is unitary in L2 µ(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' However, we shall require below (see Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1) that Kt has its spectrum in the interior of the unit circle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Therefore, we assume throughout that σ ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The proofs of the following two propositions can be found in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' For each p ∈ [1, ∞] and t ≥ 0, Kt extends uniquely to a bounded operator from Lp µ(X) to itself with operator norm ∥Kt∥Lp µ→Lp µ ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' By Cb(X) we denote the set of all bounded continuous functions on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' As the measure µ is finite, we have Cb(X) ⊂ B(X) ⊂ Lp µ(X) for all p ∈ [1, ∞].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In fact, Cb(X) is dense in each Lp µ(X), p ∈ [1, ∞), see [48, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (Kt)t≥0 is a C0-semigroup of contractions in Lp µ(X) for each p ∈ [1, ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The infinitesimal generator of the C0-semigroup (Kt)t≥0 is the (in general unbounded) operator in L2 µ(X), defined by Lψ = L2 µ- lim t→0 Ktψ − ψ t , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='9) whose domain dom L is the set of all ψ ∈ L2 µ(X) for which the above limit exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' By Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='8 and the Lumer-Phillips theorem (see [28]), the operator L is densely defined, closed4, dissipative (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', Re⟨Lψ, ψ⟩µ ≤ 0 for all ψ ∈ dom L), and its spectrum is contained in the closed left half-plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The constant function 1 is contained in dom L and L1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Moreover, if M := span{1} ⊂ L2 µ(X), then both M and M⊥ are invariant under L and all Kt, t ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 4Recall that a linear operator T, defined on a subspace dom T of a Hilbert space H, which maps to a Hilbert space K, is closed if its graph is closed in H × K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR 7 Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' It is easy to see that Kt1 = 1 for each t ≥ 0 and hence 1 ∈ dom L with L1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Hence KtM ⊂ M for all t ≥ 0 and LM ⊂ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Now, if ψ ⊥ 1, then ⟨Ktψ, 1⟩µ = � Ktψ dµ = � ψ dµ = ⟨ψ, 1⟩µ = 0, which shows that also KtM⊥ ⊂ M⊥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The relation LM⊥ ⊂ M⊥ follows from (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' □ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Representation of Koopman Operators on the RKHS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Using the integral operator E, it is possi- ble to represent the Koopman operator with the aid of a linear operator on H, which is based on kernel evaluations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' This construction mimics the well-known kernel trick used frequently in machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' To begin with, for any x, y ∈ X define the rank-one operator Cxy : H → H by Cxyψ := ⟨ψ, Φ(y)⟩Φ(x) = ψ(y)Φ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' For t ≥ 0 and ψ ∈ H we further define the cross-covariance operator Ct H : H → H by Ct Hψ := � � Cxyψ ρt(x, dy) dµ(x) = � (Ktψ)(x)Φ(x) dµ(x) = EKtψ = EKtE∗ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Thus, we have Ct H = EKtE∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='10) In other words, the cross-covariance operator Ct H represents the action of the Koopman semigroup through the lens of the RKHS integral operator E (see [20] for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Being the product of the two Hilbert-Schmidt operators EKt and E∗, the operator Ct H is trace class for all t ≥ 0 (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' [16, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 521]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Note that due to ρ0(x, · ) = δx, for t = 0 this reduces to the already introduced covariance operator � � Cxy ρ0(x, dy) dµ(x) = � Cxx dµ(x) = EE∗ = CH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The identity (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='10) shows that for all η, ψ ∈ H we have ⟨η, Ct Hψ⟩ = ⟨η, Ktψ⟩µ, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='11) which shows that the role of Ct H is analogous to that of the stiffness matrix in a traditional finite- dimensional approximation of the Koopman operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In this analogy, the covariance operator CH plays the role of the mass matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Empirical estimators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Next, we introduce empirical estimators for Ct H based on finite data (xk, yk), k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' , m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We consider two sampling scenarios for fixed t > 0: (1) The xk are drawn i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' from µ, and each yk ∼ µ is obtained from the conditional distribution ρt(xk, ·), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', yk|(xk = x) ∼ ρt(x, ·) for µ-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' x ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' For example, yk can be obtained by simulating the SDE (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1) starting from xk until time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (2) µ is ergodic and both xk and yk are obtained from a single (usually long-term) simulation of the dynamics Xt at discrete integration time step ∆t > 0, using a sliding-window estimator, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', x0 = X0 ∼ µ, xk = Xk∆t, and yk = Xk∆t+t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Moreover, we assume that there exists a Riesz basis (ψj)∞ j=0 of L2 µ(X) consisting of eigenfunc- tions of the generator L with corresponding eigenvalues µj satisfying �∞ j=0 e2(Re µj)∆t < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' It easily follows from the discussion in Appendix B that the last assumption on the generator L and on the decay of its eigenvalues µj is equivalent to the similarity of L to an (unbounded) normal operator N such that eN∆t ∈ L(L2 µ(X)) is Hilbert-Schmidt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' If the assumption holds with ψj = Sej, where (ej) is an orthonormal basis of L2 µ(X), the operator N is given by N = � j µj⟨ · , ej⟩ej with dom N = {ψ : (µj⟨ψ, ej⟩) ∈ ℓ2} and L = SNS−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The condition �∞ j=0 e2(Re µj)∆t < ∞ then obviously means that the eigenvalues of eN∆t form an ℓ2 sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 8 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PHILIPP, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' SCHALLER, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' WORTHMANN, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PEITZ, AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' N ¨USKE Recall that the joint distribution of two random variables X and Y is given by dPX,Y (x, y) = dPY |X=x(y) · dPX(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Set X = xk and Y = yk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Then, in both cases (1) and (2), we have PX = µ and PY |X=x(B) = P(yk ∈ B|xk = x) = P(Xt ∈ B|X0 = x) = ρt(x, B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In other words, for the joint distribution µ0,t of xk and yk we have dµ0,t(x, y) = dρt(x, ·)(y) · dµ(x) = ρt(x, dy) · dµ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' More explicitly, µ0,t(A × B) = � A ρt(x, B) dµ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Now, since Ct H = � � Cxy ρt(x, dy) dµ(x) = � Cxy dµ0,t(x, y) = E � Cxk,yk � , for the empirical estimator for Ct H we choose the expression �Cm,t H = 1 m m−1 � k=0 Cxk,yk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='12) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' VARIANCE OF THE EMPIRICAL ESTIMATOR In case (1), the law of large numbers [3, Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4] and, in case (2), ergodicity [2] ensures the expected behavior lim m→∞ ∥ �Cm,t H − Ct H∥HS = 0 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' However, this is a purely qualitative result, and nothing is known a priori on the rate of this convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The main result of this section, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1, contains an exact expression for the Hilbert-Schmidt vari- ance of the empirical estimator �Cm,t H based on m data points, which then yields probabilistic estimates for the expression ∥ �Cm,t H − Ct H∥HS, see Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Here, our focus is on the estimation from a single ergodic trajectory, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', case (2) above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' While the broader line of reasoning partially resembles that of our previous paper [38], we require additional steps due to the infinite-dimensional setting introduced by the RKHS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1 and its proof, we will be concerned with evolving kernels kt : X × X → R, defined by kt(x, x′) := � � k(y, y′) ρt(x, dy) ρt(x′, dy′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We have kt(x, x′) = � � ⟨Φ(y), Φ(y′)⟩ ρt(x, dy) ρt(x′, dy′) = �� Φ(y) ρt(x, dy), � Φ(y′) ρt(x′, dy′) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The integrals in the last expression are well defined as limits in H for µ-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' x, x′ ∈ X as � � ∥Φ(y)∥ ρt(x, dy) dµ(x) = � � � ϕ(y) ρt(x, dy) dµ(x) = � � ϕ(x) dµ(x) ≤ ∥ϕ∥1/2 1 , see (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' This shows that kt is well defined ((µ ⊗ µ)-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=') and that it is a positive definite kernel on its domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Moreover, k0 = k and |kt(x, x′)| ≤ � � ϕ(y′) � � ϕ(y) ρt(x, dy) ρt(x′, dy′) = (Kt√ϕ)(x) · (Kt√ϕ)(x′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR 9 In particular, kt ∈ L2 µ⊗µ(X 2) with ∥kt∥L2 µ⊗µ ≤ ∥ϕ∥1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' By Φt we denote the corresponding feature map, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', Φt(x) = kt(x, ·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Note that not necessarily Φt(x) ∈ H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Finally, we define Φt,x := Φ(x)Φt(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We are now in the position to formulate our first main result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Setting zk = (xk, yk), k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' , m, the Hilbert-Schmidt variance of the empirical estimator can be written as E � ∥ �Cm,t H − Ct H∥2 HS � = 1 m � E0(t) + 2 m−1 � k=1 m−k m E � ⟨Czk − Ct H, Cz0 − Ct H⟩HS � � , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1) where E0(t) := E � ∥Cz0 − Ct H∥2 HS � = ⟨Ktϕ, ϕ⟩µ − ⟨k, kt⟩L2 µ⊗µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In case (1), E � ∥ �Cm,t H − Ct H∥2 HS � = 1 mE0(t), whereas in case (2) we have E � ∥ �Cm,t H − Ct H∥2 HS � = 1 m � �E0(t) + 2 ∞ � j=1 dj,tqj 1 − qj � 1 − 1 m · 1 − qm j 1 − qj �� � , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='2) with qj = eµj∆t, dj,t = ⟨cj,t, ψj⟩µ, and cj,t(x) = ⟨Φt,x, �ψj⟩µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Before proving Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1 in Subsection 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1 below, let us comment on its statements and draw some conclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (a) Note that, by ergodicity of the invariant measure µ, the generator L has no eigenvalues on the imaginary axis, except the simple zero eigenvalue (see Proposition D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1 in the Appendix).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In contrast, if we drop the ergodicity assumption, we have E � ∥ �Cm,t H − Ct H∥2 HS � = 1 m � �E0(t) + 2 ∞ � j=ν0 dj,tqj 1 − qj � 1 − 1 m · 1 − qm j 1 − qj �� � + m − 1 m ν0−1 � j=1 dj,t, where ν0 = #{j : µj ∈ 2πi ∆t Z} is the number of eigenvalues of L of the form 2kπi ∆t , k ∈ Z, counting multiplicities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Obviously, the last term does not decay to zero as m → ∞ if �ν0−1 j=1 dj,t ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (b) The definition of cj,t requires Φt,x to be in L2 µ(X) for µ-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' x ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' This will in fact be proved in Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='6 below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In the following, we let σ2 m := E0(t) + 2 ∞ � j=1 dj,tqj 1 − qj � 1 − 1 m · 1 − qm j 1 − qj � and σ2 ∞ := E0(t) + 2 ∞ � j=1 dj,tqj 1 − qj .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Then E � ∥ �Cm,t H − Ct H∥2 HS � = σ2 m m and σ2 m → σ2 ∞ as m → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Both infinite series converge absolutely as (qj) ∈ ℓ2 by assumption, and (dj,t) ∈ ℓ2 as shown in the proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We can therefore interpret σ2 ∞ as asymptotic variance of the estimator ˆCm,t H , similar to our previous results in [38, Lemma 6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' An upper bound on the variance can be obtained as follows: 10 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PHILIPP, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' SCHALLER, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' WORTHMANN, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PEITZ, AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' N ¨USKE Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In case (2), for all m ∈ N we have σ2 m ≤ ⟨Ktϕ, ϕ⟩µ � 1 + 4B Aδq ∥q∥ℓ2 � , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='3) where A and B denote the lower and upper Riesz bounds of (ψj), respectively, q = (qj)∞ j=1 , and δq = inf j≥1 |1 − qj| > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' First of all, by Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='6, E0(t) = ⟨Ktϕ, ϕ⟩µ − ⟨k, kt⟩L2 µ⊗µ ≤ ⟨Ktϕ, ϕ⟩µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We have |1 − qj| ≥ δq and |qj| ≤ 1 for all j ≥ 1 and hence 1 |1 − qj| · ����1 − 1 m · 1 − qm j 1 − qj ���� ≤ 1 δq � 1 + 1 m m−1 � k=0 |qj|k � ≤ 2 δq .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' This and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='7) imply (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' □ Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We have the following probabilistic bound on the estimation error: P � ∥Ct H − �Cm,t H ∥HS > ε � ≤ � � � � � � � � � � � � � σ2 m mε2 , in case (2), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4) E0(t) mε2 , in case (1), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='5) 2 e − mε2 8∥k∥2∞ , in case (1) with bounded kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='6) In particular, the above also holds upon replacing the left-hand side by P � ∥EKtψ − �Cm,t H ψ∥ > ε � for ψ ∈ H, ∥ψ∥ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The inequalities (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='5) are an immediate consequence of Markov’s inequality, applied to the random variable ∥Ct H − �Cm,t H ∥2 HS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The inequality (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='6) follows from Ct H − �Cm,t H = 1 m �m−1 k=0 (Ct H − Czk), Hoeffding’s inequality for Hilbert space-valued random variables [43, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='5] (see also [30, Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='2]), and (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='6 below) ∥Ct H − Cxy∥HS ≤ ∥Ct H∥HS + ∥Cxy∥HS = � ⟨k, kt⟩L2 µ⊗µ + � ϕ(x)ϕ(y) ≤ 2∥k∥∞, since also ∥kt∥∞ ≤ ∥k∥∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The estimate ∥EKtψ − �Cm,t H ψ∥ = ∥EKtE∗ψ − �Cm,t H ψ∥ = ∥(Ct H − �Cm,t H )ψ∥ ≤ ∥Ct H − �Cm,t H ∥HS finally yields the last claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' □ Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Under additional assumptions (boundedness of the kernel, mixing, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' ), other concen- tration inequalities than Markov’s, such as, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', [3, Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='12] (α-mixing) or [46, Th´eor`eme 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1] (β-mixing), might lead to better estimates than (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Let t ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Then Φt,x ∈ L2 µ(X) for µ-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' x ∈ X with ∥Φt,x∥2 µ ≤ ϕ(x)(Ktϕ)(x) · ⟨Ktϕ, ϕ⟩µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Moreover, for every t ≥ 0 we have ∥Cxy∥2 HS = ϕ(x)ϕ(y) and ∥Ct H∥2 HS = ⟨k, kt⟩L2 µ⊗µ = � � Φt,x(y) dµ(y) dµ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR 11 Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We estimate |Φt,x(x′)|2 = |k(x, x′)kt(x, x′)|2 ≤ ϕ(x)ϕ(x′)(Kt√ϕ)2(x) · (Kt√ϕ)2(x′) ≤ ϕ(x)(Ktϕ)(x) · ϕ(x′)(Ktϕ)(x′), where we have applied Jensen’s inequality to (Kt√ϕ)(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' This proves the first inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Next, if (fj) ⊂ H denotes the Mercer basis corresponding to k, then ⟨Cxy, Cx′y′⟩HS = � i ⟨Cxyfi, Cx′y′fi⟩ = � i fi(y)fi(y′)k(x, x′) = k(x, x′)k(y, y′) This proves ∥Cxy∥2 HS = ϕ(x)ϕ(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Moreover, it yields ∥Ct H∥2 HS = ���� � Cxy dµ0,t(x, y) ���� 2 HS = � � k(x, x′)k(y, y′) dµ0,t(x, y) dµ0,t(x′, y′) = � � k(x, x′) �� � k(y, y′) ρt(x, dy) ρt(x′, dy′) � dµ(x′) dµ(x) = ⟨k, kt⟩L2 µ⊗µ, as claimed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' □ Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' First of all, we have E � ∥ �Cm,t H − Ct H∥2 HS � = E ���� 1 m m−1 � k=0 (Czk − Ct H) ��� 2 HS � = E � 1 m2 m−1 � k,ℓ=0 � Czk − Ct H, Czℓ − Ct H � HS � = E � 1 m2 m−1 � k=0 ∥Czk − Ct H∥2 HS + 2 m2 m−1 � k=0 m−1 � ℓ=k+1 � Czk − Ct H, Czℓ − Ct H � HS � = 1 mE � ∥Cz0 − Ct H∥2 HS � + 2 m2 m−1 � k=1 (m − k)E � ⟨Czk − Ct H, Cz0 − Ct H⟩HS � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' where we exploited that E[⟨Czk − Ct H, Czℓ − Ct H⟩HS] only depends on the difference ℓ − k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Let us compute the first term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Since E[Cz0] = Ct H and thus E[⟨Cz0, Ct H⟩HS] = ∥Ct H∥2 HS, E � ∥Cz0 − Ct H∥2 HS � = E � ∥Cz0∥2 HS � − ∥Ct H∥2 HS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' For ψ ∈ H we have ∥Cz0ψ∥2 = ∥ψ(y0)Φ(x0)∥2 = ψ(y0)2ϕ(x0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Using the Mercer basis (fi) ⊂ H corresponding to k in H (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='5), we obtain E � ∥Cz0∥2 HS � = E � � i ∥Cz0fi∥2� = E � � i fi(y0)2ϕ(x0) � = E[ϕ(x0)ϕ(y0)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Note that the latter equals (ϕ(x) = k(x, x) by definition) E[ϕ(x0)ϕ(y0)] = � ϕ(x) � ϕ(y) ρt(x, dy) dµ(x) = � ϕ(x)(Ktϕ)(x) dµ(x) = ⟨Ktϕ, ϕ⟩µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We obtain E � ∥Cz0 − Ct H∥2 HS � = E[ϕ(x0)ϕ(y0)] − ⟨k, kt⟩L2 µ⊗µ = ⟨Ktϕ, ϕ⟩µ − ⟨k, kt⟩L2 µ⊗µ = E0(t) and thus (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Case (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In this case, zk and zℓ are independent for k ̸= ℓ, so that E � ⟨Czk − Ct H, Czℓ − Ct H⟩HS � = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 12 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PHILIPP, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' SCHALLER, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' WORTHMANN, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PEITZ, AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' N ¨USKE Hence, the statement of the theorem for case (1) follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Case (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Here, the cross terms do not vanish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In fact, E � ⟨Czk − Ct H, Cz0 − Ct H⟩HS � = E[⟨Czk, Cz0⟩HS] − ∥Ct H∥2 HS = E � � i ⟨Czkfi, Cz0fi⟩ � − ∥Ct H∥2 HS = E �� � i fi(yk)fi(y0) � k(xk, x0) � − ∥Ct H∥2 HS = E � k(yk, y0)k(xk, x0) � − ∥Ct H∥2 HS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Now, E � k(yk, y0)k(xk, x0) � = � � � � k(y′, y)k(x′, x) ρt(x′, dy′) ρk∆t(x, dx′) ρt(x, dy) dµ(x) = � � k(x, x′) �� � k(y, y′) ρt(x, dy) ρt(x′, dy′) � ρk∆t(x, dx′) dµ(x) = � � k(x, x′)kt(x, x′) ρk∆t(x, dx′) dµ(x) = � �� [Φ(x)Φt(x)](x′) ρk∆t(x, dx′) � dµ(x) = � [Kk∆tΦt,x](x) dµ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Hence, E � ⟨Czk − Ct H, Cz0 − Ct H⟩HS � = � (Kk∆tΦt,x)(x) dµ(x) − ⟨k, kt⟩L2 µ⊗µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Let us now exploit the assumptions on the spectral properties of the generator L in case (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' For µ-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' x ∈ X, we have Φt,x = ∞ � j=0 cj,t(x)ψj, the series converging in L2 µ(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Therefore, KsΦt,x = ∞ � j=0 cj,t(x)Ksψj = ∞ � j=0 cj,t(x)eµjsψj, and thus (for k ≥ 1) � � Kk∆tΦt,x � (x) dµ(x) = � ∞ � j=0 cj,t(x)eµjk∆tψj(x) dµ(x) = ∞ � j=0 dj,t · eµjk∆t = ∞ � j=0 dj,t · qk j .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' This series converges absolutely for each t ≥ 0 due to our assumption that � j |qj|2 < ∞ and since for each j ∈ N0 we have by Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='6 that ∞ � j=0 |dj,t|2 ≤ B2 ∞ � j=0 ∥cj,t∥2 µ = B2 � ∞ � j=0 |⟨Φt,x, �ψj⟩µ|2 dµ(x) ≤ B2 A2 � ∥Φt,x∥2 µ dµ(x) ≤ B2 A2 ⟨Ktϕ, ϕ⟩2 µ, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='7) where A and B are the Riesz bounds of (ψj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR 13 Without loss of generality, we may assume that µ0 = 0 with ψ0 = 1 and µ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' , µν0−1 ∈ 2πi ∆t Z, and ψk ∈ 1⊥ for k ≥ 1, see Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The duality relations then imply �ψ0 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Now, c0,t(x) = ⟨Φt,x, 1⟩µ = � k(x, y)kt(x, y) dµ(y) and hence d0,t = ⟨c0,t, 1⟩µ = � c0,t(x) dµ(x) = � � k(x, y)kt(x, y) dµ(y) dµ(x) = ⟨k, kt⟩L2 µ⊗µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='8) This implies E � ⟨Czk − Ct H, Cz0 − Ct H⟩HS � = ∞ � j=0 dj,t · qk j − ⟨k, kt⟩L2 µ⊗µ = ∞ � j=1 dj,t · qk j and therefore E � ∥ �Cm,t H − Ct H∥2 HS � = 1 mE0(t) + 2 m ∞ � j=1 dj,t m−1 � k=1 (1 − k m)qk j = 1 m � �E0(t) + 2 ν0−1 � j=1 dj,t m−1 � k=1 (1 − k m)qk j + 2 ∞ � j=ν0 dj,t m−1 � k=1 (1 − k m)qk j � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The identity m−1 � k=1 � 1 − k m � qk = � q 1−q � 1 − 1 m · 1−qm 1−q � if q ̸= 1 m−1 2 if q = 1 finally yields (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' □ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' BOUND ON THE KOOPMAN PREDICTION ERROR The kernel cross-covariance operator Ct H can also be used to approximate the predictive capabilities of the Koopman operator, for observables in H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Approximating the full Koopman operator involves the inverse of the co-variance operator, which becomes an unbounded operator on a dense domain of definition in the infinite-dimensional RKHS case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Moreover, its empirical estimator �Cm H is finite-rank and thus not even injective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' While Fukumizu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' tackle this problem in [10] by means of a regularization procedure, we choose to use pseudo-inverses instead (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We truncate the action of the Koopman operator using N terms of the Mercer series expansion and derive a bound for the prediction error for fixed truncation parameter N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' While we use similar ideas as presented in [11], we heavily rely on our new results on the cross-covariance operator, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Afterwards, we deal with the case of Koopman-invariance of the RKHS [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Here, we establish an estimate for the truncation error, which then yields a bound on the deviation from the full Koopman operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We emphasize that this error bound is extremely useful in comparison to its prior counterparts based on the assumption that the space spanned by a finite number of so-called observables (dictionary) is invariant under the Koopman operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The latter essentially requires to employ only Koopman eigenfunctions as observables, see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', [25, 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Let (ej) be the Mercer orthonormal basis of L2 µ(X) corresponding to the kernel k and let λj = ∥Eej∥µ as well as fj := � λjej (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We arrange the Mercer eigenvalues in a non-increasing way, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', λ1 ≥ λ2 ≥ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Let ψ ∈ H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Then Ktψ = ∞ � j=1 ⟨Ktψ, ej⟩µej = ∞ � j=1 ⟨Ct Hψ, ej⟩ej = N � j=1 ⟨Ct Hψ, ej⟩ej + ∞ � j=N+1 ⟨Ct Hψ, ej⟩ej.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1) 14 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PHILIPP, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' SCHALLER, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' WORTHMANN, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PEITZ, AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' N ¨USKE 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Estimation error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In the next theorem, we estimate the probabilistic error between the first sum- mand Kt Nψ = N � j=1 ⟨Ct Hψ, ej⟩ej, ψ ∈ H, and its empirical estimator, which is of the form �N j=1⟨ �Cm,t H ψ, �ej⟩�ej with approximations �ej of the ej.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Assume that the eigenvalues λj of CH are simple, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', λj+1 > λj for all j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Fix an arbitrary N ∈ N and let δN = min j=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=',N λj − λj+1 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='2) Further, let ε ∈ (0, δN) and δ ∈ (0, 1) be arbitrary and fix some5 m ≥ max{N, 2σ2 m ε2δ }.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Let now �λ1 ≥ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' ≥ �λm denote the largest m eigenvalues of �Cm H in descending order and let �e1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' , �em be corresponding eigenfunctions, respectively, such that ∥�ej∥ = �λ−1/2 j for j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' , m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' If we define �Km,t N ψ = N � j=1 ⟨ �Cm,t H ψ, �ej⟩�ej, ψ ∈ H, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='3) then, with probability at least 1 − δ, we have that ∥Kt N − �Km,t N ∥H→L2µ(X) ≤ � 1 √λN + N + 1 δNλN (1 + ∥ϕ∥1)∥ϕ∥1/2 1 � ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4) All of the above statements equally apply to case (1) upon replacing σm by E0(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (a) If we set �fj = �λ1/2 j �ej, then �Cm H = m � j=1 �λj⟨ · , �fj⟩ �fj, and thus N � j=1 ⟨ · , �ej⟩�ej = N � j=1 1 �λj ⟨ · , �fj⟩ �fj = ( �Cm H )† �QN, where �QN = �N j=1⟨ · , �fj⟩ �fj is the orthogonal projector onto the span of the first N eigenfunctions of �Cm H in H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Therefore, �Km,t N ψ = m � j=1 ⟨ �Cm,t H ψ, �ej⟩�ej = ( �Cm H )† �QN �Cm,t H ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In particular, for N = m we have �Km,t N = ( �Cm H )† �Cm,t H , which surely is one of the first canonical choices for an empirical estimator of Kt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (b) The functions �ej have unit length in the empirical L2 µ-norm: 1 m m � k=1 �ej(xk)�ej(xk) = � �Cm H �ej, �ej � = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Therefore, projecting onto the first N empirical Mercer features is the whitening transformation com- monly used in traditional EDMD [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 5By Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='3, an amount of at least m ≥ max � N , 2∥ϕ∥2 µ ε2δ � 1 + 4B Aδq ∥q∥ℓ2 �� data points suffices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR 15 Proof of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' By Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4, both events ∥Ct H − �Cm,t H ∥HS ≤ ε and ∥CH − �Cm H ∥HS ≤ ε occur with probability at least 1 − δ/2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Hence, they occur simultaneously with probability at least 1 − δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In the remainder of this proof we assume that both events occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Then all the statements deduced in the following hold with probability at least 1 − δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Let us define the intermediate approximation �Km,t N ψ = N � j=1 ⟨ �Cm,t H ψ, ej⟩ej, ψ ∈ H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Let ψ ∈ H be arbitrary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Setting C := Ct H − �Cm,t H , we have ∥Kt Nψ − �Km,t N ψ∥2 µ = ����� N � j=1 � Cψ, ej � ej ����� 2 µ = N � j=1 ��� Cψ, ej ���2 = N � j=1 ��� ψ, C∗ej ���2 ≤ ∥ψ∥2 N � j=1 ∥C∗ej∥2 ≤ ∥ψ∥2 N � j=1 1 λj ∥C∗fj∥2 ≤ ∥ψ∥2 λN N � j=1 ∥C∗fj∥2 ≤ ∥ψ∥2 λN ∞ � j=1 ∥C∗fj∥2 = ∥ψ∥2 λN ∥Ct H − �Cm,t H ∥2 HS, and thus, ∥Kt Nψ − �Km,t N ψ∥µ ≤ ∥ψ∥ √λN ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Next, we aim at estimating the remaining error �Km,t N ψ − �Km,t N ψ = N � j=1 ⟨ �Cm,t H ψ, ej⟩ej − N � j=1 ⟨ �Cm,t H ψ, �ej⟩�ej = N � j=1 λ−1 j ⟨ �Cm,t H ψ, fj⟩fj − N � j=1 �λ−1 j ⟨ �Cm,t H ψ, �fj⟩ �fj = N � j=1 λ−1 j ⟨f, fj⟩fj − N � j=1 �λ−1 j ⟨f, �fj⟩ �fj = N � j=1 � λ−1 j Pjf − �λ−1 j �Pjf � = N � j=1 λ−1 j (Pj − �Pj)f + N � j=1 (λ−1 j − �λ−1 j ) �Pjf, where f = �Cm,t H ψ, Pjf = ⟨f, fj⟩fj and �Pjf = ⟨f, �fj⟩ �fj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' By (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4), it suffices to estimate the above error in the ∥ · ∥-norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' By Theorem C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='3, the first summand can be estimated as ��� N � j=1 λ−1 j (Pj − �Pj)f ��� ≤ N � j=1 1 λj ∥Pj − �Pj∥∥f∥ ≤ N · ∥CH − �Cm H ∥ λNδN ∥f∥ ≤ N λNδN ∥f∥ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 16 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PHILIPP, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' SCHALLER, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' WORTHMANN, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PEITZ, AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' N ¨USKE For the second summand we have ��� N � j=1 (λ−1 j − �λ−1 j ) �Pjf ��� 2 = N � j=1 |λ−1 j − �λ−1 j |2∥ �Pjf∥2 = N � j=1 |λj − �λj|2 λ2 j�λ2 j ∥ �Pjf∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Now, note that ϵ < δN by assumption and therefore ∥CH − �Cm H ∥HS ≤ δN ≤ λN−λN+1 2 ≤ λN 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' For j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' , N, according to Theorem C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1 this implies �λj ≥ λj − |λj − �λj| ≥ λj − ∥CH − �Cm H ∥HS ≥ λj − λN 2 ≥ λj 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Hence, ��� N � j=1 (λ−1 j − �λ−1 j ) �Pjf ��� 2 ≤ 4 N � j=1 |λj − �λj|2 λ4 j ∥ �Pjf∥2 ≤ 4∥CH − �Cm H ∥2 HS λ4 N ∥ �QNf∥2, and thus, ��� N � j=1 (λ−1 j − �λ−1 j ) �Pjf ��� ≤ 2 λ2 N ∥f∥ε ≤ 1 λNδN ∥f∥ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' From ∥ �Cm,t H ∥ ≤ ∥ �Cm,t H − Ct H∥ + ∥Ct H∥ ≤ ∥ �Cm,t H − Ct H∥HS + ∥EKtE∗∥ ≤ ε + ∥ϕ∥1 we conclude �� �Km,t N ψ − �Km,t N ψ �� ≤ N + 1 λNδN ∥ �Cm,t H ψ∥ε ≤ N + 1 λNδN (ε + ∥ϕ∥1)∥ψ∥ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' All together, we obtain (recall (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4)) ∥Kt Nψ − �Km,t N ψ∥µ ≤ ∥Kt Nψ − �Km,t N ψ∥µ + ∥ϕ∥1/2 1 ∥ �Km,t N ψ − �Km,t N ψ∥ ≤ ∥ψ∥ √λN ε + N + 1 λNδN (ε + ∥ϕ∥1)∥ϕ∥1/2 1 ∥ψ∥ε = � 1 √λN + N + 1 δNλN (1 + ∥ϕ∥1)∥ϕ∥1/2 1 � ε · ∥ψ∥, which implies (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' □ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Projection error in case of Koopman-invariance of the RKHS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In the preceeding section, we have seen that the empirical operator �Km,t N can be written as ( �Cm H )† �Cm,t H if m = N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In the limit m → ∞, we would arrive at the operator C−1 H Ct H, which is not even well-defined for all ψ ∈ H, in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' However, if the RKHS is invariant under Kt, the above operator limit is well-defined as a bounded operator on H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In this situation we are able to extend Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1 to an estimate on the full error made by our empirical estimator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We start by defining the operator Kt H := C−1 H Ct H on its natural domain dom Kt H := {ψ ∈ H : Ct Hψ ∈ ran CH}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='5) We consider Kt H as an operator from H into itself (with domain of definition in H).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We have dom Kt H = {ψ ∈ H : Ktψ ∈ H}, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='6) and Kt H is closed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR 17 Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Note that Ct Hψ ∈ ran CH if and only if EKtψ = CHφ for some φ ∈ H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Since CHφ = Eφ and ker E = {0}, the latter is equivalent to Ktψ = φ ∈ H, which proves the representation of the domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' As to the closedness of Kt H, let (ψn) ⊂ dom Kt H and φ ∈ H such that ψn → ψ in H and Kt Hψn → φ in H as n → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The latter implies Ct Hψn → CHφ, while the first implies Ct Hψn → Ct Hψ in H as n → ∞, from which we conclude that Ct Hψ = CHφ, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', ψ ∈ dom Kt H and Kt Hψ = φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' □ If the Koopman operator leaves the RKHS H invariant (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', KtH ⊂ H), Kt H is defined on all of H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Moreover, since the canonical inclusion map E∗ : H → L2(µ) is injective, it possesses an unbounded inverse on its range H, and therefore: C−1 H Ct Hφ = C−1 H EKtE∗φ = (EE∗)−1EE∗(E∗)−1KtE∗φ = (E∗)−1KtE∗φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='7) Remarkably, invariance of H under the Koopman operator implies that the left-hand side not only repro- duces the Koopman operator on H, but actually defines a bounded operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Parts of the next proposition can be found in [22, Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='3] and [8, Theorem 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' For t > 0, the following statements are equivalent: (i) KtH ⊂ H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (ii) Kt H ∈ L(H).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (iii) ran Ct H ⊂ ran CH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' With regard to the two representations (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='5) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='6) of the domain, it is immediate that both (i) and (iii) are equivalent to dom Kt H = H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The equivalence of the latter to (ii) follows from the closed graph theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' □ Note that if one of (i)–(iii) holds, then Kt H = Kt|H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In addition to the assumptions in Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1, assume that H is invariant under the Koopman operator Kt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' For fixed N ∈ N, let δN be as in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='2), choose ε, δ, and m as in Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1 and define the empirical estimator �Km,t N as in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Then, with probability at least 1 − δ we have that ∥Kt − �Km,t N ∥H→L2µ(X) ≤ � λN+1 ∥Kt H∥ + � 1 √λN + N + 1 δNλN (1 + ∥ϕ∥1)∥ϕ∥1/2 1 � ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='8) Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' First of all, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1 implies that ∥Kt − �Km,t N ∥H→L2µ(X) ≤ ∥Kt − Kt N∥H→L2µ(X) + ∥Kt N − �Km,t N ∥H→L2µ(X) ≤ ∥Kt − Kt N∥H→L2µ(X) + � 1 √λN + N + 1 δNλN (1 + ∥ϕ∥1)∥ϕ∥1/2 1 � ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Now, for ψ ∈ H, ∥Ktψ − Kt Nψ∥2 µ = ����� ∞ � j=N+1 ⟨Ct Hψ, ej⟩ej ����� 2 µ = ∞ � j=N+1 |⟨Ct Hψ, ej⟩|2 = ∞ � j=N+1 1 λj |⟨Ct Hψ, fj⟩|2 = ∞ � j=N+1 1 λj |⟨Kt Hψ, CHfj⟩|2 = ∞ � j=N+1 λj|⟨Kt Hψ, fj⟩|2 ≤ λN+1∥Kt Hψ∥2, which proves the theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' □ We have just proved that the projection error ∥Ktψ − Kt Nψ∥µ decays at least as fast as the square roots of the eigenvalues of CH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Recall that (λj)j∈N ∈ ℓ1(N), since CH is trace class with �∞ j=1 λj = Tr(CH) = ∥E∗∥2 HS = ∥ϕ∥1, see Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 18 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PHILIPP, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' SCHALLER, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' WORTHMANN, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PEITZ, AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' N ¨USKE 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' ILLUSTRATION WITH THE ORNSTEIN-UHLENBECK PROCESS For the numerical illustration of our results, we consider the Ornstein-Uhlenbeck (OU) process on X = R, which is given by the SDE dXt = −αXt dt + dWt, where α > 0 is a positive parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Analytical Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Since all relevant properties of the OU process are available in analytical form, we can exactly calculate all of the terms appearing in our theoretical error bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Moreover, we can also compute the exact estimation and prediction errors for finite data in closed form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Let us begin by recapping the analytical results required for our analysis, which can be found in [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The invariant measure µ, and the density of the stochastic transition kernel ρt, are given by dµ(x) = �α π e−αx2 dx and dρt(x, y) = � α πv2 t exp � − α v2 t (y − e−αtx)2� dx dy, with v2 t = (1 − e−2αt)/2α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The Koopman operators Kt are self-adjoint in L2 µ(R), their eigenvalues and corresponding eigenfunctions are given by qj = e−αjt and ψj(x) = 1 � 2jαjj!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Hj( √ 2αx), j ∈ N0, where Hj are the physicist’s Hermite polynomials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We consider the Gaussian radial basis function (RBF) kernel with bandwidth σ > 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', k(x, y) = exp � −(x − y)2 σ2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Let us quickly verify that this choice of the kernel satisfies the compatibility assumptions (A1)–(A3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Indeed, (A1) is trivial as k(x, x) = 1 and (A3) follows easily from the continuity of the functions in H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' To see that H is dense in L2 µ(R) (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', (A2)), let ψ ∈ L2 µ(R) be such that ⟨ψ, Φ(y)⟩µ = 0 for all y ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The latter means that φ∗ϕσ = 0, where φ(x) = ψ(x)e−αx2 and ϕσ(x) = e−x2/σ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We apply the Fourier transform and obtain �φ · � ϕσ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Noting that the Fourier transform of a Gaussian is again a Gaussian, we get �φ = 0 and thus ψ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The Mercer eigenvalues and features with respect to the invariant measure µ of the OU process, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', the eigenvalues and eigenfunctions of the integral operator E∗E in L2 µ(R), are also available in analytical form [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' They are given by λi = � α C1 � 1 σ2C1 �i and ϕi(x) = γie−ζ2x2Hi �√αηx � , i ∈ N0, using the following constants: η = � 1 + 4 ασ2 �1/4 , γi = � η 2iΓ(i + 1) �1/2 , ζ2 = α 2 (η2 − 1), C1 = α + ζ2 + σ−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' With these results, we can compute the variance of the empirical estimator for Ct H as described in The- orem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The eigenvalues qj were already given above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The coefficients dj,t can be calculated using Mercer’s theorem as dj,t = � � k(x, x′)k(y, y′)ψj(x)ψj(x′) dµ0,t(x, y) dµ0,t(x′, y′) ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR 19 = � k,ℓ λkλℓ �� ϕk(x)ϕℓ(y)ψj(x) dµ0,t(x, y) �2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The series needs to be truncated at a finite number of terms and the integrals can be calculated by numer- ical integration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' As d0,t = ⟨k, kt⟩L2 µ⊗µ = ∥Ct H∥2 HS (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='8)), and hence ∥Ct H∥2 HS = � k,ℓ λkλℓ �� ϕk(x)ϕℓ(y) dµ0,t(x, y) �2 , (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1) the Hilbert-Schmidt norm of the cross-covariance operator Ct H can be computed similarly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Since, for the Gaussian RBF kernel, we have ϕ(x) = k(x, x) = 1 for all x, we therefore find E0(t) = � Ktϕ, ϕ � µ − ∥Ct H∥2 HS = 1 − ∥Ct H∥2 HS, completing the list of terms required by Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In addition, we notice that upon replacing ei- ther one or two of the integrals in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1) by finite-data averages, we can also calculate ∥ ˆCm,t H ∥2 HS and ⟨Ct H, ˆCm,t H ⟩HS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Therefore, the estimation error for finite data {(xk, yk)}m k=1 can be obtained by simply expanding the inner product ∥Ct H − ˆCm,t H ∥2 HS = ∥Ct H∥2 HS + ∥ ˆCm,t H ∥2 HS − 2⟨ ˆCm,t H , Ct H⟩HS, allowing us to precisely compare the estimation error to the error bounds obtained in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Besides the estimation error for Ct H, we are also interested in the prediction error, which is bounded according to Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We will compare these bounds to the actual error ∥(Kt N − ˆKm,t N )φ∥L2µ(X), for a specific observable φ ∈ H and a fixed number of N Mercer features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' For the OU process, it is again beneficial to consider Gaussian observables φ: φ(x) = 1 � 2πσ2 0 exp � −(x − m0)2 2σ2 0 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Application of the Koopman operator leads to yet another, unnormalized Gaussian observable, which is given by Ktφ(x) = 1 � 2πσ2 t exp � −(m0 − e−αtx)2 2σ2 t � , σ2 t = σ2 0 + v2 t .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The inner products of Ktφ with the Mercer eigenfunctions ϕi can be evaluated by numerical integration, providing full access to the truncated observable Kt Nφ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' On the other hand, the empirical approximation ˆKm,t N φ can be computed directly based on the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We note that ˆKm,t N φ = N � j=1 � ˆCm,t H φ, ˆej � ˆej = 1 m m � k=1 φ(yk) N � j=1 ⟨Φ(xk), ˆej⟩ ˆej = 1 m m � k=1 φ(yk) N � j=1 ˆej(xk)ˆej.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The functions ˆej can be obtained from the eigenvalue decomposition of the standard kernel Gramian matrix 1 mKX := 1 m [k(xk, xl)]m k,l=1 , as the latter is the matrix representation of the empirical covariance operator ˆCm H on the subspace span{Φ(xk)}m k=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' If 1 mKX = V ΛV ⊤ is the spectral decomposition of the Gramian, then ˆej = 1 m1/2ˆλj m � l=1 VljΦ(xl) 20 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PHILIPP, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' SCHALLER, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' WORTHMANN, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PEITZ, AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' N ¨USKE are the correctly normalized eigenfunctions according to Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Plugging this into the above, we find ˆKm,t N φ(x) = 1 m m � k=1 φ(yk) N � j=1 1 m1/2ˆλj m � l=1 Vljk(xl, xk) 1 m1/2ˆλj m � r=1 Vrjk(xr, x) = 1 mφ(Y )⊤ 1 mKX � VNΛ−2 N V ⊤ N � KX,x = 1 mφ(Y )⊤VNΛ−1 N V ⊤ N KX,x, where φ(Y ) = [φ(yk)]m k=1, KX,x = [k(xk, x)]m k=1, VN = V [IN 0m−N]⊤, ΛN = diag(�λj)N j=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Numerical Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' For the actual numerical experiments, we set α = 1, choose the elementary integration time step as ∆t = 10−2, and set the lag time to t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We compute the exact variance E[∥Ct H− ˆCm,t H ∥2 HS] by the expression given in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1, and also the coarser estimate for the variance given in Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We test three different kernel bandwidths, σ ∈ {0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='5}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' All Mercer series are truncated after the first 10 terms for σ ∈ {0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='5}, and 20 terms for σ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='05, while Koopman eigenfunction expansions are truncated after 15 terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In the first set of experiments, we use Chebyshev’s inequality to compute the maximal estimation error ∥Ct H − ˆCm,t H ∥HS that can be guaranteed with confidence 1 − δ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='9, for a range of data sizes m between m = 20 and m = 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' As a comparison, we generate 200 independent simulations of length m + t ∆t , corresponding to the sliding-window estimator with m data points, for each data size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We then compute the resulting estimation error using the expressions given in the previous section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We extract the 1 − δ-percentile of the estimation error for all trajectories, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', the maximal error that is not exceeded by 100 ∗ (1 − δ) percent of the trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In addition, we also use Chebyshev’s inequality with the i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' variance 1 mE0(t) to predict the estimation error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The comparison of these results for all data sizes m and the different kernel bandwidths is shown in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We observe that the bound from Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1 is quite accurate, over-estimating the actual error by about a factor three, and captures the detailed qualitative dependence of the estimation error on m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The coarser bound from Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='3, however, appears to discard too much information, it over-estimates the error by one to two orders of magnitude, and also does not capture the initial slope for small m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Finally, we note that for the larger kernel bandwidths, the i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' variance is indeed too small, leading to an under-estimation of the error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' This observation confirms that it is indeed necessary to take the effect of the correlation between data points into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In a second set of experiments, we test the performance of our theoretical bounds concerning the prediction of expectations for individual observables, obtained in Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' For the same three Gaussian RBF kernels as in the first set of experiments, we consider the observable φ = ϕ0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', the first Mercer feature, and choose N = 10 in the Mercer series expansion Kt Nφ and its empirical approximation ˆKm,t N φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Note that φ is a different observable depending on the bandwidth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Again, we set 1 − δ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='9, and use the bound from Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1 to bound the L2 µ-error between Kt Nφ and ˆKm,t N φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' As a comparison, we compute the actual L2 µ-error by numerical integration, using the fact that we can evaluate Kt Nφ and ˆKm,t N φ based on the discussion above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We repeat this procedure 15 times and provide average errors and standard deviations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The results for all three kernels are shown in Figure 4, and we find that our theoretical bounds are much too pessimistic in all cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' This finding highlights our previous observation that bounding the prediction error outside the RKHS still requires more in-depth research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR 21 102 103 104 m 10 2 10 1 100 101 (m) Error for Ct , t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='05, = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='050 T 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1 C 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='3 i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Data 102 103 104 m 10 2 10 1 100 101 (m) Error for Ct , t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='05, = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='100 T 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1 C 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='3 i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Data 102 103 104 m 10 2 10 1 100 101 (m) Error for Ct , t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='05, = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='500 T 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1 C 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='3 i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Data FIGURE 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Probabilistic error estimates for Ct H associated to the OU process, at lag time t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='05, and the Gaussian RBF kernel with different bandwidths σ ∈ {0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='05} (corresponding to left, center and right panels).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The blue and green curves show the es- timated error using the fine and coarse bounds from Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1 and Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='3, re- spectively, while the purple curves represent the bound obtained from the i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='-variance 1 mE0(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The red curve shows the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='9-percentile of the estimation error based on 200 independent simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 102 103 m 10 1 101 103 105 107 Prediction Error t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='05, = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='050 Prediction N = 10 Data Bound N = 10 102 103 m 10 1 101 103 105 107 Prediction Error t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='05, = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='100 Prediction N = 10 Data Bound N = 10 102 103 m 10 1 101 103 105 107 Prediction Error t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='05, = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='500 Prediction N = 10 Data Bound N = 10 FIGURE 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Comparison of the theoretical bound on the prediction error ∥Kt Nφ − ˆKm,t N φ∥µ, if φ is chosen as the first Mercer feature ϕ0, using N = 10 in the Mercer series representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The predicted error is shown in blue, error bars for the actual error obtained from 15 independent data sets are shown in red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Different panels correspond to the same kernel bandwidths as in Figure 3 above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' CONCLUSIONS We have analyzed the finite-data estimation error for data-driven approximations of the Koopman operator on reproducing kernel Hilbert spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' More specifically, we have provided an exact expression for the variance of empirical estimators for the cross-covariance operator, if a sliding-window estimator is applied to a long ergodic trajectory of the dynamical system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' This setting is relevant for many complex systems, such as molecular dynamics simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Our results present a significant improvement over the state of the art, since they concern a setting where the notorious problem of dictionary selection can be circumvented, and therefore no longer depend on the dictionary size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We have also extended the concept of asymptotic variance to an infinite-dimensional approximation space for the Koopman operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Our numerical study on the Ornstein Uhlenbeck process has shown that, even using a simple mass concentration inequality, accurate bounds on the estimation error can be obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In our second result, we have extended our estimates to a uniform bound on the prediction error for observables in the RKHS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Thereby, we have circumvented dealing with an unbounded inverse of the covariance operator by applying a finite-dimensional truncation of the associated Mercer series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In case of Koopman-invariance of the RKHS, however, we were able to find a bound on the truncation error which then yields estimates for the full approximation error.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Zhang and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Zuazua, A quantitative analysis of Koopman operator methods for system identification and predictions, Comptes Rendus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' M´ecanique, Online first (2023), 1–31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 24 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PHILIPP, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' SCHALLER, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' WORTHMANN, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PEITZ, AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' N ¨USKE APPENDIX A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PROOFS Proof of Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Let ψ ∈ H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Then (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4) follows from � |ψ(x)|2 dµ(x) = � |⟨ψ, Φ(x)⟩|2 dµ(x) ≤ ∥ψ∥2 � ϕ(x) dµ(x) = ∥ψ∥2∥ϕ∥1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Assume that (A2) holds and that ψ ∈ L2 µ(X) is such that ⟨ψ, Φ(x)⟩µ = 0 for all x ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Then 0 = � ⟨ψ, Φ(x)⟩µψ(x) dµ(x) = � � k(x, y)ψ(x)ψ(y) dµ(x) dµ(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Hence, ψ = 0 by (A2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Conversely, assume that H is dense in L2 µ(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Let ψ ∈ L2 µ(X) such that � � k(x, y)ψ(x)ψ(y) dµ(x) dµ(y) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Since the integrand equals ⟨ψ(x)Φ(x), ψ(y)Φ(y)⟩ and the integral � ψ(x)Φ(x) dµ(x) exists by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='5), we obtain � ψ(x)Φ(x) dµ(x) = 0H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' This implies that ⟨ψ, Φ(y)⟩µ = � ψ(x)k(x, y) dµ(x) = 0 for each y ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Hence, ⟨ψ, φ⟩µ = 0 for each φ ∈ H := span{Φ(x) : x ∈ X}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Now, let φ ∈ H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Then there exists a sequence (φn) ⊂ H such that ∥φn − φ∥ → 0 as n → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Therefore, |⟨ψ, φ⟩µ| = |⟨ψ, φ − φn⟩µ| ≤ ∥ψ∥µ∥φ − φn∥µ ≤ ∥ψ∥µ � ∥ϕ∥1∥φ − φn∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Hence, ⟨ψ, φ⟩µ = 0, and the density of H in L2 µ(X) implies ψ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' □ Proof of Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (a) For ψ ∈ L2 µ(X) we have ∥Eψ∥2 = � � ψ(x)ψ(y)⟨Φ(x), Φ(y)⟩ dµ(x) dµ(y) = � � k(x, y)ψ(x)ψ(y) dµ(x) dµ(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Hence, the injectivity of E follows from (A2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' If (ei) is an orthonormal basis of H, then � i ∥E∗ei∥2 µ = � i ∥ei∥2 µ = � i � |ei(x)|2 dµ(x) = � i � |⟨Φ(x), ei⟩|2 dµ(x) = � ∥Φ(x)∥2 dµ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The claim is now a consequence of ∥Φ(x)∥2 = ϕ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (b) By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1, H is dense in L2 µ(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Moreover, E∗ is compact by (a) and Schauder’s theorem [47, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (c) This follows from (a) and ker CH = ker EE∗ = ker E∗ = {0} by (A3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' □ Proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='4, the operator E∗E ∈ B(L2 µ(X)) is a positive self-adjoint trace- class operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Hence, by the well known spectral theory of compact operators (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', [12]) there exists an orthonormal basis (ej)∞ j=1 of L2 µ(X) consisting of eigenfunctions of E∗E corresponding to a summable sequence (λj)∞ j=1 of strictly positive eigenvalues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Since E∗ψ = ψ for ψ ∈ H, we have Eej = λjej and thus ej ∈ H for all j and CHej = EE∗ej = Eej = λjej.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Moreover, ⟨fi, fj⟩ = � λj/λi⟨Eei, ej⟩ = � λj/λi⟨ei, ej⟩µ = δij by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='6) so that the fj indeed form an orthonormal system in H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The completeness of (fj) in H follows from the injectivity of E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Finally, �∞ j=1 λj = Tr CH = ∥ϕ∥1 and k(x, y) = ⟨Φ(x), Φ(y)⟩ = � j ⟨Φ(x), fj⟩⟨fj, Φ(y)⟩ = � j fj(x)fj(y), which completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' □ Proof of Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Let ψ ∈ B(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' For p = ∞ we have |(Ktψ)(x)| = |Ex[ψ(Xt)]| ≤ Ex[|ψ(Xt)|] ≤ ∥ψ∥∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' If p < ∞, by Jensen’s inequality, for every convex φ : R → R we have φ ◦ Ktψ ≤ Kt(φ ◦ ψ) and thus |Ktψ|p ≤ Kt|ψ|p, which, by invariance of µ, leads to ∥Ktψ∥p p = � |Ktψ|p dµ ≤ � Kt|ψ|p dµ = � |ψ|p dµ = ∥ψ∥p p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR 25 The claim now follows by density of B(X) in Lp µ(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' □ Proof of Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Let ψ ∈ Cb(X) and fix x ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Denote the stochastic solution process of the SDE (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1) with initial value x by Xx t .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Since Xx t (ω) is continuous in t for P-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' ω ∈ Ω (see [39, Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1]), ψ(Xx t (ω)) → ψ(Xx 0 (ω)) = ψ(x) as t → 0 for P-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' ω ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Hence, by dominated convergence, Ktψ(x) = E[ψ(Xx t )] = � ψ(Xx t (ω)) dP(ω) → ψ(x) as t → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' It now follows from Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='7 and, again, dominated convergence that ∥Ktψ −ψ∥p → 0 as t → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' If ψ ∈ Lp µ(X) and ε > 0, there exists η ∈ Cb(X) such that ∥ψ − η∥p < ε/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Choose δ > 0 such that ∥Ktη − η∥p < ε/3 for t < δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Then ∥Ktψ − ψ∥p ≤ ∥Kt(ψ − η)∥p + ∥Ktη − η∥p + ∥η − ψ∥p < ε for t < δ, which proves the claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' □ APPENDIX B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' RIESZ BASES Recall that a Riesz basis [7] of a Hilbert space H is a sequence (ψj) ⊂ H satisfying span{ψj} = H and for which there exist A, B > 0 such that for all c ∈ ℓ2, A∥c∥2 ≤ ��� � j cjψj ��� H ≤ B∥c∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The constant A (B, resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=') is called a lower (upper, resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=') Riesz bound of the basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Also recall that to every Riesz basis (ψj) there exists a dual Riesz basis ( �ψj) such that ⟨ψj, �ψk⟩H = δjk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' If (ψj) has the bounds A and B, then ( �ψj) has bounds 1/B and 1/A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Every element f of H admits a representation f = � j⟨f, �ψj⟩Hψj = � j⟨f, ψj⟩H �ψj and A2∥f∥2 H ≤ � j |⟨f, ψj⟩|2 ≤ B2∥f∥2 H and B−2∥f∥2 H ≤ � j |⟨f, �ψj⟩|2 ≤ A−2∥f∥2 H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' It can furthermore be easily seen that a sequence (ψj) ⊂ H is a Riesz basis of H if and only if there exists a boundedly invertible linear operator S ∈ L(H) and an orthonormal basis (ej) of H such that ψj = Sej for all j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Then �ψj = (S−1)∗ej for all j, B = ∥S∥, and A = ∥S−1∥−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' APPENDIX C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' SOME FACTS FROM SPECTRAL THEORY In this section, let H be a Hilbert space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' If P is an orthogonal projection in H, we set P ⊥ = I − P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' For v ∈ H, ∥v∥ = 1, denote by Pv the rank-one orthogonal projection onto span{v}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We say that a linear operator on H is non-negative if it is self-adjoint and its spectrum is contained in [0, ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' For a non-negative compact operator T on H we denote by λ1(T) ≥ λ2(T) ≥ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' the eigenvalues of T in descending order (counting multiplicities).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' We set λj(T) = 0 if j > rank(T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Moreover, if T has only simple eigenvalues6, we let Pj(T) denote the orthogonal projection onto the eigenspace ker(T − λj(T)) and Qn(T) = �n j=1 Pj(T) the spectral projection corresponding to the n largest eigenvalues of T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Theorem C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1 ([12, Cor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' If T and �T are two non-negative compact operators on H, then for all j ∈ N, |λj(T) − λj( �T)| ≤ ∥T − �T∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' 6i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', dim ker(T − λ) = 1 for each eigenvalue λ of T 26 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PHILIPP, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' SCHALLER, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' WORTHMANN, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PEITZ, AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' N ¨USKE Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' For v, w ∈ H with ∥v∥ = ∥w∥ = 1 we have ∥Pv − Pw∥ = ∥P ⊥ w Pv∥ = � 1 − |⟨v, w⟩|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1) Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' First of all, the second equation in (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1) is clear, since ∥P ⊥ w Pvf∥2 = ∥⟨f, v⟩P ⊥ w v∥2 = |⟨f, v⟩|2(1 − ∥Pwv∥2) = |⟨f, v⟩|2(1 − |⟨v, w⟩|2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Second, if Pv,w denotes the orthogonal projection onto Hv,w := span{v, w}, we have ∥Pv − Pw∥ = ∥(Pv − Pw)Pv,w∥ = ∥(Pv − Pw)|Hv,w∥ = sup x∈Hv,w, ∥x∥=1 ∥(Pv − Pw)x∥, which is a two-dimensional problem in Hv,w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Now, if x ∈ Hv,w, ∥x∥ = 1, we write x = av + bw and obtain a2 + 2abγ + b2 = 1, where γ = ⟨v, w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Moreover, ⟨x, v⟩ = a + bγ, ⟨x, w⟩ = aγ + b and so ∥(Pv − Pw)x∥2 = ∥⟨x, v⟩v − ⟨x, w⟩w∥2 = ∥(a + bγ)v − (aγ + b)w∥2 = (a + bγ)2 − 2(a + bγ)(aγ + b)γ + (aγ + b)2 = a2 + 2abγ + b2γ2 − 2γ(a2γ + abγ2 + ab + b2γ) + a2γ2 + 2abγ + b2 = (1 − γ2)a2 + 2abγ − 2abγ3 + b2(1 − γ2) = (1 − γ2)(a2 + b2 + 2abγ) = 1 − |⟨v, w⟩|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Hence, the objective function is constant on {x ∈ Hv,w : ∥x∥ = 1} and (C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1) is proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' □ The next theorem is a variant of the Davis-Kahan sin(Θ) theorem (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' [57]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Theorem C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Let T and �T be non-negative Hilbert-Schmidt operators on H, let n ∈ N, assume that the largest n + 1 eigenvalues of T are simple, and set δ = min j=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=',n λj(T) − λj+1(T) 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' If ∥T − �T∥HS < δ, then for j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' , n we have ∥Pj(T) − Pj( �T)∥ ≤ ∥T − �T∥ δ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' For j ∈ N put λj = λj(T), Pj = Pj(T), �λj = λj( �T), and �Pj = Pj( �T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' By Theorem C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1, we have |λj − �λj| ≤ ∥T − �T∥HS < δ for all j, hence �λj is contained in the interval Ij = (λj − δ, λj + δ) for j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' , n + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' By assumption, sup Ij+1 ≤ inf Ij for j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' , n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' In particular, the intervals I1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' , In+1 are pairwise disjoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Now, let j ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' , n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Then for k ∈ N \\ {j} we have |�λk − λj| > δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Therefore, we have dist(λj, σ( �T)\\{�λj}) ≥ δ and thus, for f ∈ �P ⊥ j H, ∥( �T − λj)f∥ ≥ dist � λj, σ( �T| �P ⊥ j H) � ∥f∥ = dist(λj, σ( �T)\\{�λj})∥f∥ ≥ δ∥f∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' As TPj = λjPj and �P ⊥ j �T = �T �P ⊥ j , we obtain ∥T − �T∥ ≥ ∥ �P ⊥ j ( �T − T)Pj∥ = ∥ �P ⊥ j �TPj − �P ⊥ j TPj∥ = ∥( �T − λj) �P ⊥ j Pj∥ ≥ δ∥ �P ⊥ j Pj∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' The claim now follows from Lemma C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' □ ERROR BOUNDS FOR KERNEL-BASED APPROXIMATIONS OF THE KOOPMAN OPERATOR 27 APPENDIX D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' ERGODICITY AND THE GENERATOR In this section, we prove the following proposition on the spectral properties of the generator L under the ergodicity assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Proposition D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Assume that the invariant measure µ is ergodic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Then ker L = span{1} and ker(L − iωI) = {0} for ω ∈ R\\{0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' First of all, it is worth mentioning that Lψ = 0 implies Ktψ = ψ for all t ≥ 0 and that Lψ = iωψ, ω ∈ R \\ {0}, implies K2π/ωψ = ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Therefore, it suffices to show that Ktψ = ψ for some t > 0 and ψ ∈ L2 µ(X) is only possible for constant ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' For this, we consider the Markov process (Xnt)∞ n=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' For convenience, we assume w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' that t = 1 holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' By invariance of µ, the process (Xn)∞ n=0 is stationary, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=', (Xn)∞ n=0 and (Xn+1)∞ n=0 are equally distributed as X N0-valued random variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' According to [15, Lemma 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='2] there exist X-valued random variables X−k, k ∈ N, such that X := (Xn)n∈Z is also stationary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' By Pµ denote the law of the X Z-valued random variable X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' On S := X Z define the left shift T : S → S by T(xn)n∈Z := (xn+1)n∈Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Stationarity of X means that also TX ∼ Pµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' A set A ∈ BZ X := � k∈Z BX is called shift-invariant if T −1A = A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' It is easy to see that the set of shift-invariant sets forms a sub-σ-algebra I of BZ X .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Now, by [13, Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='11] and the ergodicity of µ we have Pµ(A) ∈ {0, 1} for any A ∈ I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Now, Birkhoff’s Ergodic Theorem [15, Theorem 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='6] states that lim n→∞ 1 n n−1 � k=0 f(T kX) = E � f(X)|X−1I � (D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='1) almost surely and in L1(Ω) for any f ∈ L1(S).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Given ψ ∈ L1 µ(X), let us apply this theorem to the function f = ψ ◦ π0, where the projection π0 : S → X is defined by π0(xn)n∈Z = x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' First of all, � |f| dPµ = � |ψ(x0)| dPµ((xn)n∈Z) = � |ψ(x)| dµ(x) < ∞ as Pµ ◦ π−1 0 = µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Hence, we have f ∈ L1(S).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Furthermore, we compute f(T kX) = ψ(π0(T kX)) = ψ(Xk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' For A ∈ I we have P(X−1A) = Pµ(A) ∈ {0, 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Thus, we obtain lim n→∞ 1 n n−1 � k=0 ψ(Xk) = E[f(X)] = � f dPµ = � ψ ◦ π0 dPµ = � ψ dµ almost surely and in L1(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Therefore, if ψ ∈ L2 µ(X) such that Ktψ = ψ, then Kktψ = ψ for all k ∈ N0, hence for µ-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' x ∈ X we have ψ(x) = 1 n n−1 � k=0 ψ(x) = 1 n n−1 � k=0 Kktψ(x) = 1 n n−1 � k=0 E[ψ(Xkt)|X0 = x] = E � 1 n n−1 � k=0 ψ(Xkt) ����� X0 = x � n→∞ −→ � ψ dµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Thus, ψ must indeed be (µ-essentially) constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' □ 28 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PHILIPP, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' SCHALLER, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' WORTHMANN, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' PEITZ, AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' N ¨USKE AUTHOR AFFILIATIONS F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Philipp TECHNISCHE UNIVERSIT ¨AT ILMENAU, INSTITUTE FOR MATHEMATICS, WEIMARER STRASSE 25, D-98693 ILMENAU, GERMANY Email address: friedrich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='philipp@tu-ilmenau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='de M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Schaller TECHNISCHE UNIVERSIT ¨AT ILMENAU, INSTITUTE FOR MATHEMATICS, WEIMARER STRASSE 25, D- 98693 ILMENAU, GERMANY Email address: manuel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='schaller@tu-ilmenau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='de K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Worthmann TECHNISCHE UNIVERSIT ¨AT ILMENAU, INSTITUTE FOR MATHEMATICS, WEIMARER STRASSE 25, D-98693 ILMENAU, GERMANY Email address: karl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='worthmann@tu-ilmenau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='de S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' Peitz PADERBORN UNIVERSITY, DEPARTMENT OF COMPUTER SCIENCE, DATA SCIENCE FOR ENGINEERING, GER- MANY Email address: sebastian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='peitz@upb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='de F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content=' N¨uske MAX PLANCK INSTITUTE FOR DYNAMICS OF COMPLEX TECHNICAL SYSTEMS, MAGDEBURG, GERMANY Email address: nueske@mpi-magdeburg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='mpg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dFAT4oBgHgl3EQfpB03/content/2301.08637v1.pdf'} +page_content='de' metadata={'source': 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100644 index 0000000000000000000000000000000000000000..55ed07c71bc8de9857291f1bcb82c40e86882423 --- /dev/null +++ b/9NAyT4oBgHgl3EQfQ_Zv/content/tmp_files/2301.00057v1.pdf.txt @@ -0,0 +1,975 @@ +A Mapping of Assurance Techniques for Learning Enabled +Autonomous Systems to the Systems Engineering Lifecycle +Christian Ellis1, Maggie Wigness2, and Lance Fiondella1 +Abstract—Learning enabled autonomous systems provide in- +creased capabilities compared to traditional systems. However, +the complexity of and probabilistic nature in the underlying +methods enabling such capabilities present challenges for current +systems engineering processes for assurance, and test, evalua- +tion, verification, and validation (TEVV). This paper provides +a preliminary attempt to map recently developed technical +approaches in the assurance and TEVV of learning enabled +autonomous systems (LEAS) literature to a traditional systems +engineering v-model. This mapping categorizes such techniques +into three main approaches: development, acquisition, and +sustainment. We review the latest techniques to develop safe, +reliable, and resilient learning enabled autonomous systems, +without recommending radical and impractical changes to exist- +ing systems engineering processes. By performing this mapping, +we seek to assist acquisition professionals by (i) informing +comprehensive test and evaluation planning, and (ii) objectively +communicating risk to leaders. +I. INTRODUCTION +It is widely recognized [1] that the complexity and resulting +capabilities of autonomous systems created using machine +learning methods, which we refer to as learning enabled +autonomous systems (LEAS), pose new challenges to sys- +tems engineering compared to their traditional counterparts. +Moreover, the inability to translate qualitative assessments +to quantitative metrics which measure system performance +hinder adoption. Such limitations make it difficult to produce +reliable systems, and even harder to assure [2]. Without under- +standing the capabilities and limitations of existing assurance +techniques, defining safety and performance requirements that +are both clear and testable remains out of reach. +Mature test, evaluation, verification, and validation (TEVV) +methods have been in use for decades to ensure the safety +analysis and acquisition of hardware systems [3], but fewer +TEVV methods for software are available, and even fewer +for software that improves itself through learning [4]. Initial +approaches to autonomous systems use control theory to +physically model the world and its underlying dynamics [5], +while LEAS infer and generalize statistical patterns, which +lead to the achievement of goals from a sample of pre- +collected training data points. However, due to the nature of +the environments where LEAS are fielded and the massive +size of their underlying state spaces, systems will likely +encounter states during operation they have never experienced +before, yet still being required to take action. +1 Christian Ellis is a PhD Student and Lance Fiondella is an Asso- +ciate Professor in the Department of Electrical and Computer Engineer- +ing at the University of Massachusetts Dartmouth, USA. cellis3, +lfiondella@umassd.edu +2 Maggie Wigness is a researcher at the United States Army Research +Laboratory (ARL). +Fig. 1: Recent work in assurance for LEAS is mapped to +relevant stages of the MITRE systems engineering lifecy- +cle [6], into 3 distinct categories—development, acquisition, +and sustainment. +Early work from the autonomy community identified issues +that arise from incorporating learning into autonomous sys- +tems [4] including state space explosion, operation in unpre- +dictable environments, emergent behavior, and effective hu- +man machine interaction. Assurance methods such as formal +methods [7], or reliability analysis [8] seek to provide either +certain or probabilistic guarantees on system performance. +Formal methods support verification by exhaustively search +and identifying dangerous regions of the state space and +provide techniques to avoid such states. Reliability analysis +supports test and evaluation by quantifying the probability +a system will be operational at a point in time from oper- +ational data collected throughout the systems lifecycle. The +aforementioned state space explosion makes formal methods +challenging to scale, and reliability analysis difficult to ac- +curately predict estimates. A different field of research seeks +to develop methods which explicitly consider safety during +the learning and operational stages [9]. Lastly, investments +such as the DARPA Assured Autonomy program1 seeks to +continually assure learning enabled cyber-physical systems +by constructing formal methods that assure correctness at +design time and perform runtime monitoring at operation +time. While this program has advanced the state of the +1https://www.darpa.mil/program/assured-autonomy +arXiv:2301.00057v1 [cs.SE] 30 Dec 2022 + +Transition +Concept +Operation& +Development +Maintenance +Requirements +Test& +Engineering +Evaluation +System +System +Architecture +Integration +SystemDesign +&Development +Development +Acquisition +Sustainmentart in formal methods [10] and runtime monitoring [11], a +systematic approach to identify outstanding gaps will remain +unclear unless the community makes explicit and coordinated +efforts to understand how such methods may be incorporated +into the broader systems engineering process. +Our work seeks to communicate recent technical devel- +opments in LEAS assurance with a focus on autonomous +vehicles, accompanying recent literature reviews [12] [13], by +mapping such developments to distinct steps of a well known +systems engineering model chosen due to its prevalence, +namely the v-model. Fig. 1 shows the mapping and identifies +three top level lifecycle phases: development, acquisition, and +sustainment. For each top level lifecycle phase, a section of +the paper has been dedicated to outlining recent technical de- +velopments and how they contribute to the goals of the phase. +This representation helps identify where the latest methods for +TEVV fit in the broader systems engineering process while +also enabling systematic consideration of potential sources of +defects, faults, and attacks. Note that we use the v-model only +to assist the classification of where TEVV methods fit. This is +not a recommendation to use a certain software development +lifecycle over another. +The remainder of the paper is organized as follows. Sec- +tion II outlines the specific scientific fields supporting LEAS. +Section III provides an overview of the mapping between tra- +ditional systems engineering and the state of the art in assur- +ance for LEAS. Section IV maps assurance techniques, which +assist development to design and development, and system +integration in the systems engineering lifecycle. Section V +maps assurance techniques, which assist acquisition to test +and evaluation. Section VI maps assurance techniques, which +assist sustainment to transition, operation, & maintenance. +Lastly, section VII concludes with areas this mapping can +impact. +II. METHODS SUPPORTING THE DEVELOPMENT OF +LEARNING ENABLED AUTONOMOUS SYSTEMS +This section seeks to define the fields of engineering +with significant impact on development of LEAS with a +focus on vehicles and their corresponding challenges for +assurance. In later sections (Sec. IV—VI), solutions to such +challenges are identified and categorized according to where +they reside within the systems engineering lifecycle such as +development, acquisition, or sustainment. Rather than seek to +obtain an exhaustive list of engineering fields, of which there +are many, we first provide an overview of learning enabled +autonomous vehicles and then review two key contributing +fields, including machine learning and reinforcement learning. +While there are other non-learning methods such as optimal +control theory [14], which have made large and long lasting +impacts on the development on LEAS, they are not considered +in this paper. +LEAS normally follow one of two design approaches, end- +to-end (E2E) or modular. In the E2E approach [15], a system’s +sensors act as the input to a learning algorithm. For example, a +deep neural network outputs the corresponding actions such as +steering wheel angle (lateral control) [16], torque (longitudi- +nal control) [17], or both [18]. In the modular approach [19], a +system’s sensors act as input to a perception sub-system which +is responsible for building a map and model of the world. +Such subsystems commonly include perception components +that use ML techniques such as semantic segmentation [20] or +object detection [21]. This model is then used by a planning +subsystem, which outputs a kinematically feasible trajectory +to which controls are applied [22], [23]. +While it may be possible to break down layers of E2E +neural networks into sub-components using interpretability +techniques [24], this paper specifically focuses on the modular +approach for two reasons: i) it is clear to a human what the +responsibility of each component is (increased interpretabil- +ity), and ii) the modular approach is currently more common +in autonomous vehicle designs in industry and government +implementations. While some of the underlying problems for +assurance are the same for both approaches, including those +previously mentioned [4], we explicitly consider software +assurance methods which are applicable to either perception +or planning components, or the joint-combination thereof. +A. Machine Learning +In machine learning (ML), tasks are completed by training +a model from data to perform function approximation using +a combination of mathematical optimization and statistical +techniques [25]. This results in computer programs which are +able to complete a task without constructing a set of exact +solution instructions ahead of time. There are three main +forms of learning, including supervised, unsupervised, and +reinforcement learning. In supervised learning, each training +sample from the dataset is associated with a set of features and +a corresponding label to train a model. For example, a neural +network can be trained on a dataset of images containing +handwritten digits, where each sample’s corresponding label +is 0 through 9. In unsupervised learning, each training sample +is only represented by a set of extracted features, which are +subsequently used to identify the underlying feature patterns +throughout the dataset. For example, clustering techniques +divide a dataset into k distinct groups, where all data points +in a group are similar with respect to some distance measure. +Finally, in reinforcement learning, an autonomous agent learns +the optimal way to act over time via interaction with the +environment, such as an autonomous robot learning how to +move its actuators and joints to navigate in an environment +without hitting obstacles. +Although the ability to perform complex tasks solely from +data has made ML highly successful, it is for this same +reason that ML models are difficult to assure. Among other +factors, a model’s performance depends on the data experi- +enced during training and the environment in which it was +trained [26]. Naive metrics such as the model’s accuracy +on a test set may be perceived as overconfident because +they assume most future data will be like the experienced +data. This is especially true in complex systems such as +government systems tasked with operating in contested op- + +erational environments, demonstrating the need for metrics +to assess model performance in new environments. Another +assurance challenge includes determining relevant test cases +given the state space explosion and curse of dimensionality +problems, of which the Range Adversarial Planning Tool has +been proposed [27]. Furthermore, such models are brittle to +perturbations in input, which may come from sources such as, +sensor noise or adversarial attacks [28]. Lastly, it is inevitable +that such models will fail from time to time, and explanations +of why they fail (interpretability techniques) and how to fail +gracefully (resilience techniques) are also valuable. Although +there are a variety of new assurance techniques [12] [13] that +seek to alleviate such issues, a framework does not exist to +assess their thoroughness and relative effectiveness. +B. Reinforcement Learning +Reinforcement learning (RL) is given a dedicated subsec- +tion because it is an enabler of intelligent-like capabilities +required for complex autonomous systems. Reinforcement +learning provides a framework for autonomous agents to make +decisions under uncertainty and learn from environmental +interaction [29]. Specified by a reward function, an agent +seeks to obtain an optimal policy which maximizes its reward +by taking actions over a time horizon in an environment. A +policy is a function that maps the current state to the single +action that maximizes the expected future reward. Formally, +this structure is part of a Markov Decision Process (MDP) +consisting of a state space S, an action space A, a state +transition distribution over next states T(st+1|st, a), and a +reward function R(s, a, s′) whose solution is the optimal +policy which maximizes the expected future reward π∗. Exact +RL seeks to converge to the optimal policy using tabular +techniques, requiring an agent to visit each state many times. +Conversely, approximate techniques such as deep RL [30] +allow an agent to operate in large (possibly infinite) state +and action spaces without explicitly visiting each state by +obtaining a parameterized policy. +Although RL has demonstrated its ability to mimic intel- +ligent capabilities such as beating players at Go [31], and +autonomous driving [32], there are limitations. Designing +reward functions explicitly by hand is a challenging task +that can lead to a misalignment between the reward function +specified and the true reward function the algorithm designer +intended [33]. Such value misalignment leads to unintended +consequences such as reward hacking [34], where the robot +maximizes reward in a way that the algorithm designer did +not intend while often failing to meet its goals. Furthermore, +many solutions sample inefficiently and are often brittle [35], +limiting their real world applicability. Lastly, RL can cause +a disconnect between how a programmer may interpret what +an agent has learned and the true learned concept [36]. For +example, a programmer may believe an agent has learned to +traverse to a goal grid cell, but because of the environment +setup, the agent may have actually simply learned to traverse +to a green grid cell. For systems incorporating RL, such limi- +tations and corresponding tests for each should be considered +explicitly in the assurance process. +III. OVERVIEW OF MAPPING +This paper provides a preliminary attempt to map recently +developed technical approaches in the assurance and TEVV +of learning enabled autonomous systems (LEAS) literature +to a traditional systems engineering v-model. The mapping +identifies three top level lifecycle phases: development, ac- +quisition, and sustainment. Proceeding according to the colors +in Fig. 1, the stages surrounded in the black box, including +system design & development, and system integration, assist +development and therefore are mapped to methods which +explicitly provide safety assurance during the learning process +(Sec. IV). The stage in the green box, test and evaluation, +assists the acquisition of systems and therefore is mapped to +TEVV analysis techniques which quantify the performance +of an already built system, or component (Sec. V). The stage +in the orange box, transition operation & maintenance, is +mapped to safety assurance techniques which aid sustainment +by monitoring or adapt performance of a fielded system +(Sec. VI). For each stage, applicable classes of techniques +are organized by respective subsections. +In addition to the stage of the system engineering lifecycle, +this mapping also seeks to categorize technical developments +according to their granularity. When evaluating different ap- +proaches to the same problem, the choice of performance +metrics depend on the scope of the unit under test—whole +system, learning enabled component, or a traditional com- +ponent. Interfaces at various lifecycle levels of granularity +promote systems thinking [37] about architecture. Namely, the +way a system’s components and subsystems relate, interact, +and work over time. By understanding the input paths that +contribute to a unit’s decisions, the outputs that may lead to +failures within the larger system become clearer. +Generally speaking, there are two main approaches to as- +sure LEAS—white-box techniques and black-box techniques. +White-box techniques require either a model of the system +under test, or direct access to the source code. In contrast, +black-box techniques only look at the inputs and outputs of +the system under test, and are unaware of the underlying +methods of how the system generates the outputs. White- +box techniques are better for component level assurance, +while black-box techniques are often better for system-wide +assurance. +The implementation of assurance techniques and their +accompanying metrics to quantify system performance and +safety (Sec. IV—Sec. VI) can all be used as supporting +evidence for a safety assurance case [38] to determine system +readiness level and maturity. Tools which automate trace- +ability and reproducibility throughout the system lifecycle +such as [39] can reduce the burden of collecting evidence. +The appropriate choice of assurance methods and associated +metrics is dependent on the system maturity. Initial project +milestones may focus on demonstrating anti-fragility, while +later milestones may focus on demonstrating the ability to + +accomplish a mission and accompanying capabilities. Fur- +thermore, quantitative metrics may only be applicable at +certain levels of system granularity. For example, an entire +system may be best evaluated by the outcomes of a pre- +determined mission and supporting data, while a learning +enabled component may be better evaluated by measures +specific to machine learning such as uncertainty quantifica- +tion, robustness to environmental shift, and the ability to fail +gracefully and recover from faults. Metrics which are able +to capture the performance of all approaches under test may +be preferred over metrics that measure the performance of a +certain class of algorithms. Lastly, if performance data can +be collected during the development process, one could also +perform a quantitative analysis of a system at any given time +using traditional reliability [8] and defect removal [40]. +IV. ASSURANCE ACTIVITIES TO SUPPORT SYSTEM +DEVELOPMENT +This section maps assurance methods which assist de- +velopment to system design and development, and system +integration in the systems engineering lifecycle. +A. Artificial Intelligence Safety +AI safety is a sub-field of AI which seeks to ensure that a +deployed AI systems (i) operates as the designer intended +and (ii) completes its task without harming humans. The +importance of AI safety is backed by impactful institutions +such as the Future of Life Institute2 and Machine Intelligence +Research Institute3. In the academic literature, AI safety +has been popularized by the agenda of Amodedi et al. [9], +who discuss five failure modes for AI; negative side effects, +reward hacking, scalable supervision, safe exploration, and +distributional shift. Moreover, in the context of RL, the +value alignment problem arises due to a gap in the specified +reward function and what the human actually intended [41]. +Specifically, Taylor et al. [42] discuss eight different ap- +proaches focusing on two areas of value alignment—reward +specification and techniques to avoid side effects. Burden et +al. [43] argue that the scope of AI safety problems residing +in a specific system can be characterized by three quantitative +factors; generality, capability, and control. For a literature +review of AI safety, the reader is directed to [44]. +While the works above seek to obtain safer agents by +altering the underlying methodologies, the focus is on agents +in artificial environments rather than physical robots, thereby +creating a gap between theoretical and applied research. +Moreover, most approaches assume that the system is fol- +lowing a RL paradigm, demonstrating the importance to +understand the underlying learning paradigm employed by a +project. Lastly, although AI safety approaches alone will not +be sufficient for LEAS assurance, if the methods are applied +during the learning process, such approaches are likely to +perform and test better than their non-safe counterparts, +leading to higher assurance measures. +2https://futureoflife.org/ +3https://intelligence.org/ +B. Learning from Human Feedback +Incorporating human interaction can positively impact the +performance of a LEAS because it is often easier to provide +feedback on desired behavior rather than explicitly defining it. +This is one solution to the value alignment problem mentioned +in Sec. IV-A. Such human interaction may include learning +from demonstration, intervention, or evaluation [45]. In learn- +ing from demonstration [46], the human provides a dataset +of examples mimicking how the system should operate. In +learning from intervention [47], the system operates fully +autonomously and the human takes over as required to correct +system behavior. In learning from human evaluation [48], +[49], the system completes various tasks fully autonomously, +and then a human ranks the tasks. This ranking may be +from best to worst, or answering the yes/no question, “Was +this the behavior you wanted to see the system perform?” +All of the methods mentioned fall into a sub-field known +as imitation learning [50]. Lastly, recent developments in +imitation learning attempt to incorporate safety as part of the +learning process using uncertainty quantification, creating a +new sub field known as safe imitation learning [51], [52]. +C. Uncertainty Estimation +System requirements often demand that a learning en- +abled autonomous system make a prediction, classification, +or decision at every time-step during operation. Since many +implementations contain perception systems that will likely +never be 100% accurate, the certainty or lack thereof, of a +prediction may assist in the final decision made—especially if +the outcome of such a prediction may lead to risky behavior. +The ability for a system to measure what it does and does +not know can be captured by quantifying uncertainty with +Bayesian analysis techniques [53]. There are two main types +of uncertainty, aleatoric and epistemic. Aleatoric uncertainty +measures the variance between samples in a population. +This type of uncertainty cannot be reduced with more data. +An example is the outcome of a fair coin flip. Epistemic +uncertainty measures the lack of knowledge of a population, +which is often captured in a system’s parameters. This type +of uncertainty can be alleviated by collecting more data. +An understanding of the different types of uncertainty helps +system designers understand if performance can be increased +by simply collecting more data. Additional details can be +found in the reviews on uncertainty quantification applied to +machine learning [54], neural networks [55], and computer +vision [56]. Such techniques aid at the learning enabled com- +ponent level, and can be used to quantify system confidence in +the current operational environment and thereby communicate +uncertainty (risk) to the system end users. +D. Cost-sensitive Learning +At the system level, the impact of a learning enabled +component on the whole system is measured in terms of +its ability to assist in the completion of a task. Additional +failure modes introduced by such components must be ex- +plicitly considered. Cost-sensitive learning [57] is applicable + +in classification problems where the cost associated with the +misclassification is not equal among classes. For example, +in the context of commercial autonomous vehicles, a false +positive resulting in the vehicle stopping when it did not need +to likely has lower cost than a false negative resulting in a +vehicle colliding with a pedestrian. +E. Formal Methods +Static analysis techniques such as formal methods are able +to provide guarantees on system performance without ever +operating the system [58]. Rather than attempting to discover +faults while the system is placed under operation, claims about +a system are proved or disproved algorithmically using rig- +orous mathematical methods. Such methods develop a model +of the system being tested, such as a finite-state automaton, +and then test that model against a set of specifications defined +in a formal language. There are two main approaches, formal +verification [7], which checks if a given system satisfies a set +of specifications, while program synthesis seeks to construct a +system from a set of specifications [59]. For a literature review +of formal methods in the context of autonomous robotics, the +reader is directed to [60]. +In the context of LEAS, the system is often complex +and safety is critical, thereby making formal methods an +attractive solution. Specifically, synthesis methods provide a +“correct-by-construction” approach [61], where capabilities +and required operating conditions such as safety constraints +are described as specifications and act as input to a synthesis +algorithm which outputs the appropriate system model and +optimal control policy. The vehicle’s actions are thereby guar- +anteed to stay within the operating conditions determined by +the obtained policy. However, many approaches are currently +limited to static environments, meaning a robot which is +guaranteed to satisfy the specifications in one environment +does not necessarily carry over to other environments. More- +over, many formal methods have issues scaling to large state +spaces [62] due to their exhaustive nature. However, solutions +have been proposed using clever optimization techniques such +as +[63] [64]. Nevertheless, synthesis methods can be used +to assure safety during a systems development phase, while +formal verification techniques such as model checking [7] +may be more applicable at the acquirement level. +V. ASSURANCE ACTIVITIES TO SUPPORT SYSTEM +ACQUISITION +This section maps assurance activities to support system +acquisition to test and evaluation in the systems engineering +lifecycle. +A. Autonomy Standards +Standards seek to provide safety assurances, verify capa- +bilities, and promote understanding. Several standards have +been developed to assist the design and development of +commercial autonomous vehicles such as ISO 26262 [65] and +IEC 61508 [66]. Specifically, UL 4600 [67] and ISO/PAS +21448 [68] explicitly consider autonomous vehicle capabil- +ities incorporating learning. UL 4600 employs the idea of +safety assurance cases, where system performance is argued +like a court case given evidence. Minimizing risk is the +goal while also accepting that it cannot be eliminated all to- +gether. Military focused standards include ALFUS [69] paired +with the updated ARP6128 [70], and MIL-STD-882E [71]. +Most recently, IEEE 2817 [72] (in development) seeks to +standardize verification methods specifically for autonomous +systems. Although this discussion is part of the development +subsection, the standards listed here may also be applicable +to the other two lifecycle categories identified in Figure 1. +B. Software Testing +Capabilities of autonomous systems are enabled by soft- +ware. There is no debate on the importance of software +testing, when acknowledging the severity of historic software +failures such as the patriot missile or Boeing 737 MAX. +Traditional methods such as those outlined in [73] seek +to partition the input space using graph or logic coverage +to exhaustively test a program. While traditional methods +may work for testing traditional software systems, exhaustive +methods are rendered infeasible due to the state space ex- +plosion problem. Moreover, for statistical learning algorithms +commonly applied in machine learning methods, the set of +all possible samples is often much larger than the number +of samples collected. For example, the set of all possible +images a camera may sense using the RGB spectrum with +an image size of 256 × 256 is 16, 777, 216(256∗256). This +demonstrates the importance of analyzing dataset features +and their associated effectiveness [74] to obtain a generalized +model. +In regards to software engineering—a machine learning +model is similar to traditional components, they both have +inputs and outputs. The difference is the size of the input +space and that the outputs may change on the same input at +different points in time if the model is continually learning. +However, if the model is not learning from new data, it can +be considered as a deterministic component. An inaccurate +prediction from a model can be thought of as equivalent to +a software fault [75]. However, due to the large state space, +the issue remains in the detection of such faults. The next +subsection that follows seek to identify such faults. +C. Automated Test Generation +Automated test case generation seeks to increase the ef- +fectiveness of test and evaluation by minimizing testing time, +and identifying the most impactful test cases which are likely +to contain faults. A survey of automatic test-case generation +[76] identifies five main categories—structural testing, model- +based testing, combinatorial testing, random testing, and +search-based testing. Aforementioned for LEAS, the number +of configurations is often intractable and therefore exhaustive +or tree methods are infeasible. Search-based methods seek to +alleviate this issue by using clever optimization techniques, +which identify test cases in areas (boundaries) of a systems + +configuration space that are likely to lead to system failure. +Therefore, this subsection focuses on search-based methods. +Most relevant to LEAS, Mullins et al. [27] provide a tool +which automatically identifies test cases for a system under +test with a search based optimization approach dependent on +a set of mission scenario configurations and a performance +score for each configuration. A case study using the afore- +mentioned tool in an autonomous surface vessel domain can +be found in [77]. Bridging the gap between formal verification +and automated test case generation, Akellea et al. [78] provide +a black-box method to identify test cases which do not satisfy +a provided temporal logic specification based on a dataset of +observed demonstrations. Most recently, Badithela et al. [79] +identify test cases for mission objectives by constructing a +set of constraints given a user-defined sequence of waypoints +and a reachability objective. In conclusion, recent research in +search-based automated test generation is able to handle the +state space explosion problem, while also finding the most +impactful test cases. The results from such test cases help +provide impactful evidence towards, or against the construc- +tion of safety case (UL 4600). +D. Metrics for Machine Learning +Metrics provide a quantitative analysis of performance, +clearly identifying the best solution out of a set of possible +solutions. Performance is best measured by the system’s abil- +ity to accurately make predictions in the current operational +environment which positively contribute to the larger mission +goals. Initial metrics in supervised machine learning focused +on confusion matrices and receiver operating characteristics +(ROC) with metrics such as accuracy, sensitivity, specificity, +precision, and F1 score. For regression models, statistical +measures such as mean absolute error or mean squared error +were sufficient. In the context of neural network regression, +the statistical significance of input features and an accompany- +ing statistical test may be identified [80]. In the reinforcement +learning framework, Chan et al. [81] provide a set of test and +evaluation metrics to statistically measure the variability and +risk of RL algorithms both during and after training. +Agnostic to the task (classification, regression, clustering, +etc.), neuron coverage was introduced [82], as a testing metric +analogous to code coverage [83] for traditional systems. Code +coverage measures the percentage of a code base that has been +covered by tests. High code coverage implies that few soft- +ware bugs remain, and vice versa. Similarly, neural coverage +measures the percentage neuron activations occur from the +testing dataset, seeking to obtain the same implications of +code coverage. However, recent research [84] [85] has shown +that neuron coverage is an insufficient metric for testing. +Wang et al. [86] seek to address this limitation by quantifying +the value of a test set. Addition metrics research is needed to +quantitatively measure the assurance problems outlined in [4]. +VI. ASSURANCE ACTIVITIES TO SUPPORT SYSTEM +SUSTAINMENT +This section maps assurance activities which support sys- +tem sustainment to transition, operating, and maintenance in +the systems engineering lifecycle. +A. Runtime Monitoring +Runtime monitoring observes the current state of a system +and determines if the system is satisfying or violating a set +of pre-determined specifications. This is similar to the formal +methods approach outlined in Sec. IV-E. However, runtime +monitoring occurs online (while the system is operating), +whereas most techniques from formal methods occur offline. +Kane et al. introduced EgMon [87], which detects the vio- +lation of specifications using propositional metric temporal +logic. Similarly, Zapridou et al. [88] develop an adaptive +cruise control system in the CARLA simulator and perform +runtime monitoring using signal temporal logic. Yel et al. [89] +provide a runtime monitoring technique using neural networks +for safe motion planning. In the U.S. government sector, +a Boeing team as part of the DARPA assured autonomy +program, implemented runtime monitoring in a flight simula- +tor [11]. For an overview of runtime monitoring techniques, +the reader is directed to [90]. +B. Resilience Engineering +Resilience engineering techniques seek to build systems +which remain operational subject to faults and distur- +bances [91]. Such techniques quantify the impact of degraded +performance and robustness to faults while providing predic- +tions such as the expected time until recovery [92]. In the con- +text of LEAS, resilience techniques can accommodate sensor +inaccuracies which may come from measurement limitations +in the hardware, dust or debris, and adversarial attacks [28]. +Resilience monitoring enables a system to recognize that +performance is degraded, and then adapt appropriately, such +as moving from perception based navigation to odometry +based navigation. At the time of writing there is little technical +research on the incorporation of resilience techniques to +LEAS [93], However, [94] offers an initial taxonomy on +resilience for multi-robot systems. +VII. CONCLUSION +This paper provides preliminary attempt to map recently +developed technical approaches for the assurance of LEAS +to a traditional systems engineering v-model. By doing so, +we seek to improve the acquisition process by: (i) informing +comprehensive assurance planning, (ii) promoting detailed +analysis of alternatives, and (iii) objectively communicating +risk to leaders. 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Kumar, “Beyond robustness: A taxonomy of approaches towards +resilient multi-robot systems,” arXiv preprint arXiv:2109.12343, 2021. + diff --git a/9NAyT4oBgHgl3EQfQ_Zv/content/tmp_files/load_file.txt b/9NAyT4oBgHgl3EQfQ_Zv/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..f60335745cd341e9421ccf60af2a480e55a2cea4 --- /dev/null +++ b/9NAyT4oBgHgl3EQfQ_Zv/content/tmp_files/load_file.txt @@ -0,0 +1,950 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf,len=949 +page_content='A Mapping of Assurance Techniques for Learning Enabled Autonomous Systems to the Systems Engineering Lifecycle Christian Ellis1, Maggie Wigness2, and Lance Fiondella1 Abstract—Learning enabled autonomous systems provide in- creased capabilities compared to traditional systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' However, the complexity of and probabilistic nature in the underlying methods enabling such capabilities present challenges for current systems engineering processes for assurance, and test, evalua- tion, verification, and validation (TEVV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' This paper provides a preliminary attempt to map recently developed technical approaches in the assurance and TEVV of learning enabled autonomous systems (LEAS) literature to a traditional systems engineering v-model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' This mapping categorizes such techniques into three main approaches: development, acquisition, and sustainment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' We review the latest techniques to develop safe, reliable, and resilient learning enabled autonomous systems, without recommending radical and impractical changes to exist- ing systems engineering processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' By performing this mapping, we seek to assist acquisition professionals by (i) informing comprehensive test and evaluation planning, and (ii) objectively communicating risk to leaders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' INTRODUCTION It is widely recognized [1] that the complexity and resulting capabilities of autonomous systems created using machine learning methods, which we refer to as learning enabled autonomous systems (LEAS), pose new challenges to sys- tems engineering compared to their traditional counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Moreover, the inability to translate qualitative assessments to quantitative metrics which measure system performance hinder adoption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Such limitations make it difficult to produce reliable systems, and even harder to assure [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Without under- standing the capabilities and limitations of existing assurance techniques, defining safety and performance requirements that are both clear and testable remains out of reach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Mature test, evaluation, verification, and validation (TEVV) methods have been in use for decades to ensure the safety analysis and acquisition of hardware systems [3], but fewer TEVV methods for software are available, and even fewer for software that improves itself through learning [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Initial approaches to autonomous systems use control theory to physically model the world and its underlying dynamics [5], while LEAS infer and generalize statistical patterns, which lead to the achievement of goals from a sample of pre- collected training data points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' However, due to the nature of the environments where LEAS are fielded and the massive size of their underlying state spaces, systems will likely encounter states during operation they have never experienced before, yet still being required to take action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' 1 Christian Ellis is a PhD Student and Lance Fiondella is an Asso- ciate Professor in the Department of Electrical and Computer Engineer- ing at the University of Massachusetts Dartmouth, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' cellis3, lfiondella@umassd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content='edu 2 Maggie Wigness is a researcher at the United States Army Research Laboratory (ARL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' 1: Recent work in assurance for LEAS is mapped to relevant stages of the MITRE systems engineering lifecy- cle [6], into 3 distinct categories—development, acquisition, and sustainment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Early work from the autonomy community identified issues that arise from incorporating learning into autonomous sys- tems [4] including state space explosion, operation in unpre- dictable environments, emergent behavior, and effective hu- man machine interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Assurance methods such as formal methods [7], or reliability analysis [8] seek to provide either certain or probabilistic guarantees on system performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Formal methods support verification by exhaustively search and identifying dangerous regions of the state space and provide techniques to avoid such states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Reliability analysis supports test and evaluation by quantifying the probability a system will be operational at a point in time from oper- ational data collected throughout the systems lifecycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' The aforementioned state space explosion makes formal methods challenging to scale, and reliability analysis difficult to ac- curately predict estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' A different field of research seeks to develop methods which explicitly consider safety during the learning and operational stages [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Lastly, investments such as the DARPA Assured Autonomy program1 seeks to continually assure learning enabled cyber-physical systems by constructing formal methods that assure correctness at design time and perform runtime monitoring at operation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' While this program has advanced the state of the 1https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content='darpa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content='mil/program/assured-autonomy arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content='00057v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content='SE] 30 Dec 2022 Transition Concept Operation& Development Maintenance Requirements Test& Engineering Evaluation System System Architecture Integration SystemDesign &Development Development Acquisition Sustainmentart in formal methods [10] and runtime monitoring [11],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' a systematic approach to identify outstanding gaps will remain unclear unless the community makes explicit and coordinated efforts to understand how such methods may be incorporated into the broader systems engineering process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Our work seeks to communicate recent technical devel- opments in LEAS assurance with a focus on autonomous vehicles, accompanying recent literature reviews [12] [13], by mapping such developments to distinct steps of a well known systems engineering model chosen due to its prevalence, namely the v-model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' 1 shows the mapping and identifies three top level lifecycle phases: development, acquisition, and sustainment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' For each top level lifecycle phase, a section of the paper has been dedicated to outlining recent technical de- velopments and how they contribute to the goals of the phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' This representation helps identify where the latest methods for TEVV fit in the broader systems engineering process while also enabling systematic consideration of potential sources of defects, faults, and attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Note that we use the v-model only to assist the classification of where TEVV methods fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' This is not a recommendation to use a certain software development lifecycle over another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' The remainder of the paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Sec- tion II outlines the specific scientific fields supporting LEAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Section III provides an overview of the mapping between tra- ditional systems engineering and the state of the art in assur- ance for LEAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Section IV maps assurance techniques, which assist development to design and development, and system integration in the systems engineering lifecycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Section V maps assurance techniques, which assist acquisition to test and evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Section VI maps assurance techniques, which assist sustainment to transition, operation, & maintenance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Lastly, section VII concludes with areas this mapping can impact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' METHODS SUPPORTING THE DEVELOPMENT OF LEARNING ENABLED AUTONOMOUS SYSTEMS This section seeks to define the fields of engineering with significant impact on development of LEAS with a focus on vehicles and their corresponding challenges for assurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' In later sections (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' IV—VI), solutions to such challenges are identified and categorized according to where they reside within the systems engineering lifecycle such as development, acquisition, or sustainment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Rather than seek to obtain an exhaustive list of engineering fields, of which there are many, we first provide an overview of learning enabled autonomous vehicles and then review two key contributing fields, including machine learning and reinforcement learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' While there are other non-learning methods such as optimal control theory [14], which have made large and long lasting impacts on the development on LEAS, they are not considered in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' LEAS normally follow one of two design approaches, end- to-end (E2E) or modular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' In the E2E approach [15], a system’s sensors act as the input to a learning algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' For example, a deep neural network outputs the corresponding actions such as steering wheel angle (lateral control) [16], torque (longitudi- nal control) [17], or both [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' In the modular approach [19], a system’s sensors act as input to a perception sub-system which is responsible for building a map and model of the world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Such subsystems commonly include perception components that use ML techniques such as semantic segmentation [20] or object detection [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' This model is then used by a planning subsystem, which outputs a kinematically feasible trajectory to which controls are applied [22], [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' While it may be possible to break down layers of E2E neural networks into sub-components using interpretability techniques [24], this paper specifically focuses on the modular approach for two reasons: i) it is clear to a human what the responsibility of each component is (increased interpretabil- ity), and ii) the modular approach is currently more common in autonomous vehicle designs in industry and government implementations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' While some of the underlying problems for assurance are the same for both approaches, including those previously mentioned [4], we explicitly consider software assurance methods which are applicable to either perception or planning components, or the joint-combination thereof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Machine Learning In machine learning (ML), tasks are completed by training a model from data to perform function approximation using a combination of mathematical optimization and statistical techniques [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' This results in computer programs which are able to complete a task without constructing a set of exact solution instructions ahead of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' There are three main forms of learning, including supervised, unsupervised, and reinforcement learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' In supervised learning, each training sample from the dataset is associated with a set of features and a corresponding label to train a model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' For example, a neural network can be trained on a dataset of images containing handwritten digits, where each sample’s corresponding label is 0 through 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' In unsupervised learning, each training sample is only represented by a set of extracted features, which are subsequently used to identify the underlying feature patterns throughout the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' For example, clustering techniques divide a dataset into k distinct groups, where all data points in a group are similar with respect to some distance measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Finally, in reinforcement learning, an autonomous agent learns the optimal way to act over time via interaction with the environment, such as an autonomous robot learning how to move its actuators and joints to navigate in an environment without hitting obstacles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Although the ability to perform complex tasks solely from data has made ML highly successful, it is for this same reason that ML models are difficult to assure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Among other factors, a model’s performance depends on the data experi- enced during training and the environment in which it was trained [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Naive metrics such as the model’s accuracy on a test set may be perceived as overconfident because they assume most future data will be like the experienced data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' This is especially true in complex systems such as government systems tasked with operating in contested op- erational environments, demonstrating the need for metrics to assess model performance in new environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Another assurance challenge includes determining relevant test cases given the state space explosion and curse of dimensionality problems, of which the Range Adversarial Planning Tool has been proposed [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Furthermore, such models are brittle to perturbations in input, which may come from sources such as, sensor noise or adversarial attacks [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Lastly, it is inevitable that such models will fail from time to time, and explanations of why they fail (interpretability techniques) and how to fail gracefully (resilience techniques) are also valuable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Although there are a variety of new assurance techniques [12] [13] that seek to alleviate such issues, a framework does not exist to assess their thoroughness and relative effectiveness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Reinforcement Learning Reinforcement learning (RL) is given a dedicated subsec- tion because it is an enabler of intelligent-like capabilities required for complex autonomous systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Reinforcement learning provides a framework for autonomous agents to make decisions under uncertainty and learn from environmental interaction [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Specified by a reward function, an agent seeks to obtain an optimal policy which maximizes its reward by taking actions over a time horizon in an environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' A policy is a function that maps the current state to the single action that maximizes the expected future reward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Formally, this structure is part of a Markov Decision Process (MDP) consisting of a state space S, an action space A, a state transition distribution over next states T(st+1|st, a), and a reward function R(s, a, s′) whose solution is the optimal policy which maximizes the expected future reward π∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Exact RL seeks to converge to the optimal policy using tabular techniques, requiring an agent to visit each state many times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Conversely, approximate techniques such as deep RL [30] allow an agent to operate in large (possibly infinite) state and action spaces without explicitly visiting each state by obtaining a parameterized policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Although RL has demonstrated its ability to mimic intel- ligent capabilities such as beating players at Go [31], and autonomous driving [32], there are limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Designing reward functions explicitly by hand is a challenging task that can lead to a misalignment between the reward function specified and the true reward function the algorithm designer intended [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Such value misalignment leads to unintended consequences such as reward hacking [34], where the robot maximizes reward in a way that the algorithm designer did not intend while often failing to meet its goals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Furthermore, many solutions sample inefficiently and are often brittle [35], limiting their real world applicability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Lastly, RL can cause a disconnect between how a programmer may interpret what an agent has learned and the true learned concept [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' For example, a programmer may believe an agent has learned to traverse to a goal grid cell, but because of the environment setup, the agent may have actually simply learned to traverse to a green grid cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' For systems incorporating RL, such limi- tations and corresponding tests for each should be considered explicitly in the assurance process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' OVERVIEW OF MAPPING This paper provides a preliminary attempt to map recently developed technical approaches in the assurance and TEVV of learning enabled autonomous systems (LEAS) literature to a traditional systems engineering v-model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' The mapping identifies three top level lifecycle phases: development, ac- quisition, and sustainment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Proceeding according to the colors in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' 1, the stages surrounded in the black box, including system design & development, and system integration, assist development and therefore are mapped to methods which explicitly provide safety assurance during the learning process (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' IV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' The stage in the green box, test and evaluation, assists the acquisition of systems and therefore is mapped to TEVV analysis techniques which quantify the performance of an already built system, or component (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' V).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' The stage in the orange box, transition operation & maintenance, is mapped to safety assurance techniques which aid sustainment by monitoring or adapt performance of a fielded system (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' VI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' For each stage, applicable classes of techniques are organized by respective subsections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' In addition to the stage of the system engineering lifecycle, this mapping also seeks to categorize technical developments according to their granularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' When evaluating different ap- proaches to the same problem, the choice of performance metrics depend on the scope of the unit under test—whole system, learning enabled component, or a traditional com- ponent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Interfaces at various lifecycle levels of granularity promote systems thinking [37] about architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Namely, the way a system’s components and subsystems relate, interact, and work over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' By understanding the input paths that contribute to a unit’s decisions, the outputs that may lead to failures within the larger system become clearer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Generally speaking, there are two main approaches to as- sure LEAS—white-box techniques and black-box techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' White-box techniques require either a model of the system under test, or direct access to the source code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' In contrast, black-box techniques only look at the inputs and outputs of the system under test, and are unaware of the underlying methods of how the system generates the outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' White- box techniques are better for component level assurance, while black-box techniques are often better for system-wide assurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' The implementation of assurance techniques and their accompanying metrics to quantify system performance and safety (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' IV—Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' VI) can all be used as supporting evidence for a safety assurance case [38] to determine system readiness level and maturity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Tools which automate trace- ability and reproducibility throughout the system lifecycle such as [39] can reduce the burden of collecting evidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' The appropriate choice of assurance methods and associated metrics is dependent on the system maturity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Initial project milestones may focus on demonstrating anti-fragility, while later milestones may focus on demonstrating the ability to accomplish a mission and accompanying capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Fur- thermore, quantitative metrics may only be applicable at certain levels of system granularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' For example, an entire system may be best evaluated by the outcomes of a pre- determined mission and supporting data, while a learning enabled component may be better evaluated by measures specific to machine learning such as uncertainty quantifica- tion, robustness to environmental shift, and the ability to fail gracefully and recover from faults.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Metrics which are able to capture the performance of all approaches under test may be preferred over metrics that measure the performance of a certain class of algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Lastly, if performance data can be collected during the development process, one could also perform a quantitative analysis of a system at any given time using traditional reliability [8] and defect removal [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' ASSURANCE ACTIVITIES TO SUPPORT SYSTEM DEVELOPMENT This section maps assurance methods which assist de- velopment to system design and development, and system integration in the systems engineering lifecycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Artificial Intelligence Safety AI safety is a sub-field of AI which seeks to ensure that a deployed AI systems (i) operates as the designer intended and (ii) completes its task without harming humans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' The importance of AI safety is backed by impactful institutions such as the Future of Life Institute2 and Machine Intelligence Research Institute3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' In the academic literature, AI safety has been popularized by the agenda of Amodedi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' [9], who discuss five failure modes for AI;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' negative side effects, reward hacking, scalable supervision, safe exploration, and distributional shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Moreover, in the context of RL, the value alignment problem arises due to a gap in the specified reward function and what the human actually intended [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Specifically, Taylor et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' [42] discuss eight different ap- proaches focusing on two areas of value alignment—reward specification and techniques to avoid side effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Burden et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' [43] argue that the scope of AI safety problems residing in a specific system can be characterized by three quantitative factors;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' generality, capability, and control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' For a literature review of AI safety, the reader is directed to [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' While the works above seek to obtain safer agents by altering the underlying methodologies, the focus is on agents in artificial environments rather than physical robots, thereby creating a gap between theoretical and applied research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Moreover, most approaches assume that the system is fol- lowing a RL paradigm, demonstrating the importance to understand the underlying learning paradigm employed by a project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Lastly, although AI safety approaches alone will not be sufficient for LEAS assurance, if the methods are applied during the learning process, such approaches are likely to perform and test better than their non-safe counterparts, leading to higher assurance measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' 2https://futureoflife.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content='org/ 3https://intelligence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content='org/ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Learning from Human Feedback Incorporating human interaction can positively impact the performance of a LEAS because it is often easier to provide feedback on desired behavior rather than explicitly defining it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' This is one solution to the value alignment problem mentioned in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' IV-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Such human interaction may include learning from demonstration, intervention, or evaluation [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' In learn- ing from demonstration [46], the human provides a dataset of examples mimicking how the system should operate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' In learning from intervention [47], the system operates fully autonomously and the human takes over as required to correct system behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' In learning from human evaluation [48], [49], the system completes various tasks fully autonomously, and then a human ranks the tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' This ranking may be from best to worst, or answering the yes/no question, “Was this the behavior you wanted to see the system perform?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' All of the methods mentioned fall into a sub-field known as imitation learning [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Lastly, recent developments in imitation learning attempt to incorporate safety as part of the learning process using uncertainty quantification, creating a new sub field known as safe imitation learning [51], [52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Uncertainty Estimation System requirements often demand that a learning en- abled autonomous system make a prediction, classification, or decision at every time-step during operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Since many implementations contain perception systems that will likely never be 100% accurate, the certainty or lack thereof, of a prediction may assist in the final decision made—especially if the outcome of such a prediction may lead to risky behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' The ability for a system to measure what it does and does not know can be captured by quantifying uncertainty with Bayesian analysis techniques [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' There are two main types of uncertainty, aleatoric and epistemic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Aleatoric uncertainty measures the variance between samples in a population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' This type of uncertainty cannot be reduced with more data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' An example is the outcome of a fair coin flip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Epistemic uncertainty measures the lack of knowledge of a population, which is often captured in a system’s parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' This type of uncertainty can be alleviated by collecting more data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' An understanding of the different types of uncertainty helps system designers understand if performance can be increased by simply collecting more data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Additional details can be found in the reviews on uncertainty quantification applied to machine learning [54], neural networks [55], and computer vision [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Such techniques aid at the learning enabled com- ponent level, and can be used to quantify system confidence in the current operational environment and thereby communicate uncertainty (risk) to the system end users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Cost-sensitive Learning At the system level, the impact of a learning enabled component on the whole system is measured in terms of its ability to assist in the completion of a task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Additional failure modes introduced by such components must be ex- plicitly considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Cost-sensitive learning [57] is applicable in classification problems where the cost associated with the misclassification is not equal among classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' For example, in the context of commercial autonomous vehicles, a false positive resulting in the vehicle stopping when it did not need to likely has lower cost than a false negative resulting in a vehicle colliding with a pedestrian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Formal Methods Static analysis techniques such as formal methods are able to provide guarantees on system performance without ever operating the system [58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Rather than attempting to discover faults while the system is placed under operation, claims about a system are proved or disproved algorithmically using rig- orous mathematical methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Such methods develop a model of the system being tested, such as a finite-state automaton, and then test that model against a set of specifications defined in a formal language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' There are two main approaches, formal verification [7], which checks if a given system satisfies a set of specifications, while program synthesis seeks to construct a system from a set of specifications [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' For a literature review of formal methods in the context of autonomous robotics, the reader is directed to [60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' In the context of LEAS, the system is often complex and safety is critical, thereby making formal methods an attractive solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Specifically, synthesis methods provide a “correct-by-construction” approach [61], where capabilities and required operating conditions such as safety constraints are described as specifications and act as input to a synthesis algorithm which outputs the appropriate system model and optimal control policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' The vehicle’s actions are thereby guar- anteed to stay within the operating conditions determined by the obtained policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' However, many approaches are currently limited to static environments, meaning a robot which is guaranteed to satisfy the specifications in one environment does not necessarily carry over to other environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' More- over, many formal methods have issues scaling to large state spaces [62] due to their exhaustive nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' However, solutions have been proposed using clever optimization techniques such as [63] [64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Nevertheless, synthesis methods can be used to assure safety during a systems development phase, while formal verification techniques such as model checking [7] may be more applicable at the acquirement level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' ASSURANCE ACTIVITIES TO SUPPORT SYSTEM ACQUISITION This section maps assurance activities to support system acquisition to test and evaluation in the systems engineering lifecycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Autonomy Standards Standards seek to provide safety assurances, verify capa- bilities, and promote understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Several standards have been developed to assist the design and development of commercial autonomous vehicles such as ISO 26262 [65] and IEC 61508 [66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Specifically, UL 4600 [67] and ISO/PAS 21448 [68] explicitly consider autonomous vehicle capabil- ities incorporating learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' UL 4600 employs the idea of safety assurance cases, where system performance is argued like a court case given evidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Minimizing risk is the goal while also accepting that it cannot be eliminated all to- gether.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Military focused standards include ALFUS [69] paired with the updated ARP6128 [70], and MIL-STD-882E [71].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Most recently, IEEE 2817 [72] (in development) seeks to standardize verification methods specifically for autonomous systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Although this discussion is part of the development subsection, the standards listed here may also be applicable to the other two lifecycle categories identified in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Software Testing Capabilities of autonomous systems are enabled by soft- ware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' There is no debate on the importance of software testing, when acknowledging the severity of historic software failures such as the patriot missile or Boeing 737 MAX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Traditional methods such as those outlined in [73] seek to partition the input space using graph or logic coverage to exhaustively test a program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' While traditional methods may work for testing traditional software systems, exhaustive methods are rendered infeasible due to the state space ex- plosion problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Moreover, for statistical learning algorithms commonly applied in machine learning methods, the set of all possible samples is often much larger than the number of samples collected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' For example, the set of all possible images a camera may sense using the RGB spectrum with an image size of 256 × 256 is 16, 777, 216(256∗256).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' This demonstrates the importance of analyzing dataset features and their associated effectiveness [74] to obtain a generalized model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' In regards to software engineering—a machine learning model is similar to traditional components, they both have inputs and outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' The difference is the size of the input space and that the outputs may change on the same input at different points in time if the model is continually learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' However, if the model is not learning from new data, it can be considered as a deterministic component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' An inaccurate prediction from a model can be thought of as equivalent to a software fault [75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' However, due to the large state space, the issue remains in the detection of such faults.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' The next subsection that follows seek to identify such faults.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Automated Test Generation Automated test case generation seeks to increase the ef- fectiveness of test and evaluation by minimizing testing time, and identifying the most impactful test cases which are likely to contain faults.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' A survey of automatic test-case generation [76] identifies five main categories—structural testing, model- based testing, combinatorial testing, random testing, and search-based testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Aforementioned for LEAS, the number of configurations is often intractable and therefore exhaustive or tree methods are infeasible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Search-based methods seek to alleviate this issue by using clever optimization techniques, which identify test cases in areas (boundaries) of a systems configuration space that are likely to lead to system failure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Therefore, this subsection focuses on search-based methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Most relevant to LEAS, Mullins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' [27] provide a tool which automatically identifies test cases for a system under test with a search based optimization approach dependent on a set of mission scenario configurations and a performance score for each configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' A case study using the afore- mentioned tool in an autonomous surface vessel domain can be found in [77].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Bridging the gap between formal verification and automated test case generation, Akellea et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' [78] provide a black-box method to identify test cases which do not satisfy a provided temporal logic specification based on a dataset of observed demonstrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Most recently, Badithela et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' [79] identify test cases for mission objectives by constructing a set of constraints given a user-defined sequence of waypoints and a reachability objective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' In conclusion, recent research in search-based automated test generation is able to handle the state space explosion problem, while also finding the most impactful test cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' The results from such test cases help provide impactful evidence towards, or against the construc- tion of safety case (UL 4600).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Metrics for Machine Learning Metrics provide a quantitative analysis of performance, clearly identifying the best solution out of a set of possible solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Performance is best measured by the system’s abil- ity to accurately make predictions in the current operational environment which positively contribute to the larger mission goals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Initial metrics in supervised machine learning focused on confusion matrices and receiver operating characteristics (ROC) with metrics such as accuracy, sensitivity, specificity, precision, and F1 score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' For regression models, statistical measures such as mean absolute error or mean squared error were sufficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' In the context of neural network regression, the statistical significance of input features and an accompany- ing statistical test may be identified [80].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' In the reinforcement learning framework, Chan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' [81] provide a set of test and evaluation metrics to statistically measure the variability and risk of RL algorithms both during and after training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Agnostic to the task (classification, regression, clustering, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' ), neuron coverage was introduced [82], as a testing metric analogous to code coverage [83] for traditional systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Code coverage measures the percentage of a code base that has been covered by tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' High code coverage implies that few soft- ware bugs remain, and vice versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Similarly, neural coverage measures the percentage neuron activations occur from the testing dataset, seeking to obtain the same implications of code coverage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' However, recent research [84] [85] has shown that neuron coverage is an insufficient metric for testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' [86] seek to address this limitation by quantifying the value of a test set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Addition metrics research is needed to quantitatively measure the assurance problems outlined in [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' ASSURANCE ACTIVITIES TO SUPPORT SYSTEM SUSTAINMENT This section maps assurance activities which support sys- tem sustainment to transition, operating, and maintenance in the systems engineering lifecycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Runtime Monitoring Runtime monitoring observes the current state of a system and determines if the system is satisfying or violating a set of pre-determined specifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' This is similar to the formal methods approach outlined in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' IV-E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' However, runtime monitoring occurs online (while the system is operating), whereas most techniques from formal methods occur offline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Kane et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' introduced EgMon [87], which detects the vio- lation of specifications using propositional metric temporal logic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Similarly, Zapridou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' [88] develop an adaptive cruise control system in the CARLA simulator and perform runtime monitoring using signal temporal logic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Yel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' [89] provide a runtime monitoring technique using neural networks for safe motion planning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' In the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' government sector, a Boeing team as part of the DARPA assured autonomy program, implemented runtime monitoring in a flight simula- tor [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' For an overview of runtime monitoring techniques, the reader is directed to [90].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Resilience Engineering Resilience engineering techniques seek to build systems which remain operational subject to faults and distur- bances [91].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Such techniques quantify the impact of degraded performance and robustness to faults while providing predic- tions such as the expected time until recovery [92].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' In the con- text of LEAS, resilience techniques can accommodate sensor inaccuracies which may come from measurement limitations in the hardware, dust or debris, and adversarial attacks [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Resilience monitoring enables a system to recognize that performance is degraded, and then adapt appropriately, such as moving from perception based navigation to odometry based navigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' At the time of writing there is little technical research on the incorporation of resilience techniques to LEAS [93], However, [94] offers an initial taxonomy on resilience for multi-robot systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' CONCLUSION This paper provides preliminary attempt to map recently developed technical approaches for the assurance of LEAS to a traditional systems engineering v-model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' By doing so, we seek to improve the acquisition process by: (i) informing comprehensive assurance planning, (ii) promoting detailed analysis of alternatives, and (iii) objectively communicating risk to leaders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' As indicated by the number of references in each section, most research has been done in the development of methods which explicitly consider safety assurance, while further research is needed in methods which aid the acquire- ment, and sustainment of such systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' Future work seeks to perform a case study assuring a LEAS using some of the methodologies referenced in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NAyT4oBgHgl3EQfQ_Zv/content/2301.00057v1.pdf'} +page_content=' REFERENCES [1] L.' metadata={'source': 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+Eigenvalues of QCD Dirac matrix with improved staggered quarks in the continuum +limit +Olaf Kaczmarek,1 Ravi Shanker,2, ∗ and Sayantan Sharma2 +1Fakult¨at f¨ur Physik, Universit¨at Bielefeld, D-33615 Bielefeld, Germany +2The Institute of Mathematical Sciences, a CI of Homi Bhabha National Institute, Chennai, 600113, India +We calculate the eigenmodes of the Highly Improved Staggered Quark (HISQ) matrix near the +chiral crossover transition in QCD with 2 + 1 flavors with the aim to gain more insights into its +temperature dependence. +On performing the continuum extrapolation, we do not observe any +gap opening up in the infrared part of the eigenvalue density of QCD Dirac operator, instead we +observe a peak. +The existence of the peak and oscillations of the infrared eigenmodes can be +understood in terms of an interacting ensemble of instantons. From the properties of the continuum +extrapolated eigen spectrum we further show that the anomalous UA(1) part of the chiral symmetry +is not effectively restored simultaneously along with its non-singlet counterpart. +We provide an +explanation for this observation, further showing interesting connections between the anomalous +UA(1) restoration and the change in the infrared part of the eigenvalue distribution. +PACS numbers: +12.38.Gc, 11.15.Ha, 11.30.Rd, 11.15.Kc +Introduction The eigenvalue spectrum of the quark +Dirac operator contains valuable information about the +fundamental properties of Quantum Chromodynamics +(QCD). The chiral condensate which acts as a (pseudo) +order parameter for the chiral (crossover) transition in +QCD is related to the density of near-zero eigenvalues [1]. +In fact it was shown from very general considerations that +the formation of the chiral condensate is related to the +occurrence of small eigenvalues that scale proportional +to the volume [2]. The breaking of the non-singlet part +of chiral symmetry i.e. SUA(2) × SUV (2) → SUV (2) of +QCD with physical quark masses at the crossover tem- +perature Tc = 156.5 ± 1.5 MeV [3] can also be explained +in terms of modifications in the deep infrared part of the +eigenvalue density. The flavor-singlet UA(1) part of the +chiral symmetry on the other hand, is anomalous yet is +believed to play an important role in determining the +nature of the chiral phase transition [4–6]. The temper- +ature dependence of the amount of UA(1) breaking near +the chiral crossover transition in QCD can be only deter- +mined using non-perturbative lattice techniques and is a +topic of contemporary interest in lattice QCD see for e.g. +Ref. [7, 8] for recent reviews. Whereas there are some +very compelling evidence that show UA(1) remains effec- +tively broken in 2 + 1 flavor QCD with physical quark +mass m +[9–15], even when m → 0 [16], there are lat- +tice studies which also favor an effective restoration at +Tc [17–22]. +The eigenvalue spectrum of the QCD Dirac matrix also +encodes within it some remarkable universal properties. +It was shown that the route towards achieving thermo- +dynamic limit for the infrared modes of the Dirac op- +erator is universal [23], for any number of light quark +flavors. +The existence of a non-zero chiral condensate +leads to a sum rule involving sum of inverse squares of +∗Electronic address: rshanker@imsc.res.in +these small eigenvalues [2]. These sum rules are univer- +sal irrespective of the details of the nature and type of +gauge interactions [23, 24] and could be derived from chi- +ral random matrix theory [25]. A good agreement was +demonstrated for the distribution of the small eigenvalues +and the spectral density of lattice QCD Dirac operator +and chiral random matrix theory at zero temperature on +small lattice volumes [26]. In fact universal correlations +between higher order spectral functions in a random ma- +trix theory has been derived [27] and its connection to +QCD was discussed. At finite temperature the universal +features of infrared eigenvalues can be also accounted for +within a random matrix theory [28–30]. Additionally the +infrared eigenvalue spectrum of QCD has more subtle +features. A near-zero peak of localized eigenvalues has +been observed for finite lattices, mixing with but very +different from the delocalized bulk modes whose spectral +density follows random matrix statistics [7, 31]. Whether +or not such a feature survives in the continuum limit is +yet to be ascertained. Previous studies of quark Dirac +spectrum in an instanton liquid ensemble [29, 32] at zero +temperature have observed similar peak-like feature. +With increasing temperature the localized modes +starts separating out from the random bulk modes lead- +ing to the opening up of a mobility edge [31]. The corre- +sponding temperature where a finite mobility edge sepa- +rates the bulk modes from the localized one was initially +estimated from lattice studies to be identical to Tc in dy- +namical [33–38] as well as in quenched QCD [39], remi- +niscent of an Anderson-like transition that is observed in +disordered semi-metals [40]. However independent lat- +tice studies do discuss another possible scenario where +the opening of a finite mobility edge may occur at tem- +peratures higher that Tc [41], with an intermediate phase +consisting of scale-invariant infinitely extended infrared +modes [42, 43] strongly interacting with the bulk modes +leading to a singularity at the mobility edge. +Most of the previous lattice QCD studies were ei- +ther performed in the quenched limit or with dynam- +arXiv:2301.11610v1 [hep-lat] 27 Jan 2023 + +2 +ical quarks but away from the physical point and for +finite lattice spacings. On a finite lattice, the most of- +ten used lattice discretization i.e. the staggered fermions +only has a remnant of the continuum chiral symmetry +group due to mixing of spin and flavor degrees of free- +dom. +Furthermore the anomalous part of the chiral +symmetry in the continuum is not realized exactly by +the staggered/Wilson quarks and is expected to be re- +covered only in the continuum limit. We, for the first +time study the properties of the eigenvalue spectrum of +(highly) improved dynamical staggered Dirac operator +in large volume lattices by carefully performing a con- +tinuum extrapolation. We show that the deep infrared +spectrum of QCD Dirac operator has indeed a peak of +near-zero modes which survives in continuum. These are +distinct from other infrared modes which has a linearly +rising density and a quadratic level repulsion similar to a +certain class of random matrix theories. These so-called +bulk modes are delocalized in volume as compared to the +near-zero modes and they tend to distinctly disentangle +from each other at a temperature ∼ 1.15 Tc, which is also +where UA(1) is effectively restored. +In the subsequent +sections we discuss our results and also provide a unified +physical explanation of these phenomena we observe. +Numerical Details In this work we use the gauge +configurations for 2 + 1 flavor QCD with physical quark +masses generated by the HotQCD collaboration using +Highly Improved Staggered quark (HISQ) discretization +for the fermions and tree-level Symanzik improved gauge +action. These ensembles have been previously used to +measure the equation of state of QCD both at zero and +finite baryon density [3, 44]. The Goldstone pion mass is +set to 140 MeV and the kaon mass is 435 MeV for these +configurations. We focus on five different temperatures, +one below Tc and others above Tc. +For most of these +temperatures we consider three different lattice spacings +corresponding to Nτ = 8, 12, 16, details of which are men- +tioned in Table I in Appendix A. The number of spatial +lattice sites was chosen to be Ns = 4Nτ such that the +spatial volume in each case was about 4 fm, which en- +sures that the system is close to the thermodynamic limit. +We next measure the eigenvalues of the massless HISQ +Dirac matrix on these gauge ensembles using conjugate +gradient method based algorithms. +General features of the eigenvalue spectrum of +QCD using HISQ Dirac operator in continuum +limit In this section we study in detail the eigenvalue +density ρ(λ) of the fermions in 2 + 1 flavor QCD by +performing a continuum extrapolation of the parame- +ters characterizing the eigenspectrum calculated on the +lattice with Highly Improved Staggered Quarks (HISQ) +discretization. +We first study the eigenvalue spectrum +for four different temperatures above Tc in order to un- +derstand whether the flavor singlet and non-singlet parts +of the chiral symmetry is effectively and simultaneously +restored or not. +At zero temperature it is known from chiral perturba- +tion theory [45] that the bulk eigenvalue density is +ρ(λ) = ⟨0| ¯ψψ|0⟩ +π ++ |λ|⟨0| ¯ψψ|0⟩2 +N 2 +f − 4 +32π2NfF 4π ++ .. +(1) +The intercept of the eigenvalue density gives the chiral +condensate. The ratio of the slope and the intercept of +the density as a function of λ should be proportional +to the chiral condensate. We first focus on the intercept +and the slope (linear in λ) of the eigenvalue density at the +lowest temperature T = 145 MeV, shown in the left panel +of Fig. 1, and compare with the expectations from Eq. 1. +At this temperature we could only obtain a continuum +estimate of the slope and intercept as we have data for +two lattice spacings. From the continuum estimate of the +intercept we obtain a chiral condensate ⟨0| ¯ψψ|0⟩/T 3 = +18.4. From the slope we could similarly extract its square +and hence the chiral condensate (normalized by T 3) to be +17.3 which is consistent with the one extracted from the +intercept. Thus leading features of the eigenvalue density +of QCD at 145 MeV are indeed very well represented +within chiral perturbation theory. +The bulk eigenvalue density in the chirally symmetric +phase has been studied very recently [46]. Most generally, +it can be expressed as a function of λ as +ρ(λ) +T 3 += ρ0 +T 3 + λ +T .c1(T, m) +T 2 ++ λ2 +T 2 .c2(T, m) +T ++ λ3 +T 3 c3(T, m) . +(2) +Here c1 is the coefficient that characterizes the leading- +order growth of the eigenvalue spectrum in the deep infra- +red and c2 is its next-to leading order coefficient which +eventually has a λ3-dependence predicted from perturba- +tion theory. The intercept ρ0 gives the the chiral conden- +sate. The coefficients c1,2,3 can in general be a function +of the temperature T and the light-quark mass m. +The results of the eigenvalue density ρ(λ)/T 3 as a func- +tion of λ for T > Tc are shown in the middle and right +panel of Fig. 1. On the finest available Nτ = 16 lattice, +we observe two distinct features in the eigenvalue spec- +trum, a peak of near-zero eigenvalues and the linearly +rising part, which we call as bulk modes. For T ≲ Tc, the +near-zero and the bulk eigenvalues overlap strongly mak- +ing it impossible to distinguish them apart. At higher +temperatures, the bulk eigenvalues separate out from the +deep-infrared part of the spectrum allowing for near-zero +modes to be distinctly visible. +Comparing the results +of different lattice spacings, we observe the same trend +at each temperature above Tc i.e. near-zero peak gets +smeared with the bulk for coarser lattices and becomes +more prominent in the continuum limit. This is thus a +physical feature of the eigen spectrum and not a lattice +artifact. In order to interpret its origin we recall that in +the instanton liquid model (ILM) at zero temperature, +the scaled eigenvalue (cλ) density of the Dirac operator +for Nf flavors and zero topological charge sector is dis- +tributed according to [47], +ρ(cλ) = cλ +2 +� +J2 +Nf (cλ) − JNf +1(cλ)JNf −1(cλ) +� +. +(3) + +3 + 0 + 2 + 4 + 6 + 8 + 10 + 0 + 0.05 + 0.1 + 0.15 + 0.2 + 0.25 +ρ(λ)/Τ3 +λ/T +145 MeV +Nτ= 12 += 16 + 0 + 2 + 4 + 6 + 8 + 10 + 0 + 0.1 + 0.2 + 0.3 + 0.4 + 0.5 +ρ(λ)/Τ3 +λ/T +166 MeV +Nτ = 8 += 12 += 16 + 0 + 2 + 4 + 6 + 8 + 10 + 0 + 0.1 + 0.2 + 0.3 + 0.4 + 0.5 +ρ(λ)/Τ3 +λ/T +171 MeV +Nτ = 8 += 12 += 16 +Fig. 1: Eigenvalue spectrum for HISQ Dirac operator for 3 different lattice spacings corresponding to Nτ = 8, 12, 16 at +T = 166, 171 MeV (center, right) and for two different lattice spacings, Nτ = 12, 16 respectively at T = 145 MeV (left). + 0 + 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 + 0.7 + 0 + 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 +ρ(cλ) +cλ +Nτ=16 +ILM prediction +T = 162 MeV + = 166 MeV += 171 MeV +Fig. 2: Near-zero (scaled) eigenvalue density for HISQ Dirac +operator at T = 162, 166, 171 MeV for the finest lattice spac- +ing corresponding to Nτ = 16 and its comparison with ILM +prediction available at T = 0. +To compare our data with the above formula, we take +c = V ⟨0| ¯ψψ|0⟩/T, where V is the spatial volume of the +system and Nf = 3. A comparison of near zero modes for +three different temperatures, T = 162, 166, 171 MeV, is +shown in Fig. 2 by removing the contribution of the bulk +intercept ρ0. We observe a good agreement with ILM for +T = 171 MeV, in particular, the initial few oscillations +of the small eigenvalue density as a function of cλ. +Now focusing on the bulk modes, it was shown us- +ing chiral Ward identities that in the symmetry restored +phase, the sufficient condition for UA(1) restoration ev- +ident from the degeneracy of up to 6-point correlation +functions in the scalar-pseudo-scalar sector are c1 = +O(m2) +... and c3 = c30 +O(m2)+.... The perturbative +λ3-growth in Eq. 2 can have a mass-independent coeffi- +cient which however does not lead to UA(1) breaking. We +verify whether indeed it is true even non-perturbatively +by performing a fit to the bulk part i.e. all eigenvalues +λ > λ0 with ρ(λ) +T 3 = λ +T . c1(T,m) +T 2 ++ ρ0 +T 3 . This ansatz neglects +higher powers in λ which is well justified since we are +in the deep infrared of the eigen spectrum, represented +by O(100) eigenvalues out of a total million available on +such lattice sizes. The results of the fit are discussed in +Table II. The extracted slope c1 for each temperature +T > Tc, at three different values of Nτ then allows us +to perform a continuum (∼ 1/N 2 +τ ) extrapolation of this +coefficient. We next study the m-dependence of this con- +tinuum extrapolated coefficient c1(m, T). The results of +the fits are shown in Fig. 3. It is evident from the fit +that it is more favorable that c1 is proportional to T 2 +(χ2/d.o.f=0.6) to leading order rather than c1 is propor- +tional to m2 (χ2/d.o.f=0.1). From the fit we obtain the +value of c1(m, T)/T 2 = 16.8(4). + 12 + 14 + 16 + 18 + 20 + 22 + 24 + 1.02 + 1.04 + 1.06 + 1.08 + 1.1 + 1.12 + 1.14 +c1(m,T)/T2 +T/Tc +Fig. 3: Continuum estimates for c1(m, T)/T 2 for T > Tc ob- +tained after fitting the points with a m-independent constant +(orange band) and a sum of quadratic (m2/T 2) and quartic +(m4/T 4) dependence (gray band). +This result for the slope in the continuum limit has +a very important consequence, i.e. the m-independent +term in c1 ensures that the UA(1) part of the chiral sym- +metry will remain effectively broken in the chiral limit in +the symmetry-restored phase. The coefficient of linear- +in-λ term at finite temperature is significantly larger than +its zero temperature value of 0.63 in units of T 2 +c obtained +from Eq. 1. For extracting the later we have used the +latest data for the chiral condensate and Fπ from the +FLAG review [48], for Nf = 3. A significant thermal en- +hancement in the slope of the eigen spectrum is observed +above Tc. +Moreover the slope of the eigen density for +T ≲ 1.12 Tc is distinctly different from the perturbative + +4 +λ3 rise implying significant non-perturbative effects. +The fate of UA(1) breaking in the continuum +limit Since the flavor singlet part of the chiral sym- +metry is anomalous it has no corresponding order pa- +rameter. Hence to measure whether this singlet part of +the chiral symmetry is simultaneously (and effectively) +restored along with the non-singlet part, it has been +suggested [49] to look at the degeneracies of the in- +tegrated correlators of mesons i.e., χπ − χδ. +In the +continuum, the integrated meson correlators are related +to each others through the following relations, χδ = +χσ − 4χdisc and χπ = χη + 4χ5disc. These integrated me- +son correlators are defined as χπ = +� +d4x ⟨πi(x)πi(0)⟩, +χσ = +� +d4x ⟨σ(x)σ(0)⟩, χδ = +� +d4x ⟨δi(x)δi(0)⟩ and +χη = +� +d4x ⟨η(x)η(0)⟩ where i = 1, 2, 3. +We measure +(χπ − χδ)/T 2 at the four different temperatures above +Tc, and perform a ∼ 1/N 2 +τ continuum extrapolation at +each temperature, results of which are shown in Fig. 4. +For the highest temperature we have only two data points +available corresponding to Nτ = 8, 12 for continuum ex- +trapolation hence assigned a 40% and 20% error in slope +and the intercept obtained from the fit, similar to that +obtained for the previous temperature. It is evident that +the continuum extrapolated values of this integrated cor- +relator drops to 1/6 when T/Tc changes from 1.04-1.12 +and a naive linear extrapolation of the intercept gives a +temperature around 1.14 Tc when this observable goes to +zero. In fact the values of this observable increase when +the lattice spacings are made finer. Performing contin- +uum estimates with finer lattice sizes Nτ = 16, 12 at +each temperature, gives a higher intercept than the cor- +responding extrapolation considering all three Nτ-values. +Hence the finiteness of this observable is quite robust and +we conclude that UA(1) does not get effectively restored +at Tc. + 20 + 40 + 60 + 80 + 100 + 120 + 140 + 160 + 180 + 200 + 0 + 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 +(χπ - χδ)/T2 +1/Nτ +2 +162 MeV +166 MeV +171 MeV +176 MeV +Fig. 4: The continuum estimates for χπ − χδ normalized by +the square of temperature for HISQ fermions from 3 dif- +ferent lattice spacings corresponding to Nτ = 8, 12, 16 at +T = 162, 166, 171 MeV respectively and from Nτ = 12, 16 +data at T = 176 MeV. +In the chiral symmetry restored phase, χσ = χπ and +χδ = χη hence one obtaines χπ − χδ = 4χ5,disc. Using +chiral Ward identities it is known that χ5,disc = χt/m2 +where χt is the topological susceptibility of QCD. This +allows relating the UA(1) breaking parameter to the +topological susceptibility through the relation, 1/4(χπ − +χδ)m2 +l /T 4 = χt/T 4. A comparison of these two observ- +ables is shown in Fig. 5. From the figure it is evident +that for T > 1.05 Tc, when chiral symmetry is effectively +restored, the two quantities agree with each other within +errors. This is particularly interesting since for staggered +quarks, even though the chiral and taste symmetries are +intermixed at finite lattice spacing, the symmetries of +QCD and related chiral Ward identities are recovered in +the continuum limit. + 0 + 0.005 + 0.01 + 0.015 + 0.02 + 0.025 + 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 1.11 1.12 1.13 +T/Tc +(χπ-χδ)ml +2/4T4 +χt/T4 +Fig. 5: A comparison of the integrated renormalized correla- +tor (χπ −χδ)m2 +l /4T 4 with the topological susceptibility (mea- +sured independently using gradient flow in Ref. [50]) for tem- +peratures > Tc. +Distribution of the smallest eigenvalue at finite +temperature The probability distribution of the small- +est eigenvalue of the QCD Dirac operator λmin has in- +herent information about the microscopic degrees of free- +dom. For a random matrix ensemble (at zero tempera- +ture) the smallest eigenvalue is distributed according to, +P(cλmin) = +�π +2 (cλmin)3/2I3/2(cλmin)e− 1 +2 (cλmin)2 , +(4) +At the lowest temperature T = 145 MeV, we calcu- +late the probability distribution of the smallest eigen- +value λmin at different lattice spacings and perform a +continuum estimate of the distributions, details of which +are given in Appendix B. The final outcome of the fit is +given in Fig. 6. The continuum extrapolation of the dis- +tribution shown as the orange band agrees well with the +distribution of a chiral Gaussian unitary random matrix +ensemble. In contrast, we also plot the distribution of +the lowest eigenvalue at T = 171 MeV whose continuum +extrapolation is shown as a blue band in Fig. 6. It is +evident that the lowest eigenvalue which is a part of the +near-zero peak follows a very different statistics rather +than known from a chiral RMT. + +5 + 0 + 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 + 0.7 + 0 + 1 + 2 + 3 + 4 + 5 + 6 +P(cλmin) +cλmin +T=145 MeV +=171 MeV +RMT prediction +Fig. 6: The continuum extrapolated probability distribution +of smallest eigenvalue for T = 145, 171 MeV shown as orange +and blue bands respectively and its comparison with the RMT +prediction. +Why is UA(1) effectively restored at tempera- +ture above Tc? The next question we ask is whether the +near-zero modes which arise due to interactions among +instantons can distinctly disentangle out of the bulk +modes. A similar phenomena occurs in disordered semi- +metals leading to an Anderson-like transition. In such +systems, with increasing strength of the disorder poten- +tial, there is a dynamical transition from a phase of delo- +calized electron states to that of localized states, with a +certain energy threshold i.e., the mobility edge separating +them. It is also known that near such an Anderson-like +transition, the eigenvalue spacing distribution of the dis- +ordered states follows a similar behavior as RMTs for all +spacing values except at the tails of the distribution due +to the effects of the localized states. We observe the same +features for the QCD Dirac eigen spacing distribution for +our finest Nτ = 16 lattices, detailed in Appendix C. In +addition we have performed a systematic measurement +of level-spacing distributions at different temperatures +above Tc for different lattice spacings and extracted the +parameters that characterize its functional dependence +in the same Appendix. We find that the bulk modes (ex- +cept at its higher tails) agree very well with the results +obtained for random matrices belonging to Gaussian Uni- +tary ensemble (GUE). Having shown the distinct features +of near-zero and bulk modes, we have elaborated on how +reliably we can estimate the temperature at which these +modes separate in Appendix D. We obtain the tempera- +ture of ∼ 1.15(3) Tc, which is similar to a mobility edge +that separates the near-zero from the bulk modes. +In order to interpret these results, one could visualize +the quarks moving in the background of an interacting +ensemble of instantons, where the strength of the inter- +actions changes as a function of temperature. +At the +microscopic level it is conjectured that the instantons +remain strongly correlated below Tc, subsequently tran- +sitioning to a liquid-like phase with a finite correlation +length [51] just above Tc, and eventually to a gas-like +phase at 2 Tc [13, 15]. Below Tc the intercept of the in- +frared eigenvalue density quantifies the chiral condensate +which corresponds to the breaking of the non-singlet part +of the chiral symmetry. Due to very strong correlations +the microscopic details of the interactions are lost and the +eigenvalues repel strongly similar to random matrices of +a GU ensemble. +As the temperature is increased, the +interactions weaken and indeed at ∼ 171 MeV, the near- +zero eigenvalues with an oscillating behavior, as predicted +from instanton liquid model, start to become prominent. +These eventually separate from the bulk at ∼ 1.15 Tc +analogous to opening of a mobility edge. Earlier studies +have observed screening of inter-instanton interactions +and build-up of local pockets of Polyakov loop fluctua- +tions [38, 52] above such temperatures. This is also the +region where the constituent dyons of the closely-spaced +instantons interact semi-classically and thus start to be- +come detectable [53–56]. +Incidentally this suppression of long range instanton +interactions also weakens the strength of UA(1) breaking, +allowing for its effective restoration at T ≲ 1.15 Tc. Lat- +tice studies [57, 58] have reported a jump in the electrical +conductivity around this temperature. This also suggests +that the strength of the attractive potential due to in- +stantons changes from liquid-like correlations to sparse +local hot-spots, leaving most of the quark momentum +states beyond the mobility edge to be delocalized thus +enhancing the electrical charge transport. +Conclusions In this letter we have addressed a long- +standing question of whether the flavor singlet UA(1) sub- +group of the chiral symmetry gets effectively restored si- +multaneously with the non-singlet part for QCD with two +light quark flavors at Tc. The effective restoration of the +anomalous UA(1) symmetry is a non-perturbative phe- +nomenon driven by the deep infra-red part of the QCD +Dirac eigenvalue spectrum. By carefully performing the +continuum extrapolation of the staggered Dirac spectrum +on the lattice and studying in detail its properties, we ex- +plicitly demonstrate that UA(1) remains effectively bro- +ken in the chirally symmetric phase for T ≲ 1.15 Tc. We +also provide arguments for why this conclusion should +remain unchanged even in the chiral limit. +With the increase in temperature the strength of in- +teractions between the instantons starts weakening due +to which the deep infrared part of the spectrum is sepa- +rated out of the bulk modes which happens to be around +T ∼ 1.15 Tc. The tunneling probability due to instantons +also decreases with increasing temperature which results +in lowering of the height of near-zero peak of eigenvalue +density. We show for the first time that both these phe- +nomena are possibly the reason behind the UA(1) restora- +tion, which also surprisingly happens to be around the +same temperature. Observations of such rich interplay of +phenomena in QCD matter above Tc should be quite ro- +bust, since these are made after performing a continuum +extrapolation. It will be interesting to observe further +finer details of chiral transition in the massless limit with + +6 +QCD Dirac operators which have exact chiral symmetry +on the lattice. +Acknowledgements The authors acknowledge sup- +port by the Deutsche Forschungsgemeinschaft (DFG, +German Research Foundation) through the CRC-TR 211 +’Strong-interaction matter under extreme conditions’– +Project no. 315477589 – TRR 211. S.S. acknowledges +support by the Department of Science and Technology, +Govt. of India through a Ramanujan Fellowship. The +numerical computations in this work were performed on +the GPU cluster at Bielefeld University. We thank the +Bielefeld HPC.NRW team for their support. We thank +the HotQCD Collaboration, specially Christian Schmidt +for sharing the gauge configurations and software with us. +We also acknowledge the contribution of Hiroshi Ohno +who was involved during the early stages of the project. +S.S. is grateful to Frithjof Karsch for helpful discussions +and his kind hospitality when this work was finalized. A +part of this work is based on the MILC collaboration’s +public lattice gauge theory code [59]. +Appendix A: Details of the lattice calculations +of the eigenvalue spectrum + 0 + 2 + 4 + 6 + 8 + 10 + 0 + 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 +ρ(λ)/Τ3 +λ/T +162 MeV +Nτ = 8 += 12 += 16 + 0 + 2 + 4 + 6 + 8 + 10 + 0 + 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 +ρ(λ)/Τ3 +λ/T +176 MeV +Nτ = 8 += 12 +Fig. 7: The eigenvalue spectrum for HISQ Dirac operator at +three different lattice spacings corresponding to Nτ = 8, 12, 16 +for T = 162 MeV and at Nτ = 8, 12 for T = 176 MeV. +We first tabulate the lattice sizes, gauge couplings and +the number of configurations that we have studied for +each temperature value from 145-176 MeV in Table I. As +mentioned earlier, it is important that we take the contin- +uum limit appropriately hence for each temperature we +performed calculations with three different lattice extents +Nτ = 8, 12, 16 in order to perform continuum extrapola- +tion of the parameters characterizing the eigenvalue den- +sity. We then calculated the first 60, 100, 200 eigenvalues +of the massless HISQ Dirac matrix for Nτ = 16, 12, 8 re- +spectively. We have fixed the bin size λa = 0.001 for each +Nτ for measuring the eigenvalue density and performed a +jack-knife analysis to remove any auto-correlation effects +among the data in the bins. We then fit the bulk part +i.e. all eigenvalues above an infrared cut-off λ > λ0 with +the fit ansatz ρ(λ) +T 3 = λ +T . c1(T,m) +T 2 ++ ρ0 +T 3 . The results of the +fit and the choice of cut-off at different temperatures are +mentioned in Table II. +T (MeV) +β Ns Nτ Nconfs +145 +6.285 48 12 +1530 +145 +7.010 64 16 +2860 +162 +6.423 32 +8 +250 +162 +6.825 48 12 +1960 +162 +7.130 64 16 +3390 +166 +6.445 32 +8 +400 +166 +6.850 48 12 +2100 +166 +7.156 64 16 +2190 +171 +6.474 32 +8 +280 +171 +6.880 48 12 +1980 +171 +7.188 64 16 +1040 +176 +6.500 32 +8 +240 +176 +6.910 48 12 +330 +Tab. I: The parameters for the lattice calculations +T [MeV] Nτ λ0/T +c1 +T 2 +ρ0/T 3 +145 +12 +0.1 +9.0(5) 7.30(7) +145 +16 +0.05 +9(1) +6.67(9) +162 +8 +0.2 +8.8(3) +4.1(1) +162 +12 +0.15 13.2(2) 2.69(5) +162 +16 +0.1 +17.5(5) 1.93(7) +166 +8 +0.2 +8.9(1) 3.31(5) +166 +12 +0.15 13.3(3) 1.92(6) +166 +16 +0.1 +16.6(8) 1.4(1) +171 +8 +0.2 +9.3(1) 2.38(5) +171 +12 +0.15 12.9(1) 1.19(3) +171 +16 +0.1 +17.0(5) 0.45(8) +176 +8 +0.2 +9.5(1) 1.67(4) +176 +12 +0.15 13.0(2) 0.36(6) +Tab. II: Lattice size (N 3 +σ × Nτ), temperature (T), the esti- +mated values of c1/T 2 and ρ0/T 3 after the fit of the bulk +modes by taking the lower cutoff at λ0/T. + +7 +We have shown the eigenvalue distributions for three +different temperatures at 145, 166, 171 MeV in Fig. 1. We +also have measured the eigenvalue densities at two other +temperatures at 166, 176 MeV which we show in Fig. 7. +Appendix B: Details of the calculation per- +formed for the smallest eigenvalues for T < Tc +First we have extracted the smallest eigenvalue from +each configuration for Nτ = 12, 16 and later re-scaled +to the dimensionless quantity cλmin, where the value of +⟨ ¯ψψ⟩ at finite temperature is obtained from Ref. [60]. +Keeping the bin size constant we obtained the probabil- +ity distribution of cλmin for each Nτ and then performed +a spline interpolation by taking appropriate weights pro- +portional to the errors for each data point in order to +have a smoother interpolating curve. Next we performed +a continuum extrapolation at each value of cλmin of the +interpolating function with the ansatz c + d/N 2 +τ . We as- +signed a 15% error for T = 145 MeV, as we only had +two points while performing the continuum extrapola- +tion. In Fig. 6 we find a good agreement between the +continuum extrapolated distribution of the lowest eigen- +value at T = 145 MeV and the RMT predictions from +a Gaussian Unitary ensemble. A slight discrepancy exist +for lower and higher values of cλmin. This can be due to +the fact that we use a very low but finite convergence cri- +terion while calculating the eigenvalue spectrum. Hence +we do not have any data for cλmin < 0.6. Since we are +plotting a probability distribution (of the smallest eigen- +value), the area under the curve must be unity. To pre- +serve this criterion the values of the probability densities +along the higher end of the tail lie above the RMT curve +in order to compensate for the relatively lower values in +the lower portion of the tail. +Appendix C: The level spacing distribution for +bulk modes +Next we look at the level spacing distribution of the +bulk modes. +To study the universal properties of the +eigenvalue level spacing fluctuations one has to remove +the system dependent mean. This is done by a method +called unfolding. Let λ represent eigenvalues in the as- +cending sequence for any particular gauge configuration. +The average density of the eigenvalues in the sequence i.e. +the reciprocal of the average spacing as a function of λ +is represented as ¯ρ(λ). The eigenvalue sequence can then +be unfolded using the average level-staircase function, +¯η(λ) = +� λ +λ0 dλ′¯ρ(λ′) which tells us how many eigenvalues +in this sequence are less than λ on an average. Here λ0 +labels the eigenvalue beyond which all the higher eigen- +values are bulk modes and below which are the near-zero +modes. The unfolded sequence is labeled by λuf +i += ¯η(λi), +where the index i labels the original eigenvalue whose un- +folding is performed. +When appropriately normalized, +the average spacing between the unfolded eigenvalues +equals unity. The nearest neighbor spacing distribution +is constructed by calculating the differences between con- +secutive unfolded eigenvalues λuf +i+1 − λuf +i +and organizing +them into histogram bins. This gives us a picture of how +the eigenvalue spacings fluctuate about the average which +we have plotted in Fig. 8 for four different temperatures +T = 162, 166, 171, 176 MeV and at each temperature, for +the three different lattice sizes Nτ = 8, 12, 16 except for +T = 176 MeV. We have then estimated the functional de- +pendence of these nearest neighbor spacing distributions +by two different fit ansatz, shown as solid and dotted +lines in Fig. 8. The dotted curves were obtained after +performing a fit to the lattice data points with the func- +tion f(s) = asbe−cs2, motivated by the Wigner surmise. +The solid curves on the other hand, were obtained after +fitting the points to an ansatz function f(s) = ps2e−qs2. +The values of these parameters a, b, c, p, q after perform- +ing the fits are given in Table III. It is evident that the +level repulsion between the bulk modes is quadratic simi- +lar to that of random matrices belonging to the Gaussian +unitary ensemble (GuE). However for the Nτ = 16 lat- +tices, due to the contamination with the near-zero modes +the fit of the tail is not good and can not be explained by +RMT prediction. In order to account for the long tail of +the spacing distribution we fit it to a semi-Poisson distri- +bution P(s) ∼ s2 exp (−αs) which shows strong repulsion +at small values of s but falls off slowly at large values of +s parameterized by a fit parameter α. After performing +the fit of the level separation with this ansatz, we obtain +the value of α = 3.02(7), 3.17(9), 3.3(1) for temperatures +T = 162, 166, 171 MeV respectively. +The lattice data +now do agree to this new fit ansatz reasonably well for +Nτ = 16 at all temperatures above Tc, which is evident +in Fig. 9. +T (MeV) Nτ +a +b +c +p +q +162 +8 2.91(5) 1.85(3) 1.19(1) 3.16(7) 1.26(2) +162 +12 +2.6(1) 1.69(6) 1.13(3) +3.2(1) 1.29(3) +162 +16 +2.1(4) +1.2(2) +1.0(1) +4.0(6) +1.6(1) +166 +8 2.78(5) 1.78(2) 1.16(1) 3.13(9) 1.26(2) +166 +12 +2.6(2) 1.66(7) 1.12(4) +3.2(2) 1.30(4) +166 +16 +2.1(5) +1.2(2) +1.1(2) +4.5(8) +1.8(2) +171 +8 2.74(7) 1.76(3) 1.15(2) +3.2(1) 1.27(2) +171 +12 +2.5(2) +1.6(1) 1.11(6) +3.4(3) 1.35(6) +171 +16 +1.6(4) +0.8(2) +1.0(2) +5(1) +2.0(3) +176 +8 2.77(7) 1.77(4) 1.16(2) 3.15(9) 1.27(2) +176 +12 +2.3(3) +1.4(1) 1.07(8) +3.5(3) 1.39(7) +Tab. III: The estimated values of the parameters after the fit +to different unfolded level spacing distributions. +Appendix D: Details of extraction of the mobil- +ity edge +Next, in order to estimate when these bulk modes sep- +arate from the deep-infrared peak of eigenvalues, we cal- +culate at what temperature the functional fit of the bulk +eigenvalue spectrum has a non-zero intercept along the +λ-axis which is larger than the typical width of the near- +zero peak. +In the continuum, we have already calcu- +lated the slope of the bulk eigenvalue density, which is +c1(m, T)/T 2 = 16.8(4). Looking at the eigenvalue distri- +butions in Fig.1, we can choose a typical value of λ at + +8 + 0 + 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 + 0.7 + 0.8 + 0.9 + 1 + 0 + 0.5 + 1 + 1.5 + 2 + 2.5 + 3 +P(s) +Spacing s +T=162 MeV +Nτ=16 +=12 +=8 + 0 + 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 + 0.7 + 0.8 + 0.9 + 1 + 0 + 0.5 + 1 + 1.5 + 2 + 2.5 + 3 +P(s) +Spacing s +T=166 MeV +Nτ=16 +=12 +=8 + 0 + 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 + 0.7 + 0.8 + 0.9 + 1 + 0 + 0.5 + 1 + 1.5 + 2 + 2.5 + 3 +P(s) +Spacing s +T=171 MeV +Nτ=16 += 12 +=8 + 0 + 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 + 0.7 + 0.8 + 0.9 + 1 + 0 + 0.5 + 1 + 1.5 + 2 + 2.5 + 3 +P(s) +Spacing s +T=176 MeV +Nτ=12 +=8 +Fig. 8: Unfolded level spacing distribution of bulk eigenvalues modes for different temperatures shown as a function of different +lattice spacings or equivalently, Nτ. The solid lines in each plot correspond to the two-parameter fit and the dotted curves for +three-parameter fits inspired from the Wigner surmise for Gaussian unitary random matrix ensembles. + 0 + 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 + 0.7 + 0.8 + 0.9 + 1 + 0 + 0.5 + 1 + 1.5 + 2 + 2.5 + 3 + 3.5 +P(s) +Spacing s +Nτ=16 +T=162 MeV +=166 MeV +=171 MeV +Fig. 9: A fit to the eigenvalue level spacing distribution using +a mixed ansatz for Nτ = 16 at T = 162, 166, 171 MeV. +-1 +-0.5 + 0 + 0.5 + 1 + 1.5 + 2 + 2.5 + 1 + 1.02 1.04 1.06 1.08 1.1 1.12 1.14 1.16 1.18 +ρ0/T3 +T/Tc +Fig. 10: Continuum extrapolation of the bulk intercept for +eigenvalue densities at different temperatures above Tc. 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Bielefeld (main) (2018). + diff --git a/A9FJT4oBgHgl3EQfry2f/content/tmp_files/load_file.txt b/A9FJT4oBgHgl3EQfry2f/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..807056c730ab68e68ad18326fc29090c3db93a65 --- /dev/null +++ b/A9FJT4oBgHgl3EQfry2f/content/tmp_files/load_file.txt @@ -0,0 +1,1042 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf,len=1041 +page_content='Eigenvalues of QCD Dirac matrix with improved staggered quarks in the continuum limit Olaf Kaczmarek,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='1 Ravi Shanker,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' ∗ and Sayantan Sharma2 1Fakult¨at f¨ur Physik,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Universit¨at Bielefeld,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' D-33615 Bielefeld,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Germany 2The Institute of Mathematical Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' a CI of Homi Bhabha National Institute,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Chennai,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 600113,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' India We calculate the eigenmodes of the Highly Improved Staggered Quark (HISQ) matrix near the chiral crossover transition in QCD with 2 + 1 flavors with the aim to gain more insights into its temperature dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' On performing the continuum extrapolation, we do not observe any gap opening up in the infrared part of the eigenvalue density of QCD Dirac operator, instead we observe a peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The existence of the peak and oscillations of the infrared eigenmodes can be understood in terms of an interacting ensemble of instantons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' From the properties of the continuum extrapolated eigen spectrum we further show that the anomalous UA(1) part of the chiral symmetry is not effectively restored simultaneously along with its non-singlet counterpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We provide an explanation for this observation, further showing interesting connections between the anomalous UA(1) restoration and the change in the infrared part of the eigenvalue distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' PACS numbers: 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='Gc, 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='Ha, 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='Rd, 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='Kc Introduction The eigenvalue spectrum of the quark Dirac operator contains valuable information about the fundamental properties of Quantum Chromodynamics (QCD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The chiral condensate which acts as a (pseudo) order parameter for the chiral (crossover) transition in QCD is related to the density of near-zero eigenvalues [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' In fact it was shown from very general considerations that the formation of the chiral condensate is related to the occurrence of small eigenvalues that scale proportional to the volume [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The breaking of the non-singlet part of chiral symmetry i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' SUA(2) × SUV (2) → SUV (2) of QCD with physical quark masses at the crossover tem- perature Tc = 156.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5 MeV [3] can also be explained in terms of modifications in the deep infrared part of the eigenvalue density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The flavor-singlet UA(1) part of the chiral symmetry on the other hand, is anomalous yet is believed to play an important role in determining the nature of the chiral phase transition [4–6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The temper- ature dependence of the amount of UA(1) breaking near the chiral crossover transition in QCD can be only deter- mined using non-perturbative lattice techniques and is a topic of contemporary interest in lattice QCD see for e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' [7, 8] for recent reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Whereas there are some very compelling evidence that show UA(1) remains effec- tively broken in 2 + 1 flavor QCD with physical quark mass m [9–15], even when m → 0 [16], there are lat- tice studies which also favor an effective restoration at Tc [17–22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The eigenvalue spectrum of the QCD Dirac matrix also encodes within it some remarkable universal properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' It was shown that the route towards achieving thermo- dynamic limit for the infrared modes of the Dirac op- erator is universal [23], for any number of light quark flavors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The existence of a non-zero chiral condensate leads to a sum rule involving sum of inverse squares of ∗Electronic address: rshanker@imsc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='in these small eigenvalues [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' These sum rules are univer- sal irrespective of the details of the nature and type of gauge interactions [23, 24] and could be derived from chi- ral random matrix theory [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' A good agreement was demonstrated for the distribution of the small eigenvalues and the spectral density of lattice QCD Dirac operator and chiral random matrix theory at zero temperature on small lattice volumes [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' In fact universal correlations between higher order spectral functions in a random ma- trix theory has been derived [27] and its connection to QCD was discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' At finite temperature the universal features of infrared eigenvalues can be also accounted for within a random matrix theory [28–30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Additionally the infrared eigenvalue spectrum of QCD has more subtle features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' A near-zero peak of localized eigenvalues has been observed for finite lattices, mixing with but very different from the delocalized bulk modes whose spectral density follows random matrix statistics [7, 31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Whether or not such a feature survives in the continuum limit is yet to be ascertained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Previous studies of quark Dirac spectrum in an instanton liquid ensemble [29, 32] at zero temperature have observed similar peak-like feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' With increasing temperature the localized modes starts separating out from the random bulk modes lead- ing to the opening up of a mobility edge [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The corre- sponding temperature where a finite mobility edge sepa- rates the bulk modes from the localized one was initially estimated from lattice studies to be identical to Tc in dy- namical [33–38] as well as in quenched QCD [39], remi- niscent of an Anderson-like transition that is observed in disordered semi-metals [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' However independent lat- tice studies do discuss another possible scenario where the opening of a finite mobility edge may occur at tem- peratures higher that Tc [41], with an intermediate phase consisting of scale-invariant infinitely extended infrared modes [42, 43] strongly interacting with the bulk modes leading to a singularity at the mobility edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Most of the previous lattice QCD studies were ei- ther performed in the quenched limit or with dynam- arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='11610v1 [hep-lat] 27 Jan 2023 2 ical quarks but away from the physical point and for finite lattice spacings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' On a finite lattice, the most of- ten used lattice discretization i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' the staggered fermions only has a remnant of the continuum chiral symmetry group due to mixing of spin and flavor degrees of free- dom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Furthermore the anomalous part of the chiral symmetry in the continuum is not realized exactly by the staggered/Wilson quarks and is expected to be re- covered only in the continuum limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We, for the first time study the properties of the eigenvalue spectrum of (highly) improved dynamical staggered Dirac operator in large volume lattices by carefully performing a con- tinuum extrapolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We show that the deep infrared spectrum of QCD Dirac operator has indeed a peak of near-zero modes which survives in continuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' These are distinct from other infrared modes which has a linearly rising density and a quadratic level repulsion similar to a certain class of random matrix theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' These so-called bulk modes are delocalized in volume as compared to the near-zero modes and they tend to distinctly disentangle from each other at a temperature ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='15 Tc, which is also where UA(1) is effectively restored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' In the subsequent sections we discuss our results and also provide a unified physical explanation of these phenomena we observe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Numerical Details In this work we use the gauge configurations for 2 + 1 flavor QCD with physical quark masses generated by the HotQCD collaboration using Highly Improved Staggered quark (HISQ) discretization for the fermions and tree-level Symanzik improved gauge action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' These ensembles have been previously used to measure the equation of state of QCD both at zero and finite baryon density [3, 44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The Goldstone pion mass is set to 140 MeV and the kaon mass is 435 MeV for these configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We focus on five different temperatures, one below Tc and others above Tc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' For most of these temperatures we consider three different lattice spacings corresponding to Nτ = 8, 12, 16, details of which are men- tioned in Table I in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The number of spatial lattice sites was chosen to be Ns = 4Nτ such that the spatial volume in each case was about 4 fm, which en- sures that the system is close to the thermodynamic limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We next measure the eigenvalues of the massless HISQ Dirac matrix on these gauge ensembles using conjugate gradient method based algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' General features of the eigenvalue spectrum of QCD using HISQ Dirac operator in continuum limit In this section we study in detail the eigenvalue density ρ(λ) of the fermions in 2 + 1 flavor QCD by performing a continuum extrapolation of the parame- ters characterizing the eigenspectrum calculated on the lattice with Highly Improved Staggered Quarks (HISQ) discretization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We first study the eigenvalue spectrum for four different temperatures above Tc in order to un- derstand whether the flavor singlet and non-singlet parts of the chiral symmetry is effectively and simultaneously restored or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' At zero temperature it is known from chiral perturba- tion theory [45] that the bulk eigenvalue density is ρ(λ) = ⟨0| ¯ψψ|0⟩ π + |λ|⟨0| ¯ψψ|0⟩2 N 2 f − 4 32π2NfF 4π + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='. (1) The intercept of the eigenvalue density gives the chiral condensate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The ratio of the slope and the intercept of the density as a function of λ should be proportional to the chiral condensate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We first focus on the intercept and the slope (linear in λ) of the eigenvalue density at the lowest temperature T = 145 MeV, shown in the left panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 1, and compare with the expectations from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' At this temperature we could only obtain a continuum estimate of the slope and intercept as we have data for two lattice spacings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' From the continuum estimate of the intercept we obtain a chiral condensate ⟨0| ¯ψψ|0⟩/T 3 = 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' From the slope we could similarly extract its square and hence the chiral condensate (normalized by T 3) to be 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='3 which is consistent with the one extracted from the intercept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Thus leading features of the eigenvalue density of QCD at 145 MeV are indeed very well represented within chiral perturbation theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The bulk eigenvalue density in the chirally symmetric phase has been studied very recently [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Most generally, it can be expressed as a function of λ as ρ(λ) T 3 = ρ0 T 3 + λ T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='c1(T, m) T 2 + λ2 T 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='c2(T, m) T + λ3 T 3 c3(T, m) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' (2) Here c1 is the coefficient that characterizes the leading- order growth of the eigenvalue spectrum in the deep infra- red and c2 is its next-to leading order coefficient which eventually has a λ3-dependence predicted from perturba- tion theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The intercept ρ0 gives the the chiral conden- sate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The coefficients c1,2,3 can in general be a function of the temperature T and the light-quark mass m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The results of the eigenvalue density ρ(λ)/T 3 as a func- tion of λ for T > Tc are shown in the middle and right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' On the finest available Nτ = 16 lattice, we observe two distinct features in the eigenvalue spec- trum, a peak of near-zero eigenvalues and the linearly rising part, which we call as bulk modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' For T ≲ Tc, the near-zero and the bulk eigenvalues overlap strongly mak- ing it impossible to distinguish them apart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' At higher temperatures, the bulk eigenvalues separate out from the deep-infrared part of the spectrum allowing for near-zero modes to be distinctly visible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Comparing the results of different lattice spacings, we observe the same trend at each temperature above Tc i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' near-zero peak gets smeared with the bulk for coarser lattices and becomes more prominent in the continuum limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' This is thus a physical feature of the eigen spectrum and not a lattice artifact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' In order to interpret its origin we recall that in the instanton liquid model (ILM) at zero temperature, the scaled eigenvalue (cλ) density of the Dirac operator for Nf flavors and zero topological charge sector is dis- tributed according to [47], ρ(cλ) = cλ 2 � J2 Nf (cλ) − JNf +1(cλ)JNf −1(cλ) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' (3) 3 0 2 4 6 8 10 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='25 ρ(λ)/Τ3 λ/T 145 MeV Nτ= 12 = 16 0 2 4 6 8 10 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5 ρ(λ)/Τ3 λ/T 166 MeV Nτ = 8 = 12 = 16 0 2 4 6 8 10 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5 ρ(λ)/Τ3 λ/T 171 MeV Nτ = 8 = 12 = 16 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 1: Eigenvalue spectrum for HISQ Dirac operator for 3 different lattice spacings corresponding to Nτ = 8, 12, 16 at T = 166, 171 MeV (center, right) and for two different lattice spacings, Nτ = 12, 16 respectively at T = 145 MeV (left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='7 0 2 4 6 8 10 12 14 16 18 ρ(cλ) cλ Nτ=16 ILM prediction T = 162 MeV = 166 MeV = 171 MeV Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 2: Near-zero (scaled) eigenvalue density for HISQ Dirac operator at T = 162, 166, 171 MeV for the finest lattice spac- ing corresponding to Nτ = 16 and its comparison with ILM prediction available at T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' To compare our data with the above formula, we take c = V ⟨0| ¯ψψ|0⟩/T, where V is the spatial volume of the system and Nf = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' A comparison of near zero modes for three different temperatures, T = 162, 166, 171 MeV, is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 2 by removing the contribution of the bulk intercept ρ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We observe a good agreement with ILM for T = 171 MeV, in particular, the initial few oscillations of the small eigenvalue density as a function of cλ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Now focusing on the bulk modes, it was shown us- ing chiral Ward identities that in the symmetry restored phase, the sufficient condition for UA(1) restoration ev- ident from the degeneracy of up to 6-point correlation functions in the scalar-pseudo-scalar sector are c1 = O(m2) +.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' and c3 = c30 +O(m2)+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='. The perturbative λ3-growth in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 2 can have a mass-independent coeffi- cient which however does not lead to UA(1) breaking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We verify whether indeed it is true even non-perturbatively by performing a fit to the bulk part i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' all eigenvalues λ > λ0 with ρ(λ) T 3 = λ T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' c1(T,m) T 2 + ρ0 T 3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' This ansatz neglects higher powers in λ which is well justified since we are in the deep infrared of the eigen spectrum, represented by O(100) eigenvalues out of a total million available on such lattice sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The results of the fit are discussed in Table II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The extracted slope c1 for each temperature T > Tc, at three different values of Nτ then allows us to perform a continuum (∼ 1/N 2 τ ) extrapolation of this coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We next study the m-dependence of this con- tinuum extrapolated coefficient c1(m, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The results of the fits are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' It is evident from the fit that it is more favorable that c1 is proportional to T 2 (χ2/d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='f=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='6) to leading order rather than c1 is propor- tional to m2 (χ2/d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='f=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' From the fit we obtain the value of c1(m, T)/T 2 = 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='8(4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 12 14 16 18 20 22 24 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='02 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='04 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='06 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='08 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='12 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='14 c1(m,T)/T2 T/Tc Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 3: Continuum estimates for c1(m, T)/T 2 for T > Tc ob- tained after fitting the points with a m-independent constant (orange band) and a sum of quadratic (m2/T 2) and quartic (m4/T 4) dependence (gray band).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' This result for the slope in the continuum limit has a very important consequence, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' the m-independent term in c1 ensures that the UA(1) part of the chiral sym- metry will remain effectively broken in the chiral limit in the symmetry-restored phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The coefficient of linear- in-λ term at finite temperature is significantly larger than its zero temperature value of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='63 in units of T 2 c obtained from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' For extracting the later we have used the latest data for the chiral condensate and Fπ from the FLAG review [48], for Nf = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' A significant thermal en- hancement in the slope of the eigen spectrum is observed above Tc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Moreover the slope of the eigen density for T ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='12 Tc is distinctly different from the perturbative 4 λ3 rise implying significant non-perturbative effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The fate of UA(1) breaking in the continuum limit Since the flavor singlet part of the chiral sym- metry is anomalous it has no corresponding order pa- rameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Hence to measure whether this singlet part of the chiral symmetry is simultaneously (and effectively) restored along with the non-singlet part, it has been suggested [49] to look at the degeneracies of the in- tegrated correlators of mesons i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=', χπ − χδ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' In the continuum, the integrated meson correlators are related to each others through the following relations, χδ = χσ − 4χdisc and χπ = χη + 4χ5disc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' These integrated me- son correlators are defined as χπ = � d4x ⟨πi(x)πi(0)⟩, χσ = � d4x ⟨σ(x)σ(0)⟩, χδ = � d4x ⟨δi(x)δi(0)⟩ and χη = � d4x ⟨η(x)η(0)⟩ where i = 1, 2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We measure (χπ − χδ)/T 2 at the four different temperatures above Tc, and perform a ∼ 1/N 2 τ continuum extrapolation at each temperature, results of which are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' For the highest temperature we have only two data points available corresponding to Nτ = 8, 12 for continuum ex- trapolation hence assigned a 40% and 20% error in slope and the intercept obtained from the fit, similar to that obtained for the previous temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' It is evident that the continuum extrapolated values of this integrated cor- relator drops to 1/6 when T/Tc changes from 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='04-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='12 and a naive linear extrapolation of the intercept gives a temperature around 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='14 Tc when this observable goes to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' In fact the values of this observable increase when the lattice spacings are made finer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Performing contin- uum estimates with finer lattice sizes Nτ = 16, 12 at each temperature, gives a higher intercept than the cor- responding extrapolation considering all three Nτ-values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Hence the finiteness of this observable is quite robust and we conclude that UA(1) does not get effectively restored at Tc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 20 40 60 80 100 120 140 160 180 200 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='002 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='004 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='006 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='008 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='012 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='014 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='016 (χπ - χδ)/T2 1/Nτ 2 162 MeV 166 MeV 171 MeV 176 MeV Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 4: The continuum estimates for χπ − χδ normalized by the square of temperature for HISQ fermions from 3 dif- ferent lattice spacings corresponding to Nτ = 8, 12, 16 at T = 162, 166, 171 MeV respectively and from Nτ = 12, 16 data at T = 176 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' In the chiral symmetry restored phase, χσ = χπ and χδ = χη hence one obtaines χπ − χδ = 4χ5,disc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Using chiral Ward identities it is known that χ5,disc = χt/m2 where χt is the topological susceptibility of QCD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' This allows relating the UA(1) breaking parameter to the topological susceptibility through the relation, 1/4(χπ − χδ)m2 l /T 4 = χt/T 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' A comparison of these two observ- ables is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' From the figure it is evident that for T > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='05 Tc, when chiral symmetry is effectively restored, the two quantities agree with each other within errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' This is particularly interesting since for staggered quarks, even though the chiral and taste symmetries are intermixed at finite lattice spacing, the symmetries of QCD and related chiral Ward identities are recovered in the continuum limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='005 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='015 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='025 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='03 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='04 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='05 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='06 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='07 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='08 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='09 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='11 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='12 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='13 T/Tc (χπ-χδ)ml 2/4T4 χt/T4 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 5: A comparison of the integrated renormalized correla- tor (χπ −χδ)m2 l /4T 4 with the topological susceptibility (mea- sured independently using gradient flow in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' [50]) for tem- peratures > Tc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Distribution of the smallest eigenvalue at finite temperature The probability distribution of the small- est eigenvalue of the QCD Dirac operator λmin has in- herent information about the microscopic degrees of free- dom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' For a random matrix ensemble (at zero tempera- ture) the smallest eigenvalue is distributed according to, P(cλmin) = �π 2 (cλmin)3/2I3/2(cλmin)e− 1 2 (cλmin)2 , (4) At the lowest temperature T = 145 MeV, we calcu- late the probability distribution of the smallest eigen- value λmin at different lattice spacings and perform a continuum estimate of the distributions, details of which are given in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The final outcome of the fit is given in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The continuum extrapolation of the dis- tribution shown as the orange band agrees well with the distribution of a chiral Gaussian unitary random matrix ensemble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' In contrast, we also plot the distribution of the lowest eigenvalue at T = 171 MeV whose continuum extrapolation is shown as a blue band in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' It is evident that the lowest eigenvalue which is a part of the near-zero peak follows a very different statistics rather than known from a chiral RMT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 5 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='7 0 1 2 3 4 5 6 P(cλmin) cλmin T=145 MeV =171 MeV RMT prediction Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 6: The continuum extrapolated probability distribution of smallest eigenvalue for T = 145, 171 MeV shown as orange and blue bands respectively and its comparison with the RMT prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Why is UA(1) effectively restored at tempera- ture above Tc?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The next question we ask is whether the near-zero modes which arise due to interactions among instantons can distinctly disentangle out of the bulk modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' A similar phenomena occurs in disordered semi- metals leading to an Anderson-like transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' In such systems, with increasing strength of the disorder poten- tial, there is a dynamical transition from a phase of delo- calized electron states to that of localized states, with a certain energy threshold i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=', the mobility edge separating them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' It is also known that near such an Anderson-like transition, the eigenvalue spacing distribution of the dis- ordered states follows a similar behavior as RMTs for all spacing values except at the tails of the distribution due to the effects of the localized states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We observe the same features for the QCD Dirac eigen spacing distribution for our finest Nτ = 16 lattices, detailed in Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' In addition we have performed a systematic measurement of level-spacing distributions at different temperatures above Tc for different lattice spacings and extracted the parameters that characterize its functional dependence in the same Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We find that the bulk modes (ex- cept at its higher tails) agree very well with the results obtained for random matrices belonging to Gaussian Uni- tary ensemble (GUE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Having shown the distinct features of near-zero and bulk modes, we have elaborated on how reliably we can estimate the temperature at which these modes separate in Appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We obtain the tempera- ture of ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='15(3) Tc, which is similar to a mobility edge that separates the near-zero from the bulk modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' In order to interpret these results, one could visualize the quarks moving in the background of an interacting ensemble of instantons, where the strength of the inter- actions changes as a function of temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' At the microscopic level it is conjectured that the instantons remain strongly correlated below Tc, subsequently tran- sitioning to a liquid-like phase with a finite correlation length [51] just above Tc, and eventually to a gas-like phase at 2 Tc [13, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Below Tc the intercept of the in- frared eigenvalue density quantifies the chiral condensate which corresponds to the breaking of the non-singlet part of the chiral symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Due to very strong correlations the microscopic details of the interactions are lost and the eigenvalues repel strongly similar to random matrices of a GU ensemble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' As the temperature is increased, the interactions weaken and indeed at ∼ 171 MeV, the near- zero eigenvalues with an oscillating behavior, as predicted from instanton liquid model, start to become prominent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' These eventually separate from the bulk at ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='15 Tc analogous to opening of a mobility edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Earlier studies have observed screening of inter-instanton interactions and build-up of local pockets of Polyakov loop fluctua- tions [38, 52] above such temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' This is also the region where the constituent dyons of the closely-spaced instantons interact semi-classically and thus start to be- come detectable [53–56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Incidentally this suppression of long range instanton interactions also weakens the strength of UA(1) breaking, allowing for its effective restoration at T ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='15 Tc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Lat- tice studies [57, 58] have reported a jump in the electrical conductivity around this temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' This also suggests that the strength of the attractive potential due to in- stantons changes from liquid-like correlations to sparse local hot-spots, leaving most of the quark momentum states beyond the mobility edge to be delocalized thus enhancing the electrical charge transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Conclusions In this letter we have addressed a long- standing question of whether the flavor singlet UA(1) sub- group of the chiral symmetry gets effectively restored si- multaneously with the non-singlet part for QCD with two light quark flavors at Tc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The effective restoration of the anomalous UA(1) symmetry is a non-perturbative phe- nomenon driven by the deep infra-red part of the QCD Dirac eigenvalue spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' By carefully performing the continuum extrapolation of the staggered Dirac spectrum on the lattice and studying in detail its properties, we ex- plicitly demonstrate that UA(1) remains effectively bro- ken in the chirally symmetric phase for T ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='15 Tc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We also provide arguments for why this conclusion should remain unchanged even in the chiral limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' With the increase in temperature the strength of in- teractions between the instantons starts weakening due to which the deep infrared part of the spectrum is sepa- rated out of the bulk modes which happens to be around T ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='15 Tc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The tunneling probability due to instantons also decreases with increasing temperature which results in lowering of the height of near-zero peak of eigenvalue density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We show for the first time that both these phe- nomena are possibly the reason behind the UA(1) restora- tion, which also surprisingly happens to be around the same temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Observations of such rich interplay of phenomena in QCD matter above Tc should be quite ro- bust, since these are made after performing a continuum extrapolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' It will be interesting to observe further finer details of chiral transition in the massless limit with 6 QCD Dirac operators which have exact chiral symmetry on the lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Acknowledgements The authors acknowledge sup- port by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the CRC-TR 211 ’Strong-interaction matter under extreme conditions’– Project no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 315477589 – TRR 211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' acknowledges support by the Department of Science and Technology, Govt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' of India through a Ramanujan Fellowship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The numerical computations in this work were performed on the GPU cluster at Bielefeld University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We thank the Bielefeld HPC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='NRW team for their support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We thank the HotQCD Collaboration, specially Christian Schmidt for sharing the gauge configurations and software with us.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We also acknowledge the contribution of Hiroshi Ohno who was involved during the early stages of the project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' is grateful to Frithjof Karsch for helpful discussions and his kind hospitality when this work was finalized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' A part of this work is based on the MILC collaboration’s public lattice gauge theory code [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Appendix A: Details of the lattice calculations of the eigenvalue spectrum 0 2 4 6 8 10 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='35 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='45 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5 ρ(λ)/Τ3 λ/T 162 MeV Nτ = 8 = 12 = 16 0 2 4 6 8 10 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='6 ρ(λ)/Τ3 λ/T 176 MeV Nτ = 8 = 12 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 7: The eigenvalue spectrum for HISQ Dirac operator at three different lattice spacings corresponding to Nτ = 8, 12, 16 for T = 162 MeV and at Nτ = 8, 12 for T = 176 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We first tabulate the lattice sizes, gauge couplings and the number of configurations that we have studied for each temperature value from 145-176 MeV in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' As mentioned earlier, it is important that we take the contin- uum limit appropriately hence for each temperature we performed calculations with three different lattice extents Nτ = 8, 12, 16 in order to perform continuum extrapola- tion of the parameters characterizing the eigenvalue den- sity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We then calculated the first 60, 100, 200 eigenvalues of the massless HISQ Dirac matrix for Nτ = 16, 12, 8 re- spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We have fixed the bin size λa = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='001 for each Nτ for measuring the eigenvalue density and performed a jack-knife analysis to remove any auto-correlation effects among the data in the bins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We then fit the bulk part i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' all eigenvalues above an infrared cut-off λ > λ0 with the fit ansatz ρ(λ) T 3 = λ T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' c1(T,m) T 2 + ρ0 T 3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The results of the fit and the choice of cut-off at different temperatures are mentioned in Table II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' T (MeV) β Ns Nτ Nconfs 145 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='285 48 12 1530 145 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='010 64 16 2860 162 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='423 32 8 250 162 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='825 48 12 1960 162 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='130 64 16 3390 166 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='445 32 8 400 166 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='850 48 12 2100 166 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='156 64 16 2190 171 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='474 32 8 280 171 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='880 48 12 1980 171 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='188 64 16 1040 176 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='500 32 8 240 176 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='910 48 12 330 Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' I: The parameters for the lattice calculations T [MeV] Nτ λ0/T c1 T 2 ρ0/T 3 145 12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='1 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='0(5) 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='30(7) 145 16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='05 9(1) 6.' metadata={'source': 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8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='2 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5(1) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='67(4) 176 12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='15 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='0(2) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='36(6) Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' II: Lattice size (N 3 σ × Nτ), temperature (T), the esti- mated values of c1/T 2 and ρ0/T 3 after the fit of the bulk modes by taking the lower cutoff at λ0/T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 7 We have shown the eigenvalue distributions for three different temperatures at 145, 166, 171 MeV in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We also have measured the eigenvalue densities at two other temperatures at 166, 176 MeV which we show in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Appendix B: Details of the calculation per- formed for the smallest eigenvalues for T < Tc First we have extracted the smallest eigenvalue from each configuration for Nτ = 12, 16 and later re-scaled to the dimensionless quantity cλmin, where the value of ⟨ ¯ψψ⟩ at finite temperature is obtained from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' [60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Keeping the bin size constant we obtained the probabil- ity distribution of cλmin for each Nτ and then performed a spline interpolation by taking appropriate weights pro- portional to the errors for each data point in order to have a smoother interpolating curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Next we performed a continuum extrapolation at each value of cλmin of the interpolating function with the ansatz c + d/N 2 τ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We as- signed a 15% error for T = 145 MeV, as we only had two points while performing the continuum extrapola- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 6 we find a good agreement between the continuum extrapolated distribution of the lowest eigen- value at T = 145 MeV and the RMT predictions from a Gaussian Unitary ensemble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' A slight discrepancy exist for lower and higher values of cλmin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' This can be due to the fact that we use a very low but finite convergence cri- terion while calculating the eigenvalue spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Hence we do not have any data for cλmin < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Since we are plotting a probability distribution (of the smallest eigen- value), the area under the curve must be unity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' To pre- serve this criterion the values of the probability densities along the higher end of the tail lie above the RMT curve in order to compensate for the relatively lower values in the lower portion of the tail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Appendix C: The level spacing distribution for bulk modes Next we look at the level spacing distribution of the bulk modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' To study the universal properties of the eigenvalue level spacing fluctuations one has to remove the system dependent mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' This is done by a method called unfolding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Let λ represent eigenvalues in the as- cending sequence for any particular gauge configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The average density of the eigenvalues in the sequence i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' the reciprocal of the average spacing as a function of λ is represented as ¯ρ(λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The eigenvalue sequence can then be unfolded using the average level-staircase function, ¯η(λ) = � λ λ0 dλ′¯ρ(λ′) which tells us how many eigenvalues in this sequence are less than λ on an average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Here λ0 labels the eigenvalue beyond which all the higher eigen- values are bulk modes and below which are the near-zero modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The unfolded sequence is labeled by λuf i = ¯η(λi), where the index i labels the original eigenvalue whose un- folding is performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' When appropriately normalized, the average spacing between the unfolded eigenvalues equals unity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The nearest neighbor spacing distribution is constructed by calculating the differences between con- secutive unfolded eigenvalues λuf i+1 − λuf i and organizing them into histogram bins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' This gives us a picture of how the eigenvalue spacings fluctuate about the average which we have plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 8 for four different temperatures T = 162, 166, 171, 176 MeV and at each temperature, for the three different lattice sizes Nτ = 8, 12, 16 except for T = 176 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' We have then estimated the functional de- pendence of these nearest neighbor spacing distributions by two different fit ansatz, shown as solid and dotted lines in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The dotted curves were obtained after performing a fit to the lattice data points with the func- tion f(s) = asbe−cs2, motivated by the Wigner surmise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The solid curves on the other hand, were obtained after fitting the points to an ansatz function f(s) = ps2e−qs2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The values of these parameters a, b, c, p, q after perform- ing the fits are given in Table III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' It is evident that the level repulsion between the bulk modes is quadratic simi- lar to that of random matrices belonging to the Gaussian unitary ensemble (GuE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' However for the Nτ = 16 lat- tices, due to the contamination with the near-zero modes the fit of the tail is not good and can not be explained by RMT prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' In order to account for the long tail of the spacing distribution we fit it to a semi-Poisson distri- bution P(s) ∼ s2 exp (−αs) which shows strong repulsion at small values of s but falls off slowly at large values of s parameterized by a fit parameter α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' After performing the fit of the level separation with this ansatz, we obtain the value of α = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='02(7), 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='17(9), 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='3(1) for temperatures T = 162, 166, 171 MeV respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The lattice data now do agree to this new fit ansatz reasonably well for Nτ = 16 at all temperatures above Tc, which is evident in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' T (MeV) Nτ a b c p q 162 8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='91(5) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='85(3) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='19(1) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='16(7) 1.' metadata={'source': 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+page_content='77(4) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='16(2) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='15(9) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='27(2) 176 12 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='3(3) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='4(1) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='07(8) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5(3) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='39(7) Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' III: The estimated values of the parameters after the fit to different unfolded level spacing distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Appendix D: Details of extraction of the mobil- ity edge Next, in order to estimate when these bulk modes sep- arate from the deep-infrared peak of eigenvalues, we cal- culate at what temperature the functional fit of the bulk eigenvalue spectrum has a non-zero intercept along the λ-axis which is larger than the typical width of the near- zero peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' In the continuum, we have already calcu- lated the slope of the bulk eigenvalue density, which is c1(m, T)/T 2 = 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='8(4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Looking at the eigenvalue distri- butions in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='1, we can choose a typical value of λ at 8 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5 3 P(s) Spacing s T=162 MeV Nτ=16 =12 =8 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5 3 P(s) Spacing s T=166 MeV Nτ=16 =12 =8 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} 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equivalently, Nτ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The solid lines in each plot correspond to the two-parameter fit and the dotted curves for three-parameter fits inspired from the Wigner surmise for Gaussian unitary random matrix ensembles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='3 0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5 3 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5 P(s) Spacing s Nτ=16 T=162 MeV =166 MeV =171 MeV Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 9: A fit to the eigenvalue level spacing distribution using a mixed ansatz for Nτ = 16 at T = 162, 166, 171 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='5 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='02 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='04 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='06 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='08 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='12 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='14 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='16 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='18 ρ0/T3 T/Tc Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 10: Continuum extrapolation of the bulk intercept for eigenvalue densities at different temperatures above Tc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The horizontal line corresponds to ρ0/T 3 = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='34 for the bulk spectrum when it is completely separates from near zero modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' which the near-zero and bulk modes separate out, which is most evident for the Nτ = 16 lattices at λ0/T ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Using these inputs and that the bulk modes have a linear- in-λ dependence we can calculate the value of bulk inter- cept ρ0/T 3 = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='34 at λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Next we take the values of the intercept of bulk mode density for all T > Tc from Table II and perform a continuum extrapolation with the function ρ0/T 3 + d/N 2 τ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' The continuum values, ρ0/T 3 so-obtained are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' 10 for all T > Tc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' At the highest temperature T = 176 MeV a 10% error is assigned to the data point since we could perform a con- tinuum estimate with the data available only for two Nτ values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Now fitting the continuum extrapolated values, ρ0/T 3 with the ansatz ρ0/T 3 = d1(T/Tc) + d2 we obtain d1 = −23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='1(3) and d2 = 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='3(3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Using this parametric dependence of the continuum value of the intercept as a function of temperature, we extract a T/Tc = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='15(3) when the value of ρ0/T 3 = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='34 i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=', when the near-zero modes distinctly emerge out from the bulk spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' [1] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Banks and A.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' thesis, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} +page_content=' Bielefeld (main) (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/A9FJT4oBgHgl3EQfry2f/content/2301.11610v1.pdf'} diff --git a/C9E1T4oBgHgl3EQfEANP/content/tmp_files/2301.02884v1.pdf.txt b/C9E1T4oBgHgl3EQfEANP/content/tmp_files/2301.02884v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..e0a750272fa0dad37ce0f57fdf6a7fd6ff3a0037 --- /dev/null +++ b/C9E1T4oBgHgl3EQfEANP/content/tmp_files/2301.02884v1.pdf.txt @@ -0,0 +1,1531 @@ +TunesFormer: Forming Tunes with Control Codes +Shangda Wu +Music AI and Information Technology +Central Conservatory of Music +Beijing, China +shangda@mail.ccom.edu.cn +Maosong Sun +Computer Science and Technology +Tsinghua University +Beijing, China +sms@tsinghua.edu.cn +ABSTRACT +In recent years, deep learning techniques have been applied +to music generation systems with promising results. How- +ever, one of the main challenges in this field has been the +lack of annotated datasets, making it difficult for models to +learn musical forms in compositions. To address this issue, +we present TunesFormer1, a Transformer-based melody gen- +eration system that is trained on a large dataset of 285,449 +ABC tunes. By utilizing specific symbols commonly found +in ABC notation to indicate section boundaries, Tunes- +Former can understand and generate melodies with given +musical forms based on control codes. Our objective evalu- +ations demonstrate the effectiveness of the control codes in +achieving controlled musical forms, and subjective experi- +ments show that the generated melodies are of comparable +quality to human compositions. Our results also provide in- +sights into the optimal placement of control codes and their +impact on the generated melodies. TunesFormer presents +a promising approach for generating melodies with desired +musical forms through the use of deep learning techniques. +Author Keywords +Transformer, controllable melody generation, musical form, +control codes, ABC notation +CCS Concepts +•Computing methodologies → Neural networks; •Applied +computing → Sound and music computing; +1. +INTRODUCTION +Musical form plays a crucial role in shaping the aesthetic +and expressive qualities of music. +Examples of musical +forms include verse-chorus, ABAB, and sonata forms, which +are commonly found in popular and classical music. The +ability to generate melodies with specific musical forms is a +highly sought-after feature in music generation systems, as +it allows users to create music that adheres to specific mu- +sical conventions and styles. This can be particularly useful +for music producers, composers, and educators seeking to +generate music that follows a specific form. +Deep learning techniques have gained widespread atten- +tion in recent years as a means of generating music with di- +verse styles and properties. Various approaches have been +proposed, including the use of recurrent neural networks +(RNNs) [9, 8, 22, 25], generative adversarial networks (GANs) +1https://github.com/sander-wood/tunesformer +[5, 24, 26], and Transformer models [4, 6, 13]. Among these +approaches, Transformer models [21] have proven particu- +larly effective for music generation due to their ability to +model long-range dependencies, handle variable-length in- +put sequences, and generate coherent and consistent output. +While deep learning techniques have shown promising re- +sults in generating music, a major challenge faced by mu- +sic generation systems is the ability to generate melodies +with predefined musical forms. Previous related work has +achieved some level of melody generation based on struc- +tural information, but there are limitations such as a focus +only on harmony or section length [1, 17, 28], considera- +tion of only bar-level structure [23, 29], or reliance on rules +to generate phrases and sections [3, 16]. Accurately iden- +tifying specific musical forms can be difficult for rules or +algorithms, and manually labelling this type of data is ex- +pensive due to the time and resources required, as well as +the high level of musical knowledge and understanding re- +quired. Thus, the problem of effectively teaching models to +learn musical forms from datasets remains largely unsolved. +To address the challenge of melody generation conditioned +on musical forms, we introduce TunesFormer, a Transformer- +based melody generation system trained on a large dataset +of 285,449 ABC tunes. ABC notation is a widely used text- +based representation of music that is more comprehensive +and expressive than MIDI. In addition to the symbols used +to represent pitches and rhythms, ABC notation also in- +cludes symbols to represent section boundaries and other +structural elements. +Based on these symbols, we design +several control codes that allow TunesFormer to generate +melodies with specific musical forms based on user input. +We present a thorough evaluation of TunesFormer through +both objective and subjective experiments. Our objective +evaluations demonstrate the effectiveness of the control codes +in achieving controlled musical forms, while subjective ex- +periments show that the control codes for edit distance sim- +ilarity are relevant to human subjective perception, and the +quality of the generated melodies is comparable to that of +human compositions as evaluated by professional musicians. +These experimental results also provide insight into the op- +timal placement of control codes and their impact on the +generated melodies. Overall, our results highlight the po- +tential of TunesFormer as a powerful and flexible tool for +generating melodies with desired musical forms. +The main contributions of this paper are: +• The introduction of TunesFormer, a Transformer-based +melody generation system that generates melodies with +specific musical forms using control codes. +• TunesFormer is trained on a large ABC notation dataset, +allowing it to learn a more comprehensive representa- +tion of music notation compared to systems trained +on MIDI datasets. +arXiv:2301.02884v1 [cs.SD] 7 Jan 2023 + +• We conduct both objective and subjective experiments +to comprehensively evaluate TunesFormer, demonstrat- +ing the effectiveness of the control codes. +2. +RELATED WORK +There has been a significant amount of research dedicated +to music generation using deep learning techniques. Much +of this work has focused on the use of deep neural networks +to model complex patterns in symbolic music generation, +but a significant challenge remains in generating full-length +music with consistent long-term structure. +Chen et al. explored the use of explicit structure encod- +ing in neural networks for symbolic music generation [1]. +They found that incorporating explicit structure encoding +significantly improved the quality and structure of the gen- +erated music. However, this approach relies on harmony to +guide the model in generating melodies with good structure, +without considering the actual musical form. +PopMNet [23], a model for generating structured pop mu- +sic melodies, consists of a Structure Generation Net (SGN) +and a Melody Generation Net (MGN), with the SGN gen- +erating melody structures based on pairwise relations be- +tween bars (repetition and sequence) and the MGN gener- +ating melodies based on these structures and chord progres- +sions. MELONS [29], a framework based on Transformer +for generating melodies with long-term structures, also con- +sists of a structure generation net and a melody generation +net, which are used to factor the melody generation process +into two sub-problems: structure generation and structure- +conditional melody generation. While these approaches are +able to generate melodies with clearer structures compared +to other models, they are limited to generating melodies +with pairwise relations between bars, rather than more com- +plex structural patterns. +MusicFrameworks [3] is a hierarchical music structure +representation and a multi-step generative process for cre- +ating full-length melodies guided by long-term repetitive +structure, chord, melodic contour, and rhythm constraints. +This approach allows for the customization of chords, ba- +sic melody, and rhythm structure, providing more control +over the generated melodies. However, this method requires +structural information to be extracted from existing songs +to generate new ones, which relies on hand-crafted rules and +may not always be available. +MeloForm [16] utilizes an expert system to generate a +melody by developing musical elements from motifs to phrases, +and then to sections with repetitions and variations ac- +cording to a given musical form. However, the generated +melodies may lack musical richness, so the approach also +utilizes a Transformer-based refinement model to improve +the melody without altering its musical form. While this ap- +proach allows for precise control of musical form, the model +does not learn the concept of musical form from the data +and relies on an expert system in the generation process. +A predictive deep network [2] models polyphonic music +using a novel graphical representation, inspired by tonnetz +from music theory, in a deep neural network. This tonnetz- +inspired representation is evaluated using a dataset of clas- +sical music and is found to produce musical sequences that +are more tonally stable and contain more repeated patterns +than sequences generated by pianoroll-based models. CM- +HRNN [8], a conditional melody generation model based on +a hierarchical recurrent neural network, generates melodies +with long-term structures based on given chord accompani- +ments. Both approaches learn long-term dependencies, re- +sulting in the implicit generation of melodies with repetitive +patterns, although these patterns do not represent specific +musical forms. +MorpheuS [10] is a music generation system that can gen- +erate polyphonic pieces with a given tension profile and +long- and short-term repeated pattern structures. A math- +ematical model for tonal tension is used to quantify the +tension profile and state-of-the-art pattern detection algo- +rithms are utilized to extract repeated patterns in a tem- +plate piece. These patterns are then used to constrain long- +term structure in the generated pieces. However, this ap- +proach is limited to the generation of music with predefined +tension profiles and does not consider the incorporation of +additional constraints or variables in the music generation +process. +Zhang et al. +proposed a harmony-aware learning ap- +proach [28] for generating structured pop music, which can +improve the structure and quality of the generated music. +Naruse et al. developed a method for generating pop mu- +sic with controllable phrase lengths [17] using a deep neu- +ral network and adding PHRASE and BAR COUNTDOWN events. +However, neither of these approaches explicitly captures the +relationships between sections. +3. +METHODOLOGY +3.1 +Data Representation +In this research, we aim to generate score information for +music [7, 20], rather than performance information [12, 18]. +Thus, the data representation used must effectively encode +sheet music. +The three most commonly used symbolic music formats +are ABC notation, MusicXML, and MIDI. ABC notation is +designed for simplicity and was originally intended for use +with folk music, while MusicXML is geared towards the ex- +change of musical notation. MIDI, on the other hand, is +focused on the sequencing of instrument sounds at a low +level, rather than higher-level musical concepts. Most pre- +vious works on symbolic music information retrieval and +generation [11, 13, 27] utilize MIDI as the data represen- +tation due to its popularity. +However, in this study, we +adopt ABC notation as our data representation due to its +advantages for score-oriented music generation over MIDI. +One advantage of ABC notation is that it can distinguish +enharmonic notes (e.g., B#3 and C4), while MIDI assigns +numerical codes to specific pitches without considering note +names. +This means that MIDI is unable to differentiate +between enharmonic notes. +Additionally, for music generation tasks, ABC notation +can accurately represent complex durations, while MIDI re- +quires a trade-off between accuracy and sequence length +or vocabulary size. This can result in quantization errors +where certain notes cannot be accurately represented due +to pre-defined time resolution (e.g., 16th notes). +Furthermore, ABC notation includes a comprehensive set +of musical symbols found in sheet music, including impor- +tant elements like ornamentation and articulation that are +not explicitly represented in MIDI, as shown in Fig. +1. +More importantly, some symbols used to indicate section +boundaries in ABC notation can serve as the basis for con- +trol codes. While MusicXML also has these advantages over +MIDI, it is based on XML, which can be more complex and +time-consuming to work with compared to ABC notation, +which is based on ASCII and therefore easier to use with +fewer errors. +Overall, the use of ABC notation for score-oriented mu- +sic generation allows for a more accurate and comprehen- +sive representation of music while maintaining simplicity, +enabling the generation of more complex and musically co- + +(a) ABC notation +(b) MusicXML +(c) MIDI +Figure 1: Excerpts from Nocturne Op. 9 No. 2 (E Flat Major) rendered by MuseScore 4 in different formats. While (a) and +(b) are essentially the same, (c) does not distinguish between enharmonic notes and loses many musical symbols. +herent melodies. This makes ABC notation a better choice +for music generation systems compared to MIDI, partic- +ularly for tasks that require a greater level of detail and +control over the generated music. +3.2 +Control Codes +Control codes are symbols that are added to the ABC no- +tation representation to indicate the desired musical form +of the generated melodies. +The most important information in musical forms lies in +the number of sections and the similarity between the indi- +vidual sections. For example, the musical form ABA’ refers +to a structure with three sections, where there is a main +section A followed by a contrasting section B (dissimilar) +and then the main section reappears as the recapitulation +A’ (similar) but with some slight variation. +Incorporating control codes that specify the number of +bars in each section can provide an additional level of con- +trol. These control codes can effectively influence the pacing +and flow of the music, as the number of bars in each sec- +tion can significantly impact the overall structure and form +of the piece. For instance, melodies with the same struc- +ture but different numbers of bars in each section, such as +A8B8A8 and A4B8A4, exhibit distinct musical characteristics +due to the varied length of their sections. +Based on the above reasons, we add the following control +codes to each ABC tune in the dataset through an auto- +mated process to indicate its musical form: +• Number of Bars (NB): controls the number of bars +in a section of the melody. For example, users could +specify that they want a section to contain 8 bars, and +TunesFormer would generate a section that fits within +that structure. It counts on the bar symbol |. +• Number of Sections (NS): controls the number of sec- +tions in the entire melody. This can be used to create a +sense of structure and coherence within the melody, as +different sections can be used to create musical themes +or motifs. It counts on several symbols that are com- +monly used in ABC notation and can be used to rep- +resent section boundaries: [|,||,|],|:,::, and :|. +• Edit Distance Similarity (EDS): controls the similar- +ity level between the current section c and a previous +section p in the melody. +It is based on the Leven- +shtein distance [14] lev(c, p), and can be formalised as +follows: +eds(c, p) = 1 − +lev(c, p) +max(|c|, |p|) +(1) +where |c| and |p| are the string length of two sections. +The EDS control code is discretized into 11 levels, +ranging from 0 (no match at all) to 10 (exact match). +To investigate the impact of different placements of these +control codes on generated melodies, we designed the fol- +lowing five placements: +• Global Placement (GP): all control codes are placed at +the beginning of the ABC notation. +• Section-based Placement (SP): NB and EDS control +codes are placed at the beginning of each section to +indicate the number of bars and the similarity of the +edit distances in that section. +• Section Countdown Placement (SCP): similar to section- +based placement, but NS control codes are also placed +at the beginning of each section to indicate the num- +ber of sections remaining in the piece. +• Bar Countdown Placement (BCP): similar to section- +based placement, but NB control codes are placed at +the beginning of each bar to indicate the number of +bars remaining in the section. +• Section & Bar Countdown Placement (SBCP): a com- +bination of SCP and BCP, with NS control codes placed +at the beginning of each section and NB control codes +placed at the beginning of each bar. This placement +allows for both the countdown of sections and bars to +be presented in the piece. +Fig. 2 shows an example of an ABC tune with control +codes using the GP. Other placements of control codes can +be found in Appendix A. The tune header includes the time +signature and key signature, and the tune body consists of +three sections, each with 8 bars. +The first control code +[SECS_3] specifies there are 3 sections in the tune, and + +a tempo +fpatempo +fp3Tune Body I +[SECS_3][BARS_8][SIM_3][BARS_8][SIM_10][SIM_3][BARS_8] +L:1/4 +M:4/4 +K:C +“C” E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/ F A |“G” A G“C” C2 | +E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/“D” F D |“G” A G“C” C2 || +“C” e e“G” d d/d/ |“Am” c A“Em” G E | “F” F3/2 G/ A F |“C” E/E/G/G/ c G | +e e“G” d d/d/ |“Am” c A“Em” G E |“F” F3/2 G/“G” A B | “C” d c c2 || +“C” E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/ F A |“G” A G“C” C2 | +E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/“D” F D |“G” A G“C” C2 |] +Control Codes +Tune Header +Tune Body II +Tune Body III +Figure 2: An example of the GP. For the purpose of demon- +stration, it is separated into several sections. +the following control code [BARS_8] indicates the first sec- +tion has 8 bars. The next two control codes [SIM_3] and +[BAR_8] indicate that the EDS between tune body II and +tune body I is approximately 0.3, and tune body II has 8 +bars. The last three control codes [SIM_10], [SIM_3] and +[BARS_8] specify that tune body III is identical to tune +body I while dissimilar to tune body II, and has 8 bars. +3.3 +Model Architecture +TunesFormer is a Transformer-based language model that +utilizes the GPT-2 small [19] architecture as its basis, which +is a decoder-only, unidirectional Transformer. The GPT-2 +small architecture is a deep learning model that consists of +12 layers, each with a hidden size of 768 and 12 attention +heads. +This allows TunesFormer to effectively learn and +recognize complex patterns and structures in ABC notation. +To accurately represent the independent semantics of each +character in ABC notation, we employ character-level tok- +enization. In addition, we also include control codes as spe- +cial tokens. During inference, these control codes can either +be provided by users as prompts or generated by Tunes- +Former itself, allowing for a high degree of flexibility in the +music generation process. +We trained TunesFormer from scratch using the learning +rate α = 10−4, with a 1,000-step linear warmup and learning +rate decay. We trained a total of 30 epochs with a batch +size of 32, using the AdamW [15] optimizer with β1 = 0.9, +β2 = 0.999, ϵ = 10−8, and a weight decay coefficient of +0.01. +We also use automatic mixed precision to improve +the efficiency of the training process. +4. +EXPERIMENTS +4.1 +Dataset +The dataset used to train and evaluate TunesFormer is +collected from two sources: The Session2 and ABCnota- +tion.com3. The Session is a community website focused on +Irish traditional music, while ABCnotation.com is a website +that provides a standard for folk and traditional music nota- +tion in the form of ASCII text files. The combined dataset +consists of 285,449 ABC tunes, with 99% (282,595) of the +tunes used as the training set and the remaining 1% (2854) +used as the evaluation set. +To ensure consistency and standardization among the ABC +tunes in the dataset, we first converted them all into Mu- +sicXML format and then re-converted them back into ABC +notation. In order to focus solely on the musical content, +we removed any natural language elements (such as titles, +composers, and lyrics) and unnecessary information (such +as reference numbers and sources). +2https://thesession.org +3https://abcnotation.com +0.0000 +0.1000 +0.2000 +0.3000 +0.4000 +0.5000 +0.6000 +0.7000 +0.8000 +0.9000 +1.0000 +GP +SP +SCP +BCP +SBCP +Eval Set +Figure 3: Results of bar length accuracy at different settings. +As depicted in Fig. 4, in this dataset, 99.4% of the pieces +have no more than 8 sections and 99.1% of the sections have +no more than 32 bars. Therefore, we set an upper limit of +8 for the number of sections and 32 for the number of bars. +4.2 +Objective Experiments +We present the objective experimental results to evaluate +the effectiveness of TunesFormer in generating controlled +musical forms. We measured the bar length accuracy, sec- +tion number accuracy, bar number accuracy, and Edit Dis- +tance Similarity (EDS) of the generated tunes in each of +the five placements: Global Placement (GP), Section-based +Placement (SP), Section Countdown Placement (SCP), Bar +Countdown Placement (BCP), and Section & Bar Count- +down Placement (SBCP). The evaluation set consisted of +2854 tunes, which were used as a benchmark for compari- +son. To provide context for our evaluation, we analyzed the +distribution of the number of sections, number of bars per +section, and EDS of the tunes in the dataset. +We first measure the bar length accuracy at different set- +tings to evaluate the grammatical correctness of the tunes +generated by TunesFormer. Bar length accuracy refers to +the correctness of the number of beats in each bar in a tune, +as defined by the time signature. For example, in a 4/4 time +signature, there are 4 beats per bar and the quarter note re- +ceives one beat. To maintain grammatical correctness, the +total number of beats in each bar must match the time sig- +nature. Bar length accuracy is therefore a measure of how +well TunesFormer can generate melodies that adhere to the +specified time signature. +In order to evaluate the bar length accuracy of Tunes- +Former, we generated 100 tunes in each setting and com- +pared them to 2854 tunes from the evaluation set. Upon +manual examination, we found that almost all inaccuracies +in the generated tunes were due to incomplete bars at the +beginning and end of sections, which are still grammati- +cally correct. +We conducted independent samples t-tests +and found that there were no statistically significant dif- +ferences between the accuracy of the generated tunes in +each setting and the evaluation set, with the exception of +the SCP and BCP settings which had slightly lower accu- +racy. However, this difference was not statistically signifi- +cant as indicated by a p-value> 0.05. These results suggest +that TunesFormer is able to generate grammatically correct +tunes under all settings. +To verify the effectiveness of the control codes for different +placements, we conducted three separate experiments: +• Bar number accuracy: we used the NS and NB control +codes to specify the number of sections (1 section) and +the number of bars (1-32 bars), while the EDS control +codes were generated by TunesFormer itself. To de- +termine the accuracy of the bar number, we compared + +0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +1 +2 +3 +4 +5 +6 +7 +8 +0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +1 +1 +2 +3 +4 +5 +6 +7 +8 +GP +SP +SCP +BCP +SBCP +(b) Section Number Accuracy +(e) Section Number Distribution +0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +1 +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +GP +SP +SCP +BCP +SBCP +EDS +0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +1 +1 +3 +5 +7 +9 +11 +13 +15 +17 +19 +21 +23 +25 +27 +29 +31 +GP +SP +SCP +BCP +SBCP +0 +0.05 +0.1 +0.15 +0.2 +0.25 +0.3 +0.35 +1 +3 +5 +7 +9 +11 13 15 17 19 21 23 25 27 29 31 +(a) Bar Number Accuracy +(c) Edit Distance Similarity Comparison +(d) Bar Number Distribution +(f) Edit Distance Similarity Distribution +0 +0.05 +0.1 +0.15 +0.2 +0.25 +0.3 +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +Figure 4: Evaluating the effectiveness of control codes in TunesFormer for generating controlled musical forms. The green +dotted line in (c) is the theoretical EDS values at each level. +the actual number of bars generated to the NB con- +trol codes. For each setting, we generated 100 tunes, +resulting in a total of 5 placements × 32 bar numbers +× 100 tunes = 16,000 tunes. +• Section number accuracy: we used the NS control code +to specify the number of sections (1-8 sections), while +the NB and EDS control codes were generated by +TunesFormer itself. To determine the accuracy of the +section number, we compared the actual number of +sections generated to the NS control code. For each +setting, we generated 100 tunes, resulting in a total +of 5 placements × 8 section numbers × 100 tunes = +4000 tunes. +• Edit distance similarity comparison: we used the NS +and EDS control codes to specify the number of sec- +tions (2 sections) and the similarity level (0-10 levels), +while the NB control codes were generated by Tunes- +Former itself. To compare the average edit distance +similarity values at each EDS level, we compared them +to the theoretical EDS values. For each setting, we +generated 100 tunes, resulting in a total of 5 place- +ments × 11 levels × 100 tunes = 5500 tunes. +The results are provided in Fig. 4, which includes plots +for bar number accuracy (Fig. 4a), section number accuracy +(Fig. 4b), and edit distance similarity comparison (Fig. 4c). +In Fig. 4a, it is shown that TunesFormer generally has high +accuracy in generating the correct number of bars when the +number specified is 17 or less for all placements. However, +when the number of bars specified exceeds 17, there is a +noticeable decrease in accuracy for the GP, SP, and SCP. +This decrease in accuracy is likely due to the distribution of +the number of bars in the dataset, as shown in Fig. 4d. A +higher proportion of a certain number of bars corresponds +to more of its NB control codes being learned by Tunes- +Former, resulting in a more robust representation of those +control codes. Both the BCP and SBCP, which insert NB +control codes before each bar, have higher accuracy in gen- +erating the correct number of bars regardless of the number +specified. +Fig. 4b demonstrates a similar trend in section number +accuracy: TunesFormer can generate the correct number of +sections almost 100% of the time for all placements, except +the GP, SP, and BCP when the number of specified sec- +tions is greater than 6. This is also due to the distribution +of the number of sections in the dataset, as shown in Fig. +4e. Both the SCP and SBCP, which insert NS control codes +before each section, have higher accuracy in generating the +correct number of sections regardless of the number speci- +fied. However, because the distribution of section numbers +is not as concentrated as bar numbers, not using the section +countdown does not have as much of an impact on accuracy +as the bar countdown. +Fig. 4c presents the results of the EDS comparison. The +ability of TunesFormer to generate sections with specified +levels of similarity to the reference sections was evaluated by +comparing the average EDS values of the generated tunes +to the specified EDS levels. Overall, TunesFormer performs +well at most EDS levels for all placements, with the av- +erage EDS values consistently close to the specified levels. +However, for EDS levels less than 2, all placements except +for GP exhibit a statistically significant difference from the +theoretical EDS values. This deviation from the expected +results is not due to the distribution of EDS levels in the +dataset, as levels 0 and 1 outnumber level 2. Rather, it is +likely caused by the fact that when the EDS between two +sections is at a low level, their bar lengths are often signif- +icantly different. The model is more likely to capture this +pattern when all control codes are placed at the beginning +(GP). This suggests that the placement of control codes +has a significant impact on the ability of TunesFormer to +generate sections with a low level of EDS similarity. +Overall, the SBCP performs well in both bar and section +number accuracy, while the GP performs best in EDS. +4.3 +Subjective Experiments +In our subjective experiments, we sought to assess the qual- +ity of generated tunes in various settings and evaluate the +relevance of the EDS control code to human subjective per- + +1 +1.5 +2 +2.5 +3 +3.5 +4 +4.5 +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +Subjective Similarity Score +Similarity Level +Figure 5: Subjective similarity scores of selected tunes from +the evaluation set. +ception. We recruited music school students who majored +in music as participants. +We randomly selected 100 tunes with two sections from +our evaluation set, with 10 tunes at each level of similarity +ranging from 0 to 9. We excluded tunes with a similarity +level of 10, as two identical sections would be the same in +terms of subjective perception. For each tune, participants +were asked to rate its similarity to the control code on a scale +of 1 (completely dissimilar) to 5 (exact match), resulting in +a total of 100 ratings. +Participants were presented with +sheet music for the selected tunes, with section boundaries +marked, as well as audio of the tunes. They were asked to +select the most appropriate description of the tune from five +options based on their subjective perception: +• Completely dissimilar: the two sections have no simi- +larity in terms of melody, rhythm, or structure, or the +two sections are too far apart in length. +• Mildly dissimilar: the two sections do not share the +motif or theme and are significantly different in the +overall structure and melody. +• Moderately similar: the two sections have a similar +structure and some shared motifs, but there are still +significant differences in terms of rhythm and pitch. +• Highly similar: the two sections have a very similar +structure and many shared motifs, but with noticeable +differences in rhythm or pitch. +• Exact match: the two sections are identical in every +aspect, including melody, rhythm, and structure. +As shown in Fig. 5, the subjective similarity scores ob- +tained from our study participants were strongly correlated +with the calculated similarity levels. +The Pearson corre- +lation coefficient for this relationship was 0.948, indicating +that EDS can be used as a reliable measure of similarity in +melody generation, as it is closely related to the subjective +perception of similarity. +Furthermore, Fig. 5 shows that when the EDS similarity +level is below 4, the two sections are perceived as dissimilar +by our participants, and vice versa. Based on these findings, +we can conclude that setting the EDS control codes to a +similarity level above 4 will result in the target section being +perceived as similar to the reference section, while setting +the control codes to a level below 4 will result in the target +section being perceived as dissimilar to the reference section. +To evaluate the quality of the tunes generated by Tunes- +Former under different settings, we conducted a subjective +evaluation in which participants rated 10 randomly selected +tunes from the evaluation set and 10 tunes generated from +1 +1.5 +2 +2.5 +3 +3.5 +4 +4.5 +GP +SP +SCP +BCP +SBCP +Eval Set +Figure 6: Results of subjective ratings for generated tunes +quality compared to the evaluation set. +scratch for each placement on a scale ranging from 1 (poor +quality) to 5 (excellent quality). +The results, depicted in Fig. 6, show that the mean rat- +ings of the generated tunes were generally similar across +all placement settings, with values ranging from 3.03 to +3.47. However, the insertion of control codes before each bar +(BCP) resulted in a statistically significantly lower mean +rating compared to the evaluation set, with a p-value < +0.05. This suggests that the BCP may negatively impact +the perceived quality of the generated tunes. In contrast, +when the section countdown was introduced (SBCP), the +ratings increased. +This may be because the insertion of +too many NB control codes can reduce the quality of the +generation, while NS control codes enhance TunesFormer’s +understanding of the relationships between sections while +only slightly increasing the sequence length. +The evalu- +ation set had a higher mean rating compared to all other +placements, although the difference was not statistically sig- +nificant. +These results demonstrate that TunesFormer is +capable of generating tunes of comparable quality to those +in the evaluation set under all settings (except BCP). +5. +CONCLUSIONS +In this paper, we present TunesFormer, a melody gener- +ation system that leverages the power of Transformer and +is trained on a large dataset of 282,595 ABC notation tunes. +By utilizing control codes, TunesFormer can generate melodies +that match a given musical form. Our results indicate that +TunesFormer can generate high-quality melodies that are +comparable to those in the evaluation set. +Through objective experiments, we demonstrate the ef- +fectiveness of these control codes in achieving the desired +number of sections and bars, as well as in achieving a spe- +cific level of edit distance similarity. Subjective experiments +also show that edit distance similarity is highly relevant to +the human subjective perception of similarity. +However, +we also find that the insertion of control codes before ev- +ery bar may negatively impact the perceived quality of the +generated melodies. 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Melons: generating melody with long-term +structure using transformers and structure graph, +2021. +APPENDIX +A. +EXAMPLES OF VARIOUS PLACEMENTS +[SECS_3] +L:1/4 +M:4/4 +K:C +“C” E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/ F A |“G” A G“C” C2 | +E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/“D” F D |“G” A G“C” C2 || +“C” e e“G” d d/d/ |“Am” c A“Em” G E | “F” F3/2 G/ A F |“C” E/E/G/G/ c G | +e e“G” d d/d/ |“Am” c A“Em” G E |“F” F3/2 G/“G” A B | “C” d c c2 || +“C” E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/ F A |“G” A G“C” C2 | +E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/“D” F D |“G” A G“C” C2 |] +Control Codes +Tune Header +Tune Body II +[SIM_10][SIM_3][BARS_8] +[BARS_8] +[SIM_3][BARS_8] +Control Codes +Control Codes +Control Codes +Tune Body I +Tune Body III +Figure 7: Section-based Placement (SP): NB and EDS con- +trol codes are inserted before each section of the tune. +L:1/4 +M:4/4 +K:C +“C” E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/ F A |“G” A G“C” C2 | +E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/“D” F D |“G” A G“C” C2 || +“C” e e“G” d d/d/ |“Am” c A“Em” G E | “F” F3/2 G/ A F |“C” E/E/G/G/ c G | +e e“G” d d/d/ |“Am” c A“Em” G E |“F” F3/2 G/“G” A B | “C” d c c2 || +“C” E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/ F A |“G” A G“C” C2 | +E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/“D” F D |“G” A G“C” C2 |] +Tune Header +Tune Body II +[SECS_1][SIM_10][SIM_3][BARS_8] +[SECS_3][BARS_8] +[SECS_2][SIM_3][BARS_8] +Control Codes +Control Codes +Control Codes +Tune Body I +Tune Body III +Figure 8: Section Countdown Placement (SCP): NS control +codes are inserted before each section of the tune as a count- +down of the number of sections remaining in the tune. +[SECS_3] +L:1/4 +M:4/4 +K:C +[BARS_8] “C” E3/2 D/“G” G3/2“C” E/ | +[BARS_7] c G E G | +[BARS_6] “G” D3/2 E/ F A | +[BARS_5] “G” A G“C” C2 | +[BARS_4] E3/2 D/“G” G3/2“C” E/ | +[BARS_3] c G E G | +[BARS_2] “G” D3/2 E/“D” F D | +[BARS_1] “G” A G“C” C2 || +Control Codes +Tune Header +[SIM_3] +Control Codes +Tune Body I +& +Control Codes +Tune Body II +& +Control Codes +[BARS_8] “C” e e“G” d d/d/ | +[BARS_7] “Am” c A“Em” G E | +[BARS_6] “F” F3/2 G/ A F | +[BARS_5] “C” E/E/G/G/ c G | +[BARS_4] e e“G” d d/d/ | +[BARS_3] “Am” c A“Em” G E | +[BARS_2] “F” F3/2 G/“G” A B | +[BARS_1] “C” d c c2 || +[SIM_10][SIM_3] +Control Codes +[BARS_8] “C” E3/2 D/“G” G3/2“C” E/ | +[BARS_7] c G E G | +[BARS_6] “G” D3/2 E/ F A | +Tune Body III +& +Control Codes +… +Figure 9: +Bar Countdown Placement (BCP): NB control +codes are inserted before each bar of the tune as a count- +down of the number of bars remained in the section. +[SECS_3] +L:1/4 +M:4/4 +K:C +[BARS_8] “C” E3/2 D/“G” G3/2“C” E/ | +[BARS_7] c G E G | +[BARS_6] “G” D3/2 E/ F A | +[BARS_5] “G” A G“C” C2 | +[BARS_4] E3/2 D/“G” G3/2“C” E/ | +[BARS_3] c G E G | +[BARS_2] “G” D3/2 E/“D” F D | +[BARS_1] “G” A G“C” C2 || +Control Codes +Tune Header +[SECS_2][SIM_3] +Control Codes +Tune Body I +& +Control Codes +Tune Body II +& +Control Codes +[BARS_8] “C” e e“G” d d/d/ | +[BARS_7] “Am” c A“Em” G E | +[BARS_6] “F” F3/2 G/ A F | +[BARS_5] “C” E/E/G/G/ c G | +[BARS_4] e e“G” d d/d/ | +[BARS_3] “Am” c A“Em” G E | +[BARS_2] “F” F3/2 G/“G” A B | +[BARS_1] “C” d c c2 || +[SECS_1][SIM_10][SIM_3] +Control Codes +[BARS_8] “C” E3/2 D/“G” G3/2“C” E/ | +[BARS_7] c G E G | +[BARS_6] “G” D3/2 E/ F A | +Tune Body III +& +Control Codes +… +Figure 10: Section & Bar Countdown Placement (SBCP): +NS and NB control codes are inserted before each section +and bar of the tune respectively, which allows for both the +countdown of sections and bars to be presented in the piece. + +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +15 +16 +17 +18 +19 +20 +21 +22 +23 +24 +25 +26 +27 +28 +29 +30 +31 +32 +33 +34 +35 +36 +37 +38 +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +15 +16 +17 +18 +19 +20 +21 +22 +23 +24 +25 +26 +27 +28 +29 +30 +31 +32 +33 +34 +35 +36 +37 +38 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +1.0 +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +15 +16 +17 +18 +19 +20 +21 +22 +23 +24 +25 +26 +27 +28 +29 +30 +31 +32 +33 +34 +35 +36 +37 +38 +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +15 +16 +17 +18 +19 +20 +21 +22 +23 +24 +25 +26 +27 +28 +29 +30 +31 +32 +33 +34 +35 +36 +37 +38 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +1.0 +(a) Hey Jude - NB Control Codes Only +(b) Hey Jude - NB and NS Control Codes Only +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +15 +16 +17 +18 +19 +20 +21 +22 +23 +24 +25 +26 +27 +28 +29 +30 +31 +32 +33 +34 +35 +36 +37 +38 +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +15 +16 +17 +18 +19 +20 +21 +22 +23 +24 +25 +26 +27 +28 +29 +30 +31 +32 +33 +34 +35 +36 +37 +38 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +1.0 +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +15 +16 +17 +18 +19 +20 +21 +22 +23 +24 +25 +26 +27 +28 +29 +30 +31 +32 +33 +34 +35 +36 +37 +38 +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +15 +16 +17 +18 +19 +20 +21 +22 +23 +24 +25 +26 +27 +28 +29 +30 +31 +32 +33 +34 +35 +36 +37 +38 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +1.0 +(c) Hey Jude - All Control Codes +(d) Hey Jude - Original +Figure 11: Visualisations of the self-similarity matrices of “Hey Jude” with form A9A’9B12A"9. (a), (b) and (c) are generated +by TunesFormer with A9 (the first 9 bars) from the original composition (d) as the prompt. +B. +CASE STUDY OF CONTROL CODES +Fig. 11 presents visualizations of the self-similarity matrices of several melodies. Fig. 11a-c were generated by TunesFormer- +GP using the first nine bars of the original tune “Hey Jude” (Fig. 11d) as the prompt with different control codes specified. +Fig. 11a was generated using only the NB control codes, which indicate the number of bars in the melody. The resulting +melody exhibits a less cohesive structure than the original tune, with fewer clear phrase boundaries and a less distinct musical +form. This suggests that while the NB control codes are important in generating melodies with a certain number of bars, +they are not sufficient in achieving the same level of structural cohesiveness as the original tune. +Fig. 11b specifies the NB and NS control codes, which indicate the number of sections and the number of bars within +each section, respectively. +The EDS control codes, which indicate the relationships between sections, are generated by +TunesFormer itself. This generation strategy is similar to the approach used in [17], but the resulting self-similarity matrix +is significantly different from the original tune as TunesFormer is not specified in terms of the relationships between sections. +Fig. 11c uses all control codes from the original tune to form the structure of the generated tune. It is clear that Fig. 11c +is very close to Fig. 11d, demonstrating the importance of EDS control codes for constructing well-structured melodies. It +should be noted that the use of the same musical form does not mean that the content of the original tune is also copied. +Overall, Fig. 11a-c show that while the NB control codes are important in generating melodies with a certain number +of bars, they are not sufficient in achieving the same level of structural cohesiveness as the original tune. The introduction +of NS control codes improves the structure of the generated melodies, but the EDS control codes are crucial in achieving a +melody with a similar structure to the original tune. + diff --git a/C9E1T4oBgHgl3EQfEANP/content/tmp_files/load_file.txt b/C9E1T4oBgHgl3EQfEANP/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..d1e287ed5a2507bbb433a22ce4616470dfaef247 --- /dev/null +++ b/C9E1T4oBgHgl3EQfEANP/content/tmp_files/load_file.txt @@ -0,0 +1,906 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf,len=905 +page_content='TunesFormer: Forming Tunes with Control Codes Shangda Wu Music AI and Information Technology Central Conservatory of Music Beijing, China shangda@mail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='ccom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='cn Maosong Sun Computer Science and Technology Tsinghua University Beijing, China sms@tsinghua.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='cn ABSTRACT In recent years, deep learning techniques have been applied to music generation systems with promising results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' How- ever, one of the main challenges in this field has been the lack of annotated datasets, making it difficult for models to learn musical forms in compositions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' To address this issue, we present TunesFormer1, a Transformer-based melody gen- eration system that is trained on a large dataset of 285,449 ABC tunes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' By utilizing specific symbols commonly found in ABC notation to indicate section boundaries, Tunes- Former can understand and generate melodies with given musical forms based on control codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Our objective evalu- ations demonstrate the effectiveness of the control codes in achieving controlled musical forms, and subjective experi- ments show that the generated melodies are of comparable quality to human compositions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Our results also provide in- sights into the optimal placement of control codes and their impact on the generated melodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' TunesFormer presents a promising approach for generating melodies with desired musical forms through the use of deep learning techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Author Keywords Transformer, controllable melody generation, musical form, control codes, ABC notation CCS Concepts Computing methodologies → Neural networks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' •Applied computing → Sound and music computing;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' INTRODUCTION Musical form plays a crucial role in shaping the aesthetic and expressive qualities of music.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Examples of musical forms include verse-chorus, ABAB, and sonata forms, which are commonly found in popular and classical music.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The ability to generate melodies with specific musical forms is a highly sought-after feature in music generation systems, as it allows users to create music that adheres to specific mu- sical conventions and styles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' This can be particularly useful for music producers, composers, and educators seeking to generate music that follows a specific form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Deep learning techniques have gained widespread atten- tion in recent years as a means of generating music with di- verse styles and properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Various approaches have been proposed, including the use of recurrent neural networks (RNNs) [9, 8, 22, 25], generative adversarial networks (GANs) 1https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='com/sander-wood/tunesformer [5, 24, 26], and Transformer models [4, 6, 13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Among these approaches, Transformer models [21] have proven particu- larly effective for music generation due to their ability to model long-range dependencies, handle variable-length in- put sequences, and generate coherent and consistent output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' While deep learning techniques have shown promising re- sults in generating music, a major challenge faced by mu- sic generation systems is the ability to generate melodies with predefined musical forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Previous related work has achieved some level of melody generation based on struc- tural information, but there are limitations such as a focus only on harmony or section length [1, 17, 28], considera- tion of only bar-level structure [23, 29], or reliance on rules to generate phrases and sections [3, 16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Accurately iden- tifying specific musical forms can be difficult for rules or algorithms, and manually labelling this type of data is ex- pensive due to the time and resources required, as well as the high level of musical knowledge and understanding re- quired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Thus, the problem of effectively teaching models to learn musical forms from datasets remains largely unsolved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' To address the challenge of melody generation conditioned on musical forms, we introduce TunesFormer, a Transformer- based melody generation system trained on a large dataset of 285,449 ABC tunes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' ABC notation is a widely used text- based representation of music that is more comprehensive and expressive than MIDI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' In addition to the symbols used to represent pitches and rhythms, ABC notation also in- cludes symbols to represent section boundaries and other structural elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Based on these symbols, we design several control codes that allow TunesFormer to generate melodies with specific musical forms based on user input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' We present a thorough evaluation of TunesFormer through both objective and subjective experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Our objective evaluations demonstrate the effectiveness of the control codes in achieving controlled musical forms, while subjective ex- periments show that the control codes for edit distance sim- ilarity are relevant to human subjective perception, and the quality of the generated melodies is comparable to that of human compositions as evaluated by professional musicians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' These experimental results also provide insight into the op- timal placement of control codes and their impact on the generated melodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Overall, our results highlight the po- tential of TunesFormer as a powerful and flexible tool for generating melodies with desired musical forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The main contributions of this paper are: The introduction of TunesFormer, a Transformer-based melody generation system that generates melodies with specific musical forms using control codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' TunesFormer is trained on a large ABC notation dataset, allowing it to learn a more comprehensive representa- tion of music notation compared to systems trained on MIDI datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='02884v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='SD] 7 Jan 2023 We conduct both objective and subjective experiments to comprehensively evaluate TunesFormer, demonstrat- ing the effectiveness of the control codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' RELATED WORK There has been a significant amount of research dedicated to music generation using deep learning techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Much of this work has focused on the use of deep neural networks to model complex patterns in symbolic music generation, but a significant challenge remains in generating full-length music with consistent long-term structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' explored the use of explicit structure encod- ing in neural networks for symbolic music generation [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' They found that incorporating explicit structure encoding significantly improved the quality and structure of the gen- erated music.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' However, this approach relies on harmony to guide the model in generating melodies with good structure, without considering the actual musical form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' PopMNet [23], a model for generating structured pop mu- sic melodies, consists of a Structure Generation Net (SGN) and a Melody Generation Net (MGN), with the SGN gen- erating melody structures based on pairwise relations be- tween bars (repetition and sequence) and the MGN gener- ating melodies based on these structures and chord progres- sions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' MELONS [29], a framework based on Transformer for generating melodies with long-term structures, also con- sists of a structure generation net and a melody generation net, which are used to factor the melody generation process into two sub-problems: structure generation and structure- conditional melody generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' While these approaches are able to generate melodies with clearer structures compared to other models, they are limited to generating melodies with pairwise relations between bars, rather than more com- plex structural patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' MusicFrameworks [3] is a hierarchical music structure representation and a multi-step generative process for cre- ating full-length melodies guided by long-term repetitive structure, chord, melodic contour, and rhythm constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' This approach allows for the customization of chords, ba- sic melody, and rhythm structure, providing more control over the generated melodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' However, this method requires structural information to be extracted from existing songs to generate new ones, which relies on hand-crafted rules and may not always be available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' MeloForm [16] utilizes an expert system to generate a melody by developing musical elements from motifs to phrases, and then to sections with repetitions and variations ac- cording to a given musical form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' However, the generated melodies may lack musical richness, so the approach also utilizes a Transformer-based refinement model to improve the melody without altering its musical form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' While this ap- proach allows for precise control of musical form, the model does not learn the concept of musical form from the data and relies on an expert system in the generation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' A predictive deep network [2] models polyphonic music using a novel graphical representation, inspired by tonnetz from music theory, in a deep neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' This tonnetz- inspired representation is evaluated using a dataset of clas- sical music and is found to produce musical sequences that are more tonally stable and contain more repeated patterns than sequences generated by pianoroll-based models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' CM- HRNN [8], a conditional melody generation model based on a hierarchical recurrent neural network, generates melodies with long-term structures based on given chord accompani- ments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Both approaches learn long-term dependencies, re- sulting in the implicit generation of melodies with repetitive patterns, although these patterns do not represent specific musical forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' MorpheuS [10] is a music generation system that can gen- erate polyphonic pieces with a given tension profile and long- and short-term repeated pattern structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' A math- ematical model for tonal tension is used to quantify the tension profile and state-of-the-art pattern detection algo- rithms are utilized to extract repeated patterns in a tem- plate piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' These patterns are then used to constrain long- term structure in the generated pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' However, this ap- proach is limited to the generation of music with predefined tension profiles and does not consider the incorporation of additional constraints or variables in the music generation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' proposed a harmony-aware learning ap- proach [28] for generating structured pop music, which can improve the structure and quality of the generated music.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Naruse et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' developed a method for generating pop mu- sic with controllable phrase lengths [17] using a deep neu- ral network and adding PHRASE and BAR COUNTDOWN events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' However, neither of these approaches explicitly captures the relationships between sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' METHODOLOGY 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='1 Data Representation In this research, we aim to generate score information for music [7, 20], rather than performance information [12, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Thus, the data representation used must effectively encode sheet music.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The three most commonly used symbolic music formats are ABC notation, MusicXML, and MIDI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' ABC notation is designed for simplicity and was originally intended for use with folk music, while MusicXML is geared towards the ex- change of musical notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' MIDI, on the other hand, is focused on the sequencing of instrument sounds at a low level, rather than higher-level musical concepts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Most pre- vious works on symbolic music information retrieval and generation [11, 13, 27] utilize MIDI as the data represen- tation due to its popularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' However, in this study, we adopt ABC notation as our data representation due to its advantages for score-oriented music generation over MIDI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' One advantage of ABC notation is that it can distinguish enharmonic notes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=', B#3 and C4), while MIDI assigns numerical codes to specific pitches without considering note names.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' This means that MIDI is unable to differentiate between enharmonic notes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Additionally, for music generation tasks, ABC notation can accurately represent complex durations, while MIDI re- quires a trade-off between accuracy and sequence length or vocabulary size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' This can result in quantization errors where certain notes cannot be accurately represented due to pre-defined time resolution (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=', 16th notes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Furthermore, ABC notation includes a comprehensive set of musical symbols found in sheet music, including impor- tant elements like ornamentation and articulation that are not explicitly represented in MIDI, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' More importantly, some symbols used to indicate section boundaries in ABC notation can serve as the basis for con- trol codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' While MusicXML also has these advantages over MIDI, it is based on XML, which can be more complex and time-consuming to work with compared to ABC notation, which is based on ASCII and therefore easier to use with fewer errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Overall, the use of ABC notation for score-oriented mu- sic generation allows for a more accurate and comprehen- sive representation of music while maintaining simplicity, enabling the generation of more complex and musically co- (a) ABC notation (b) MusicXML (c) MIDI Figure 1: Excerpts from Nocturne Op.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 9 No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 2 (E Flat Major) rendered by MuseScore 4 in different formats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' While (a) and (b) are essentially the same, (c) does not distinguish between enharmonic notes and loses many musical symbols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' herent melodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' This makes ABC notation a better choice for music generation systems compared to MIDI, partic- ularly for tasks that require a greater level of detail and control over the generated music.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='2 Control Codes Control codes are symbols that are added to the ABC no- tation representation to indicate the desired musical form of the generated melodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The most important information in musical forms lies in the number of sections and the similarity between the indi- vidual sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' For example, the musical form ABA’ refers to a structure with three sections, where there is a main section A followed by a contrasting section B (dissimilar) and then the main section reappears as the recapitulation A’ (similar) but with some slight variation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Incorporating control codes that specify the number of bars in each section can provide an additional level of con- trol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' These control codes can effectively influence the pacing and flow of the music, as the number of bars in each sec- tion can significantly impact the overall structure and form of the piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' For instance, melodies with the same struc- ture but different numbers of bars in each section, such as A8B8A8 and A4B8A4, exhibit distinct musical characteristics due to the varied length of their sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Based on the above reasons, we add the following control codes to each ABC tune in the dataset through an auto- mated process to indicate its musical form: Number of Bars (NB): controls the number of bars in a section of the melody.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' For example, users could specify that they want a section to contain 8 bars, and TunesFormer would generate a section that fits within that structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' It counts on the bar symbol |.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Number of Sections (NS): controls the number of sec- tions in the entire melody.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' This can be used to create a sense of structure and coherence within the melody, as different sections can be used to create musical themes or motifs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' It counts on several symbols that are com- monly used in ABC notation and can be used to rep- resent section boundaries: [|,||,|],|:,::, and :|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Edit Distance Similarity (EDS): controls the similar- ity level between the current section c and a previous section p in the melody.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' It is based on the Leven- shtein distance [14] lev(c, p), and can be formalised as follows: eds(c, p) = 1 − lev(c, p) max(|c|, |p|) (1) where |c| and |p| are the string length of two sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The EDS control code is discretized into 11 levels, ranging from 0 (no match at all) to 10 (exact match).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' To investigate the impact of different placements of these control codes on generated melodies, we designed the fol- lowing five placements: Global Placement (GP): all control codes are placed at the beginning of the ABC notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Section-based Placement (SP): NB and EDS control codes are placed at the beginning of each section to indicate the number of bars and the similarity of the edit distances in that section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Section Countdown Placement (SCP): similar to section- based placement, but NS control codes are also placed at the beginning of each section to indicate the num- ber of sections remaining in the piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Bar Countdown Placement (BCP): similar to section- based placement, but NB control codes are placed at the beginning of each bar to indicate the number of bars remaining in the section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Section & Bar Countdown Placement (SBCP): a com- bination of SCP and BCP, with NS control codes placed at the beginning of each section and NB control codes placed at the beginning of each bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' This placement allows for both the countdown of sections and bars to be presented in the piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 2 shows an example of an ABC tune with control codes using the GP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Other placements of control codes can be found in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The tune header includes the time signature and key signature, and the tune body consists of three sections, each with 8 bars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The first control code [SECS_3] specifies there are 3 sections in the tune,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' and ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='a tempo ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='fpatempo ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='fp3Tune Body I ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[SECS_3][BARS_8][SIM_3][BARS_8][SIM_10][SIM_3][BARS_8] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='L:1/4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='M:4/4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='K:C ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“C” E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/ F A |“G” A G“C” C2 | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/“D” F D |“G” A G“C” C2 || ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“C” e e“G” d d/d/ |“Am” c A“Em” G E | “F” F3/2 G/ A F |“C” E/E/G/G/ c G | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='e e“G” d d/d/ |“Am” c A“Em” G E |“F” F3/2 G/“G” A B | “C” d c c2 || ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“C” E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/ F A |“G” A G“C” C2 | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/“D” F D |“G” A G“C” C2 |] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Control Codes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Tune Header ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Tune Body II ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Tune Body III ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Figure 2: An example of the GP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' For the purpose of demon- stration, it is separated into several sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' the following control code [BARS_8] indicates the first sec- tion has 8 bars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The next two control codes [SIM_3] and [BAR_8] indicate that the EDS between tune body II and tune body I is approximately 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='3, and tune body II has 8 bars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The last three control codes [SIM_10], [SIM_3] and [BARS_8] specify that tune body III is identical to tune body I while dissimilar to tune body II, and has 8 bars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='3 Model Architecture TunesFormer is a Transformer-based language model that utilizes the GPT-2 small [19] architecture as its basis, which is a decoder-only, unidirectional Transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The GPT-2 small architecture is a deep learning model that consists of 12 layers, each with a hidden size of 768 and 12 attention heads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' This allows TunesFormer to effectively learn and recognize complex patterns and structures in ABC notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' To accurately represent the independent semantics of each character in ABC notation, we employ character-level tok- enization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' In addition, we also include control codes as spe- cial tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' During inference, these control codes can either be provided by users as prompts or generated by Tunes- Former itself, allowing for a high degree of flexibility in the music generation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' We trained TunesFormer from scratch using the learning rate α = 10−4, with a 1,000-step linear warmup and learning rate decay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' We trained a total of 30 epochs with a batch size of 32, using the AdamW [15] optimizer with β1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='9, β2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='999, ϵ = 10−8, and a weight decay coefficient of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' We also use automatic mixed precision to improve the efficiency of the training process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' EXPERIMENTS 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='1 Dataset The dataset used to train and evaluate TunesFormer is collected from two sources: The Session2 and ABCnota- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='com3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The Session is a community website focused on Irish traditional music, while ABCnotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='com is a website that provides a standard for folk and traditional music nota- tion in the form of ASCII text files.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The combined dataset consists of 285,449 ABC tunes, with 99% (282,595) of the tunes used as the training set and the remaining 1% (2854) used as the evaluation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' To ensure consistency and standardization among the ABC tunes in the dataset, we first converted them all into Mu- sicXML format and then re-converted them back into ABC notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' In order to focus solely on the musical content, we removed any natural language elements (such as titles, composers, and lyrics) and unnecessary information (such as reference numbers and sources).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 2https://thesession.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='org 3https://abcnotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='com 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='0000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='1000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='2000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='3000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='4000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='5000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='6000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='7000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='8000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='9000 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='0000 GP SP SCP BCP SBCP Eval Set Figure 3: Results of bar length accuracy at different settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' As depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 4, in this dataset, 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='4% of the pieces have no more than 8 sections and 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='1% of the sections have no more than 32 bars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Therefore, we set an upper limit of 8 for the number of sections and 32 for the number of bars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='2 Objective Experiments We present the objective experimental results to evaluate the effectiveness of TunesFormer in generating controlled musical forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' We measured the bar length accuracy, sec- tion number accuracy, bar number accuracy, and Edit Dis- tance Similarity (EDS) of the generated tunes in each of the five placements: Global Placement (GP), Section-based Placement (SP), Section Countdown Placement (SCP), Bar Countdown Placement (BCP), and Section & Bar Count- down Placement (SBCP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The evaluation set consisted of 2854 tunes, which were used as a benchmark for compari- son.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' To provide context for our evaluation, we analyzed the distribution of the number of sections, number of bars per section, and EDS of the tunes in the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' We first measure the bar length accuracy at different set- tings to evaluate the grammatical correctness of the tunes generated by TunesFormer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Bar length accuracy refers to the correctness of the number of beats in each bar in a tune, as defined by the time signature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' For example, in a 4/4 time signature, there are 4 beats per bar and the quarter note re- ceives one beat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' To maintain grammatical correctness, the total number of beats in each bar must match the time sig- nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Bar length accuracy is therefore a measure of how well TunesFormer can generate melodies that adhere to the specified time signature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' In order to evaluate the bar length accuracy of Tunes- Former, we generated 100 tunes in each setting and com- pared them to 2854 tunes from the evaluation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Upon manual examination, we found that almost all inaccuracies in the generated tunes were due to incomplete bars at the beginning and end of sections, which are still grammati- cally correct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' We conducted independent samples t-tests and found that there were no statistically significant dif- ferences between the accuracy of the generated tunes in each setting and the evaluation set, with the exception of the SCP and BCP settings which had slightly lower accu- racy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' However, this difference was not statistically signifi- cant as indicated by a p-value> 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' These results suggest that TunesFormer is able to generate grammatically correct tunes under all settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' To verify the effectiveness of the control codes for different placements, we conducted three separate experiments: Bar number accuracy: we used the NS and NB control codes to specify the number of sections (1 section) and the number of bars (1-32 bars), while the EDS control codes were generated by TunesFormer itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' To de- termine the accuracy of the bar number, we compared 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='7 1 2 3 4 5 6 7 8 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='9 1 1 2 3 4 5 6 7 8 GP SP SCP BCP SBCP (b) Section Number Accuracy (e) Section Number Distribution 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='9 1 0 1 2 3 4 5 6 7 8 9 10 GP SP SCP BCP SBCP EDS 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='9 1 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 GP SP SCP BCP SBCP 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='35 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 (a) Bar Number Accuracy (c) Edit Distance Similarity Comparison (d) Bar Number Distribution (f) Edit Distance Similarity Distribution 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='3 0 1 2 3 4 5 6 7 8 9 10 Figure 4: Evaluating the effectiveness of control codes in TunesFormer for generating controlled musical forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The green dotted line in (c) is the theoretical EDS values at each level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' the actual number of bars generated to the NB con- trol codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' For each setting, we generated 100 tunes, resulting in a total of 5 placements × 32 bar numbers × 100 tunes = 16,000 tunes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Section number accuracy: we used the NS control code to specify the number of sections (1-8 sections), while the NB and EDS control codes were generated by TunesFormer itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' To determine the accuracy of the section number, we compared the actual number of sections generated to the NS control code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' For each setting, we generated 100 tunes, resulting in a total of 5 placements × 8 section numbers × 100 tunes = 4000 tunes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Edit distance similarity comparison: we used the NS and EDS control codes to specify the number of sec- tions (2 sections) and the similarity level (0-10 levels), while the NB control codes were generated by Tunes- Former itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' To compare the average edit distance similarity values at each EDS level, we compared them to the theoretical EDS values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' For each setting, we generated 100 tunes, resulting in a total of 5 place- ments × 11 levels × 100 tunes = 5500 tunes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The results are provided in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 4, which includes plots for bar number accuracy (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 4a), section number accuracy (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 4b), and edit distance similarity comparison (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 4c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 4a, it is shown that TunesFormer generally has high accuracy in generating the correct number of bars when the number specified is 17 or less for all placements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' However, when the number of bars specified exceeds 17, there is a noticeable decrease in accuracy for the GP, SP, and SCP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' This decrease in accuracy is likely due to the distribution of the number of bars in the dataset, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 4d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' A higher proportion of a certain number of bars corresponds to more of its NB control codes being learned by Tunes- Former, resulting in a more robust representation of those control codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Both the BCP and SBCP, which insert NB control codes before each bar, have higher accuracy in gen- erating the correct number of bars regardless of the number specified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 4b demonstrates a similar trend in section number accuracy: TunesFormer can generate the correct number of sections almost 100% of the time for all placements, except the GP, SP, and BCP when the number of specified sec- tions is greater than 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' This is also due to the distribution of the number of sections in the dataset, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 4e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Both the SCP and SBCP, which insert NS control codes before each section, have higher accuracy in generating the correct number of sections regardless of the number speci- fied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' However, because the distribution of section numbers is not as concentrated as bar numbers, not using the section countdown does not have as much of an impact on accuracy as the bar countdown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 4c presents the results of the EDS comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The ability of TunesFormer to generate sections with specified levels of similarity to the reference sections was evaluated by comparing the average EDS values of the generated tunes to the specified EDS levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Overall, TunesFormer performs well at most EDS levels for all placements, with the av- erage EDS values consistently close to the specified levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' However, for EDS levels less than 2, all placements except for GP exhibit a statistically significant difference from the theoretical EDS values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' This deviation from the expected results is not due to the distribution of EDS levels in the dataset, as levels 0 and 1 outnumber level 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Rather, it is likely caused by the fact that when the EDS between two sections is at a low level, their bar lengths are often signif- icantly different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The model is more likely to capture this pattern when all control codes are placed at the beginning (GP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' This suggests that the placement of control codes has a significant impact on the ability of TunesFormer to generate sections with a low level of EDS similarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Overall, the SBCP performs well in both bar and section number accuracy, while the GP performs best in EDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='3 Subjective Experiments In our subjective experiments, we sought to assess the qual- ity of generated tunes in various settings and evaluate the relevance of the EDS control code to human subjective per- 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='5 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='5 3 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='5 4 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='5 0 1 2 3 4 5 6 7 8 9 Subjective Similarity Score Similarity Level Figure 5: Subjective similarity scores of selected tunes from the evaluation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' ception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' We recruited music school students who majored in music as participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' We randomly selected 100 tunes with two sections from our evaluation set, with 10 tunes at each level of similarity ranging from 0 to 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' We excluded tunes with a similarity level of 10, as two identical sections would be the same in terms of subjective perception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' For each tune, participants were asked to rate its similarity to the control code on a scale of 1 (completely dissimilar) to 5 (exact match), resulting in a total of 100 ratings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Participants were presented with sheet music for the selected tunes, with section boundaries marked, as well as audio of the tunes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' They were asked to select the most appropriate description of the tune from five options based on their subjective perception: Completely dissimilar: the two sections have no simi- larity in terms of melody, rhythm, or structure, or the two sections are too far apart in length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Mildly dissimilar: the two sections do not share the motif or theme and are significantly different in the overall structure and melody.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Moderately similar: the two sections have a similar structure and some shared motifs, but there are still significant differences in terms of rhythm and pitch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Highly similar: the two sections have a very similar structure and many shared motifs, but with noticeable differences in rhythm or pitch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Exact match: the two sections are identical in every aspect, including melody, rhythm, and structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 5, the subjective similarity scores ob- tained from our study participants were strongly correlated with the calculated similarity levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The Pearson corre- lation coefficient for this relationship was 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='948, indicating that EDS can be used as a reliable measure of similarity in melody generation, as it is closely related to the subjective perception of similarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Furthermore, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 5 shows that when the EDS similarity level is below 4, the two sections are perceived as dissimilar by our participants, and vice versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Based on these findings, we can conclude that setting the EDS control codes to a similarity level above 4 will result in the target section being perceived as similar to the reference section, while setting the control codes to a level below 4 will result in the target section being perceived as dissimilar to the reference section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' To evaluate the quality of the tunes generated by Tunes- Former under different settings, we conducted a subjective evaluation in which participants rated 10 randomly selected tunes from the evaluation set and 10 tunes generated from 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='5 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='5 3 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='5 4 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='5 GP SP SCP BCP SBCP Eval Set Figure 6: Results of subjective ratings for generated tunes quality compared to the evaluation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' scratch for each placement on a scale ranging from 1 (poor quality) to 5 (excellent quality).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The results, depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 6, show that the mean rat- ings of the generated tunes were generally similar across all placement settings, with values ranging from 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='03 to 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' However, the insertion of control codes before each bar (BCP) resulted in a statistically significantly lower mean rating compared to the evaluation set, with a p-value < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' This suggests that the BCP may negatively impact the perceived quality of the generated tunes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' In contrast, when the section countdown was introduced (SBCP), the ratings increased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' This may be because the insertion of too many NB control codes can reduce the quality of the generation, while NS control codes enhance TunesFormer’s understanding of the relationships between sections while only slightly increasing the sequence length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The evalu- ation set had a higher mean rating compared to all other placements, although the difference was not statistically sig- nificant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' These results demonstrate that TunesFormer is capable of generating tunes of comparable quality to those in the evaluation set under all settings (except BCP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' CONCLUSIONS In this paper, we present TunesFormer, a melody gener- ation system that leverages the power of Transformer and is trained on a large dataset of 282,595 ABC notation tunes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' By utilizing control codes, TunesFormer can generate melodies that match a given musical form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Our results indicate that TunesFormer can generate high-quality melodies that are comparable to those in the evaluation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Through objective experiments, we demonstrate the ef- fectiveness of these control codes in achieving the desired number of sections and bars, as well as in achieving a spe- cific level of edit distance similarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Subjective experiments also show that edit distance similarity is highly relevant to the human subjective perception of similarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' However, we also find that the insertion of control codes before ev- ery bar may negatively impact the perceived quality of the generated melodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' On the other hand, the introduction of a small number of NS control codes can enhance Tunes- Former’s understanding of the relationships between sec- tions and improve the quality of the generated melodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' These findings have important implications for the design and development of melody generation systems, and have the potential to facilitate the creation of more controlled and expressive musical forms.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Qin, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Musicbert: Symbolic music understanding with large-scale pre-training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' In C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Zong, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Xia, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Li, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Navigli, editors, Findings of the Association for Computational Linguistics: ACL/IJCNLP 2021, Online Event, August 1-6, 2021, volume ACL/IJCNLP 2021 of Findings of ACL, pages 791–800.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Association for Computational Linguistics, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' [28] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Qiu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Wang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Zhou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Structure-enhanced pop music generation via harmony-aware learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' In J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Magalh˜aes, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Bimbo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Satoh, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Sebe, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Alameda-Pineda, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Jin, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Oria, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Toni, editors, MM ’22: The 30th ACM International Conference on Multimedia, Lisboa, Portugal, October 10 - 14, 2022, pages 1204–1213.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' ACM, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' [29] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Zou, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Zou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Zhao, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Zhang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Zhang, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Melons: generating melody with long-term structure using transformers and structure graph, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' APPENDIX A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='EXAMPLES OF VARIOUS PLACEMENTS ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[SECS_3] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='L:1/4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='M:4/4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='K:C ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“C” E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/ F A |“G” A G“C” C2 | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/“D” F D |“G” A G“C” C2 || ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“C” e e“G” d d/d/ |“Am” c A“Em” G E | “F” F3/2 G/ A F |“C” E/E/G/G/ c G | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='e e“G” d d/d/ |“Am” c A“Em” G E |“F” F3/2 G/“G” A B | “C” d c c2 || ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“C” E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/ F A |“G” A G“C” C2 | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/“D” F D |“G” A G“C” C2 |] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Control Codes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Tune Header ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Tune Body II ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[SIM_10][SIM_3][BARS_8] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_8] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[SIM_3][BARS_8] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Control Codes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Control Codes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Control Codes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Tune Body I ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Tune Body III ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Figure 7: Section-based Placement (SP): NB and EDS con- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='trol codes are inserted before each section of the tune.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='L:1/4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='M:4/4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='K:C ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“C” E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/ F A |“G” A G“C” C2 | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/“D” F D |“G” A G“C” C2 || ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“C” e e“G” d d/d/ |“Am” c A“Em” G E | “F” F3/2 G/ A F |“C” E/E/G/G/ c G | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='e e“G” d d/d/ |“Am” c A“Em” G E |“F” F3/2 G/“G” A B | “C” d c c2 || ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“C” E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/ F A |“G” A G“C” C2 | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='E3/2 D/“G” G3/2“C” E/ | c G E G |“G” D3/2 E/“D” F D |“G” A G“C” C2 |] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Tune Header ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Tune Body II ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[SECS_1][SIM_10][SIM_3][BARS_8] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[SECS_3][BARS_8] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[SECS_2][SIM_3][BARS_8] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Control Codes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Control Codes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Control Codes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Tune Body I ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Tune Body III ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Figure 8: Section Countdown Placement (SCP): NS control ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='codes are inserted before each section of the tune as a count- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='down of the number of sections remaining in the tune.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[SECS_3] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='L:1/4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='M:4/4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='K:C ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_8] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“C” E3/2 D/“G” G3/2“C” E/ | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_7] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='c G E G | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_6] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“G” D3/2 E/ F A | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_5] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“G” A G“C” C2 | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_4] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='E3/2 D/“G” G3/2“C” E/ | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_3] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='c G E G | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_2] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“G” D3/2 E/“D” F D | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_1] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“G” A G“C” C2 || ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Control Codes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Tune Header ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[SIM_3] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Control Codes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Tune Body I ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='& ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Control Codes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Tune Body II ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='& ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Control Codes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_8] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“C” e e“G” d d/d/ | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_7] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“Am” c A“Em” G E | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_6] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“F” F3/2 G/ A F | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_5] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“C” E/E/G/G/ c G | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_4] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='e e“G” d d/d/ | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_3] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“Am” c A“Em” G E | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_2] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“F” F3/2 G/“G” A B | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_1] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“C” d c c2 || ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[SIM_10][SIM_3] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Control Codes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_8] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“C” E3/2 D/“G” G3/2“C” E/ | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_7] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='c G E G | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_6] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“G” D3/2 E/ F A | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Tune Body III ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='& ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Control Codes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='… ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Figure 9: ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Bar Countdown Placement (BCP): NB control ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='codes are inserted before each bar of the tune as a count- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='down of the number of bars remained in the section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[SECS_3] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='L:1/4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='M:4/4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='K:C ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_8] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“C” E3/2 D/“G” G3/2“C” E/ | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_7] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='c G E G | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_6] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“G” D3/2 E/ F A | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_5] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“G” A G“C” C2 | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_4] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='E3/2 D/“G” G3/2“C” E/ | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_3] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='c G E G | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_2] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“G” D3/2 E/“D” F D | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_1] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“G” A G“C” C2 || ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Control Codes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Tune Header ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[SECS_2][SIM_3] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Control Codes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Tune Body I ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='& ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Control Codes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Tune Body II ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='& ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Control Codes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_8] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“C” e e“G” d d/d/ | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_7] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“Am” c A“Em” G E | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_6] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“F” F3/2 G/ A F | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_5] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“C” E/E/G/G/ c G | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_4] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='e e“G” d d/d/ | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_3] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“Am” c A“Em” G E | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_2] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“F” F3/2 G/“G” A B | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_1] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“C” d c c2 || ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[SECS_1][SIM_10][SIM_3] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Control Codes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_8] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“C” E3/2 D/“G” G3/2“C” E/ | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_7] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='c G E G | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='[BARS_6] ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='“G” D3/2 E/ F A | ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Tune Body III ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='& ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Control Codes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='… ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='Figure 10: Section & Bar Countdown Placement (SBCP): ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='NS and NB control codes are inserted before each section ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='and bar of the tune respectively,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' which allows for both the countdown of sections and bars to be presented in the piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 0.' metadata={'source': 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+page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='0 (a) Hey Jude - NB Control Codes Only (b) Hey Jude - NB and NS Control Codes Only 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content='0 (c) Hey Jude - All Control Codes (d) Hey Jude - Original Figure 11: Visualisations of the self-similarity matrices of “Hey Jude” with form A9A’9B12A"9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' (a), (b) and (c) are generated by TunesFormer with A9 (the first 9 bars) from the original composition (d) as the prompt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' CASE STUDY OF CONTROL CODES Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 11 presents visualizations of the self-similarity matrices of several melodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 11a-c were generated by TunesFormer- GP using the first nine bars of the original tune “Hey Jude” (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 11d) as the prompt with different control codes specified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 11a was generated using only the NB control codes, which indicate the number of bars in the melody.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The resulting melody exhibits a less cohesive structure than the original tune, with fewer clear phrase boundaries and a less distinct musical form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' This suggests that while the NB control codes are important in generating melodies with a certain number of bars, they are not sufficient in achieving the same level of structural cohesiveness as the original tune.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 11b specifies the NB and NS control codes, which indicate the number of sections and the number of bars within each section, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The EDS control codes, which indicate the relationships between sections, are generated by TunesFormer itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' This generation strategy is similar to the approach used in [17], but the resulting self-similarity matrix is significantly different from the original tune as TunesFormer is not specified in terms of the relationships between sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 11c uses all control codes from the original tune to form the structure of the generated tune.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' It is clear that Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 11c is very close to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 11d, demonstrating the importance of EDS control codes for constructing well-structured melodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' It should be noted that the use of the same musical form does not mean that the content of the original tune is also copied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' Overall, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' 11a-c show that while the NB control codes are important in generating melodies with a certain number of bars, they are not sufficient in achieving the same level of structural cohesiveness as the original tune.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} +page_content=' The introduction of NS control codes improves the structure of the generated melodies, but the EDS control codes are crucial in achieving a melody with a similar structure to the original tune.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/C9E1T4oBgHgl3EQfEANP/content/2301.02884v1.pdf'} diff --git a/CNE2T4oBgHgl3EQfnwjC/content/2301.04012v1.pdf b/CNE2T4oBgHgl3EQfnwjC/content/2301.04012v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8ade1688afa8f8510e8ec8d07efa5b11ea06259d --- /dev/null +++ b/CNE2T4oBgHgl3EQfnwjC/content/2301.04012v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1129992afef4b7f1419aedc41511a503ef1d50df02b81967cf091d9c7c2fea73 +size 2796862 diff --git a/CNE2T4oBgHgl3EQfnwjC/vector_store/index.pkl b/CNE2T4oBgHgl3EQfnwjC/vector_store/index.pkl new file mode 100644 index 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b/CdAzT4oBgHgl3EQfGftE/content/tmp_files/2301.01028v1.pdf.txt @@ -0,0 +1,46892 @@ +NEW INFORMATION +TECHNOLOGIES, +SIMULATION +AND AUTOMATION +MONOGRAPH +Scientific publication (issue) +Editor-in-Chief +Sergii Kotlyk +Velychko V., Voinova S., Granyak V., Gurskiy O. Zavertailo K., Ivanova L., Kotlyk D., +Kotlyk S., Kudriashova A., Kunup T., Malakhov K., Pikh I., Punchenko N., Senkivskyy V., +Sergeeva O. Sokolova O., Fedosov S., Khoshaba O.,Tsyra O., Chaplinskyy Y. +IOWA STATE UNIVERSITY DIGITAL PRESS +2022 + + + + + +MINISTRY OF EDUCATION AND SCIENCE OF UKRAINE +ODESA NATIONAL UNIVERSITY OF TECHNOLOGY + + + + + + + + +NEW INFORMATION TECHNOLOGIES, +SIMULATION AND AUTOMATION + + + + + +MONOGRAPH +Scientific publication (issue) + + + + + +Editor-in-Chief +Sergii Kotlyk + + + + + + + +IOWA STATE UNIVERSITY DIGITAL PRESS +2022 + + + + +UDC 004.01/08 +H73 +Recommended by the Academic Council of +The Odesa National University of Technology +(Protocol № 11 dated 05.04.2022) +Reviewers: +Оlexandr Romanyuk, DSc, Prof., Vinnytsia National Technical University +Valery Plotnikov, DSc, Prof., Odesa National Academy of Food Technologies +Оlexandr Shpinkovski, PhD, Docent, Odesа Polytechnic State University + + +Editor-in-Chief +Sergii Kotlyk +PhD, Docent, Odesa National University of Technology +Team of Authors: +Velychko V., Voinova S., Granyak V., Gurskiy O., Zavertailo K., Ivanova L., Kotlyk D., +Kotlyk S., Kudriashova A., Kunup T., Malakhov K., Pikh I., Punchenko N., Senkivskyy V., +Sergeeva O., Sokolova O., Fedosov S., Khoshaba O., Tsyra O., Chaplinskyy Y. + +H73 +New +information +technologies, +simulation +and +automation: +Monograph / Velychko V., Voinova S., Granyak V., et al; Editor-in-Chief Kotlyk S. +Iowa State University Digital Press. +The monograph summarizes and analyzes the current state of development of computer and +mathematical simulation/modeling, the automation of management processes, the use of +information technologies in education, the design of information systems and software +complexes, the development of computer telecommunication networks and technologies — most +areas that are united by the term Industry 4.0. +The monograph will be useful both for experts and employees of companies engaged in the +field of IT and automation, as well as for educators, masters, students and postgraduates of higher +educational institutions, and everyone interested in issues related to Industry 4.0. +DOI https://doi.org/10.31274/isudp.2022.121 +ISBN 978-617-7867-37-0 (Print) +ISBN 978-1-958291-01-6 (e-book) + +© 2022 Velychko V., Voinova S., Granyak V., et al + + + + + + +Preface + +The fourth industrial revolution (Industry 4.0) envisages a new approach to +production based on the mass introduction of information technologies into the industry, +large-scale automation of business processes, and the spread of artificial intelligence. +The benefits of the Fourth Industrial Revolution are obvious: increased productivity, +more significant safety for employees due to the reduction of jobs in hazardous working +conditions, increased competitiveness, fundamentally new products, and much more. +However, it also has shortcomings that can negatively affect society's development, +thus, studying the evolution of Industry 4.0 directions is a necessary condition for the +practical application of modern science. +The monograph summarizes and analyzes the current state of development of +computer and mathematical simulation/modeling, the automation of management +processes, the use of information technologies in education, the design of information +systems and software complexes, the development of computer telecommunication +networks and technologies — most areas that are united by the term Industry 4.0. +The monograph was compiled based on the results of the XIV International +Scientific and Practical Conference "Information Technologies and Automation - +2021", which took place in October 2021 at The Odesa National University of +Technology (the former Odesa National Academy of Food Technologies). +The range of problems presented in the monograph is extremely wide — the +application of information technologies for the design of post-printing processes and +new food products, the development of decision-making theory, mathematical +simulation/modeling in ferroelectric polymers and polarized films, the development of +logic control algorithms, the automation of maintenance of powerful electric machines +and shipping mooring systems, applications of information technologies in education, +digital health and distribution between computing complexes. +The presented monograph is a significant help to experts, educators, students, +graduate students who are trying to learn about the current state of science in the field +of Industry 4.0. This information can be used to solve a wide range of problems in the +specified sections that arise both in the educational process and in research and scientific +plans. + + + +Одеса +«Екологія» +2022 +МІНІСТЕРСТВО ОСВІТИ І НАУКИ УКРАЇНИ +Одеський національний технологічний університет +НОВІ ІНФОРМАЦІЙНІ +ТЕХНОЛОГІЇ, МОДЕЛЮВАННЯ +ТА АВТОМАТИЗАЦІЯ +Монографія +За загальною редакцією +С. В. Котлика + +УДК 004.01/08 + +Н73 +Колектив авторів: +В. Ю. Величко, С. О. Воінова, В. Ф. Граняк, О. О. Гурський, К. С. Завертайло, +Л. В. Іванова, Д. О. Котлик, С. В. Котлик, А. В. Кудряшова, Т. В. Кунуп, +К. С. Малахов, І. В. Піх, Н. О. Пунченко, В. М. Сеньківський, О. Є. Сергєєва, +О. П. Соколова, С. Н. Федосов, О. М. Хошаба, О. В. Цира, Ю. П. Чаплінський +Рецензенти: +О. Н. Романюк, д. т. н., професор, зав. кафедри програмного забезпечення +Вінницького національного технічного університету; +В. М. Плотніков, д. т. н., професор, зав. кафедри інформаційних технологій +та кібербезпеки Одеської національної академії харчових технологій; +О. А. Шпинковський, к. т. н., доцент кафедри інформаційних систем Дер- +жавного університету «Одеська політехніка» +Рекомендовано до друкування рішенням вченої ради Одеської націо- +нальної академії харчових технологій (протокол № 11 від 5 квітня 2022 р.) +© Величко В. Ю., Воінова С. О., +Граняк В. Ф. та ін., 2022 +Н73 + + + + + + + + + + + + + + + +ISBN 978-617-7867-37-0 (Print) + + +Нові + +інформаційні + +технології, + +моделювання + +та + +автомати- + +зація + +: монографія / кол. авт. + +: В. + +Ю. + +Величко, С. + +О. + +Воінова, + +В. + +Ф. + +Граняк [та ін.] + +; за заг. ред. С. + +В. + +Котлика. + +— Одеса + +: Еко- + +логія, 2022. + +— 724 с. +ISBN 978-617-7867-37-0 (Print) + + +У + +монографії + +узагальнено + +і + +проаналізовано + +рівень + +сучасного + +стану + +розвитку + +комп’ютерного + +та + +математичного + +моделювання, + +автоматизації + +процесів + +управління, + +застосування + +інформаційних + +технологій + +в + +освіті, + +проектування інформаційних систем і програмних комплексів, розвитку + +комп’ютерних телекомунікаційних мереж та технологій + +— більшості на- + +прямків, які об’єднуються терміном Індустрія 4.0. + + +Монографія буде корисною як для фахівців і працівників фірм, зайня- + +тих в галузі ІТ і автоматизації, так і для викладачів, магістрів, студентів і + +аспірантів вищих навчальних закладів, і всіх, хто цікавиться питаннями, + +пов’язаними з Індустрією 4.0. +УДК 004.01/08 + +3 +Зміст +Передмова . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 +Розділ I +МАТЕМАТИЧНЕ І КОМП’ЮТЕРНЕ МОДЕЛЮВАННЯ +СКЛАДНИХ ПРОЦЕСІВ +Контекстно-онтологічна системна оптимізація проблемно- +орієнтованої підтримки прийняття рішень +(Чаплінський Ю. П.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 +Теоретичні основи інформаційної технології прогностичного +оцінювання якості проєктування післядрукарських процесів +(Сеньківський В. М., Піх І. В., Кудряшова А. В.) . . . . . . . . . . . . . . . 44 +Thermally stimulated processes and pyroelectricity in ferroelectric +polymers (Sergeeva A. E.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 +Distribution of ferroelectric polarization in poled PVDF +and P(VDF-TFE) films (Fedosov S. N.) . . . . . . . . . . . . . . . . . . . . . . 179 +Розділ ІІ +АВТОМАТИЗАЦІЯ ТА УПРАВЛІННЯ ТЕХНОЛОГІЧНИМИ +ПРОЦЕСАМИ +Технологічний розвиток судноплавства, систем швартування +судноплавства майбутнього (Пунченко Н. О., Цира О. В.) . . . . . 220 +Автоматичний синтез мереж Петрі при розробці алгоритмів +логічного управління (Гурський О. О.) . . . . . . . . . . . . . . . . . . . . . . 291 +Система автоматизованого контролю технічного стану +та діагностування потужних обертових електричних машин +(Граняк В. Ф.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 +Розділ ІІІ +НОВІ ІНФОРМАЦІЙНІ ТЕХНОЛОГІЇ В ОСВІТІ +Автоматизована інформаційна система обліку підвищення +кваліфікації викладачів (Іванова Л. В., Котлик Д. О.) . . . . . . . . 385 +Системний підхід при організації навчального процесу +у закладах вищої освіти з застосуванням нових +інформаційних технологій (Воінова С. О.) . . . . . . . . . . . . . . . . . . 453 + +4 +Розділ IV +ПРОЕКТУВАННЯ ІНФОРМАЦІЙНИХ СИСТЕМ +І ПРОГРАМНИХ КОМПЛЕКСІВ +Ukrvectōrēs та vHealth: інтелектуальні сервіси підтримки +дистанційної медичної реабілітаційної допомоги +(Величко В. Ю., Малахов К. С.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494 +Fundamentals of computer echolocation in distributer structures +(Khoshaba O. M.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577 +Застосування математичних моделей та програмного +забезпечення для проектування нових харчових продуктів +(Котлик С. В., Соколова О. П.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596 +Розділ V +КОМП’ЮТЕРНІ ТЕЛЕКОМУНІКАЦІЙНІ МЕРЕЖІ +ТА ТЕХНОЛОГІЇ +Методика рівномірного розподілу завдань +між обчислювальними комплексами (Завертайло К. С.) . . . . . 658 +Актуальність розвитку мережі NGN (Кунуп Т. В.) . . . . . . . . . . . 689 +Список авторів . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 720 + +5 +Передмова +Четверта промислова революція (Індустрія 4.0) передбачає новий +підхід до виробництва, що базується на масовому впровадженні інфор- +маційних технологій у промисловість, масштабній автоматизації біз- +нес-процесів та поширенні штучного інтелекту. +Переваги Четвертої промислової революції очевидні: підвищення +продуктивності, велика безпека працівників за рахунок скорочення +робочих місць у небезпечних умовах праці, підвищення конкуренто- +спроможності, принципово нові продукти та багато іншого. Однак +вона має й недоліки, які можуть негативно впливати на розвиток сус- +пільства, тому вивчення розвитку напрямів Індустрії 4.0 — необхідна +умова практичного застосування сучасної науки. +У колективній монографії представлені результати практичних і тео- +ретичних досліджень в області комп’ютерного та математичного моделю- +вання, автоматизації процесів управління, застосування інформаційних +технологій в освіті, проектування інформаційних систем і програмних +комплексів, розвитку комп’ютерних телекомунікаційних мереж та тех- +нологій — більшості напрямків, які об’єднуються терміном Індустрія 4.0. +Монографія складена за підсумками проведення XIV Міжнародної +науково-практичної конференції «Інформаційні технології та автома- +тизація — 2021», яка відбулася в жовтні 2021 року в Одеському націо- +нальному технологічному університеті (колишня Одеська національна +академія харчових технологій). +Спектр представлених у монографії проблем надзвичайно широ- +кий — застосування інформаційних технологій для проектування піс- +лядрукарських процесів і нових харчових продуктів, розвиток теорії +прийняття рішень, математичне моделювання в сегнетоелектричних +полімерах і поляризованих плівках, розробка алгоритмів логічного +управління, автоматизація обслуговування потужних електричних ма- +шин і систем швартування судноплавства, застосування інформаційних +технологій в освіті та розподіл між обчислювальними комплексами. +Представлена монографія являє собою істотну підмогу фахівцям, +викладачам, студентам, аспірантам, які намагаються дізнатися про +сучасний стан науки в галузі Індустрія 4.0. Ця інформація може бути +використана для вирішення широкого кола проблем в зазначених роз- +ділах, що виникають як в навчальному процесі, так і в дослідницькому +і науковому планах. + +6 +Розділ I +МАТЕМАТИЧНЕ І КОМП’ЮТЕРНЕ МОДЕЛЮВАННЯ +СКЛАДНИХ ПРОЦЕСІВ +КОНТЕКСТНО-ОНТОЛОГІЧНА СИСТЕМНА ОПТИМІЗАЦІЯ +ПРОБЛЕМНО-ОРІЄНТОВАНОЇ ПІДТРИМКИ +ПРИЙНЯТТЯ РІШЕНЬ +Чаплінський Ю. П. +Показана актуальність використання знання-орієнтованих підходів до +прийняття рішень, що базується на використанні системної оптимізації, +онтологій та контексту. Описана технологія підтримки прийняття рішень +для розв’язання управлінських задач, яка ґрунтується на методології сис- +темної оптимізації. Досліджуються різні ситуації при прийнятті рішень в +рамках запропонованої технології. Процес прийняття рішень на основі сис- +темної оптимізації розглядається через модель певного контексту. Визна- +чені контекстна онтологія та її складові, які дозволяють розпізнати, зро- +зуміти, представити та підтримати розв’язання задачі прийняття рішень. +Представлені онтологія шарів та онтологія аспектів. +The actuality of the usage of knowledge-oriented decision-making approach +based on the use of system optimization, ontologies and context is shown. The de- +cision — making technology for solving management problems, which is based on +the methodology of system optimization, is described. Various situations of decision +making within proposed technology are researched. The decision-making process +based on system optimization through the model of some context is considered. Con- +textual ontology and its components, which allow to recognize, understand, present +and support the solution of the decision-making problem are identified. The ontology +of layers and the aspects ontology are presented. +Сьогодні комплексна та системна підтримка прийняття рішень є +домінуючим динамічним діловим середовищем. Це визначається ха- +рактерними рисами сучасного прийняття рішень: інтеграція наукових +знань, зростання кількості міждисциплінарних проблем, комплекс- +ність проблем та необхідність їх вивчення у єдності технічних, еконо- +мічних, соціальних, психологічних, управлінських та інших аспектів; +ускладнення аналізованих проблем та об’єктів; динамічність ситуацій +прийняття рішень; дефіцитність ресурсів; підвищення рівня стандар- + +7 +тизації та автоматизації елементів виробничих та управлінських про- +цесів; глобалізація конкуренції, виробництва, кооперації, стандарти- +зації тощо; підвищення ролі людського фактора в управлінні та ін. +При цьому прийняття рішень відбується як через горизонталь- +ні перехресні вузли, так і через вертикальні перехресні ієрархічні +зв’язки, при цьому можливо отримання раніше недоступної інфор- +мації, що в подальшому дає змогу розвивати нові знання та розумін- +ня. При цьому неможливо із загального процесу прийняття рішен- +ня виділити будь-які окремі задачі, оскільки вони об’єднані в одну +загальну задачу. Це означає, що діяльність як окремих людей, так і +підприємств все більшою мірою залежить від наявних у них знань як +одного з найцінніших ресурсів і можливості їхнього ефективного ви- +користання. +Управління знаннями сьогодні розглядається як потужна конку- +рентна перевага на підприємстві, орієнтованому на постійні зміни +ділових процесів. Під представленням знань розуміється їх структу- +ризація з метою формалізації процесів рішення задач у певній про- +блемній області. +Такий розгляд прийняття рішень визначає перехід від вузькодис- +циплінарного прийняття рішень до взаємодіючої множини предмет- +них областей, що об’єднує різні аспекти розгляду: представлення, +зміст, інтерпретацію та використання; постійної зміни середовища +прийняття рішень, постійного накопичення нових знань, викорис- +тання активних знань. +Слід також зазначити, що знання в таких складних предметних об- +ластях дуже швидко змінюються або застарівають, з’являються нові +задачі та нові методи розв’язання. При цьому необхідно розглядати +мультидисциплінарні сфери, що пов’язані з відповідною прикладною +проблемою, їх взаємодію та інтеграцію. +Результати розв’язання задач прийняття рішень є результатом по- +єднання та інтеграції знань, розуміння та ідей розв’язання множин +взаємопов’язаних задач з різних предметних областей, кожна з яких +має свої специфічні передумови. Вони характеризуються різноманіт- +ністю, багатовимірністю, багаторівневістю. Реалізацію ефективного +прийняття рішень будемо розглядати на основі методології систем +підтримки прийняття рішень, основою якої є між-/мульти-/транс- +дисциплінарність, контекст та онтологія, як засоби розуміння та +представлення предметних областей і процесів прийняття рішень та +інтеграції методів системного, процесного та ситуаційного аналізу. + +8 +В рамках такого прийняття рішень людині, що приймає рішення +(ЛПРу), необхідно врахувати множину властивостей, що визнача- +ються та використовуються одночасно. Це вимагає розгляду проце- +сів, структур, ресурсів, навколишнього середовища, а також взаємодії +між акторами процесу прийняття рішень. Для цього необхідно ви- +користовувати тільки ті особливості дійсності, які є найважливіши- +ми для ситуації чи проблеми. При цьому необхідно сконцентрувати +увагу на деяких конкретних характеристиках, які визначаються через +точки зору (аспекти розгляду). Це надає можливість використовувати +аспекти або точки зору для того, щоб формулювати, розв’язувати та +керувати складними та взаємозв’язними ситуаціями, які можуть ба- +зуватися не тільки на знаннях окремої предметної області, а на деякій +сукупності проблемних областей. При цьому необхідно розуміти від- +ношення між елементами середовища прийняття рішень. +Тому є актуальною є задача розв’язання проблемних ситуацій з ви- +користанням відповідних інтелектуальних засобів, що розроблені на +принципах інженерії знань для сукупності певних проблемних облас- +тей. При цьому необхідно використовувати та враховувати когнітив- +ні знання («знаю, що»); прикладні знання застосування («знаю, як»); +системне розуміння («знаю, чому»); особисту мотивацію («хочу знати, +чому»). Для цього всі знання, що використовуються, розглядаються в +розрізі знань, що описують контент, та знань, що описують контекст. +З іншого боку, прийняття рішень у системах управління описуєть- +ся взаємозалежними задачами. При чому, як правило, такі задачі ви- +являються несумісними через їхню структуру, що склалася, та обме- +жуючі фактори, так званими «вузькими місцями», до яких відносять +вимоги до функціонування системи, обсяги фінансування; наявність +достатніх людських ресурсів, виробничі можливості підприємств, +нормативні чи фактичні годинні етапи життєвого циклу виробництва +продукції тощо. При чому прийняття рішень в таких задачах вима- +гає врахування таких особливостей, системності, альтернативності, +неспільності (суперечності), багатокритеріальності, врахування ду- +мок аналітиків та експертів. Застосування традиційних методів для +розв’язання таких задач у класичній постановці, тобто знаходження +розв’язання в незмінній протягом рішення моделі, вимагає внесення +всіх варіацій параметрів (нових технологій, додаткових ресурсів) до +початкової постановки, а це веде до надмірної розмірності задачі, і, +отже, складнощів розв’язання задачі і неможливості отримання рі- +шення за прийнятний час і прийнятної точності. + +9 +Таким особливостям задач прийняття рішень задовольняє техно- +логія системної оптимізації, яка була запропонована В. М. Глушко- +вим [1]. Суть якої полягає в цілеспрямованій зміні моделей прийняття +рішень для досягнення спільності й у виборі найбільш прийнятного +рішення поставленої задачі, що формулюються як задачі багатокри- +теріального лінійного програмування та для різних видів припусти- +мих варіацій параметрів. +Створення різних засобів підтримки прийняття рішень — це без- +перервний процес формування, уточнення вимог та розв’язання. +При цьому необхідно враховувати, що функціонування систем від- +бувається в умовах інформаційної та реалізаційної неоднорідності, +розподіленості та автономності інформаційних ресурсів системи. +Інформаційна неоднорідність ресурсів полягає в різноманітності їх- +ніх прикладних контекстів. Реалізаційна неоднорідність джерел про- +являється у використанні різноманітних комп’ютерних платформ, +засобів управління базами даних, моделей даних і знань і таке інше. +Таким чином, потрібна підтримка розвитку систем та підсистем до +складніших, інтегрованих систем, що базуються на інтероперабель- +ній взаємодії компонентів. Реалізація такої підтримки прийняття +рішень базується на підтримці повного циклу прийняття рішень для +того, щоб пройти від формулювання проблеми, визначення відповід- +них моделй та алгоритмів розв’язання до використання розв’язувача, +вимагає застосування знань для прийняття рішень для конкретної за- +дачі з врахуванням навичок та досвіду користувача. +Метою роботи є представлення онтологокерованої підтримки +прийняття управлінських рішень на основі методів та алгоритмів +системної оптимізації й онтологічних методів представлення та об- +робки знань з урахуванням контекстів розв’язання задач прийняття +рішень. +Для врахування цих особливостей і властивостей прикладних +систем управління та багатьох інших вимог, що виникають в процесі +функціонування різних систем управління, потрібна побудова єдиної +технології прийняття рішень, що дозволяє виробляти найбільш при- +йнятні рішення. При цьому вибір того або іншого рішення не пови- +нен порушувати системність розгляду і цілісність процесу прийняття +рішень. Слід зазначити, що сучасне розв’язання задач вимагає вико- +ристання інформації різного походження. +Це визначає необхідність зрозуміти складність проблеми, взяти +до уваги різноманіття оточуючого світу та науковий розгляд про- + +10 +блеми, поєднати абстрактне і конкретне знання, розвивати знання +та діяльність в напрямку досягнення результатів. При цьому необ- +хідно враховувати, що використання інформації та знань у проце- +сі прийняття рішень, як правило, відбувається в контексті складної +структури процесу прийняття рішень, який часто формується за до- +помогою ряду чинників. Такі системи з точки зору прийняття рішень +включають: +• наявність складного змістовного об’єкта (системи), з яким +пов’язана загальна проблема (задача) прийняття рішення; +• розбиття даної системи на взаємозв’язані підсистеми, з відповід- +ною декомпозицією загального завдання на підзадачі; +• наявність спільної мети при розподілі функцій по підсистемах; +• фізична або віртуальна відособленість кожної з підсистем; мож- +ливість відносно самостійного вибору своїх станів; +• наявність засобів обміну станами між підсистемами, а також +засобів узгодження, подолання протиріч і синхронізації процедур +розв’язання підзадач. +В роботі [2] пропонується розглядати прийняття рішень в рамках +трьох етапів: аналіз, розробка та вибір. Аналіз (опис системи, розу- +міння поведінки системи, оцінка поточної ситуації, формулювання +цілей) включає в себе пошук середовища для умов виклику прийнят- +тя рішення. Розробка (формулювання моделі, генерація альтернатив) +належить до створення, розробки та аналізу можливих варіантів дій, в +той час як вибір (оцінка впливу альтернатив, оцінка та прийняття рі- +шення, пояснення: візуалізація та спілкування) включає в себе вибір +напрямку дій з наявних. Основною частиною підтримки прийняття +рішень є збір, оцінка, організація та перетворення цієї інформації в +форми, що придатні для аналізу. +Для успішної розробки та впровадження систем підтримки при- +йняття рішень (СППР) необхідно [3; 4]: участь кінцевих користувачів +в розробці СППР; проектування СППР для потреб кінцевих користу- +вачів, а не потреб, як їх розуміє розробник; гнучкість, адаптивність та +оновлюваність системи; простий інтерфейс, який вимагає обмежено- +го часу для навчання користування системою; візуальне відображен- +ня результатів; врахування факторів, що стосуються якості системи, +якості інформації та представлення інформації. +Область прийняття рішень будемо розглядати як багаторівневу +структуру, що включає область проблем, область моделей, область ме- +тоду та область реалізацій. Область прийняття рішень можна деком- + +11 +позувати на елементарні об’єкти, кожен з яких описується сукупніс- +тю атрибутів. В рамках такого розгляду необхідно визначити поняття +та конструкції, за якими можуть бути визначені природа, структура та +представлення процесу формування та прийняття рішень та відповід- +них складових областей, що описують такий процес. +В роботі під прийняттям рішень будемо розуміти інтерактив- +ний процес нагромадження, обробки, використання та поширення +знань, що дає можливість обміну інформацією, знаннями і досвідом +та підвищення рівня інформованості, можливість отримання та ви- +роблення усвідомленого вибору між альтернативними рішеннями, +можливість підвищення фахового рівня. Метою такого процесу є +розв’язання проблем: надання знанням доступності та корисності, +так, що відповідні достовірна інформація та знання, що впливають +на прийняття рішень та розуміння проблеми, будуть донесені відпо- +відному користувачу в відповідному форматі в відповідний час. Та- +ким чином, підтримка прийняття рішень, що реалізована як певна +система прийняття рішень, повинна відповідати SMART-критеріям, +тобто рішення мають бути конкретними, вимірними, погодженими, +реалістичними, чітко прив’язаними до часу та простору. +Будемо розуміти під підтримкою прийняття рішень інтелектуаль- +ну комп’ютерну технологію посилення можливостей ЛПР у процесі +спостереження за станом предметної області, діагностики проблем- +них ситуацій і цілей дій, планування дій і генерацію способів їх реа- +лізації, формування раціональних варіантів рішень з використанням +експертних знань і методів моделювання та оптимізації. При цьому +прийняття рішень реалізується на основі інформаційних моделей да- +них; на основі логічних моделей; на основі формальних моделей; на +основі типових рішень або прецедентів. Під основними етапами при- +йняття рішень будемо розглядати: +• моніторинг і збір достовірних даних про процеси функціону- +вання системи; +• розпізнавання, прогнозування розвитку й оцінка штатних і кри- +тичних ситуацій, що мають місце у діяльності системи; +• постановку цілей і пошук альтернативних дій з їх досягнення в +умовах ситуацій, що складаються в підсистемах підприємства і в сис- +темі в цілому; +• адекватну оцінку можливих способів дій, аналіз наслідків і вибір +найбільш ефективних з них з комплексним аналізом всього спектру +характеристик альтернативних рішень; + +12 +• організацію виконання рішень, що включає оцінку і вибір на- +прямів робіт з реалізації рішень, конкретних заходів і термінів, роз- +поділ ресурсів для реалізації рішень; +• контроль виконання рішень на основі оцінки і порівняння ста- +нів і результатів (проміжних у зіставленні з бажаними кінцевими) ді- +яльності, оцінку якості рішень, що приймалися, і правильності орга- +нізації їх вироблення. +Прийняття рішень можна представити у вигляді багаторівневої +системи, що складається з сукупності завдань, що знаходяться на +різних рівнях ієрархії та відповідають за певну функцію чи діяльність +та пов’язані з відповідною логічною структурою. Прийняття рішень +в такій системі будемо розглядати як через горизонтальні перехрес- +ні вузли (перетину кордону), так і через вертикальні перехресні іє- +рархічні зв’язки (перетин ієрархічних рівнів), при цьому можливо +отримання раніше недоступної інформації, що в подальшому дає +змогу розвивати нові знання та розуміння. Кожна задача, що від- +повідає конкретному напрямку(ам) діяльності, може мати підзадачі. +Задача та підзадачі описуються відповідними формалізованими за- +вданнями, які описуються комплексами взаємопов’язаних моделей. +Формалізовані моделі реалізуються певними методами, алгорит- +мами. Сам процес будемо розглядати як систему, яка складається +з деякого набору підсистем (етапів) та їх елементів (процедур, дій, +операцій), які взаємодіють між собою, кількість та склад яких мо- +жуть змінюватись у залежності від умов та розв’язуваних завдань. +При цьому інтеграція рішень, що приймаються, в рамках підсистем +досягається за рахунок прийняття узгоджених рішень у завданнях, а +інтеграція управління усією системою в цілому буде отримана шля- +хом узгодження дій між пов’язаними підсистемами, що належать +одному або різним рівням. +Визначимо, що між різними підсистемами, функціональними за- +дачами (підзадачами), моделями можливі різні види взаємодії. Така +взаємодія може реалізовуватися через відношення прямого підпо- +рядкування, інформаційного обміну, функціонального підпоряд- +кування, функціонального узгодження і координації. Відношення +прямого підпорядкування і функціонального підпорядкування є +базою для опису побудови системи управління за організаційною та +функціональною ознаками. Ці відношення можуть бути задані при +визначенні ієрархії функціональних задач, що розв’язуються окре- +мими підсистемами, та пріоритетів їхньої взаємодії. Відношення ін- + +13 +формаційного обміну визначається при описі взаємодій окремої під- +системи (задачі) з іншими підсистемами (задачами) у рамках цілісної +системи. Це може бути задано при визначенні для даної підсистеми +деякої нормативно-довідкової інформації, яку використовує у про- +цесі реалізації своїх функцій дана підсистема або задача. Відношення +функціонального узгодження і координації визначається при описі +функціональних задач підсистеми. Це відношення задається вхід- +ними і вихідними параметрами функціональних задач підсистеми, +а також ресурсами підсистеми. Відношення функціонального узго- +дження і координації реалізується в процесі розв’язання конкретних +взаємозв’язаних задач, що виникають всередині системи управлін- +ня. Тип зв’язків між окремими підсистемами визначається в процесі +опису організаційно-функціональної структури системи управління. +При реалізації прийняття рішень будемо розрізняти три стратегії +прийняття рішень. Це — створення, інтеграція та адаптація. Створен- +ня означає «абсолютно нову проблему», або «на порожньому місці» +концепцію розв’язання проблеми в ситуації, коли не існує відповід- +ної моделі, методу та/або алгоритму розв’язання, що могло би ви- +користовувався як основа для прийняття рішень. Це важливо, якщо +деяка частина з процесу прийняття рішень має бути спроектована +без підтримки існуючого. Інтеграція означає концепцію розв’язання +проблеми, згідно з якою побудовано процес розв’язання проблеми, +збираючи компоненти з існуючого. Чим більше компонентів багато- +кратного використання, з яких складений процес прийняття рішень, +тим легше процес інтеграції. Адаптація означає концепцію процесу +прийняття рішень, згідно з якою побудовано розв’язання проблеми, +знижуючись або змінюючи деяку частину(и) існуючого, або розши- +рюючи існуюче деякою новою частиною(ами). +Розв’язання задач на основі системної оптимізації можна предста- +вити в вигляді послідовності людино-машинних процедур, що вклю- +чають формування моделі початкової задачі в термінах предметної +області, переведення сформованої моделі в область задач, наприклад, +математичного програмування, та розв’язання задачі математичного +програмування в багатокритеріальній постановці. +При цьому рішення задачі складається з перевірки здійснимос- +ті вимог за якістю функціонування системи (директивні вимоги) в +області власних можливостей системи, і в разі їх нездійсненності — +знаходження «вузьких місць», вироблення заходів, спрямованих на +усунення нездійсненності директивних вимог, і в виборі найбільш + +14 +прийнятного рішення. Таким чином, видно, що системна оптиміза- +ція дає можливість представлення рішення досить складних задач у +вигляді послідовності рішення простіших задач. +При реалізації системної оптимізації враховується те, що обмін +інформацією про рішення, які приймаються, здійснюються між за- +дачами (етапами) з чітко вираженими зв’язками та існує пріоритет в +прийнятті рішень між задачами (етапами) як з точки зору правил їх +взаємодії, так і часу їх виконання. +1) Аналіз виконання управлінських рішень, отримані з зада- +чі (етапу), що має більший пріоритет за взаємодією чи за часом +розв’язання, або заданих власними цілями з функціонування даної +задачі (етапу), в рамках існуючих можливостей задачі (етапу), що +розв’язується. +У разі неможливості реалізації цих рішень задачею (етапом) по- +трібно виконати такі кроки: +• підготувати пропозиції щодо бажаної та можливої зміни отри- +маних рішень; +• ініціювати процес взаємодії з відповідними задачами (етапами). +2) Пошук управлінських рішень з урахуванням власних можли- +востей завдання (етапу) й існуючих взаємних зв’язків з іншими за- +дачами (етапами). +3) Визначення завдань наступного завдання (етапу) для реалізації +отриманих рішень. +В ході процесу взаємодії при пошуки узгоджених рішень структура +взаємодії, тобто множина взаємопов’язаних задач (етапів) і відповід- +них осіб, які приймають рішення, не може бути задана заздалегідь. Ця +структура генерується безпосередньо під час пошуку рішення. +У відповідності з цим інструментарій повинен забезпечити: +• передачу і прийом управлінських рішень або генерацію власно- +го напрямку(ів) рішення поставленого завдання (такі рішення буде- +мо називати директивними); +• модельне представлення власних можливостей і інтересів дано- +го завдання (етапу), директивних рішень і взаємних зв’язків з іншими +задачами (етапами); +• ініціювання процесу взаємодії з відповідними особами, які при- +ймають рішення; +• формування модельного представлення задач пошуку узгодже- +них рішень з урахуванням можливостей даного завдання (етапу); +• методи і алгоритми визначення розв’язку сформованих задач. + +15 +Такий розгляд дозволяє запропонувати підхід до реалізації вза- +ємодії між підсистемами і відповідно певними задачами (та нада- +лі його використати при розгляді певних моделей, формалізованих +задач тощо), що базується на понятті відношення пріоритету вза- +ємодії. Це відношення на множині взаємопов’язаних локальних за- +дач визначає характер впливу відповідних підсистем і задач один на +одного. Таке відношення може бути розглянуте як відношення не- +строгого порядку R , визначене таким чином: якщо K — множина +взаємопов’язаних задач, то iRj ( ,i j +K +∈ +) означає, що задача i має +пріоритет у прийнятті рішення по відношенню до задачі j , тобто її +рішення є обов’язковими (директивними) для задачі j і входять в її +модель як деякі параметри. Це відношення визначає відношення прі- +оритету взаємодії. Оскільки R є відношенням нестрогого порядку, то +воно розбиває множину взаємопов’язаних задач на класи еквівалент- +ності, які розглянемо в подальшому. Опишемо реалізацію відношень. +Для цієї мети ми введемо такі позначення (без врахування структури +системи): I — множина підсистем системи, +lI — множина задач для +l -ї структурної одиниці (підсистеми); +Припустимо, що задачі прийняття рішень в структурній одиниці +структуровані, а задача вибору рішення у всій системі в цілому має +бути сформульована через інтеграцію розподілених підсистем і відпо- +відно через інтеграцію задач, що реалізуються в підсистемах. +Для формалізації специфічних проблем інтеграції функціональ- +них задач введемо позначення: xp — вектор, що визначає вибір дії +в p -й функціональній задачі; +{ +, +} +p +p +j +p +s +s +j +J += +∈ + — вектор, що визна- +чає вплив (відношення функціонального узгодження і координа- +ції) інших функціональних задач, які описують множину +, +p +p +J +J +I +∈ +, +на p -ту функціональну задачу; +{ +, +} +p +p +j +p +z +z +j +Z += +∈ + — вектор, що ви- +значає відношення інформаційного обміну інших функціональних +задач, які описують множину +, +p +p +Z +Z +I +∈ +, з p -ю функціональною +задачею; +{ +, +, +} +p +p +p +ji +l +u +u +j +J +i +I += +∈ +∈ + — вектор директивного впливу (під- +порядкування) через пріоритет взаємодії на p -ту функціональну за- +дачу, який може визначати дію як інших функціональних задач l -ї +підсистеми, так і інших функціональних задач підсистем, що мають +директивні взаємозв’язки з цією задачею, що визначають множину +, +p +p +J +J +I +∈ +. +При цьому визначимо вектори: +{ +, +} +j +v +p +p +p +s +s +j +J += +∈ +, +{ +, +} +j +z +p +p +p +z +z +j +Z += +∈ +, +{ +, +, +} +j +p +p +pi +u +l +u +u +j +J +i +I += +∈ +∈ +, які описують відповідні вектори та множини, + +16 +що визначають вплив, інформаційний обмін та директивний вплив +даної задачі на інші задачі. +В рамках СППР взаємодія між множиною підсистем багаторівне- +вої системи та множинами супутніх задач в цих підсистемах, які від- +повідають за різні напрямки діяльності системи, реалізується через +принцип системності. +Принцип незалежності в функціонуванні СППР підсистем базу- +ється на тому, що кожна підсистема за своєю функціональною зада- +чею може робити свій вибір власної дії, яка описується вектором xp, у +відповідності зі своєю власною моделлю вибору. Така дія дасть змогу +розв’язання задачі самоуправління з виконання підсистемою своєї +функціональної діяльності. Проте принцип цілісності вимагає побу- +дови такої моделі задачі вибору рішень, область припустимих рішень +якої враховувала б вплив підсистем та функціональних задач. +З цією метою введемо такі типи припустимих областей задач при- +йняття рішень в СППР: +0( +) +p +D z + — область, що визначає область ви- +бору припустимих рішень (дій) на підставі власних можливостей від- +повідної підсистеми в p -й функціональній задачі при виборі власних +рішень +p +x з урахуванням вектора +p +z ; +0( +) +p +D s + — область припустимих +рішень +p +x p -ї функціональної задачі, що визначається вектором +ps ; +0( +) +p +D u + — область припустимих рішень +p +x , що описує директивну об- +ласть, утворену вектором +p +u . +Як відомо, більшість задач прийняття рішення розв’язується при +врахуванні деякої множини +1, +J +M += + характеристик оцінки рішення +* +p +x +, яке може визначитися в кількісній або якісній шкалі за допо- +могою множини критеріальних функцій +* +{ ( +), +} +p +i +f +f x +i +J += +∈ +, при цьому +критерії можуть носити як кількісний, так і якісний характер. +Перш за все припустимо, що +0 +0 +0 +( +) +( +) +( +) +p +p +p +D z +D s +D u +≠ ∅ + + +. В дано- +му випадку ми зможемо розв’язати задачу та знайти +* +p +x + у врахуван- +ням множини критеріальних функцій f та припустимих областей. +Якщо +0 +0 +0 +( +) +( +) +( +) +p +p +p +D z +D s +D u += ∅ + + + та +0 +0 +( +) +( +) +p +p +D z +D u += ∅ + +, то об- +ласть +0( +) +p +D u + не має припустимих рішень з областю +0( +) +p +D z + з вра- +хуванням впливу інших задач, і нам необхідно змінювати область +0( +) +p +D z + за рахунок можливостей задачі з метою одержання сумісності +з областю +0( +) +p +D u + або у разі неможливості досягнення сумісності фор- +мувати обмеження на вектор +p +u з метою інформування більш пріо- +ритетної задачі про неможливість розв’язання задачі. + +17 +Якщо +0 +0 +0 +( +) +( +) +( +) +p +p +p +D z +D s +D u += ∅ + + + і +0 +0 +( +) +( +) +p +p +D z +D u +≠ ∅ + +, то область +0( +) +p +D s + не має припустимих рішень з областю +0( +) +p +D z + з урахуванням +директивного впливу, і нам необхідно формувати вектор +ps для мно- +жини +, +p +p +J +J +I +∈ + з метою реалізації процедури узгодження рішень +взаємопов’язаних задач. +Зазначимо, що модель задачі, метод та алгоритм розв’язання за- +дач можуть не тільки бути з області математичного програмування, а і +описуватися в області інформаційних та логічних моделей. +У випадку реалізації стратегії створення формалізований опис +де якої локальної задачі, що формулюється як задача математично- +го програмування та розв’язується в системі підтримки прийняття +рішень. Оскільки будь-яка математична модель задачі прийняття +рішення включає декілька критеріїв оптимальності і системи об- +межень, що описує множину припустимих альтернатив, то всі види +впливу на цю модель можуть бути зведені до впливу на критерій і +впливу на обмеження. Розглянемо останній з них. В цьому випад- +ку множина обмежень локальної задачі включатиме обмеження, що +описують зв’язки з іншими задачами, і обмеження, що описують ло- +кальну область припустимих рішень. +Розглянемо модель локальної задачі прийняття рішення у багато- +рівневій організаційній системі, яка має загальний вигляд: +{ +xi +i +M +C += +, +0 +X , +1 +( +) +i +X u − +, +( ) +i +X u +, +( ) +U x , +1 +( +) +i +U +x + +}, де i — індекс зада- +чі, що розглядається ( +1, +i +I +M +∈ += +), +{ +( ) +, +1, +} +xi +xi +i +j +C +C +x +extr j +J +N += +→ +∈ += + — +множина оцінок вибору рішення задачі +i +M ; +0 +i +X — область можливих рішень, що визначається локальними об- +меженнями задачі +i +M (область +0( +) +p +D z +; +1 +( +) +i +X u − + — область бажаних рішень, яка визначається обмеження- +ми, які називають директивними (область +0( +) +p +D u +); +( ) +i +X u + — область рішень, яка визначається з урахуванням ком- +промісних зв’язків із завданнями, які володіють однаковими з даним +завданням пріоритетами взаємодії (область +0( +) +p +D s +); +( ) +U x — область змінних u , яка залежить від рішення +*x даної за- +дачі (вектор +ps ); +1 +( +) +i +U x + + — область змінних, що характеризують вплив даної задачі на +пов’язані з нею завдання з меншим пріоритетом взаємодії (вектор +p +u ). +Наявність у завданнях прийняття рішення локальних цілей та прі- +оритетів взаємодії призводить до різних ситуацій взаємодії між від- + +18 +повідними завданнями. Ці ситуації визначаються взаємним розташу- +ванням областей відносно одна одної. +Таким чином, процес прийняття рішень може складатися з послі- +довності етапів, кожен з яких включає такі елементи: +1. визначення рішень локальних задач з урахуванням результатів, +отриманих на попередніх етапах; +2. узгодження рішень пов’язаних локальних задач. +Перший етап полягає в аналізі моделей локальних задач. Якщо +припустимих рішень в локальній задачі не існує, то виникає необхід- +ність у цілеспрямованій зміні області +0 +i +X для виконання директив- +них вимог, що визначаються областю +1 +( +) +i +X u − +, де +1 +iu − отримано при +розв’язанні більш пріоритетних задач. Така задача корекції +0 +i +X інтер- +претується як задача системної оптимізації [5]. +Таким чином рішення локальної задачі +1 +( , +, +) +i +i +y +x u +u +− += + (локальне +припустиме рішення) буде знайдено безпосередньо або буде отри- +мано в результаті розв’язання задачі системної оптимізації, тобто +1 +0 +( +) +i +X +X u − +≠ ∅ + +. +Оскільки рішення y визначено без врахування області зв’язків +( ) +i +X u +, то значення параметра u визначені незалежно в кожній із +пов’язаних задач і можуть не збігатися. Тоді узгодження рішень по- +лягає у знаходженні таких локально допустимих (оптимальних, +компромісних) рішень, для яких значення параметрів зв’язку рівні. +Можливі підходи до реалізації алгоритмів узгодження рішень по па- +раметрах зв’язку наведено в [6]. +У разі відсутності таких узгоджених рішень необхідне корегування +моделей пов’язаних задач для досягнення сумісності в просторі па- +раметрів u , яка може бути зведена до задачі системної оптимізації. +Основною проблемою при цьому є вибір напрямку і величини коре- +гування областей +0 +i +X , +1 +( +) +i +X u − +. Отримане рішення y визначить зна- +чення параметра +1 +iu + , що характеризує вплив даної задачі на пов’язані +з нею задачі з меншим пріоритетом. +Розглянемо формулювання локальної задачі як задачу лінійного +математичного програмування, що розв’язується в системі підтрим- +ки прийняття рішень. В цьому випадку множина +xi +C + задається через +деяку множина критеріальних функцій +1 +* +, +n +i +ij +j +j +f +c +x +extr i +I += += +→ +∈ +∑ +; об- +ласть директивних вимог +g +D щодо функціонування системи управ- +ління визначається множиною +*( ) +0 +{ : +, +1, }, +g +g +j +j +D +x x +x +j +n += += += + або областю + +19 +{ : +, +1, }, +g +b +u +j +j +j +P +x x +x +x +j +n += +≤ +≤ += + або областю +0 +2 +1 +{ : +* +, +}; +n +g +g +ij +j +i +j +D +x +a +x +u i +Q += += +≤ +∈ +∑ +область +припустимих +рішень +описується +множиною +0 +0 +0 +1 +{ : +* +, +, +0, +1, } +n +ij +j +i +j +j +D +x +b +x +b i +Q x +j +n += += +≤ +∈ +≥ += +∑ +. +Згідно з методологією системної оптимізації, необхідність у +розв’занні задачі системної оптимізації виникає у разі неспільності +області директивних вимог +g +D та області припустимих рішень +0 +D . +Основна мета алгоритмів системної оптимізації полягає в побудові +нової області припустимих рішень відповідно до первинної області +0 +D і додаткової обмеженої області варіацій +, +, +, +1, +ij +i +b +b i +Q j +n +Δ +Δ +∈ += + па- +раметрів +, +ij +i +b b , що будується в процесі рішення з урахуванням того, +узгоджуються директивні вимоги й інтереси даної системи управ- +ління +g +D чи ні, в якій існуватимуть рішення із значеннями по всіх +критеріальних функціях більшими або рівними значеннями крите- +ріїв, що задаються вимогами людини, що приймає рішення (ЛПР), +в області директивних вимог +g +D . Ці алгоритми носять ітераційний +характер. +Збіжність процедур в рамках системної оптимізації реалізується +через ітераційне відсікання неприпустимих варіантів рішення, при +цьому гарантується, що припустимі варіанти не будуть відсікатися. +Що в підсумку дає нам можливість або отримати рішення поставле- +ної задачі, або зробити висновок про неможливість розв’язання по- +ставленої задачі. +Перевірка виконання вимог +g +D в області +0 +D проводиться або +прямою підстановкою +*( ) +g +x +x += + в систему обмежень області +0 +D при +0 +g +g +D +D += + або на основі якого-небудь методу лінійного програмуван- +ня для областей та у разі порожнього перетину +g +D і +0 +D можливі різ- +ні випадки взаєморозташування області +g +D та області +0 +D щодо кри- +теріальних функцій, які в загальному випадку можуть бути такими: +1. Всі точки директивної області +g +D мають кращі значення за всі- +ма критеріями в порівнянні зі значеннями, що досягаються у відпо- +відних їм за перевагою точках області +0 +D , тобто повне узгодження. +2. Для будь-якої точки з директивної області +g +D в області припус- +тимих рішень +0 +D існує точка з кращими значеннями за всіма крите- +ріями одночасно, тобто директивні вимоги не узгоджуються з цілями +даної системи, що задані набором критеріальних функцій. + +20 +3. Тільки частину точок директивної області +g +D дає поліпшення +значень за всіма критеріями одночасно, тобто вимоги лише частково +узгоджуються з цілями даної системи. +У разі виконання другого варіанту ЛПРу потрібно перевизначити +область директивних вимог +g +D , оскільки в області +g +D не будуть ви- +конуватися вимоги до значень критеріальних функцій. +З урахуванням інших варіантів розташування, а також з урахуван- +ням вигляду директивних областей можна виділити обмеження об- +ласті, які перешкоджають спільності й узгодженості рішень з +g +D і +області припустимих рішень +0 +D і які називають суттєвими обмежен- +нями. Множину індексів суттєвих обмежень позначимо як +0 +Q . +У разі директивної області вигляду +0 +g +D суттєвими обмеженнями +будуть співвідношення, що порушуються при підстановці +*g +x +x += +. +При виділенні суттєвих обмежень можна розглянути випадки з +урахуванням заданої множини критеріїв і без урахування цільових +функцій. +При врахуванні критеріїв після з’ясування реалізованого варі- +анту узгодження виділяється множина точок, яку будемо називати +областю захоплення і яка апроксимує область +g +D при реалізації +першого варіанту або будується область захоплення +g +g +X +D +⊆ + (яка +містить точки, що мають кращі значення за всіма критеріями одно- +часно в порівнянні з розв’язками області +0 +D ) при реалізації третьо- +го варіанту. +Якщо ж вирішується задача системної оптимізації без ураху- +вання множини критеріальних функцій, то визначення суттєвих +обмежень залежить від вибраної ЛПРом області захоплення +g +X , +g +g +X +D +⊆ +, яка може описуватися паралелепіпедом або деякою об- +ластю або точкою +*' +*' +, +g +x +x +D +∈ +. При цьому задачу системної опти- +мізації будемо розв’язувати відносно деякої точки +* +* +, +g +g +g +x +x +X +∈ +, яка +є вершиною відповідного багатокутника. Отримана область захо- +плення +g +X визначить відповідні множину точок і множину індек- +сів суттєвих обмежень, щодо яких будемо розв’язувати задачу сис- +темної оптимізації. +Для приналежності заданої області захоплення +g +X змінній моделі +будується система обмежень, що описує область P . +Для визначення можливості зміни параметрів моделі задачі для +досягнення вимог з +0 +D і отже можливості рішення самої задачі сис- + +21 +темної оптимізації, так і сформованої локальної задачі, вихідної по- +будуємо перетин області P варіації параметрів обмежень множини +0 +Q і області +0P припустимих варіацій цих параметрів. +Якщо +0 +P +P ≠ ∅ + +, то область зміни параметрів моделі буде обме- +жена і це дозволить вирішити задачу побудови нової моделі +1 +D , в +якій виконуються вимоги з області +0 +D . +В цьому випадку необхідно або змінювати чи перевизначити +ЛПРом свої вимоги або обмеження +0P . +Для корекції області припустимих варіацій +0P можна зокрема по- +будувати параллелепіпед, який вписано в область P , на основі якого +ЛПР зможе задати або відкорегувати обмеження області +0P , так що +0 +P +P ≠ ∅ + +. +Задача вибору варіацій параметрів +, +, +, +1, +ij +i +b +b i +Q j +n +Δ +Δ +∈ += + при непо- +рожньому перетині областей P і +0P зводиться до задачі оптимізації, в +якій як критерії вибрані витрати, що пов’язані зі змінами параметрів +моделі ( +) +, +) +C +B +b +Δ +Δ +. +Якщо функцію витрат побудувати неможливо, то задача вибору +формується як багатокритеріальна задача, в якій кожен параметр ви- +ступає як окремий критерій і залежно від фізичної суті може макси- +мізуватися або мінімізуватися. +Таким чином, нова область допустимих рішень згідно з умовами +побудови в новій області +1 +D , забезпечується здійснимість вимог за- +дачі і існують розв’язки зі значеннями критеріїв не гірше бажаних. +Умови розв’язання задачі системної оптимізації дозволяють алго- +ритму сходитися до відповідного ефективного рішення задачі. Цей +процес ітераційний. Збіжність процедур у рамках системної оптимі- +зації реалізується через ітераційне відсікання недопустимих варіантів +рішення, при цьому гарантується, що допустимі варіанти не будуть +відсікатися. Це в підсумку дає нам можливість отримання рішення +поставленого завдання або дає можливість зробити висновок про не- +можливість вибору варіанту інвестиційного проекту або неможли- +вість реалізувати даний проект. +У разі реалізації стратегії адаптація та інтеграції можна викорис- +тати апарат прецедентів, який допомагає визначити рішення для по- +точної ситуації на основі прецедентів, які вже мали місце у минуло- +му при розв’язанні подібних задач. В загальному випадку прецедент +може включати такі компоненти: опис задачі (проблемної ситуації); +рішення задачі (діагноз із проблемної ситуації і рекомендації ЛПР), + +22 +результат (або прогноз) застосування рішення, результат використан- +ня знайденого рішення. +До основних переваг технології прецедентів можна віднести мож- +ливість безпосередньо використовувати досвід, накопичений систе- +мою, без інтенсивного залучення експертів в тій чи іншій предметній +області, а також можливість виключення отримання помилкового рі- +шення. Істотними недоліками цього підходу є зниження продуктив- +ності системи при великій кількості прецедентів у базі прецедентів і +неможливість отримання рішення задач, для яких немає прецедентів +у бібліотеці прецедентів (БП) системи. +В цьому випадку процес підтримки прийняття рішень формаль- +но представляється як: +{ +, +}, +, ( +), +СППР +KB Rule Case M S M +Dec +=< +> , де +{ +, +} +KB Rule Case — база знань, що містить множину правил Rule та мно- +жину Case прецедентів. +( +) +1 +2 +, +,..., +, +n +Case +x x +x Sol += +, де +1 +2 +, +,..., +n +x x +x — пара- +метри ситуації, яка описує даний прецедент, N — кількість параметрів +для опису прецедента, а +1 +2 +, +,..., +n +X +X +X — області допустимих значень +відповідних параметрів, Sol — рішення (діагноз, рекомендації ЛПР). +{ } +i +Rule +R += +, де +iR — i-те правило, +1,..., +i +I += +. Правила +iR +Rule +∈ + визна- +чаються в такій формі: +' +1 +1 +1 +, , +,..., +, +; +,..., +; , +, , +n +n +m +b +A a U +a U +P +P b U S S +< +> , де +ia +A +∈ + +є передумови проблемної ситуації (ПС); +i +U +U +∈ + — необхідні оцінки +міри упевненості в передумовах; +V +P +P +∈ + є предикати, +1, +0 +V +m +≥ +≥ +; +b +B +∈ + — укладення c оцінкою міри упевненості +b +U ; S — початкова +проблемна ситуація (ПС); +'S — проблемна ситуація, що виникає в +результаті прийнятого рішення. +1 +{ +,..., +} +N +M +M +M += + — множина моде- +лей, що реалізують функції процесу прийняття рішень; +( +) +S M — мо- +дуль, що реалізує функцію вибору необхідної моделі (моделей) для +даної задачі; Dec — модуль формування рішень на основі бази знань. +Це дозволяє реалізувати званий цикл прецедентів або цикл навчання +за прецедентами, що включає такі етапи: +• витягання найбільш відповідного (подібного) прецедента (пре- +цедентів) для проблемної ситуації, що склалася, з бібліотеки преце- +дентів (БП); +• повторне використання витягнутого прецедента для спроби +розв’язання поточної проблеми; +• перегляд та адаптація в разі потреби отриманого рішення відпо- +відно до поточної проблеми; +• збереження знову прийнятого рішення як частини нового пре- +цеденту. + +23 +Пошук рішення на основі прецедентів полягає в визначенні міри +схожості поточної ситуації з ситуаціями прецедентів з БП. При цьому +враховуються ваги параметрів для ситуацій з БП, задані експертом. +Міра схожості залежить від близькості поточної ситуації до ситуації +прецедента і визначається за допомогою алгоритму пошуку найближ- +чого сусіда за допомогою простого зіставлення поточної ситуації з си- +туацією прецедента (кожен параметр для опису ситуацій з БП розгля- +дається як одна з координат). В результаті визначається відстань D +між поточною ситуацією і ситуацією прецедента і максимальна від- +стань +max +D + на основі меж діапазонів параметрів для ситуацій преце- +дентів. Потім обчислюється значення міри схожості +max +1 +/ +sim +D +D += − +. +Для цього можна використати метод найближчого сусіда (найближ- +чих сусідів) (К найближчих сусідів). +Необхідно враховувати, що міркування на основі прецедентів +може не привести до необхідного рішення проблемної ситуації, що +виникла, наприклад, у разі відсутності подібної (аналогічної) ситу- +ації у БП. Ця проблема може бути розв’язана через можливість по- +повнення БП безпосередньо в процесі міркування (висновку). Це +може включати: визначення існуючої практики, яка є прийнятою та +реалізованою; використання часткової стратегії автоматизації узго- +дження розрізненої інформації з декількох джерел інформації на +основі математичних моделей та експертних систем; використання +стратегічної мети усунення невизначеності, неповноти інформації та +врахування суб’єктивної експертної інформації від декількох джерел +інформації. +Як показує вищепредставлене, процес прийняття рішень склада- +ється з декількох етапів. На кожному етапі розв’язуються свої зада- +чі. Задача приймає вхідні дані і виробляє певний результат. Вхідни- +ми для задач є ситуації, кожна з яких представляє собою множину +пов’язаних відношеннями об’єктів предметної області. Виділяється +клас проблемних ситуацій, тобто ситуацій, в яких значення атрибутів +деяких об’єктів виходять за область нормальних значень або критич- +но близько підходять до її кордонів. Результатом рішення задачі може +бути повідомлення, ситуація або задача. Повідомлення — це оста- +точний результат рішення задачі, який користувач приймає до відо- +ма. Ситуація — це результат, який може бути підданий подальшому +аналізу. Ситуація може являти собою наслідки прийнятих рішень або +ж початкові рішення, які повинні привести до бажаних результатів. +Якщо в якості розв’язання отримано кілька ситуацій — альтернатив, + +24 +то може бути згенерована нова задача, яка буде оцінювати отримані +альтернативи і вибирати з них найбільш прийнятні. Для розв’язання +задач використовуються різні методи підтримки прийняття рішень. +Деякі з них можуть мати комп’ютерну реалізацію, тобто можуть бути +реалізовані в деякому програмному модулі, який, у свою чергу, інтер- +претується тим чи іншим розв’язувачем. Інші методи можуть не мати +програмної підтримки. В цьому випадку використовується текстовий +(можливо, формалізований) опис методу, а в якості розв’язувача, ін- +терпретуючого такий модуль, виступає людина — учасник процесу +прийняття рішень. Учасниками можуть бути ЛПРи, власники про- +блеми, різні активні групи, експерти та фахівці з прийняття рішень. +Таким чином, представлення знань про розв’язання задачі за до- +помогою технології системної оптимізації необхідно описати: +• моделі, що описують вихідне завдання та виникають у процесі +реалізації технології системної оптимізації; +• методи та алгоритми розв’язання сформованих моделей; +• процес розв’язання задачі за допомогою технології системної +оптимізації. Цей процес реалізується через певні етапи [5]. +Таким чином, для реалізації системної оптимізації необхідно опи- +сати та використовувати підходи та засоби для: +• формування рішень з урахуванням даних. Тут розглядається об- +ласть деталізованих даних, тобто пошук інформації з використанням +засобів СУБД як в окремих базах даних, так у загальному сховищі +даних, область агрегованих показників, тобто збір у сховище даних +відповідної інформації, її узагальнення та агрегація, гіперкубічне по- +дання та багатовимірний аналіз (оперативна аналітична обробка да- +них (OLAP)), сфера закономірностей, тобто пошук функціональних +та логічних закономірностей у накопиченій інформації, побудова +моделей та правил, які пояснюють знайдені аномалії та/або прогно- +зують розвиток деяких процесів (інтелектуальна обробка даних (Data +Mining)); +• формування рішень на основі логічних моделей та правил (при- +йняття рішень на основі продукційних моделей, семантичних мереж +тощо); +• формування рішень на основі математичних моделей (оптимі- +зація через використання аналітичних формул, оптимізація через ал- +горитми, оптимізація вибору з багатьох альтернатив тощо); +• формування рішень на основі типових рішень або прецедентів +(типові рішення та моделі, прецеденти проблемних ситуацій). + +25 +При цьому необхідно розглядати різні аспекти прийняття рішень. +Такими можуть бути, наприклад, поведінковий аспект (описує ситуа- +ції прийняття рішень та порядок, в якому розглядаються завдання та +в якому виконуються відповідні дії), організаційний аспект (описує +структуру середовища прийняття рішень, ресурси та засоби та визначає +організаційну структуру, в якій розв’язання задачі виконується або буде +виконуватися, і відносини між елементами структури), інформаційний +аспект (описує інформацію, яка використовується при прийнятті рі- +шень, як вона представляється та як вона може застосовуватись). +В рамках такого представлення прийняття рішень необхідно іден- +тифікувати модель предметної області; визначити взаємодії між за- +дачами та відповідними моделями на підставі відносин пріоритетів +взаємодії; визначити усі види впливу даної задачі (моделі) на інші +задачі (моделі); визначити всі можливі випадки активізації даної за- +дачі (моделі) як для локальних ситуацій прийняття рішення, так і для +розподіленого прийняття рішень; визначити можливі схеми реаліза- +ції даної задачі (моделі) в відповідній предметній області; визначити +множини даних, на яких реалізується дана задача (модель) і які опи- +сують результат розв’язання задачі на вибраній моделі. +При цьому прийняття рішень будемо описувати через три вимі- +ри (світи) розуміння процесу прийняття рішень: світ 1: реальний світ +(прикладний світ), світ 2: формальний світ (формальні моделі, мето- +ди, алгоритми тощо) та світ 3: світ програмного забезпечення (про- +грамні засоби, платформи тощо). +При реалізації прийняття рішень в розрізі моделей реалізується +ефект тріади: за допомогою сприйняття та концептуалізації побуду- +вати модель прикладної області (модель представляється з точки зору +опису (об’єкти, процеси, відношення, властивості та характеристики) +та з точки зору діяльності (визначення процесів, побудова концепту- +альної моделі) і за допомогою знаків або мови, зробити формалізацію +відносин (вплив, регулювання, управління) та створити формалізо- +вану модель, наприклад, символьну модель (модель представляється +з точки зору опису, як математична модель, та з точки зору діяльнос- +ті через визначення структури моделі, оцінку параметрів, достовірні +властивості та характеристики). Зв’язок між формальною моделлю та +моделлю програмного забезпечення (модель обчислювань, програмні +модулі та визначення програмної концепції, узгодження програмних +модулів) визначає методи та алгоритми, які необхідні для розв’язання +формальної системи. + +26 +Основою для використання знань та реалізації процесу прийняття +рішень за допомогою системної оптимізації, представлення відпо- +відного інтегрованого середовища прийняття рішень, взаємодії між +складовими частинами середовища, опису предметних областей та +розв’язання задач в такому середовищі є онтологія, як засіб явного +розуміння та представлення областей та процесів прийняття рішень. +Під онтологією [7] будемо розуміти систему, що описує структу- +ру певної проблемної області або множини проблемних областей та +складається з множини класів понять, пов’язаних відношеннями, їх +визначень та аксіом, що задають обмеження на інтерпретацію цих +понять в рамках даної проблемної області або їх множини. +Така онтологія [8] базується на взаємопов’язаній множині онто- +логій, що представляє собою багаторівневу асоціативну структуру, +що включає метаонтологію або онтологію верхнього рівня, базову +онтологію, контекстну онтологію, множина онтологій представ- +лення процесу прийняття рішень, що включає представлення задач +та їх розв’язання на рівні проблемної області, онтологій предмет- +но-формального та формального представлення та реалізацій цього +процесу, онтологію реалізацій, що включає опис програмного забез- +печення для підтримки прийняття рішень, онтологію представлен- +ня користувача та взаємодії з ним, модель машини виведення, що +асоціюється з побудованою онтологічною моделлю. Мета онтоло- +гії полягає у забезпеченні інтегрованої концептуальної основи для +того, щоб вона була визначена, зрозуміла, структурована та пред- +ставляла явища при прийнятті рішень за допомогою систем під- +тримки прийняття рішень. Метаонтологія розглядається як засіб +інтеграції різних складових реалізації процесу підтримки прийняття +рішень та найбільш загального його опису. Сутностями метаонто- +логії є такі поняття, як об’єкт, атрибут, значення, відношення і т. п., +наприклад, описувати метаінформацію на основі моделі Захмана. +Мета базової онтології полягає у забезпеченні ключових понять та +конструкцій для того, щоб визначити, зрозуміти, структурувати та +представити основні принципи області прийняття рішень, в рамках +якої функціонує СППР. Контекстна онтологія реалізує контекстну +систему, що допомагає розпізнати, зрозуміти та представити при- +йняття рішень через контексти та в межах контекстів. Множина он- +тологій представлення процесу прийняття рішень розглядається як +компонента бази знань при роботі з конкретною проблемною об- +ластю та є, у свою чергу, шаблоном для побудови динамічної ком- + +27 +поненти бази знань, що змінюється при переході від дослідження +однієї конкретної задачі до іншої. Онтологія реалізацій, що включає +опис програмного забезпечення для підтримки прийняття рішень: +функціональний, поведінковий, організаційний та інформаційний. +При цьому опис ґрунтується на функціональних (що робить про- +грамне забезпечення) та нефункціональних вимогах (обмеження +використання). Онтологія представлення користувача та взаємодії +з ним реалізує формування моделі сценарію та компонентів діалогу +(автоматично або автоматизовано). +Реалізація онтологічного представлення перш за все базується +на визначенні та взаємодії понять та термінів для опису предметних +областей та розв’язання певних задач у відповідних предметних об- +ластях. Будемо розглядати проблемну область прийняття рішень як +множину предметних областей та задач, що розв’язуються в них. +Таке онтологічне представлення складається з консолідованого пред- +ставлення певних проблемних областей, через які прийняття рішень +може бути представлене та визначене на основі вибраної точки зору +(стан проблеми або проблемної області, поведінка проблеми або про- +блемної області та розв’язання проблеми). +Поняття та терміни, що стосується проблемної області, включа- +ють такі поняття: об’єкт, задача (проблема), модель (формулювання +проблеми), методологія (сценарій, метод, алгоритм), система харак- +теристик (властивостей), що їх описують, значення, відношення. +Об’єкт — термін або поняття (сутність), що визначається семантич- +ним представленням та з яким пов’язані відповідні властивості, ре- +алізується певний зв’язок з іншим терміном(ами), з задачами та мо- +делями, що ініціювали присутність цього терміна. Задача — кожен +екземпляр цього класу визначає задачу для конкретного об’єкта, має +ідентифікатор, вказує на об’єкт та термін або властивість та значення +властивості, що ініціюють цю задачу тощо. Модель — кожен екземп- +ляр цього класу визначає опис об’єкта на певній мові, зокрема фор- +малізованій, що складений з метою вивчення його властивостей. До +такого опису вносяться, наприклад, чинники, що впливають на вибір +моделі, такі як період часу, змінні рішення, критерії оцінки, числові +параметри та відношення, включаючи математичні. Моделі інтегру- +ються в класи моделей. Є кілька класів моделей для прийняття рішень, +які, у свою чергу, можуть бути розв’язані декількома альтернативни- +ми методами. Кожен клас моделі краще підходить для представлення +певних видів процесів прийняття рішень. Властивість — певна ознака, + +28 +що характеризує термін, має властивості, аналогічні класу термінів. +Окрім цього він вказує на екземпляри класу значень, які визначають +його в задачах. Значення — визначають дані, що використовуються +при пошуку в семантичному представленні, вказують на задачу та на +властивість, рішенням якої воно є. Відношення — визначає зв’язок +між двома термінами та вказує на терміни або властивості та об’єкти +знань. Інші терміни визначають ті поняття, що пов’язані з системою +характеристик (структура, обмеження, середовище, контекст, рівень +узагальнення тощо), проблемою (предмет проблеми, проблема верх- +нього рівня, проблема нижнього рівня, методи (сценарії) рішення, +складність проблеми, атомна проблема, складена проблема, опис +проблеми, проблемна тема, контекст проблеми, власність проблеми, +відповідальність за проблему, оцінка проблеми, проблемна область, +вплив на проблеми, вплив з проблем, ініціювання, час, взаємодія, ак- +тор тощо), моделлю (мета, обмеження, контекст, проблемна область, +проблема, методологія, об’єкти, вхідні параметри, вихідні параметри, +інші параметри, умови, тригери (який випадок запускає), передумови +(що на початку), післяумови (що в кінці) та пов’язані знанням про- +блемної області (область знання, функціональні знання, структурне +знання, знання обробки тощо). Поняття з прийняття рішень, вклю- +чаючи системну оптимізацію, пов’язані між собою відношеннями +класифікації, узагальнення, агрегації та групування, асоціативними +відношеннями, визначення яких здійснюється через представлення +проблемної та предметних областей. +В рамках такого підходу прийняття рішень базується на представ- +ленні багаторівневої системи управління та розглядається через один +або декілька взаємопов’язаних контекстів (модель певного контек- +сту), в яких хтось (актор) щось робить (дія) з деяких причин (цілі) +для когось (об’єкт) за допомоги деякого (об’єкта), десь (місце знахо- +дження) та іноді (час). Представлення контексту складається зі зміс- +ту, що базується на онтологіях, які охоплюють певну частину моделі +контексту. +Для опису контексту необхідно знайти поняття та конструкції, які +визначають природу, структуру та представлення процесу формуван- +ня та прийняття рішень і відповідних складових областей, які опису- +ють такий процес. Контекст повинен бути описаний стандартизова- +ним способом. Представлення знань процесу прийняття рішень має +підтримувати операції, що необхідні для представлення контексту та +управління ним. + +29 +Контекст будемо розглядати як концептуальну або інтелектуальну +конструкцію, яка складається з понять в межах відповідних контекст- +них областей та допомагає нам зрозуміти, проаналізувати та викорис- +товувати природу, значення та ефекти через елементарні сутності у +відповідному середовищі або обставинах. Також контекст представ- +ляє ціле, що визначається через певні сутності, які є важливими для +даного розгляду. +Це дозволяє розглядати контекст як будь-яку інформацію, яка +може бути використана для опису ситуації, в якій щось існує чи від- +бувається та яка може допомогти пояснити ситуацію та визначити +напрямок її розв’язання. Ця ситуація залежить від знань, світогля- +ду, практики та обставин, які можуть бути використані для побудови +«нескінченної і частково відомої сукупності припущень» [8], які ви- +значають інтегральне розв’язання проблем та які забезпечують умови +для створення, підтримки та застосування знань. +При цьому, по-перше, контекст є невід’ємною властивістю випад- +ків взаємодії, а не є стабільним об’єктивним набором функцій, які +зовнішньо характеризують діяльність. Контекст залишається кри- +тично важливим для розуміння, контекстуалізації та нерозуміння +форм діяльності та інформації, але саме в контексті природи необхід- +но постійно домовлятися та переглядати його. По-друге, ці контекст- +ні властивості беруть на себе їх значення або релевантність через їх +зв’язок з формами практики, тобто займаються діями навколо арте- +фактів та інформації, яка робить ці артефакти значущими та актуаль- +ними для людей. Тоді сенс технології не може бути відірваний від спо- +собів, яким люди мають його використовувати. +Такі моделі контексту мають давати змогу розв’язувати проблеми, +що характеризуються контекстно-залежними властивостями: +• неоднорідність та мобільність; +• відносини та залежності; +• своєчасність; +• недосконалість; +• міркування; +• відповідність формалізму прийняття рішень; +• ефективне контекстне забезпечення. +Розгляд використання контексту в проблемних областях допо- +магає виявити всі семантичні відношення, надати всю необхідну ін- +формацію та правильні інтерпретації для прийняття рішень, оскільки +використання інформації в процесі прийняття рішень, як правило, + +30 +відбувається в контексті складної структури процесу прийняття рі- +шень, який часто формується за допомогою ряду чинників. +Як показано в [10], контекстна система допомагає розпізнати, +зрозуміти та подати відповідні елементи прийняття рішень як кон- +тексти та в рамках контекстів. Контекстом є будь-яка інформація, +яка може бути використана або характеризує відповідну проблемну +область. +Контекст є важливим фактором у процесі прийняття рішень, до- +помагає визначити, яка інформація необхідна для підтримки при- +йняття рішень та представляється множиною взаємопов’язаних ком- +понентів [11]. +В [12] визначено, що контекст можна розглялати як представлен- +ня проблеми, беручи до уваги такі властивості контексту [12; 13]: +• контекст — це форма інформації, тобто контекст розглядається +як те, що може бути відомо, представлено та закодовано; +• контекст є вичерпним, тобто вважається можливим сказати, що +заздалегідь визначається як контекст для конкретного використання; +• контекст є стабільним, тобто, коли контекст може відрізнятися +від застосування до програми, він не відрізняється від екземпляра до +примірника взаємодії з додатком; +• контекст та діяльність є розділеними, тобто контекст викорис- +товується для опису особливостей середовища, в межах якого здій- +снюється діяльність, але елементи діяльності не належать до самого +контексту та не розглядаються як контексти. +Основним недоліком багатьох існуючих систем, що базуються на +контексті, є неможливість реалізації динамічного опису контексту. +Існуючі контекстні моделі є «статичними» або обмеженими. +Для того, щоб додати до властивостей контексту динамізму, буде- +мо розглядати контекст, який можна охарактеризувати як: виникає +через простір і час; причинно-наслідковий процес прийняття рішень; +визначений, але не обов’язково передбачуваний; семантична інтер- +претація відносин між актором, завданням або діяльністю та сере- +довищем, в яких вони знаходяться; обмежувальні критерії, за допо- +могою яких можна моделювати цілеспрямовану діяльність. +Обмеження контексту також зменшує складність часу обчислення +потенційних рішень для діяльності. Ми використовуємо такі обме- +жувальні критерії: наявність даних або відсутність; повнота; набори +включення / виключення; часові межі; просторові межі; область ді- +яльності. + +31 +Контекст розглядається як динамічні відношення між актором, +цілеспрямованим завданням та оточенням, в яких вони знаходяться. +Такий розгляд дозволяє контекстним зв’язкам виникати, змінювати- +ся або зникати через час і простір та охоплювати складність просторо- +во-часової динаміки. Ми застосовуємо таке представлення контексту, +оскільки воно дозволяє нам моделювати контекстну динаміку таким +чином, що виникає в процесі розв’язання задачі, а не тільки вибира- +ється на етапі формулювання проблеми та процесу розв’язання зада- +чі. Модель контексту передбачає суб’єктивний погляд на проблемні +рішення ситуації. Таким чином, ми моделюємо контекст з практич- +ної точки зору та представляємо структуру контексту, яка успадкову- +ється від традиційних моделей контексту. +Такий погляд використовує позицію щодо властивостей контек- +сту. По-перше, замість того, щоб розглядати контекст як інформа- +цію, він стверджує, що контекстуальність є реляційною властивіс- +тю, яка визначається між об’єктами, діями, задачами, середовищем +і т. д. Тобто щось є або не є контекстом; Навпаки, вона може або не +може бути контекстуально актуальною для розв’язання певної зада- +чі. По-друге, можна стверджувати, що множина контекстних функ- +цій визначається динамічно. По-третє, можна стверджувати, що +контекст є особливим для кожного випадку проблеми, задачі, діяль- +ності, дії тощо. Контекст — це властивість, що пов’язана з певними +налаштуваннями, окремими випадками проблем, задач, середовищ, +дій та особами, що беруть участь у процесі прийняття рішень. По- +четверте, замість того, щоб розглядати контекст та контент як два +відокремленими об’єкта, можна стверджувати, що контекст вини- +кає в результаті діяльності. Іншими словами, контекст необхідно +розглядати не тільки як проблему представлення, а й як проблему +взаємодії. +Оскільки контекст розглядається як множина динамічних відно- +шень між актором, цілеспрямованою діяльністю, ресурсами, мож- +ливостями, часом, розташуванням та середовищем, в яких вони зна- +ходяться або використовуються. Це дозволяє контекстним зв’язкам +виникати, змінюватися або зникати через час і простір та охоплюва- +ти складність просторово-часової динаміки. Ми застосовуємо таке +представлення контексту, оскільки воно дозволяє нам моделювати +контекстну динаміку таким чином, що виникає в процесі розв’язання +задачі, а не тільки вибирається на етапі формулювання проблеми та +процесу розв’язання задачі. + +32 +Для опису контексту необхідно з’ясувати поняття та конструкції, +які визначають природу, структуру та представлення процесу форму- +вання та прийняття рішень і відповідних складових областей, які опи- +сують такий процес. Контекст має бути описаний стандартизованим +способом. Представлення знань процесу прийняття рішень повинне +підтримувати операції, що необхідні для представлення контексту та +управління ним. +Для нагромадження, інтерпретації, подання та управління кон- +текстом пропонується загальна модель управління контекстом. +Контекст на онтологія складається з трьох основних компонентів: +контексту семантики (онтологія), даних екземплярів контексту та +контексту, що пов’язаний з правилами. Онтологія представляє се- +мантики, концепти і відношення в рамках контексту. Така онтоло- +гія утворюється в результаті злиття онтології, що описує абстрактні, +конкретні контексти та контексти реалізації. Правила є аксіомами +виведення, які використовують контекстно-орієнтовані системи для +отримання рішення та міркування щодо дій, які необхідно виконати. +Ці правила мають два джерела; правила, які явно визначені, та прави- +ла, які неявно отримані самою системою. +Складність в реалізації прийняття рішень полягає в необхідності +синтезу різних точок зору зацікавлених сторін на проблему, управлін- +ня великою кількістю інформації, що стосується завдання, та розу- +міння рішень, які визначили такий розгляд задачі прийняття рішень +та самого процесу прийняття рішень. Крім того, знання, пов’язані з +проблемою, розподіляються серед різних зацікавлених сторонім як +власників проблеми та ЛПРами. +Це визначає необхідність розгляду процесів прийняття рішень на +основі представлення багаторівневої системи управління та прийнят- +тя рішення в ній через модель певного контексту [14]. +Контекстна онтологія +cntxt +O + з урахуванням результатів [10] вклю- +чає компонентні онтології: онтологія контексту, онтологія шарів і +онтологія точок зору допомагають розпізнати, зрозуміти та пред- +ставити відповідні явища як контексти та в межах контекстів. За- +гальна мета контекстної онтології полягає в тому, щоб визначити +поняття та конструкції, які допомагають нам зрозуміти природу, +цілі та значення окремих сутностей. Таким чином, замість того, щоб +розглядати проблемну область як базову структуру сутностей, он- +тологія контексту визначає розгляд сутності в контексті від спеці- +альних ролей або значень. Така онтологія представляється у вигляді + +33 +взаємопов’язаної множини онтологій, що є асоціативною структу- +рою такого вигляду (рис. 1): + +, +, +cntxt +ctx +layer +aspect +O +O +O +O += +, +де +ctx +O + — онтологія контексту; +layer +O + — онтологія шарів; +aspect +O + — онто- +логія аспектів (точок зору). +Онтологія +Онтологія аспектів (точок зору) +Онтологія контексту +Контекстна область +Контекст +Система аспектів +Аспект +Контекстні +Області +Вимір +Онтологія шарів +Шар +Система шарів +Аспекти +Онтологія +Контекстні +Області +Аспекти +Онтологія +Контекстні +Області +Аспекти +області +області +області + +Рис. 1. Складові контекстної онтології у взаємозв’язках +Онтологія +ctx +O + визначає такі контекстні області: область мети/ +результату, область актора, область процесу/дії, область об’єкта, об- +ласть середовища, область можливостей, область засобів, область +представлення, область розташування та область часу. Контекст ви- +значається як конструкція, яка складається з понять в межах десяти +контекстних областей. Кожна контекстна область визначається від- +повідними поняттями та конструкціями. Онтологія контексту +ctx +O + + +34 +містить деталізовані поняття та конструкції контекстних областей та +міжобласних відношень. +Онтологія шарів +layer +O + підтримує структуру прийняття рішень та +описує відношення на загальному рівні складових прийняття рішень +та їх реалізацію на відповідних рівнях: проблема, модель, метод та ре- +алізація в рамках системи результатів, системи об’єктів, системи ви- +користання та системи управління. Онтологія шарів +layer +O + забезпечує +поняття та конструкції для розуміння та структуризації прийняття +рішень, особливо через поняття СППР, системи об’єктів та системи +використання та також служить концептуальною основою для того, +щоб структурувати прийняття рішень за чотирма шарами (реалізація, +метод, модель та проблема). +Онтологія аспектів (точок зору) +aspect +O + отримується з онтології ша- +рів та онтології контексту. Онтологія +aspect +O + підтримує множину ви- +значених аспектів розгляду для конкретного представлення процесу +прийняття рішень в СППР та структурування сприйняття складових +прийняття рішень, зокрема з системної, концептуальної, функціо- +нальної, інформаційної та реалізаційної точок зору. +Ієрархічна організація, формальний характер, стандартизова- +ність, підтримка ефективної аргументації, підтримка різних рівнів +абстракції та взаємодій є одними з головних особливостей контекст- +ної онтології. +При цьому контекст розглядається на абстрактному, конкретному +та реалізаційному рівнях [14]. Абстрактний контекст є онтологічною +моделлю багаторівневої системи, побудованої на підставі інтегра- +ції знань прикладних проблемних областей, що розглядаються при +функціонуванні системи та релевантні конкретній задачі. Конкрет- +ний контекст є представленням певного абстрактного контексту для +конкретної задачі в відповідності з існуючими даними та визначе- +ними вимогами до процесу прийняття рішень. Контекст реалізації є +представленням кожного конкретного контексту в рамках існуючих +реалізацій, зокрема програмного забезпечення. +На підставі виявлених властивостей контексту та задач, що ви- +никають при використанні контексту, сформульовані вимоги до +управління контекстом. Контекст повинен бути описаний стан- +дартизованими способами, що забезпечують незалежність способу +представлення від платформи, модель представлення знань повин- +на підтримувати операції, необхідні для представлення контексту +та управління ним. Контекст має надавати релевантну, реальну та + +35 +доступну інформацію для розв’язання конкретної задачі або для ро- +зуміння поточної ситуації, що включається в контекст, інформація +повинна містити безпосередньо одержувані дані, історію отриман- +ня цих даних і знання, які на даний момент відомі взаємодіючим +об’єктам. +Будемо розглядати контекст як конструкцію, що складається з +понять в межах відповідних контекстних областей та описується +онтологією контексту через таку структуру контекстних областей +[14]: + +, +, +, +, +, +, +, +, +, +AR +A +PA +O +E +ctx +ctx +ctx +ctx +ctx +ctx +F +Fclt +R +Plc +T +ctx +ctx +ctx +ctx +ctx +O +O +O +O +O +O +O +O +O +O +O += +. +На загальному рівні +ctx +O + описується контекстними областями: +AR +ctx +O + — мета/результат, +A +ctx +O + — актор, +PA +ctx +O + — процес/дія, +O +ctx +O + — +об’єкт, +E +ctx +O + — середовище, +F +ctx +O + — можливості, +Fclt +ctx +O + — засоби, +R +ctx +O + — +представлення, +Plc +ctx +O + — розташування, +T +ctx +O + — час. +Для показу контекстних областей будемо використовувати класи +об’єктів, відношень та атрибутів, що дає можливість представляти їх +як семантичні аспекти, де семантика умов та відношень між ними +визначені явним чином (роблячи кожен аспект формальною онтоло- +гією). Використання таких категорій дозволяє зробити формалізацію +таких аспектів в логіці опису (дескрипційна логіка) (DL). +Контекстні поняття взаємозв’язані через контекстні відношен- +ня, включаючи внутрішньобласні, міжобласні та міжконтекстні +відношення, тобто такі відношення включають не тільки відно- +шення між компонентами однієї області, а й відношення між ін- +шими контекстами. Такі поняття та конструкції необхідні для того, +щоб визначити, зрозуміти, структурувати та представити сутності +як контексти та/або в межах контекстів, щоб зрозуміти природу, +цілі та значення відповідних сутностей задач та процесу прийняття +рішень. +Для розв’язання будь-якої задачі необхідно описати процес при- +йняття рішень, який ґрунтується на онтології контекстів за спеціалі- +зацією. Це будемо реалізовувати через онтологію шарів +w +layer +O +. +Онтологія шарів допомагає розпізнати, зрозуміти та представити +структуру прийняття рішень на основі контекстів. Онтологія шарів +описує відношення складових прийняття рішень на загальному рів- +ні та їх реалізацію на відповідних рівнях: проблема, модель, метод та + +36 +реалізація в рамках системи реалізації, системи об’єктів, системи ви- +користання та системи управління. +Ми визначаємо онтологію шарів, яка забезпечує поняття та кон- +струкції, щоб визначити, зрозуміти, структурувати та представити +статичні та динамічні особливості представлення процесу прийняття +рішень в розрізі чотирьох шарів. +, +w +s +layer +layer +layer +O +O +O += + — онтологія шарів. +w +layer +O + містить поняття та +конструкції, які пов’язані з процесом прийняття рішень в ціло- +му. +s +layer +O + представляє процес прийняття рішень структуровано та +пов’язано з визначеною системою шарів +w +layer +O +. +Ми будемо розрізняти +, +, +, +w +w +w +w +w +layer +layer +layer +layer +layer +O +Prblm +Mdl +Mth +Rlztn += + як +систему з чотирьох шарів: проблема, модель, метод та реалізація. Роз- +глянемо деякі з них. В будь-якому контексті, що охоплює розв’язання +задач, людина використовує конструкції, які можуть допомогти ви- +значити, проаналізувати, розробити та реалізувати розв’язання про- +блеми. +Поняття та конструкції +w +layer +O + отримуються з базової онтології [15], +онтології контексту [14], онтології шару +s +layer +O + та онтології точок зору +та взаємодіють з онтологіями предметно-формального та формаль- +ного представлення, онтологією реалізацій, що включає опис про- +грамного забезпечення для підтримки прийняття рішень, онтологією +представлення користувача та взаємодії з ним. +Шар +, +Pr, +w +prb +layer +Prblm +Level View +Rel += + забезпечує поняття та кон- +струкції для того, щоб визначити, зрозуміти, структурувати і пред- +ставити сутності з точки зору проблеми в межах множини проблем +СППР, що можуть бути розв’язані в рамках системи прийняття рі- +шень. Контекст проблеми (задачі) пов’язаний з контекстами моде- +лі. Поняття та конструкції +w +layer +Prblm + отримуються з базової онтології +[15], онтології контексту [14], онтології шару +s +layer +O + та онтології точок +зору та взаємодіють з онтологіями предметно-формального та фор- +мального представлення. Контекст проблеми пов’язаний з контек- +стами моделі. +Іншим шаром є моделі, що описує онтологія +w +layer +Mdl +: +, +, +w +mdl +layer +Mdl +Level ViewP Rel += +, яка забезпечує поняття та конструк- +ції для того, щоб визначити, зрозуміти, структурувати і представити +сутності з точки зору моделей в межах моделі системи. Будемо виді- +ляти такі основні точки зору до поняття моделі: +w +layer +Mdl + розглядається +з системної, концептуальної та реалізаційної точок зору. Визначен- + +37 +ня моделі має завжди висувати на перший план аспекти з цих трьох +точок зору. Модель будемо розглядати як сутність, що використову- +ється, щоб допомогти або дозволити розуміння, комунікацію, аналіз, +розробку та/або виконання деякої іншої сутності, до якої звертається +модель. Модель будемо представляти в одній з трьох форм, а саме як +концептуальна конструкція (опис), як вираз на певній мові або як ре- +алізація. Контекст моделі пов’язаний з контекстами методу та кон- +текстами проблеми. +Наступним шаром є методи, які описуються через онтологію +w +layer +Mth +. Знання методів +w +layer +Mth + складається з чотирьох компонентів: +знання процесу виконання методу, знання проблемної області, зна- +ння технологій реалізації та знання поведінки користувача. Знан ня +процесу виконання означає знання, які стосуються виконання мето- +ду. Знання проблемної області означає знання, яке стосується реаліза- +ції прийняття рішень, її системи використання та її системи об’єктів. +В кожній проблемній області є власні специфіки, які необхідні, щоб +знати та виконати метод. Знання технології означає знання, яке сто- +сується пошуку, використання та налаштування апаратного та про- +грамного забезпечення для прийняття рішень у визначеній задачі. +Знання поведінки користувача означає знання, що визначають осо- +бливості проблем людини та її поведінки, а також соціальні та органі- +заційні аспекти, які мають бути взяті до уваги в розробці та в організа- +ції роботи методу. Метод забезпечує явне знання в формі принципів, +процедур і т. д. Методи можна розділити на технології, сценарії, меха- +нізми та алгоритми. Технологія включає мову представлення та про- +цедуру. Контекст методу пов’язаний з контекстами моделі та контек- +стами реалізації. Цільові контексти методу влючають контексти, для +яких було визначено модель. +Механізми та алгоритми використовуються процедурою при- +йняття рішень, що описуються через шар реалізації +w +layer +Rlztn +: +, +, +w +rlztn +layer +Rlztn +Level ViewP Rel += +. Вони можуть або бути загальними, +тобто застосованими до усіх мов, що можуть бути використаними +при прийнятті рішень, визначеними, тобто застосованими тільки до +особливих мов, або гібридними, тобто з певними частинами, що є за- +гальними та визначеними частинами, що є визначеними або присто- +совуваними. Контекст реалізації пов’язаний з контекстами методу. +Щоб включити інформацію і знання та їх використати в різних +формах та на різних шарах, будемо розрізняти чотири види систем, +які тісно пов’язані з прийняттям рішень: + +38 +1. ті, які описують інформацію та знання, +2. ті, які пов’язані зі накопиченням, зберіганням, обробкою та за- +стосуванням інформації, +3. ті, які використовують інформацію, +4. ті, які управляють та можливо змінюються на основі результатів +прийняття рішень та використання інформації. +Таким чином будемо розглядати систему +s +layer +O +, що інтегрує сис- +тему об’єктів +layer +So +, систему реалізацій +layer +Sr +, систему використання +layer +Su + та систему управління +layer +Sm +: +, +, +, +s +layer +layer +layer +layer +layer +O +Sr +So +Su +Sm += + +— +контекстні +знання, +що +пов’язані з прийняттям рішень: система реалізацій +layer +Sr +, система +об’єктів +layer +So +, система використання +layer +Su +, система управління +layer +Sm +. +layer +Sr + можна визначити як систему, що описує акторів, інформа- +цію та дані, засоби та розташування і яка збирає, зберігає, оброб- +лює та поширює інформацію про результати, що представляється +системою об’єктів, для того, щоб реалізувати та/або поліпшити дії +системи використання. Структурно +layer +Sr + складається з акторів, дій, +інформації та даних, засобів (включаючи програмне забезпечення) +та розташування, визначає відповідні результати на рівнях прийнят- +тя рішень, які реалізують розв’язання задачі. +layer +Sr + існує для надан- +ня інформації, що відповідає критеріям релевантності, своєчасності +тощо, для того, щоб задовольнити потреби користувачів у результа- +тах процесу прийняття рішень. +layer +Sr + — функціональна одиниця, яка +збирає, зберігає, оброблює та поширює інформацію про результати +прийняття рішень, що представляються системою об’єктів +layer +So +, +та для того, щоб реалізувати та/або покращити дії системи викорис- +тання +layer +Su +. Користувачі системи реалізацій +layer +Sr + є акторами, що +бажають підвищити рівень знань про систему об’єктів +layer +So + за до- +помогою системи реалізацій. Це також вносить зміни в здатність +користувачів виконувати завдання, які стосуються системи управ- +ління +layer +Sm +. +layer +So + представляє систему, що збирає, зберігає, обробляє та по- +ширює інформацію для та внаслідок інтересів системи використання +layer +Su +. Межа +layer +So + повністю визначається інтересами системи вико- +ристання +layer +Su +. +layer +So + є частиною дійсності, яку розглядають як про- +блемну область для прийняття рішень. + +39 +layer +Su + можна представити як систему, яка використовує послуги, +забезпечені системою реалізації +layer +Sr +, в процесі прийняття рішень +для того, щоб планувати та виконати зміни (тобто зміни стану (пе- +реходи) за допомогою системи управління +layer +Sm +. Актори в системі +використання +layer +Su + — користувачі, програмні компоненти системи +реалізацій +layer +Sr +. В рамках +layer +Su + ми можемо розрізнити два види ко- +ристувачів: кінцеві користувачі, які збільшують своє знання, взаємо- +діючи безпосередньо з СППР; непрямі користувачі, які збільшують +своє знання, отримуючи результати СППР через користувачів СППР. +layer +Su + можна класифікувати за різними критеріями, наприклад, роз- +глядати на стратегічному, тактичному або оперативному рівнях. Ре- +зультати +layer +Su + можуть стосуватися людини-актора, програми-акто- +ра. +layer +Su + можна визначити як систему, яка використовує послуги, що +реалізуються системою реалізації +layer +Sr +, для прийняття рішень або ін- +ших дій, щоб планувати та виконати зміни (тобто зміни стану) в сис- +темі управління +layer +Sm +. +layer +Sm + — система, яка використовує систему +використання +layer +Su +. +Між системою реалізацій +layer +Sr +, системою об’єктів +layer +So +, сис- +темою використання +layer +Su + та системою управління +layer +Sm + існують +певні відношення. Інформаційні об’єкти системи реалізацій пред- +ставляють сутності системи об’єктів. Також інформаційні об’єкти +системи використання представляють сутності системи об’єктів. +Відношення між системи об’єктів і іншими системами залежить від +того, чи ці системи перетинаються чи не перетинаються. Ми може- +мо визначити чотири різних випадки щодо того, в якій частина сис- +тема об’єктів є частиною інших систем. В першому випадку система +об’єктів повністю не перетинається з іншими системами. Це означає, +наприклад, що інформація збирається з абсолютно різних сутностей +у порівнянні з тими, які знаходяться під впливом системи викорис- +тання. Це, звичайно, дуже рідкісна ситуація. В другому випадку сис- +тема об’єктів збігається з системою управління. В третьому випадку +система об’єктів перетинається з системою використання. В цьому +випадку система реалізацій використовується, наприклад, для пла- +нування, контролю або виконання роботи в системі використання. +Нарешті система об’єктів може перетинатися з системою реалізацій. +Як показано вище, третьою складовою контекстної онтології +ctx +O + +є онтологія аспектів (точок зору) +aspect +O +. + +40 +Поняття аспекту або точки зору не має чіткого визначення, тому +будемо використовувати аспект (точку зору) як певний спосіб розгля- +ду або оцінювання. Використання аспекту призводить до обмеженої +або визначеної концепції певних сутностей та їх властивостей в ре- +альності. Щоб отримати та пов’язати ці представлення, визначається +певна структура. +Онтологія аспектів (точок зору) + +, +, +, +, +, +, +Sys +Cncpt +Man +Inf +aspect +aspect +aspect +aspect +aspect +Rlz +aspect +aspect +aspect +VofP +VofP +VofP +VofP +O +VofP +Dim +Rel += +, +де +Sys +aspect +VofP + — системна точка зору, що відбиває склад взаємодіючих +у процесах об’єктів проблемної області та відбиває взаємодію у про- +цесах прийняття рішень; +Cncpt +aspect +VofP + — концептуальна точка зору, що відбиває зміст об’єктів +проблемної області та їх взаємодію в процесах прийняття рішень; +Man +aspect +VofP + — точка зору управління, що відбиває події та правила, які +виникають, використовуються та впливають на виконання процесів +прийняття рішень; +Inf +aspect +VofP + — інформаційна точка зору, що відбиває взаємозв’язок +функцій (дій) щодо перетворення об’єктів у процесах прийняття рі- +шень; +Rlz +aspect +VofP + — реалізаційна точка зору, яка описує засоби реалізації +елементів СППР та прийняття рішень; +aspect +Dim + — виміри розгляду точок зору; +aspect +Rel + — відношення точок зору. +В цьому випадку контекст є як результатом інтеграції релевантних +сформованих вимог до розв’язання задачі частин декількох онтоло- +гій. Під інтеграцією розуміється інтеграція декількох частин вихідних +онтологій, результатом якої є уніфікована онтологія або контекст, +в якому однаково представлені знання з інтегрованих частин, і по- +вністю підтримується логічний висновок, що заданий в цих частинах, +та які можуть бути отримані з множини однорідних або різнорідних +джерел. +Системна точка зору базується на системі об’єктів та системі ви- +користання, яка складається з пов’язаних точок зору розгляду кож- +ного з шарів та пов’язаних контекстних областей. Тут визначають, +наприклад, для проблеми, за яких умов може виникнути, які можуть + +41 +існувати впливи на проблему щодо започаткування або використан- +ня, як може бути використана, які існують або були реалізовані кон- +тексти моделі, методу та реалізації тощо. Для шару метод визначає, +які контексти моделі мають бути враховані стосовно методу, які є цілі, +можливі актори та обмеження використання методу з урахуванням як +контекстів проблеми та моделі, так і контексту реалізації тощо. +Концептуальна точка зору розглядає прийняття рішень через се- +мантичний зміст інформаційних об’єктів, який означає, що точка +зору адресується контексту системи об’єктів. Ця точка зору зосере- +джується на концептуальному змісті відповідних об’єктів у врахуван- +ням структурної та динамічної складових. +З управлінської точки зору система розглядається як система +управління з відповідними подіями та правилами функціонування +такої системи. Для цього визначають акторів (людина, програмна +система), як вони можуть взаємодіяти, де вони знаходяться, як мо- +жуть бути сфомульовані відповідні процедури та алгоритми в рамках +відповідних шарів тощо. +З інформаційної точки зору розглядається система, що базується +на системі об’єктів, яка вважається функціональною структурою ін- +формаційної обробки мети, дій та об’єктів, незалежно від будь-яких +особливостей представлення, реалізації та використання, тобто ви- +значається, яка інформація обробляється і чому, які дії та правила об- +міну та обробки тощо. +З реалізаційної точки зору розглядається система, що базується на +системі реалізації, яка пов’язана з конкретним організаційним, управ- +лінським та технологічним контекстами, тобто визначаються актори, +що виконують дії в процесі реалізації прийняття рішень, як вони вза- +ємодіють і де вони розташовані, де та як зберігаються необхідні дані, +які засоби використовуються та коли, яке апаратне та програмне за- +безпечення використовуються, і як вони пов’язані між собою тощо +Відношення між точками зору можуть бути побудовані на декіль- +кох критеріях. Оскільки неможливо знайти щось, що покривало би +всі необхідні особливості прийняття рішень та забезпечувало необ- +хідні поняття та конструкції. При цьому вибір критеріїв визначає, що +точки зору повинні підтримати структурований розгляд багатогран- +них особливостей процесу прийняття рішень. Критерії мають дозво- +ляти розглянути кожну точку зору з урахування процесу прийняття +рішень, що дозволяє визначити, що відповідає точці зору та що має +бути проігноровано. + +42 +Представлена система аспектів (точок зору) розглядається з трьох +вимірів: вимір розкладання, концептуальний вимір, незалежність ре- +алізації — вимір залежності. +Використання точок зору, таких як системна, інформаційна, +управлінська, надає можливість руху вздовж вимірювання розкла- +дання, тобто від «чорного ящика» до системи, яка складена з цілей, +дій та об’єктів. У цьому процесі переважно застосовані принципи +розкладання та спеціалізації. +Системна, управлінська та реалізаційна точки зору дають змогу +проаналізувати зміни вздовж виміру розкладання, з одного боку, та +вздовж незалежності реалізації — вимірювання залежності, з іншого +боку. +Таким чином, може бути отримано певне ієрархічне представлен- +ня системи точок зору, що будується на критерії залежності реаліза- +ції, оскільки кожний шар визначає більш конкретні поняття, і відно- +шення, що розгорнуті на нижчих рівнях абстракції. Отже об’єкти, що +реалізуються через певні інформаційні об’єкти, дії, що розділені на +дії людини та дії програмної системи, і тимчасові конкретні специфі- +кації. У цьому процесі визначаються ієрархія мети, засобів, структури +розкладання дії, структура розкладання об’єкта. +Такий розгляд контексту в рамках задач прийняття рішень до- +зволяє, не впливаючи безпосередньо на процес прийняття рішень, +обмежити його лише значущими для даного контексту правилами / +процедурами. Це дозволяє: 1) логічно виводити новий контекст з на- +явних; 2) повторно використовувати контекст за допомогою засто- +сування контекстів вищих рівнів абстракції, їх інтеграції та конкре- +тизації для відповідних умов і завдань; 3) отримувати контекст більш +високого рівня абстракції з відповідного розглянутого контексту; +4) розбивати контекст на складові відповідні логічно пов’язані вну- +трішньо узгоджені контексти. +Реалізація інтегрованого погляду на прийняття рішень через сис- +тему аспектів (точок зору) надає можливість використання інформа- +ції, яка міститься в декількох контекстах та визначає контекст, який +може бути використаний, наприклад, прикладною програмою для +розв’язання певних завдань, підвищити достовірність контекстної +інформації. Аспекти або точки зору дозволяють використовувати +тільки ту частину даних, інформації або знань, яка є релевантною для +задачі, що розв’язується. Також вони дозволяють копіювати фраг- +менти контексту, повторно використовувати їх для інших цілей тощо. + +43 +Використання системної оптимізації, яке базується на викорис- +танні знань у вигляді онтології та контексту, дає можливість внести +до організації процесу прийняття рішень ряд важливих властивостей, +перш за все дає можливість перейти до безперервного аналізу ситуацій +та планування дій, забезпечує проведення корекції процесу прийнят- +тя рішень без порушення технологічної цілісності та взаємозв’язків, +допускає багатоваріантність рішень та можливість їх отримання за +різними критеріями і моделями, будує взаємопов’язану систему під- +готовки та вибору рішень, як для даної проблеми, так і для взаємодії +з іншими комплексами проблем і завдань, дозволяє приймати рішен- +ня з урахуванням наслідків їх реалізації. При цьому в рамках таких +технологій вдасться врахувати взаємозалежність рішень, негативні +наслідки реалізації, обмеження поведінки, інформаційні обмеження, +час та середовище, що постійно змінюється, визначеність, ризик, не- +визначеність тощо. +Результати роботи використано в рамках науково-дослідної робо- +ти «Розробити типові онтологокеровані процедури системної опти- +мізації для розв’язання прикладних задач». +СПИСОК ВИКОРИСТАНОЇ ЛІТЕРАТУРИ +1. Глушков В. М. О системной оптимизации. Кибернетика. 1980. № 5. С. 89– +90. +2. Sharifi A., M. van Herwijnen M., van den Toorn W. Spatial Decision Support +Systems: Theory and Practice. ITC Lecture notes, 2004. +3. Westmacott S. Developing decision support systems for integrated coastal man- +agement in the tropics: Is the ICM decision-making environment too complex +for the development of a useable and useful DSS?” Journal of Environmental +Management. 2001. No 62. P. 55–74. +4. Bharati P., Chaudhury A. An empirical investigation of decision-making satis- +faction in web-based decision support systems. Decision Support Systems. 2004. +No 37. P. 187–197. +5. Чаплінський Ю. П. Алгоритми системної оптимізації для різних припус- +тимих варіацій параметрів. Проблеми інформатизації та управління. 2007. +№ 1. С. 163–168. +6. Волкович В. Л., Коленов Г. В. Метод раздельного решения взаимосвязан- +ных оптимизационных задач. Изв. АН СССР. Сер. Техн. киберн. 1990. № 6. +С. 28–43. +7. Чаплінський Ю. П. Онтологічне представлення процесів прийняття +рішень. Проблеми інформатизації та управління. 2009. № 2. С. 146– +151. + +44 +8. Чаплінський Ю. П. Онтологічні складові підтримки прийняття управлін- +ських рішень. Наукові праці НУХТ. 2013. № 48. С. 65–68. +9. Porzel R. Contextual Computing: Models and Applications. (Cognitive Tech- +nologies). Springer Verlag, 2010. +10. Leppдnen M. Towards an Ontology for Information Systems Development — +A Contextual Approach. Contemporary Issues in Database Design and Informa- +tion Systems Development / K. Siau (Ed.). IGI Global. 2007. P. 1–36. +11. Hinton A. Understanding Context: Environment, Language, and Information +Architecture. Sebastopol, CA: O’Reilly Media, Inc, 2014. +12. Dourish P. What we talk about when we talk about context. Personal and +ubiquitous computing. 2004. No 8. P. 19–30. +13. Bettini C., Brdiczka O., Henricksen K. et al. A survey of context modelling and +reasoning techniquesю Pervasive and Mobile Computing. 2010. No 6. P. 161– +180. +14. Чаплінський Ю. П., Субботіна О. В. Онтологія та контекст при розв’язанні +прикладних задач прийняття рішень. Штучний інтелект. 2016. № 2. +С. 147—155. +15. Чаплінський Ю. П., Надточій В. І. Базова онтологія в прийнятті рішень. +Проблеми інформатизації та управління. 2016. № 2. С. 45–51. +ТЕОРЕТИЧНІ ОСНОВИ ІНФОРМАЦІЙНОЇ ТЕХНОЛОГІЇ +ПРОГНОСТИЧНОГО ОЦІНЮВАННЯ ЯКОСТІ +ПРОЄКТУВАННЯ ПІСЛЯДРУКАРСЬКИХ ПРОЦЕСІВ +Сеньківський В. М., Піх І. В., Кудряшова А. В. +Розроблення інформаційної технології прогностичного оцінювання якос- +ті проєктування післядрукарського опрацювання книжкових видань на +первинному етапі передбачає опис предметної області, зокрема означення +особливостей реалізації, послідовності післядрукарських процесів та пере- +бігу їх проєктування. На основі теоретичного обґрунтування та експертних +висловлювань виокремлено ключові фактори впливу та здійснено функціо- +нальне моделювання визначених процедур. Наведено контекстні діаграми, де +основними функціями систем є реалізація та проєктування післядрукарських +процесів. Описано процес декомпозиції кожної з них. Для формалізації наведе- +них знань та отримання можливості встановлення оптимального розв’язку +основної та побічних задач застосовано розроблені онтології проєктування +післядрукарських процесів. +Внаслідок аналізу предметної області відбувається синтезування +моделі пріоритетного впливу факторів на якість проєктування після- + +45 +друкарських процесів. Зокрема описано особливості побудови семантич- +ної мережі та опису зв’язків між факторами за допомогою логіки пре- +дикатів, встановлено пріоритетності впливу факторів на досліджувані +процеси методами математичного моделювання ієрархій та ранжування +факторів. +Наступним етапом є оптимізація моделі пріоритетного впливу фак- +торів на якість проєктування післядрукарських процесів, що полягає у по- +кращенні вхідних даних, та здійснюється за методом аналізу ієрархій, який +передбачає розв’язання ряду задач: побудову матриці попарних порівнянь; +обчислення компонент та нормалізацію значень головного власного векто- +ра матриці; перевірку результатів оптимізації за критерієм максимального +значення головного власного вектора, нормативних значень індексу узгодже- +ності та відношення узгодженості; синтез оптимізованої моделі. +Для встановлення оптимальної альтернативи реалізації проєктування +післядрукарських процесів обрано два методи: багатофакторний вибір аль- +тернатив на основі лінійного згортання критеріїв та на основі нечіткого від- +ношення переваги. +Отримання конкретного кількісного показника якості реалізації дослі- +джуваного процесу реалізовано методами та засобами нечіткої логіки. +На основі виокремлених етапів побудовано структурно-функціональну +модель та IDEF0-моделі інформаційної технології. +The development of the information technology for prognostic assessment of the +design quality of post-press processing of book editions at the initial stage involves the +description of the subject area, including the characteristics of implementation, se- +quence of post-press processes and the course of their design. Key factors of influence +have been identified and functional modelling of certain procedures has been carried +out on the basis of theoretical substantiation and expert statements. Contextual dia- +grams are presented, where the main functions of the systems are the implementation +and design of post-press processes. The process of decomposition of each of them +is described. To formalize the knowledge and get the opportunity to establish the +optimal solution of the main and secondary problems, it is suggested to develop an +ontology of design of post-press processes. +As a result of the analysis of the subject area, a model of the priority influence of +factors on the design quality of post-press processes is synthesized. In particular, the +paper describes the features of constructing a semantic network and describing the +relationships between factors using predicate logic, prioritizing factors by mathemat- +ical modelling of hierarchies and factors ranking. +The next step is to optimize the model of priority influence of factors on the de- +sign quality of post-press processes, which consists in improving the input data and +is carried out by the method of hierarchy analysis, which involves solving a number +of problems: the construction of a matrix of pairwise comparisons; the calculation of +components and the normalization of the values of the main eigenvector; checking +the results of optimization by the criterion of the maximum value of the main eigen- + +46 +vector, the normative values of the consistency index and the consistency ratio; the +synthesis of an optimized model. +To establish the optimal alternative for the implementation of design of post- +press processes, two methods have been chosen: a multifactor selection of alterna- +tives based on linear convergence of criteria and on the basis of fuzzy benefit ratio. +Obtaining a specific quantitative indicator of the quality of implementation of the +studied process is presented by methods and means of fuzzy logic. +The structural-functional model and IDEF0-models are constructed on the ba- +sis of the selected stages of the information technology. +Постановка проблеми. Завершальний етап технології виготовлення +книжкової продукції, до якого відносяться брошурувально-палітурні +процеси, часто помилково ототожнюють із набором механічних, ци- +клічно повторюваних дій, позбавляючи їх високоінтелектуальної ін- +формаційної складової. Такий підхід призводить до підвищення ймо- +вірності часткового чи повного відбракування тиражу. Типовою хибою +є також невідповідність виготовленої продукції її функціональним та +експлуатаційним характеристикам. Так, для прикладу, стосовно видан- +ня, яке повинно служити десятиліття, застосовують клейове скріплен- +ня органічного походження, непридатне для забезпечення прийнятих +вимог, та обирають невідповідний оздоблювальний матеріал [79]. +Останніми роками використовується моделювання вказаних про- +цесів за допомогою комп’ютерної техніки та спеціального програмно- +го забезпечення [5; 59]. Важливо враховувати той факт, що обладнання +для виконання окремих операцій брошурувально-палітурних проце- +сів та матеріали, що використовуються для різних видів продукції, є +індивідуальними [7; 9; 17; 19; 24; 35]. Активно застосовується прин- +цип вертикального проєктування, при якому розрізняють процедури +аналізу і синтезу. У результаті синтезу створюються описи об’єктів, які +відображають їхню структуру і параметри [11; 13]. Вибір технології та +післядрукарського устаткування залежить від виду друкованої продук- +ції, її призначення, обсягів виробництва, економічних та фінансових +показників діяльності друкарень [1; 23; 31; 37; 74; 75]. Суттєвою про- +блемою є дотримання стандартів на виготовлення видань, метрологіч- +ні характеристики, що стосуються якості у поліграфії, моделювання +бізнес-процесів [40; 45; 77], що є важливими чинниками планування +та ефективного функціонування поліграфічних підприємств [79]. +Слід зазначити, що автоматизація з використанням комп’ютери- +зованих технологій не приносить очікуваних результатів, адже засто- +совані процедури не пов’язуються при цьому в єдину, нероздільну + +47 +систему. За таких умов доцільним та необхідним є поопераційний +інформаційний супровід, наслідком якого стане прогностичне оці- +нювання якості майбутньої продукції. Подібний підхід при наявності +умов невизначеності вимагає виокремлення ключових факторів впли- +ву на якість проєктування післядрукарських процесів, встановлення +міри важливості кожного з них та пріоритетності впливу на досліджу- +ваний процес; формування, розрахунку та багатокритеріального оці- +нювання альтернативних варіантів реалізації післядрукарських про- +цесів на основі лінійного згортання критеріїв та нечітких відношень +переваги і визначення оптимального з них; обчислення інтегрально- +го показника рівня якості проєктування післядрукарських процесів; +розроблення інформаційної технології прогностичного оцінювання +вказаних процедур, що слугуватиме методологічною основою для +отримання продукції належної якості [79]. +Основним завданням дослідження є розроблення інформаційної +технології прогностичного оцінювання якості проєктування після- +друкарських процесів, що передбачає виконання таких підпорядко- +ваних завдань: +– проаналізувати етапи проєктування та реалізації післядрукар- +ських процесів, дослідити основні операції та функції, розробити он- +тологію; +– виокремити фактори впливу на якість проєктування післядру- +карських процесів та сформувати семантичні мережі зв’язків між +ними; +– синтезувати та оптимізувати моделі пріоритетного впливу фак- +торів на якість проєктування післядрукарських процесів; +– визначити оптимальні альтернативні варіанти реалізації за ме- +тодами багатофакторного вибору альтернатив на основі лінійного +згортання критеріїв та нечіткого відношення переваги; +– побудувати функції належності лінгвістичних змінних і розраху- +вати їх значення із використанням нечітких логічних рівнянь; +– визначити інтегральний показник якості проєктування після- +друкарських процесів шляхом дефазифікації нечітких множин за +принципом центра ваги; +– розробити структурно-функціональну модель інформаційної +технології прогностичного оцінювання якості проєктування після- +друкарських процесів; +– розробити IDEF0-моделі інформаційної технології прогностич- +ного оцінювання якості проєктування післядрукарських процесів. + +48 +Виклад суті дослідження. Незважаючи на багатовікову історію зу- +силь вчених та практиків, скерованих на формування узагальнюючих +методів, способів та засобів апріорного оцінювання якості процесів, +пов’язаних з виробництвом різнорідної продукції, проблема на сьо- +годні до кінця не вирішена. Спробуємо пояснити причини такого +стану. +Найчастіше поняття «якість» співвідносять з виробом, що на +перший погляд є логічним, оскільки споживача цікавить насам- +перед добротність саме готової продукції [12; 47]. І тут постає ди- +лема — що вважати якістю і як її трактувати. Адже користувачі у +переважній більшості не знайомі зі стандартами, тому кожний по- +своєму оцінює товар, не кажучи вже про те, що його не цікавлять +деталі технології виготовлення. У цьому випадку якість стає кате- +горією суб’єктивною. З іншого боку, наявність і строге дотримання +нормативів і стандартів якості, згідно з якими оцінюється продукція +і розробляються вимоги до технології, машин та режимів реалізації +процесів та окремих процедур, стають об’єктивною передумовою +отримання якісних результатів. +Загальною парадигмою як підсумок до сказаного слугує той факт, +що якість виступає в ролі апостеріорної категорії, отриманої для ха- +рактеристики виходу виробничого процесу у статичному режимі. +У цьому випадку якість — це сукупність властивостей продукції, які +обумовлюють задоволення потреб користувача у відповідності з її +призначенням [47]. +Основна увага пропонованого дослідження буде звернена на дина- +міку формування якості книжкових видань, тобто механізм апріорно- +го встановлення прогнозованого показника критерію ефективності, +як оцінки якості видавничо-поліграфічних етапів засобами сучасних +інформаційних технологій. Враховуючи сказане, можна стверджува- +ти факт існування упорядкованих взаємозв’язків між рівнями техно- +логічного процесу випуску книжкових видань. Структурування ходу +дослідження встановить послідовність дій, а також підтвердить ефек- +тивність та більш строго обґрунтує логіку застосування інформаційної +концепції до прогнозування якості поліграфічної продукції. +З огляду на сказане, на початку ери становлення електронних ін- +формаційних засобів могло здатися, що друковану продукцію чекає +повний занепад, про що в останні роки йшли серйозні дискусії. Од- +нак дані про темпи та обсяги випуску друкованих видань (особливо +книжкових) в Україні свідчать про те, що скептики традиційної (па- + +49 +перової) поліграфії не врахували багатьох суттєвих чинників. Так, у +публікації [4] вказано на фактори, що свідчать про відродження укра- +їнського книгарства. +На початок третього тисячоліття в Україні склався добрий гурт +професійно підготовлених і рішуче налаштованих на працю видавців +і друкарів різних форм власності, які вміло продовжують кращі тра- +диції своїх попередників на книговидавничому полі. +Незважаючи на економічні негаразди, в українському суспільстві +існує стабільно високий попит на добротну українську книгу: худож- +ню, навчальну, наукову, пізнавальну, довідкову тощо. +За прикладом країн Західної Європи Україна все більше починає +відчувати вплив щорічного ярмаркового буму в книжковій справі. +Створено групи приватних видавництв в обласних центрах, які за +короткий час своєї діяльності змогли серйозно заявити про себе на +загальнодержавному рівні. +Технологія виготовлення друкованої продукції є складовою час- +тиною інформаційних технологій, адже від оперативності та доско- +налості друкарських процесів та охоплення ними усіх сфер суспільної +діяльності залежать обсяги та швидкість розповсюдження інформа- +ції — основи існування та поступу людства. Інформаційні видавничо- +поліграфічні технології належать до одного з видів сучасних техно- +логій, пов’язаних з виготовленням як паперових, так і електронних +носіїв даних і знань. Як різновид соціальних інформаційних техноло- +гій, вони породжені суспільною необхідністю удосконалення проце- +су виготовлення твердих та електронних носіїв інформації. Ця техно- +логія виникла не через появу комп’ютерної техніки як такої, а через +суспільне усвідомлення можливості організувати видавничий процес +більш ефективно, оперативно включитися в загальнолюдську інфор- +маційну систему, стати її активним джерелом і споживачем у реальній +інформаційній ситуації. І ця технологія активно впроваджується у ви- +давничий процес, є ефективною, найбільш автоматизованою техно- +логією виготовлення книги, журналу, газети чи іншої друкованої та +«електронної» продукції [3; 36; 48; 65; 66]. +Останніми роками поліграфічні корпорації створили та успішно +використовують концептуально нову інформаційну технологію ор- +ганізації та функціонування видавничо-поліграфічного комплексу, +названу терміном «робочий потік» (Workflow) [8; 14; 39; 49; 71]. Він +забезпечує послідовність реалізації конкретних операцій, пов’язаних +з даними, відображеними форматами файлів PDF, СІР3, СІР4, про- + +50 +грамним та апаратним забезпеченням, а також взаємодію апаратно- +го і програмного забезпечення. Мета полягала в тому, щоб об’єднати +технічно й організаційно потоки даних Workflow і перекинути міст +між клієнтами, друкарнями і брошурувальними підрозділами. Ці по- +токи використовуються для обробки цифрової інформації на всіх ета- +пах поліграфічного виробництва; вони забезпечують інтеграцію сис- +тем CtP (Computer to Plate) з цифровим Workflow, а також з системами +кольоропроби. Сюди входять процеси прийому даних, виробництво, +коректура, управління кольорами, поділ на кольори, спуск полос і їх +виведення. +На сучасному етапі спостерігається тенденція зменшення тиражів. +Це привело до появи друку на вимогу PoD (Print on Demand). Кож- +на система PoD має своє призначення і свої можливості. Спільним є +те, що друкарські комунікації здійснюються за допомогою цифрових +способів друку, а також післядрукарських технологій, орієнтованих +на нього. +Аналіз теперішнього стану технологій друкарства та системних +і програмних засобів їх реалізації свідчить про відсутність на даний +час універсального механізму апріорного оцінювання ефективності +реалізації етапів, стадій чи окремих операцій видавничо-поліграфіч- +ного циклу саме на інформаційному рівні, що унеможливлює апрі- +орне досягнення очікуваної якості за допомогою автоматизованих +систем, орієнтованих на експертно-прогностичне вирішення вказа- +ної проб леми. +Підставою для формування структурно-функціональної моделі +інформаційної технології прогностичного оцінювання якості проєк- +тування післядрукарських процесів є виокремлення та систематиза- +ція основних етапів інформаційної технології [10; 32; 46; 67]. +Етап 1. Аналіз предметної області +1.1. Узагальнений опис операцій та технологій післядрукарського +опрацювання книжкової продукції +Післядрукарські процеси — це сукупність послідовних дій, на- +правлених на перетворення віддрукованих аркушів та інших кон- +струкційних елементів у готову книгу [35; 61]. +Післядрукарське опрацювання книжкових видань можна розді- +лити на два великі блоки: брошурувальні та палітурні процеси. До +брошурувальних процесів належать: виготовлення зошитів, комп- +лектування та скріплення блоків. Можливе також з’єднання блоків + +51 +з обкладинками та обрізування з трьох сторін. До палітурних процесів +належать: опрацювання книжкових блоків, виготовлення та оздоб- +лення палітурок, з’єднання книжкових блоків з палітурками, кінцеве +опрацювання книг [6; 35]. Розглянемо згадані операції детальніше. +Виготовлення зошитів полягає в зіштовхуванні, розрізуванні арку- +шів на частини, фальцюванні, пресуванні та приклеюванні додатко- +вих елементів. Зіштовхування виконується для покращення точності +підрізання та розрізання аркушів. Ця операція полягає у вирівнюван- +ні країв аркушів за горизонтальним та вертикальним краями пачки. +Розрізування — це поділ друкарських чи палітурних аркушів на части- +ни. Фальцювання полягає у згинанні аркушів у визначеному поряд- +ку з фіксацією згинів з метою одержання зошитів бажаного формату +та конструкції. Фальцювання класифікується за такими ознаками: +число згинів (однозгинне, двозгинне, трьохзгинне, чотирьохзгинне, +багатозгинне), взаємне розміщення згинів (паралельне, перпенди- +кулярне, комбіноване), розміщення згинів на аркуші (симетричне, +зміщене), число полос (одинарне, двійником, четверником), число +аркушів (один, два і більше, більше чотирьох згинів). Пресування і +упаковування зошитів здійснюється для зручності транспортування +та зберігання перед наступними операціями. В якості додаткових еле- +ментів можуть бути приєднані форзаци, ілюстрації, частини аркушів. +Комплектування блока — це операція, спрямована на розміщен- +ня аркушів або сфальцьованих зошитів у правильній послідовності +в межах книжкового блоку. Є два основні способи комплектування: +вкладанням (для видань обсягом до 64–80 сторінок; аркуші встав- +ляються один в один) та підбиранням (для видань обсягом понад 80 +сторінок; сфальцьовані аркуші накладають один на одного). Скріп- +лення зошитів скомплектованого блоку може здійснюватися шит- +тям дротом, шиттям нитками або за допомогою незшивних спосо- +бів. Якщо покривним матеріалом є обкладинка, то здійснюється +з’єднання книжкового блоку з обкладинкою та обрізування з трьох +сторін [6; 9; 35]. +Якщо покривним матеріалом є палітурка, то подальше опрацю- +вання книжкових блоків може полягати у пресуванні, заклеюванні +корінця, сушінні блоку, обтискуванні корінця, обрізуванні блоку з +трьох сторін, зафарбовуванні обрізів, зміні форми корінця, каширу- +ванні, приклеюванні лясе, наклеюванні капталу, наклеюванні смужки +паперу, гільзи тощо. Виготовлення палітурки загально може склада- +тися з трьох основних операцій: розкрій покривного матеріалу, збір та + +52 +з’єднання деталей, круглення корінця. При потребі покривний мате- +ріал оздоблюється. Вставлення блоку в палітурку виконується одним +з чотирьох способів: звичайне вставлення, на гільзу, «глухе», в кишені. +Після вставлення блоків у палітурки здійснюється пресування книг, +штрихування, обгортання книг суперобкладинкою. Завершальною +операцією є пакування книжкової продукції [6; 9; 35; 76]. +Таким чином, виготовлення книжкових видань в обкладинці пе- +редбачає виконання лише брошурувальних процесів, а в палітурці — +брошурувальних і палітурних. Загалом брошурувально-палітурне ви- +робництво характеризується неабиякою варіативністю операцій, що +пов’язано зі значною кількістю елементів виробів, різновидами на- +півфабрикатів, тривалим технологічним ланцюжком, різноманітніс- +тю матеріалів. Разом з використанням класичних методів опрацюван- +ня спостерігається постійне вдосконалення напрямків автоматизації +післядрукарських процесів та бажання прогностичного оцінювання +результатів діяльності. Проєктування досліджуваних процесів є клю- +човим етапом для досягнення успішної реалізації необхідних опера- +цій і забезпечення якості книжкового видання [35; 76]. +1.2. Функціональне моделювання післядрукарського опрацювання +книжкової продукції +З огляду на системний характер проєктування післядрукарських +процесів, його доцільно розглядати та досліджувати як певну сис- +тему. При вивченні системи використовуються системний підхід та +системний аналіз. Системний підхід полягає у дослідженні об’єкта +як системи, виявленні та дослідженні сукупності відношень і зв’язків +у ньому. Основними принципами системного підходу є принцип +взаємозв’язку, принцип багатоплановості, принцип багатомірнос- +ті, принцип ієрархічності, принцип різнопорядковості, принцип +динамічності. Системний аналіз являє собою сукупність методів та +алгоритмів, спрямованих на вирішення проблеми. Основною ідеєю +системного аналізу є перетворення складної проблеми у чітку по- +слідовність знань, розв’язок яких є уже відомим або до яких можна +застосувати відомі методи вирішення. Процедура системного аналізу +складається з двох частин: аналізу та синтезу. Аналіз полягає у роз- +кладанні основної проблеми на підпроблеми та застосуванні опти- +мальних методів їх вирішення. Об’єднання окремих розв’язків під- +проблем в один загальний розв’язок проблеми називається синтезом. +Фактично аналіз та синтез є дзеркальними процедурами. Перш ніж + +53 +застосовувати системний аналіз, необхідно чітко сформулювати про- +блему, яка потребує вирішення, та визначити межі системи в яких +буде вирішуватися дана проблема. +Розрізняють два підходи системного аналізу. Перший полягає у +застосуванні математичних прийомів, зокрема теорії оптимізації та +дослідження операцій. При цьому ставиться математична задача, ме- +тою якої є знайдення оптимального проєкту системи чи/та найкра- +щого режиму її функціонування. Основою другого підходу є логіка +системного аналізу, яка використовується у тих випадках, коли засто- +сування математичного підходу є неефективним. +Логіка системного аналізу випливає зі специфіки задач, для вирі- +шення яких він застосовується, та реалізованого підходу. Системний +аналіз застосовують для погано структурованих задач. При наявності +невизначеностей у системному аналізі, метою якого є вплив на ви- +бір способу дії, присутні такі елементи, як проблема та проблемати- +ка, цілі, засоби для досягнення цілей, альтернативи, ресурси, які по- +трібні для кожної альтернативи, моделі, критерії вибору оптимальної +альтернативи. +Етап формулювання проблеми полягає у її розширенні до про- +блематики, тобто виявленні системи пов’язаних із нею проблем, без +врахування яких ключова проблема не може бути розв’язана. Наступ- +ним за важливістю є етап виявлення цілей, на якому визначається, +що потрібно зробити для розв’язання проблеми. Цілі є антиподом +проблеми. На наступних етапах визначається, яким чином потрібно +розв’язати проблему [59]. +Підвищенню ефективності та удосконаленню післядрукарсько- +го опрацювання книжкових видань сприяє використання сучас- +них методів системного аналізу, які реалізовуються за допомогою +комп’ютерної техніки та спеціальних програмних продуктів — CASE- +технологій. CASE-засоби підтримують процеси аналізу і формулю- +вання вимог до різноманітних складних систем, процеси створення +і супроводження інформаційних систем тощо. Одним з напрямів +CASE-технологій є SADT-технології, спрямовані на створення, ана- +ліз та подальше використання моделей складних систем [59]. На базі +SADT-методології розроблена методологія IDEF0-моделі, що перед- +бачає побудову контекстних діаграм деревовидної структури, ство- +рених за принципом декомпозиції. Контекстну діаграму познача- +ють як А-0, а діаграму декомпозиції першого рівня — А0. Стрілками +типу вхід (те, що опрацьовується) є множина значень +{ +} +1,..., +n +I +I +I += +, + +54 +стрілками типу керування (процедури та стратегії управління) — +множина +{ +} +1,..., +n +C +C +C += +, стрілками типу вихід (результат) — множи- +на +{ +} +1,..., +n +O +O +O += +, а стрілками типу механізми (необхідні ресурси) — +множина +{ +} +1,..., +n +M +M +M += + [40; 77]. +Основною функцією є реалізація післядрукарських процесів. +Зв’язок системи із навколишнім середовищем ілюструється такими +граничними стрілками: I1 — віддруковані аркуші, I2 — покривний +матеріал, I2 — інші матеріали, C1 — нормативно-технічна та техно- +логічна документація, C2 — проєкт, C3 — альтернативи реалізації, +O1 — рівень якості післядрукарських процесів, O2 — готові видання, +M1 — брошурувально-палітурне устаткування, інші знаряддя праці, +M2 — особовий склад працівників, експерти з предметної області, за- +цікавлені особи. +Проаналізуємо інформаційне навантаження компонент множин +граничних стрілок IDEF0 моделі реалізації післядрукарських процесів: +Граничні стрілки типу «Вхід» (Input): +– +1I (віддруковані аркуші). Результатом додрукарського опрацю- +вання авторських оригіналів та друкування накладу є віддруковані +паперові аркуші, які надходять на дільницю післядрукарського опра- +цювання. +– +2I (покривний матеріал). Аркуші покривного матеріалу, які слу- +гують для виготовлення обкладинок чи палітурок (залежно від харак- +теристик). +– +3I (інші матеріали). Матеріали для скріплення, оздоблення тощо. +Граничні стрілки типу «Контроль» (Control): +– +1 +C (нормативно-технічна та технологічна документація). До +нормативно-технічної документації належать технічні вимоги та за- +конодавчі положення, зокрема: закони, стандарти, технічні умови, +кодекси усталеної практики та ін. +– +2 +C (проєкт). Визначає перебіг усіх технологічних дій, направле- +них на реалізацію післядрукарських процесів. +– +3 +C (альтернативи реалізації). Парето-оптимальні альтернативи, +визначені оцінюванням нечітких відношень на заданій множині аль- +тернатив. +Граничні стрілки типу «Вихід» (Output): +– +1 +O (рівень якості післядрукарських процесів). Результат, отри- +маний внаслідок реалізації післядрукарського опрацювання книжко- +вих видань. + +55 +Реалізація +післядрукарських +процесів +Віддруковані аркуші +Рівень якості +післядрукарських +процесів +Брошурувально- +палітурне +устаткування, інші +знаряддя праці +Особовий склад +працівників, експерти з +предметної області, +зацікавлені особи +Альтернативи +реалізації +Проєкт +Нормативно-технічна +та технологічна +документація +Готові видання +Покривний матеріал +Інші матеріали +Рис. 1. Контекстна діаграма А-0 моделі IDEF0 реалізації +післядрукарських процесів +– +2 +O (готові видання). Книжкові видання в обкладинках чи палі- +турках, готові до розповсюдження. +Граничні стрілки типу «Механізми» (Mechanism): +– +1 +M (брошурувально-палітурне устаткування, інші знаряддя +праці). Устаткування, необхідне для реалізації післядрукарських про- +цесів. Можливе також використання спеціалізованих знарядь праці +при виконанні деяких операцій вручну. +– +2 +M (особовий склад працівників, експерти з предметної облас- +ті, зацікавлені особи). Реалізація післядрукарських процесів передба- +чає участь працівників брошурувально-палітурної дільниці, кількість +та кваліфікація яких залежать від обсягу та рівня автоматизації вироб- +ництва. Можливе залучення профільних експертів, зокрема науков- +ців та інших зацікавлених осіб. +Процес функціональної декомпозиції контекстної діаграми, на- +веденої на рис. 1, полягає у її розділенні на функції нижчого порядку +та встановленні напрямів граничних стрілок, що сприяє деталізації +діяльності в межах досліджуваного процесу [77]. +Діаграма першого рівня декомпозиції А0 моделі IDEF0 реалізації +післядрукарських процесів містить такі функціональні блоки: +– РБП (реалізація брошурувальних процесів). + +0212101CC5M1M256 +– РПП (реалізація палітурних процесів). +Діаграма другого рівня декомпозиції А1 моделі IDEF0: +– ВЗ (виготовлення зошитів). +– КБ (комплектування блоків). +– СБ (скріплення блоків). +– ВО (виготовлення обкладинок). +– ПБО (покриття блоків обкладинками). +– КОВО (кінцеве опрацювання видань в обкладинках). +Діаграма другого рівня декомпозиції А2 моделі IDEF0: +– ОБ (опрацювання блоків). +– ВОП (виготовлення та оздоблення палітурок). +– ЗБП (з’єднання блоків з палітурками). +– КОК (кінцеве опрацювання книг). +Для відображення ієрархічної залежності функцій доцільно вико- +ристовувати діаграму дерева вузлів. +1.3. Аналіз факторів впливу на якість проєктування післядрукар- +ських процесів. Розроблення онтології +Проєктування післядрукарських процесів є ключовим етапом для +досягнення успішної реалізації необхідних операцій і забезпечення +якості книжкового видання. +Важливим моментом при дослідженні післядрукарських процесів +вважатимемо наявність технологічних характеристик чи параметрів, +від яких залежить результативність проходження видання у загально- +му циклі його виготовлення. Узагальнюючи подібні чинники, вво- +димо поняття факторів, що стають основними елементами моделей +визначення пріоритетності впливу факторів на хід реалізації та про- +гностичного оцінювання якості післядрукарських процесів. Встанов- +лення пріоритетності компонент сформованої множини слугуватиме +раціоналізації післядрукарських процесів та сприятиме отриманню +готової продукції очікуваної якості. +Проєктування післядрукарських процесів слугує усвідомлено- +му та впорядкованому виконанню запланованих технологічних дій, +направлених на перетворення віддрукованих аркушів та інших кон- +струкційних елементів у завершене книжкове видання високої якос- +ті. Відсутність етапу проєктування унеможливлює отримання про- +гнозованого результату. +Нехай +{ +} +1 +2 +3 +4 +5 +6 +7 +8 +, +, +, +, +, +, +, +R +R R R R R R R R += +— множина факторів про- +єктування післядрукарських процесів, де +1 +R — показники видання; + +57 +2 +R — конструкційні особливості; +3 +R — умови експлуатації; +4 +R — тип +виробництва; +5 +R — матеріали; +6 +R — тип обладнання; +7 +R — техноло- +гічні та економічні розрахунки; +8 +R — схема технологічного процесу. +Розглянемо детальніше кожен фактор досліджуваного процесу. +Показники видання. До основних показників книжкового видання +відносяться: вид і тип видання, формат видання та його обсяг. +Вид видання — це сукупність видань, що об’єднані за однією чи +кількома типологічними ознаками. До таких типологічних ознак +належать: знакова природа інформації, спосіб виготовлення, пері- +одичність, матеріальна конструкція, склад основного тексту, мовна +ознака, ступінь аналітико-синтетичного перероблення інформації, +цільове призначення, характер інформації, структура, повторюва- +ність випуску, обсяг, формат. За знаковою природою інформації ви- +дання поділяються на текстові, нотні, картографічні (атлас, мапа, +карта), образотворчі (альбоми, образотворчі картки, образотворчі +плакати, художні репродукції, естампи, наочні посібники), видан- +ня брайлівським шрифтом. За способом виготовлення розрізняють +друковані та електронні видання. За періодичністю: неперіодичні, +серіальні, періодичні, продовжувані. За матеріальною конструкцією: +блочне видання (кодексне видання), книжкове видання (книга-пе- +рекрутка, алігат), журнальне видання (журнал-перекрутка, алігат), +аркушеве видання (плакат, буклет, газетне видання, карткове ви- +дання), комплектне видання, комбіноване видання, книжка-іграш- +ка. За складом основного тексту бувають такі види: моновидання, +полівидання (збірник, альманах, антологія), вибрані твори, зі- +брання творів (академічне видання). Види видань за мовною озна- +кою: оригінальне, перекладне, одномовне, багатомовне (видання з +паралельним текстом), паралельне видання. За ступенем аналіти- +ко-синтетичного перероблення інформації: інформаційне видання +(бібліографічне, реферативне (експрес-інформація, інформаційний +листок), оглядове), дайджест. За цільовим призначенням: офіційне, +суспільно-політичне, наукове, науково-популярне, популярне, ви- +робничо-практичне, навчальне, літературно-художнє, релігійне, до- +відкове, рекламне, видання для дозвілля. За характером інформації: +офіційне (нормативно-правове видання, нормативне видання (стан- +дарт, технічні умови), нормативно-інструктивне (інструкція), науко- +ве (монографія, автореферат дисертації, препринт, тези доповідей, +тези повідомлень, матеріали конференції, матеріали з’їзду, матеріали +симпозіуму, збірник наукових праць), виробничо-практичне (прак- + +58 +тичний порадник, практичний посібник, методичні рекомендації, +методичні настанови, методичний посібник, пам’ятка, паспорт (на +вибір), навчальні (навчальна програма, підручник, навчальний по- +сібник (навчально-методичний посібник, навчальний наочний по- +сібник, хрестоматія, практикум, робочий зошит), довідкові і реклам- +ні (енциклопедія (енциклопедичний словник), мовний словник, +лінгвістичний словник, довідник, каталог, путівник, прейскурант, +проспект, афіша). За структурою: однотомне видання, багатотомне +видання, серія (підсерія), серійне видання, додаток. За повторюва- +ністю випуску: перше, повторне (перевидання (видання без змін, +доповнене видання, перероблене видання, виправлене видання), +передрук (репринтове видання, факсимільне видання), нове. За об- +сягом видання поділяються на такі види: книга, брошура, листівка +(аркушівка). За форматом видання бувають: мініатюрне, малофор- +матне, портативне, фоліант. Окремо виділяють види періодичних та +продовжуваних видань [1; 59]. +Також книжкові видання бувають звичайного, покращеного та су- +венірно-подарункового (рекламного) типу. До звичайного типу нале- +жать видання, що видаються великими накладами, без або з невели- +кою кількістю ілюстрацій в одну чи дві фарби: вибрані твори, зібрання +творів, окремі видання, масові серії, масові рекламно-інформаційні +видання. Видання покращеного типу призначені для довготривалого +використання, містять середню кількість ілюстрацій в три або чоти- +ри фарби: вибрані твори, зібрання творів, збірники, окремі видання, +навчальні видання, покращені серії. Для видань сувенірно-подарун- +кового типу характерні невеликі наклади, високоякісні матеріали, +велика кількість багатоколірних ілюстрацій, нестандартні формати, +великі поля, додаткове оздоблення та пакування, підвищена ціна. До +них належать: видання виготовлені за індивідуальним замовленням, +сувенірні, подарункові, ювілейні, факсимільні видання [35; 59]. +Формат видання вказує на розмір готового книжкового блоку в +міліметрах або друкарського аркуша в сантиметрах і частку аркуша. +Обирається видавництвом, за погодженням з друкарнею. Залежить +здебільшого від виду та типу видання. При поліграфічному відтво- +ренні книжкових видань формат умовно позначають розміром арку- +ша паперу в сантиметрах та часткою аркуша (долею) та вказують у +випускних даних [2; 51; 59]. +Формат у міліметрах для видання в обкладинці визначають за роз- +мірами книги після обрізки з трьох боків. Формат у міліметрах для + +59 +видання в палітурці визначають за розмірами книжкового блока, об- +різаного з трьох сторін. При цьому максимальні відхилення у форма- +тах не можуть перевищувати 1 мм по ширині та 1 мм по висоті. +Формати аркушів та відповідні формати книжкових видань регла- +ментуються ДСТУ 4489:2005. Основні формати книжкових видань +наведені у таблицях 1–3. При цьому на довжину аркуша для рулонних +машин вказує машинний напрям паперу [2]. +Також за форматом і часткою аркуші бувають великі, середні, ма- +ленькі та мініатюрні. Загалом використовують 22 формати книжко- +вих видань. Окремо виділяють формат друкування, який не завжди +співпадає з форматом видання. +Подальший вибір технологічного процесу виготовлення видання +та необхідного устаткування за ідеальних умов залежить від обраного +формату [51]. В тих випадках, коли про альтернативний вибір дру- +карні не йдеться, а можливості обраної є обмеженими, залежність є +оберненою, адже формат обирається з огляду не лише на тематичні +та експлуатаційні вимоги видання, а й варіативність наявного устат- +кування та економічна доцільність того чи іншого варіанту виготов- +лення. +Також виділяють формат сторінки складання (формат набору), +тобто ширину і довжину сторінки без полів. Вимірюється в друкар- +ських одиницях. Бувають текстові, ілюстраційні і змішані сторінки +складання. +Таблиця 1 +Формати книжкових видань для 1/8 частки аркуша +Формат арку- +ша паперу, мм +Позначка +формату +аркуша* +Формат книжкових видань +Сфальцьова- +ного аркуша +видання +оптимальний +мінімальний +840 M×1080 +270×420 +265×410 +262×408 +700 M×1080 +270×350 +265×340 +262×338 +700 M×1000 +B1 +250×350 +245×340 +242×338 +700 M×900 +225×350 +220×340 +217×338 +610 M×860 +RA1 +215×305 +210×297 +208×295 +600 M×900 +225×300 +220×290 +205×275 +600 M×840 +A1 +210×300 +205×290 +202×288 +500 M×700 +B2 +175×250 +169×239 +165×235 +460 М×640 +SRA2 +160×225 +148×210 +145×208 +*Згідно з ISO 216 та ISO 217. +М — розмір вздовж машинного напряму паперу. + +60 +Таблиця 2 +Формати книжкових видань для 1/16 частки аркуша +Формат арку- +ша паперу, мм +Позначка +формату +аркуша* +Формат книжкових видань +Сфальцьова- +ного аркуша +видання +оптимальний +мінімальний +890×1240 M +222×310 +210×297 +208×295 +860×1220 M +RA0 +215×305 +210×297 +208×295 +840×1080 M +210×270 +205×260 +192×255 +750×900 M +185×225 +182×216 +179×213 +700×1000 M +B1 +175×250 +169×239 +165×235 +700×900 M +175×225 +170×215 +167×213 +600×900 M +150×225 +145×215 +142×213 +600×840 M +A1 +150×210 +145×200 +142×198 +*Згідно з ISO 216 та ISO 217. +М — розмір вздовж машинного напряму паперу. +Таблиця 3 +Формати книжкових видань для 1/32 частки аркуша +Формат арку- +ша паперу, мм +Позначка +формату +аркуша* +Формат книжкових видань +Сфальцьова- +ного аркуша +видання +оптимальний +мінімальний +1000 M×1400 +B0 +175×250 +169×239 +165×235 +890 M×1240 +155×222 +148×210 +145×208 +880 M×1120 +140×220 +136×210 +133×208 +860 M×1220 +RA0 +152×215 +148×210 +145×208 +840 M×1080 +135×210 +130×200 +127×188 +750 M×900 +112×187 +107×177 +104×175 +700 M×1080 +135×175 +130×165 +127×163 +700 M×1000 +B1 +125×175 +120×165 +117×163 +700 M×900 +112×175 +107×165 +104×163 +600 M×900 +112×150 +107×140 +104×138 +600 M×840 +105×150 +100×140 +97×138 +*Згідно з ISO 216 та ISO 217. +М — розмір вздовж машинного напряму паперу. +Поля сторінки — це незаповнені ділянки навколо сторінки складан- +ня, розміри яких визначаються різницею формату сторінки та формату +сторінки складання. Кожна сторінка має чотири поля: верхнє (голов- +кове), нижнє (хвостове), зовнішнє (переднє) і внутрішнє (корінцеве). +Оптимальні розміри полів завжди є пропорційними одне до одного. + +61 +Рекомендовані розміри сторінки складання та полів для певних +форматів залежать від варіантів оформлення видань (перший — най- +більш економний, з невеликими полями; другий — звичайний, з се- +редніми полями; третій — покращений, з великими полями) [2; 59]. +Таблиця 4 +Рекомендовані розміри полів +Формат паперу, см +та частка аркуша +Формат сторінки +складання, кв. +Розміри полів до обрізування +(корінцеве, верхнє, зовнішнє, +нижнє), мм +Перший варіант оформлення +60×84/32 +9, 13, 15, 20 +60×90/32 +9, 13, 18, 20 +70×90/32 +9, 13, 18, 23 +75×90/32 +9, 13, 18, 21 +70×100/32 +9, 13, 21, 23 +70×108/32 +3 +6 7 4 +× +9, 13, 18, 23 +84×108/32 +3 +6 9 4 +× +9, 13, 18, 23 +60×84/16 +3 +3 +6 +9 +4 +4 +× +11, 16, 17, 19 +60×90/16 +3 +1 +6 +10 +4 +2 +× +11, 16, 17, 20 +70×90/16 +1 +8 10 4 +× +11, 16, 20, 25 +75×90/16 +3 +1 +8 +10 +4 +4 +× +11, 16, 19, 25 +70×100/16 +1 +8 11 2 +× +11, 16, 20, 27 +70×108/16 +1 +8 12 2 +× +11, 16, 20, 29 +84×108/16 +3 +1 +9 +12 +4 +2 +× +11, 16, 23, 29 +60×84/8 +3 +9 +14 +4 × +13, 18, 21, 30 +60×90/8 +1 +1 +10 +14 +2 +4 +× +13, 18, 23, 26 +70×100/8 +12 17 +× +13, 18, 21, 26 +70×108/8 +13 17 +× +13, 18, 23, 26 +84×108/8 +3 +13 20 4 +× +13, 18, 23, 29 +Другий варіант оформлення +60×84/32 +1 +1 +4 +6 +4 +4 +× +11, 16, 18, 22 + +62 +Продовження табл. 4 +Формат паперу, см +та частка аркуша +Формат сторінки +складання, кв. +Розміри полів до обрізування +(корінцеве, верхнє, зовнішнє, +нижнє), мм +60×90/32 +1 +1 +4 +6 +2 +4 +× +11, 16, 20, 22 +70×90/32 +1 +1 +4 +7 +2 +2 +× +11, 16, 20, 24 +75×90/32 +1 +1 +4 +8 +2 +4 +× +11, 16, 20, 22 +70×100/32 +1 +5 7 2 +× +11, 16, 24, 24 +70×108/32 +3 +1 +5 +7 +4 +2 +× +11, 16, 21, 24 +84×108/32 +3 +1 +5 +9 +4 +2 +× +11, 16, 21, 23 +60×84/16 +1 +1 +6 +9 +2 +2 +× +13, 18, 20, 21 +60×90/16 +1 +1 +6 +10 +2 +4 +× +13, 18, 20, 23 +70×90/16 +3 +7 +10 +4 × +13, 18, 22, 27 +75×90/16 +1 +8 +10 +2 × +13, 18, 21, 27 +70×100/16 +3 +1 +7 +11 +4 +4 +× +13, 18, 22, 30 +70×108/16 +3 +1 +7 +12 +4 +4 +× +13, 18, 22, 31 +84×108/16 +1 +1 +9 +12 +2 +4 +× +13, 18, 26, 31 +60×84/8 +1 +3 +9 +13 +2 +4 +× +16, 20, 23, 33 +60×90/8 +1 +10 +14 +4 × +16, 20, 24, 28 +70×100/8 +3 +3 +11 +16 +4 +4 +× +16, 20, 23, 29 +70×108/8 +3 +3 +12 +16 +4 +4 +× +16, 20, 25, 29 +84×108/8 +3 +1 +12 +20 +4 +2 +× +16, 20, 25, 31 +Третій варіант оформлення +60×84/32 +4 6 +× +13, 18, 20, 24 +60×90/32 +1 +4 +6 +4 × +13, 18, 23, 24 +70×90/32 +1 +1 +4 +7 +4 +4 +× +13, 18, 20, 27 +75×90/32 +1 +4 +8 +4 × +13, 18, 20, 25 + +63 +Закінчення табл. 4 +Формат паперу, см +та частка аркуша +Формат сторінки +складання, кв. +Розміри полів до обрізування +(корінцеве, верхнє, зовнішнє, +нижнє), мм +70×100/32 +3 +1 +4 +7 +4 +4 +× +13, 18, 26, 27 +70×108/32 +1 +1 +5 +7 +2 +4 +× +13, 18, 23, 27 +84×108/32 +1 +1 +5 +9 +2 +4 +× +13, 18, 23, 26 +60×84/16 +1 +1 +6 +9 +4 +4 +× +16, 20, 22, 24 +60×90/16 +1 +6 +10 +4 × +16, 20, 22, 25 +70×90/16 +1 +3 +7 +9 +2 +4 +× +16, 20, 24, 29 +75×90/16 +1 +3 +8 +9 +4 +4 +× +16, 20, 23, 30 +70×100/16 +1 +7 +11 +2 × +16, 20, 24, 32 +70×108/16 +1 +7 +12 +2 × +16, 20, 24, 24 +84×108/16 +1 +9 +12 +4 × +16, 20, 27, 24 +60×84/8 +1 +1 +9 +13 +4 +2 +× +18, 22, 26, 35 +60×90/8 +1 +3 +10 +13 +4 +4 +× +18, 22, 27, 31 +70×100/8 +1 +1 +11 +16 +2 +2 +× +18, 22, 25, 31 +70×108/8 +1 +1 +12 +16 +2 +2 +× +18, 22, 27, 31 +84×108/8 +1 +1 +12 +20 +2 +4 +× +18, 22, 27, 34 +Обсяг — це кількість сторінок або аркушів в одному примірнику +видання. Розрізняють такі види аркушів: паперовий, фізичний, умов- +ний, авторський, обліково-видавничий. Паперовий аркуш — облікова +одиниця виміру кількості паперу, необхідного для друкування видан- +ня. Один паперовий аркуш дорівнює двом фізичним аркушам. Фізич- +ний друкарський аркуш — це фізичний обсяг видання, що дорівнює +площі аркушу визначеного формату (84×108 см, 84×90 см, 70×100 см +та ін.), задрукованого з однієї сторони. Кількість фізичних аркушів у +два рази більша за кількість паперових аркушів. Умовний друкарський +аркуш — облікова одиниця обсягу видання, площею 60×90 см, при- + +64 +значена для порівняння обсягу видань різних форматів. Вираження +фізичних друкарських аркушів в умовних друкарських аркушах і на- +впаки здійснюється за допомогою коефіцієнта переведення: + +, +фа +пр +уа +S +K +S += + +(1) +де +фа +S + — площа фізичного аркуша, +уа +S + — площа умовного аркуша. +Тоді обсяг видання в умовних друкарських аркушах визначається +за формулою: + +, +уа +фа +пр +O +O +K += +⋅ + +(2) +де +фа +O + — обсяг в фізичних аркушах. +Авторський аркуш — облікова одиниця обсягу твору. Один ав- +торський аркуш містить 40000 знаків прозового тексту (в тому числі +пробіли, розділові знаки, цифри тощо) або 700 рядків віршованого +тексту, або 3000 см2 ілюстрацій. +Обліково-видавничий аркуш призначений для вимірювання об- +сягу авторського твору з урахуванням матеріалів, доданих видавни- +цтвом. Визначається так само, як і авторський аркуш, але враховує +об’єкти, що не є наслідком авторської праці (видавничу анотацію, +зміст, титульні елементи, вихідні та випускні дані, передмову, дані на +обкладинці, палітурці, суперобкладинці, колонцифру тощо). +Обсяг видання в аркушах слугує для обліку робіт, уніфікації ви- +дань, підрахунку витрат та здійснення технологічних розрахунків. +Кількість умовних та обліково-видавничих аркушів зазначається +у випускних відомостях книги. Ще однією обліковою одиницею об- +сягу видання є кількість сторінок, що зазначається в бібліографіч- +ному описі. Від обсягу видання залежать вид та тип покрівельного +матеріалу, спосіб фальцювання та комплектування, технологія скрі- +плення книжкового блоку та ін. [35; 51; 59]. +Конструкційні особливості. Враховується спосіб комплектування, +спосіб скріплення книжкового блоку, вид і тип покрівельного матері- +алу, наявність та вид додаткових елементів. +Комплектування книжкових блоків відбувається двома способа- +ми: вкладанням та підбиранням. Комплектування вкладанням по- +лягає у вкладанні сфальцьованих аркушів один в один, використову- +ється для невеликих за обсягом видань. Накладання сфальцьованих +зошитів або аркушів один на один називається комплектуванням ви- +дань підбиранням (для видань обсягом понад 80 сторінок) [35]. + +65 +Способи скріплення поділяються на швейні, безшвейні і комбі- +новані. При швейному скріпленні використовують дріт або нитки, +при безшвейному — клей чи механічні способи. Також виділяють +позошитне та поблочне скріплення. При позошитному скріпленні +блок повинен бути скомплектованим підбиранням. Тоді кожен зо- +шит один за одним прошивається через фальц і скріплюється (швей- +не скріплення). При поблочному скріпленні блок комплектується +вкладанням або підбиранням і скріплюється за один робочий цикл +(швейне, незшивне клейове чи комбіноване скріплення). Поблочний +спосіб скріплення є економічнішим, особливо для видань великого +об’єму. +Скріплення дротом найчастіше використовується для видань із +малим чи середнім терміном використання, зазвичай для брошур і +книжок у м’якій обкладинці. Забезпечує високу продуктивність, міц- +ність та низьку собівартість. Є чотири способи шиття дротом: ушив- +кою, вшиттям, врознім, зустрічними скобами. +При шитті ушивкою дротяні скоби проходять через згин корінця +і загинаються всередину книги. Для запобігання корозії використо- +вується дріт із покриттям або іноді латунний дріт. Шиття ушивкою +застосовується до блоків, скомплектованих вкладанням із накинутою +зверху обкладинкою. +Шиття вшиттям дроту використовується для видань, скомплекто- +ваних підбиранням. Прошивання здійснюється дротяними скобами +на відстані 4–5 мм від краю корінця. Кінці скоби загинаються пара- +лельно до спинки скоби на корінцевому полі останньої сторінки. Для +закриття спинки та ніжок скоби приклеюють обкладинку. +Шиття дротом врознім використовується для видань у палітур- +ках. При цьому скоби загинаються поверх блока на корінець. Шит- +тя врознім може бути як поблочним (для видань, скомплектованих +вкладанням), так і позошитним. +Шиття дротом зустрічними скобами використовується для бло- +ків товщиною більше 15 мм, скомплектованих підбиранням. Зазви- +чай застосовується для виготовлення відкритих календарів. Міцність +забезпечується невеликою відстанню між ніжками скоб (не менше +5 мм). +Шиття блоків нитками є одним з найбільш розповсюджених та +надійних способів скріплення, дозволяє обробляти зошити на поопе- +раційному обладнанні та потокових лініях. Є чотири способи шиття +нитками: впрострочку, вшиттям, позошитне, позошитне на марлі. + +66 +Шиття нитками впрострочку використовується для видань неве- +ликого обсягу, скомплектованих вкладанням. Прошивання здійсню- +ється неперервним швом вздовж усього згину. +Шиття вшиттям ниток застосовується до блоків, скомплектова- +них підбиранням. Прошивання здійснюється вздовж усього корінця +з відступом від краю 4–5 мм. +Позошитне шиття полягає у послідовному прошиванні корінце- +вих згинів. Відбувається не лише зшиття кожного аркуша, а й зоши- +тів між собою. Допускається зшиття блоків на корінцевому матеріалі, +наприклад, на марлі (для книг у палітурках), та без нього (для книг в +обкладинках та палітурках). +Незшивне скріплення здійснюється за допомогою клейових плі- +вок чи різних механічних пристроїв. +Незшивне клейове скріплення реалізується різними клеями та у +різний спосіб і поділяється так: з повним зрізанням, частковим зрі- +занням і без зрізання корінцевих фальців. +Незшивне клейове скріплення з повним зрізанням корінцевих фаль- +ців при застосуванні полівінілацетатної дисперсії (холодне скріплення) +здійснюється шляхом утворення клейової плівки внаслідок випарову- +вання води з клею та його часткового вбирання папером. Обладнання, +що використовується для незшивного клейового скріплення з повним +зрізанням корінцевих фальців при застосуванні термоклеїв (гаряче +скріплення), повинно мати підігрівач бачка з клеєм, а при застосуванні +полівінілацетатної дисперсії (холодне скріплення) — стіл з підігрівом чи +сушильну секцію. Загалом більшість операцій при холодному та гарячо- +му скріпленнях є однаковими чи подібними, тож часто використовують +універсальне обладнання, яке можна переналаштовувати. +Незшивне клейове скріплення з частковим руйнуванням корінце- +вих фальців характеризується вищою міцністю порівняно з попере- +днім способом, за рахунок збереження частини фальців. При цьому +клей склеює зошити між собою та проникає у прорізи, склеюючи +аркуші. Блоки комплектуються підбиранням, а обсяг зошитів стано- +вить 8 чи 16 сторінок. Можливі такі способи: скріплення блоків за +допомогою шнурів чи ниток у прорізах на корінці; скріплення блоків +з прорізами, канавками поперек корінця; «флекстабіль», скріплен- +ня блоків з вирубуванням окремих зон; скріплення блоків з зошитів, +перфорованих за корінцем. +Незшивне клейове скріплення без руйнування корінцевих фаль- +ців поділяється на такі способи: скріплення однозгинних зошитів, + +67 +скріплення дво- і тризгинних зошитів у корінцевих згинах вузькими +смужками рідкого холодного клею, скріплення зошитів за корінцеви- +ми фальцами з використанням термоклею, незшивне клейове скріп- +лення з попереднім нанесенням на середину корінцевих полів сму- +жок холодного поліамідного клею. +Механічні незшивні способи скріплення призначені для з’єднання +блоків за допомогою механічних замків. При цьому блоки складають- +ся з окремих аркушів. Застосовуються для виготовлення дитячих ви- +дань, рекламних проспектів, каталогів, альбомів та ін. +Швейно-клейове скріплення (комбіноване) здійснюється за до- +помогою термониток. При цьому блоки повинні бути скомплектова- +ні підбиранням. Шиття відбувається при фальцюванні [9; 35; 75]. +Виділяють чотири типи обкладинок та п’ять типів палітурок. +Обкладинка — зовнішній покрівельний матеріал, що скріплюєть- +ся з книжковим блоком без застосування форзаців. Розрізняють чо- +тири типи обкладинок. +Тип 1 — проста обкладинка для покриття блока наопашки. Засто- +совується для видань обсягом до 64 сторінок. Обкладинка складаєть- +ся з одного аркушу, який накидається на зошит і скріплюється з ним +дротяними скобами чи нитками. Блок при цьому зазвичай комплек- +тується вкладанням. Найчастіше виготовляється з паперу, який, для +збільшення довговічності, може бути покритий прозорим полімер- +ним шаром з однієї або двох сторін. +Тип 2 — проста обкладинка для звичайного покриття блока. Скріп- +люється з книжковим блоком шляхом приклеювання по корінцю. +Містить подвійне бігування. На відміну від обкладинки типу 1 може +бути покрита прозорим полімерним шаром тільки з зовнішнього боку +(щоб була змога приклеїти її по корінцю). Блок комплектується під- +биранням. При відкриванні основне навантаження припадає на біги, +тому може виникати відривання обкладинки від книжкового блока. +Тип 3 — проста обкладинка для покриття блока врозпуск. Скріп- +люється з книжковим блоком шляхом приклеювання. При цьому +клей наноситься не лише на корінець, а й на бокові сторони блоку (на +кілька міліметрів корінцевого поля першої та останньої сторінки). +Блок комплектується підбиранням. Такий тип обкладинки найбільш +поширений, адже є довговічнішим за тип 2. Це пов’язано з наявністю +чотирьох бігувань. +Тип 4 — складена обкладинка з обкантованим корінцем. Матеріа- +лом боковин може бути папір або палітурний картон, а як обкантовку + +68 +використовують палітурний матеріал. Характеризується значно ви- +щою міцністю та складністю виготовлення порівняно з обкладинками +типів 1, 2 та 3. Зазвичай застосовується для видань великого обсягу. +Тобто, за конструкцією обкладинки типи 1, 2, 3 складаються з од- +нієї деталі, а обкладинка типу 4 з боковин обкладинки та обкантовки +[13; 35]. +Палітурка — цупкий, захисний зовнішній покрівельний елемент +книги, який скріплюється з книжковим блоком за допомогою форза- +ців. Розрізняють п’ять типів палітурок. +Тип 5 — складена. Складається з картонних боковин, корінця, від- +ставу, вкритих різними покрівельними матеріалами. Для видань тов- +щиною до 10 мм можна виготовляти без розставів. Використовується +для дитячої, художньої, наукової літератури, підручників для серед- +ньої школи, невеликих за обсягом довідників. Характеризується не- +високою собівартістю, достатньою міцністю та великими можливос- +тями оформлення. Може задруковуватися з подальшим лакуванням +чи припресовуванням плівки, що підвищує довговічність та стійкість +до стирання. +Тип 6 — палітурка з однієї деталі. Складається з одного суцільного +матеріалу. Зазвичай використовується для довідникових видань ма- +лого формату та для паперово-білових виробів. +Тип 7 — суцільнокрита. Складається з картонних боковин та від- +ставу, вкритих суцільним покрівельним матеріалом. Для видань тов- +щиною до 10 мм можна виготовляти без розставів. Характеризується +невеликою собівартістю та більшою міцністю, порівняно з палітурка- +ми типів 5, 8 та 9. Завдяки своїм характеристикам отримала широке +застосування, зокрема для покриття підручників для закладів вищої +та професійно-технічної освіти, передплатних, науково-популярних, +наукових видань. +Тип 8 — палітурка з накладними боковинками і накладним ко- +рінцем. Складається з картонних боковинок, відставу, накладних +боковинок, обкладених покрівельним матеріалом з усіх сторін, та +накладного корінця. Характеризується невисокою міцністю, серед- +ньою собівартістю, привабливим виглядом. Використовуються при +виготовленні наукових, науково-довідкових, науково-популярних +видань. +Тип 9 — палітурка з накладними боковинками і обкантованим ко- +рінцем. Складається з картонних боковинок, накладних боковинок +та обкантовувального матеріалу. Зазвичай слугує для покриття під- + +69 +ручників для початкової та середньої школи, довідкових та науково- +популярних видань [35]. +Видання також може мати додаткові елементи: форзаци (для +скріп лення книжкових блоків з палітурками та оформлення видань), +ілюстрації (для оформлення видань). Форзаци поділяються за та- +кими характеристиками: характером оформлення (прості незадру- +ковані, виготовлені з кольорового паперу та незадруковані, фонові, +декоративно-орнаментні, тематичні), кількістю задрукованих сторін +(односторонні, двосторонні), фарбовістю (однофарбові, двофарбові, +багатофарбові), способом приєднання (приклейні, пришивні, про- +шивні), конструкцією (суцільнопаперові, обкантовані, прикантова- +ні, накидні, складені). Додаткові ілюстративні елементи класифіку- +ються залежно від місця розміщення в зошиті та способу приєднання +до нього: приклейки (прості, складнофальцьовані, з окантуванням, в +рамку, на стержень, на паспарту (на стержні, з плюром), з відігнутим +фальцем, з бігуванням), вклейки (в роз’єм зошитів, з розрізуванням +фальців зошитів, прості, складнофальцьовані), накидки, вкладки, +окремий зошит. Додатковими елементами також можуть бути части- +ни аркушів — зошити з іншою кількістю сторінок, ніж основні. Обсяг +додаткових зошитів повинен бути кратним чотирьом [35]. +Умови експлуатації. Цей фактор містить дві основні складові: тер- +мін та інтенсивність експлуатації книжкових видань. +Термін служби — це календарний час експлуатації видання чи +його довговічність, які залежать від конструкційних особливостей, +інформаційної цінності, місця його використання та вікової категорії +читачів [35]. +За віковою категорією видання поділяються на ті, що призначені +для дорослих читачів та для дітей. Крім того дітей-читачів поділяють +за швидкістю читання (досвідчені та читачі-початківці) та за віком +(дошкільнята (до 6 років включно), читачі молодшого шкільного віку +(від 7 до 10 років), читачі середнього шкільного віку (від 11 до 14 ро- +ків) та читачі старшого шкільного віку (від 15 до 17 років). Звісно, що +зазвичай видання для дітей молодшого шкільного віку будуть менш +довговічними, ніж для старшого [70]. +Виділяють малий (до 2 років), середній (до 5–10 років) та великий +(до 20 років і більше) термін служби видань [35]. +За терміном використання також розрізняють видання для три- +валого, разового та разового тривалого користування. Видання для +тривалого користування можуть неодноразово перечитуватися од- + +70 +ним чи кількома читачами впродовж великого проміжку часу. На- +приклад, мистецькі видання, літературна класика, вузькопрофільні +видання. Видання для разового використання актуальні недовготри- +валий період, зазвичай використовуються лише один раз та втрача- +ють своє функціональне призначення. До таких видань належать +програми святкових заходів, концертів, конференцій тощо. Видання +для разового тривалого користування призначені для читання одним +користувачем один раз протягом відносно тривалого часу, після чого +можуть бути використані іншим читачем за тим самим принципом. +Сюди відносяться навчально-методичні матеріали, зокрема методич- +ні вказівки, робочі програми тощо [70]. +Інтенсивність експлуатації визначається числом подвійних пере- +гинів елементів книги. Чим більша кількість перегинів, тим вищою +є інтенсивність експлуатації. Розрізняють малу та велику інтенсив- +ність. При чому вона не залежить від терміну служби, адже, напри- +клад, при малому терміні службі інтенсивність експлуатації може +бути як малою, так і великою [35]. +Тип виробництва. Тип виробництва — багатоскладова характе- +ристика організаційного та технічного рівнів виробництва, яка по- +ширюється на обсяг виробництва, номенклатуру продукції, характер +завантаження робочих місць, випуск однотипної продукції, собівар- +тість продукції та кваліфікацію робітників. Іншими словами, це рі- +вень постійного завантаження робочих місць однотипною роботою. +Розрізняють такі типи організації виробничого процесу: одиничне, +серійне, масове та змішане. +Одиничне виробництво характеризується високою собівартістю +продукції, тривалим терміном виробництва, великою часткою руч- +ної праці та відсутністю закріплених операцій за робочими місцями. +Впроваджується при наявності великої кількості номенклатур при +невеликих тиражах, зазвичай для випуску книг на замовлення (Book +on Demand). +При серійному виробництві виготовляється обмежений асор- +тимент продукції, тобто робота проводиться з певними партіями. +Характеризується значною механізацією праці, паралельно-послі- +довним переміщенням предметів праці, закріпленням періодично +повторюваних операцій за визначеними робочими місцями, великою +номенклатурою, однак меншою, ніж при одиничному виробництві. +Собівартість книжкової продукції також нижча, ніж при одиничному +виробництві. Буває дрібно-, середньо- та великосерійне виробництво. + +71 +Масове виробництво характеризується виготовленням книжко- +вої продукції великими накладами на вузькоспеціалізованих робочих +місцях. Характерною є висока механізація, автоматизація виробни- +чого процесу та значно нижча собівартість продукції. Можливе ви- +користання потокових ліній [38]. +Матеріали. Основними матеріалами, характеристики яких врахо- +вуються при проєктуванні післядрукарських процесів, є вид і параме- +три паперу, на якому друкується наклад; палітурні матеріали; матері- +али для скріплення книжкових блоків; оздоблювальні матеріали та ін. +Загальними для всіх видів паперу є такі вимоги: +– достатня механічна міцність; +– незасміченість; +– однорідність товщини, щільності та структури в межах однієї +партії та всередині кожного аркуша; +– вологість 6–8 %; +– чітка прямокутна форма аркушів (допустимі відхилення косини +не більше 2 мм). +Будову та структуру паперу характеризують такі параметри, як +товщина, маса квадратного метра, щільність, пористість. +Товщина є основною характеристикою, що впливає на механічні +та оптичні властивості паперу. Папір товщиною від 0,03 до 0,25 мм +використовують для друкування (зазвичай 0,07–0,1 мм). Матеріал із +більшою товщиною, але до 3 мм називається картоном. Товщина па- +перу визначає масивність видання та його економічні показники. Для +прикладу, від товщини корінця книги залежать витрати палітурних +матеріалів. Чим тонший папір, тим компактніший книжковий блок. +Ще одним важливим показником характеристики паперу є маса +квадратного метра, яка пропорційна середній товщині паперу. Для +друкування використовують папір масою від 30 до 250 г/м2. Матеріал +масою більше 250 г/м2 називають картоном. Сорти паперу однакової +маси можуть мати різну товщину та щільність. +На щільність паперу впливає кількість наповнювача, ступінь +розмелу волокон, каландрування паперу тощо. Для друкування ви- +користовують папір щільністю від 0,5 до 1,35 г/м2. Щільність паперу +пов’язана з його пористістю. +Пористість — це ступінь присутності порожнин у міжволокнис- +тому просторі паперу. Чим більша пористість, тим вища вбирна здат- +ність паперу та, відповідно, швидкість всотування фарби. Однак при +значній пористості зменшується контрастність друкарських відбитків. + +72 +Неоднорідність структури пов’язана з технологічними особливос- +тями виготовлення паперу і спостерігається між поперечними і по- +здовжніми волокнами. Поперечному напрямку притаманні менша +цупкість, більше розширення структури при зволоженні (ніж видо- +вження структури при зволоженні у поздовжньому напрямку). Ви- +значення напрямку паперу здійснюється за допомогою дослідження +на надрив, де при перпендикулярному розриві аркуша в поперечно- +му напрямку виникає рваний надрив, а в поздовжньому — гладкий. +Також різниться лицевий та зворотній бік паперу. Лицевий бік глад- +кіший, адже при виготовленні зворотній бік контактує з сіткою. Ці +особливості важливі не лише при друкуванні, а й при брошуруваль- +но-палітурних процесах. Наприклад, фальцювання краще відбува- +ється вздовж напрямку відливу. Для уникнення поперечних складок і +хвилеподібності поверхні блоку напрям волокон для книжкового ви- +дання повинен бути паралельним корінцю блоку. +Важливим показником характеристики поверхні паперу є глад- +кість. Чим вища гладкість, тим краща якість віддрукованих зобра- +жень, тому для друкування високоякісних ілюстраційних видань ви- +користовують гладкий крейдяний папір. +До механічних властивостей паперу належать міцність та дефор- +мація. Міцність — це здатність паперу чинити опір руйнуванню під +дією механічних сил. Властивості міцності та деформації залежать +від складу та структури: наявності наповнювача, поверхневої про- +клейки, ступеня розробки рослинних волокнистих напівфабрикатів +та каландрування, вологості паперу. При дослідженні міцності папе- +ру послуговуються такими характеристиками: міцність на розрив і +видовження, міцність на згин, міцність на надрив, міцність поверх- +ні до стирання. Деформація паперу виникає під дією навантаження. +Розрізняють зворотну (зникає при відсутності тиску) та незворотну +(залишається після припинення навантаження) деформацію. Кожна +з них використовується для певних цілей, наприклад, при тисненні на +палітурці потрібно, аби рельєф залишався, а не зникав з часом, а при +високому друку — навпаки. За характером деформація поділяється на +пружну, еластичну та пластичну. Пружність — це властивість, що до- +зволяє паперу змінювати свою форму під час дії механічних сил, а піс- +ля припинення цієї дії миттєво відновлювати початкову форму. Елас- +тичність дозволяє поступово відновлювати форму після припинення +дії механічних сил. Пластична деформація є незворотною, адже папір +не може відновити свою початкову форму після усунення напруги. + +73 +До оптичних властивостей паперу належать білизна, глянець, про- +зорість, світлопроникність. Білизна — здатність паперу рівномірно +відбивати світло, характеризується коефіцієнтом відбивання (відно- +шення кількості відбитого світла поверхнею паперу до кількості світ- +ла, що падає на цю поверхню). В цілому білизна паперу коливається +від 60 до 98 %, а оптимальною для читання вважається від 70 до 80 %. +Глянець — частково дзеркальне відбивання світла від поверхні. За +цим показником папір буває глянцевим (глянець може доходити до +75–80 %) і матовим (до 30 %). Прозорість — один з випадків світло- +проникності, який визначає здатність паперу пропускати крізь себе +світло без розсіювання. Зазвичай це негативне явище, яке призводить +до видимості надрукованого на зворотному боці паперу. +Друкарський папір поділяється на групи за певними ознаками: +– призначенням: для офсетного, високого, глибокого способів +друку; +– форматом: аркушевий, рулонний; +– видом друкарської продукції: книжково-журнальний, газетний, +картографічний та ін.; +– волокнистим складом; +– масою метра квадратного тощо. +Класифікація паперу у різних країнах відрізняється [19]. +Картон у поліграфії використовується для виготовлення палітурок +(палітурний картон), суцільнокартонних обкладинок (кольоровий +пресшпан), упаковки різного виду (крейдяний хром-ерзац коробко- +вий). Також використовують гофрований картон. Поверхня палітур- +ного картону повинна бути гладкою, рівною, нежолобленою, без плям +і складок. Є чотири марки палітурного картону: А (для ручного та ме- +ханічного виготовлення палітурок, для виготовлення палітурок з при- +клеєним ззовні покривним матеріалом), Б (для виготовлення футлярів +книг, палітурок до малоформатних видань, палітурок з приклеєним +ззовні покривним матеріалом), В (для виготовлення суцільнокартон- +них палітурок типу 6 без поверхневої проклейки), Г (для виготовлення +палітурок з приклеєним ззовні покривним матеріалом) [19]. +Форзацний папір використовується для виготовлення форзаців. +Щільність форзацного паперу становить 900 кг/м3, а ступінь проклей- +ки 1 мм. Якщо вказані показники вищі спостерігається ускладнення +фальцювання, погіршення сприйняття клею та скручування. Неба- +жаною також є підвищена пористість, що призводить до надмірного +намокання при склеюванні. Неоднорідність щільності спричиняє жо- + +74 +лоблення, утворення пухирців та зморшок. Недостатня міцність уне- +можливлює задруковування. При намащуванні клеєм деформація і на- +хил до скручування повинні бути мінімальними. В цілому форзацний +папір повинен бути достатньо міцним на згин та розрив, адже забезпе- +чує довговічність видання. Форзацний папір поділяється на дві марки: +А (для незадрукованих форзаців) та О (для багатофарбових форзаців). +Для виготовлення обкладинок та обклейки палітурок використо- +вують обкладинковий папір трьох марок: А (глазурований), Б (ма- +товий), В (містить волокна деревної маси та поступається міцністю +маркам А та Б). Такий папір не повинен змінювати розмір при зволо- +женні і повинен мати високу міцність на розрив і згин. +Папір для відставу має масу 210 г/м2. Повинен бути пружним, +щільним, цупким, не ламким. +Для склеювання корінця книжкового блоку використовують міц- +ний, непроклеєний та неглазурований папір, який добре сприймає +клей. +Покривні матеріали повинні відповідати таким вимогам: +– мати високу міцність на надрив, розрив та стирання; +– мати достатню щільність, аби глибоко не всмоктувати клеї та +фарби; +– витримувати багаторазові згини впродовж тривалого часу; +– бути водо- та світлостійкими; +– сприймати друкарські фарби та тиснення фольгою; +– мати естетичний вигляд тощо. +Основними властивостями палітурного матеріалу є колір, яскра- +вість, художньо-технічні елементи, що визначаються призначенням +та змістом видання. За видом основа покривних палітурних матеріа- +лів може бути ткана, паперова та неткана [19; 35]. +Зазвичай як тканеву основу покривних палітурних матеріалів +використовують міткаль — міцну тканину простого полотняно- +го переплетення, що слугує основою для виготовлення палітурного +коленкору й ледерину. Також можуть використовувати дук (сильно +апретована, товста бавовняна тканина, з рідким полотняним пере- +плетенням; призначена для виготовлення суцільнотканинних оправ +високохудожніх видань), рогожку (міцна, груба бавовняна тканина, +з рідким полотняним переплетенням, зафарбована у природні кольо- +ри волокон; призначена для виготовлення суцільнотканинних оправ +високохудожніх видань) та шифон (міцна і тонка шовкова тканина; +використовується для приклейки форзаца та як стержні для вкле- + +75 +йок). Коленкор — це бавовняна тканина полотняного переплетення, +що просочена розчином з крохмального клею, каоліну та барвника. +Коленкор не використовують для видань із тривалим терміном ко- +ристування, адже швидко брудниться, а від надмірної вологості може +пліснявіти та загнивати. Ледерин — це палітурний матеріал з нітро- +целюлозним покриттям, який виготовляється на основі міткалі з +просоченням крохмально-каоліновим розчином і нітроцелюлозним +покриттям на лицевому боці. Йому властива міцність, водостійкість, +світло- і термостійкість, стійкість до згинання. Ззовні нагадує шкіру. +Має підвищену жорсткість, тож вимагає використання дуже липкого +клею. З часом спостерігається старіння цього матеріалу, що призво- +дить до підвищення жорсткості, крихкості та руйнування згинів. +До покривних матеріалів на паперовій основі належать: ледерин +на папері, папвініл, тевін та ін. Ледерин на папері — це міцний ізо- +ляційний папір, що виготовляється з волокон небіленої сульфатної +хвойної целюлози, покритий шаром нітроцелюлозної сульфатної +плівки. Значно дешевший, ніж ледерин на тканевій основі. Зазвичай +застосовується для виготовлення палітурок малоформатних видань. +Папвініл — це матеріал з полівінілхлоридним покриттям, що має ви- +соку водостійкість, міцність до стирання і згинання, однак з часом +може розтріскуватися. Зовні подібний до шкіри. Тевін — покривний +матеріал з вініловим покриттям, має широку колірну гаму та витри- +мує понад 2000 подвійних згинів. +До покривних матеріалів на нетканій основі належать: неткор, сін- +тоніт, сканвініл, ламінар, маленіт. Неткор покритий крохмально-као- +ліновим покриттям, а його нетканева основа складається зі склеєних +між собою лавсанових і віскозних волокон. Використовується для ви- +готовлення палітурок масових видань. Сінтоніт покритий нітроцелю- +лозою, зовні подібний до ледерину, використовується для виготовлен- +ня палітурок об’ємних видань. Сканвініл покритий полі хлорвінілом, +за властивостями нагадує папвініл, використовується для оформлен- +ня палітурок цінних видань. Ламінар — дубльований палітурний мате- +ріал, який складається з несклеєних нетканих та паперових полотен, +використовується для виготовлення палітурок художніх та наукових +видань. Основа маленіту виготовляється з нетканого нітроцелюлозно- +го полотна з відходів низькосортної бавовняної пряжі. +Виділяють також покривні матеріали без основи — пластмасова +плівка товщиною від 0,2 до 0,45 мм, яку використовують для виготов- +лення паперо-білових товарів, а не книжкових видань. + +76 +Для виготовлення оправ ювілейних та подарункових альбомів +можуть застосовувати шкіру. Це ефектний, однак дорогий матеріал. +Найчастіше використовують гладку козячу шкіру товщиною від 0,4 +до 1 мм — сап’ян. Окрім звичайного, буває ще левантський сап’ян — +зі шкіри гірського козла. Сап’ян з тисненням на лицевому боці нази- +вають шагреневою шкірою. Також застосовують товсту, м’яку телячу +шкіру (опойок) та шкіру жирового дублення, що отримують зі шкір +лосів, оленів, овець та диких кіз (замшу) [19]. +Для скріплення книжкових блоків використовують дріт, нитки, +термонитки, марлю, каптал, матеріал для обклейки корінців, клеї +тощо. +Для скріплення ушивкою застосовують дріт поліграфічний або +стальний низьковуглецевий загального призначення, іноді — латун- +ний дріт. Для видань, скомплектованих вкладанням і масою папе- +ру основного тексту до 80 г/м2 діаметр дроту варіюється в межах від +0,4 до 0,7 мм залежно від товщини блоку. Якщо маса паперу більша +80 г/ м2, то діаметр дроту від 0,45 до 0,7 мм. Маса 1000 м дроту зале- +жить від діаметру дроту і обирається в межах від 5,9 до 39,45 кг. При +шитті дротом в рознім можуть використовуватися бавовняна полігра- +фічна марля НШ та дротяні скоби кількістю від 2 до 4 шт, залежно від +висоти видання. Під час шиття вшиттям дроту використовують від 2 +до 3 скоб (залежно від висоти видання) з товщиною дроту від 0,4 до +0,85 мм (залежно від товщини корінця). Шиття дротом зустрічними +скобами передбачає розміщення скоб на відстані не менше ніж 5 мм +одна від одної. +Стальний дріт, що використовується у поліграфії, повинен мати +однакову товщину, гладку блискучу поверхню, бути м’яким та гнуч- +ким. Для уникнення корозії дріт можуть покривати тонким шаром +міді, олова, цинку або лаку. +Для зшивання зошитів також застосовують бавовняні нитки, син- +тетичні та термонитки. Бавовняні нитки складаються з шести скру- +чених між собою ниток, просочених крохмальними речовинами. +Вони мають стабільні властивості, практично не плутаються, не об- +риваються, не розрізають папір під час зшивання. Синтетичні нитки +удвічі міцніші за бавовняні, хоча й значно тонші та економічніші, од- +нак дорожчі та можуть різати папір при зшиванні, плутатися та роз- +тягуватися. Майже не обриваються та не торочаться. Виготовлені з +поліамідних полімерів. Бавовняні та синтетичні нитки іноді поєдну- +ють. Термонитки застосовують для скріплення блоків у корінцевих + +77 +фальцах. Вони виготовлені з віскозного шовку, покритого поліпропі- +леном. Використання термониток уможливлює автоматизацію бро- +шурувально-палітурних процесів [19; 35]. +Поліграфічна марля — це бавовняна тканина з рідким полотняним +переплетенням. Виробляється двох марок: НШ та БО. Марля НШ за- +стосовується для шиття ниткошвейними машинами. Є добре апре- +тованою та просоченою клеєм, що забезпечує достатню жорсткість. +Марля БО характеризується меншою жорсткістю та використовуєть- +ся для наклеювання корінця у блокообробних агрегатах. Попри неви- +соку міцність вона значно зміцнює корінець. Замінником марлі БО +може бути мікрокрепірований папір [19]. +Для наклеювання видань на корінець у блокообробних агрегатах +та для окантовки корінця при безшвейному клейовому скріпленні чи +скріпленні термонитками можуть використовувати мікрокрепірова- +ний папір. +В обклеювально-каптальних машинах і агрегатах для обклейки +корінця використовують папір з сульфатної целюлози масою від 60 +до 80 г/м2. +Для видань обсягом понад 10 аркушів використовують каптал, +який являє собою стрічку шириною від 13 до 15 см з потовщеним кра- +єм в 1,5–2 мм і виготовляється тканням різнокольорових шовкових, +напівшовкових та бавовняних ниток [19; 35]. +При виготовленні поліграфічної продукції також застосовують +клеї, які повинні легко і рівномірно розмащуватися, добре змочувати +матеріал, мати високу швидкість скріплювання, бути світлими, щоб +не залишати плям, не вступати в хімічні реакції з матеріалами, що +скріплюються, не пліснявіти, не старіти та ін. Усі палітурні клеї поді- +ляються на групи: водяної дисперсії (латексний, ПВАД та ін.), водя- +них клейових розчинів (кістковий, крохмальний, декстриновий), тер- +мопластичних полімерів (термоклеї), у вигляді розчинів у органічних +розчинниках, термореактивні клеї. До клеїв рослинного походження +належать крохмальний та декстриновий клеї. Клеями тваринного по- +ходження є кістковий, казеїновий. Синтетичні клеї: полівінілацетат- +ний, епоксидний, латексний на основі бутадієнстирольного каучуку, +карбоксиметилцелюлозний, термоклей, клеї у вигляді розчинів у ор- +ганічних розчинниках. В цілому вибір клею залежить від характеру +поліграфічного матеріалу та умов склеювання. Для прикладу, при +склеюванні пористого паперу доцільно застосовувати в’язкий клей, а +для приклеювання пружного покривного матеріалу — більш липкий. + +78 +Для заклеювання корінця можна використати палітурні клеї з хоро- +шою еластичністю та високою міцністю клейової плівки [19]. +У подарункових чи мистецьких виданнях часто використовують +лясе — закладку у вигляді шовкової стрічки шириною від 3 до 8 мм, +зазвичай червоного кольору. Також лясе може бути виготовленою +з товстого паперу чи пластмаси, мати орнамент чи медальйон. +Для оздоблення палітурних матеріалів здійснюють тиснення палі- +турною фольгою, лакування, припресовування плівки. +Палітурна фольга використовується для нанесення кольорово- +го чи металевого зображення шляхом тиснення. Фольга може бути +на паперовій або лавсановій основі, є багатошаровим матеріалом. +Буває кольорова, бронзова, «ювілейна» та голографічна. Кольорова +фольга буває різних кольорів та відтінків, що уможливлює втілення +найрізноманітніших ідей оформлення поліграфічної продукції. Її по- +верхня буває матовою та глянцевою. Відбитки є стійкими до впливу +зовнішніх факторів. Тиснення бронзовою фольгою візуально нага- +дує тиснення золотом, однак з часом тьмяніє, тож рідко використо- +вується. «Ювілейній» фользі притаманний хороший блиск, який не +тьмяніє з часом. Вона міцно тримається на палітурному матеріалі. +Завдяки розсіювання відбитого світла голографічна фольга створює +ефект об’ємності зображення. За іншими властивостями нагадує +«ювілейну». При виборі фольги слід враховувати її сумісність з інши- +ми. Фольга, виготовлена на водяних розчинах, не буде друкуватися +по фользі, що виготовлена на спиртових розчинах. На якість відбит- +ків впливають: питомий тиск; температура штампа; швидкість та час +тиснення; вид, характер та вологість покривних матеріалів; характер +та площа друкарських елементів штампа; відповідність адгезійного +шару фольги поверхні друкарського матеріалу; вид і товщина матері- +алу декеля [19; 34; 35]. +Лакування служить для додаткового оздоблення поліграфічної +продукції, захисту від стирання, підвищення міцності та довговічнос- +ті. За призначенням лаки поділяються на: ґрунтувальні (створюють +адгезійний шар для подальшого нанесення іншого лаку чи фарби), +матові, глянцеві, підвищеної стійкості до стирання, для термозва- +рювання за допомогою ультразвуку, для термозварювання за допо- +могою мікрохвильових пристроїв, для полегшення або ускладнення +руху задруковуваного пакувального матеріалу, для каландрування, +спеціального призначення. Лакове покриття може наноситися як +на сухий, так і на мокрий відбиток на лакувальних машинах або в + +79 +лакувальних секціях. Для цього застосовують такі типи лаків: дру- +карські (на масляній основі), дисперсійні, лаки ультрафіолетового +закріплення, лаки на основі летких розчинників. Друкарські лаки +містять смоли, льняну оліфу, алкіди, сикативи та ін. і закріплюються +вибірковим всмоктуванням та окислювальною полімеризацією нена- +сичених сполук. Головними компонентами дисперсійних лаків є по- +лімери на основі стирола-акрилата. Закріплення відбувається через +всмоктування і випаровування води, у зв’язку з цим окремі полімерні +частинки зближуються і, внаслідок зростання капілярного тиску, мі- +крочастинки з’єднуються в однорідну плівку. Лаки ультрафіолетового +закріплення поділяються на такі види: радикального і катіонного за- +кріплення (за вийнятком лаків, що накладаються офсетним спосо- +бом зі зволоженням — засобами радикальної полімеризації). Лаки на +основі летючих розчинників закріплюються шляхом випаровування +спирту. Основними недоліками цих лаків є надмірна липкість та ви- +сокий рівень забруднення навколишнього середовища. +Припресовування плівки підвищує вологостійкість матеріалу, +міцність, довговічність, надає блиску та естетичного вигляду. Для +оздоблення покривних матеріалів застосовують синтетичні полі- +мерні плівки, які повинні бути міцними, безбарвними, прозорими, +еластичними, не призводити до скручування та жолоблення відбит- +ку, якнайменше деформуватися в процесі старіння, мати рівномірну +товщину. Виокремлюють три способи припресовування плівки: кле- +йовий, безклейовий, спосіб перенесення. Клейовий спосіб полягає у +нанесенні на плівку тонкого клейового шару, який висихає під дією +інфрачервоних променів. Потім плівка розігрівається разом з відбит- +ком і припресовується до нього. Таким способом оздоблюють видан- +ня в обкладинках типів 1, 2, 3, 4 та у палітурках типів 6, 7, 8, 9, а також +суперобкладинки. При цьому використовують ацетилцелюлозні, по- +ліпропіленові, поліетилентерефталатні плівки та клеї (розчин полі- +мерів у летких органічних розчинниках), латекси (водяні дисперсії +полімерів). Вид і склад клею обирається залежно від плівки та паперу. +Припресовуванням плівки безклейовим способом називається про- +цес з’єднання поліграфічної продукції з термопластичними поліме- +рами чи плівками (поліетилтерефталатними, поліамідними, цело- +фановими та ін.) із нанесеним заздалегідь клейовим шаром. Плівка +нагрівається, підплавляється і припресовується до поверхні матеріа- +лу. Такий спосіб використовується для оздоблення видань у палітур- +ках типу 5, 7, 8, 9. За способом перенесення на відбиток наноситься + +80 +прозора плівка (поліетилентерефталатна) на основі. Згодом основа +відділяється та може бути використана повторно. Цей спосіб вико- +ристовують для оздоблення обкладинок та суперобкладинок [19; 35]. +Тип обладнання. На основі ключових характеристик видання та +схеми технологічного процесу здійснюється вибір обладнання. +Для кожної операції може бути обране специфічне обладнання. +Також обладнання може бути універсальним, з можливістю зміни на- +лаштувань. +Для розрізування і підрізування паперових аркушів чи палітурних +матеріалів використовують одноножеві паперорізальні машини. При +відсутності спеціалізованого устаткування вони можуть також ви- +користовуватися для обрізування книжкових блоків з трьох сторін. +В цілому поділяються на три категорії: малі (ширина стопи до 70 см), +середні (до 90 см), великі (більше 90 см). Також існують два способи +різання: марзанний (ніж у кінці руху врізається у пластмасову деталь, +розташовану нижче стопи, — марзан) і безмарзанний (для розрізуван- +ня використовується ніж та контрніж). Одноножеві різальні машини +характеризуються такими параметрами: довжина різу, мінімальна +та максимальна відстань від площини подавача до лінії різу, шири- +на переднього стола, зусилля тиску притискача, швидкість роботи, +мінімальна та максимальна швидкість подавача, пружність голов- +ного приводу, відстань від підлоги до поверхні стола, маса машини. +В якості допоміжних пристроїв паперорізальних машин можуть бути: +«повітряна подушка» (пневматична система для полегшення ручного +пересування або повороту стопи), гідравлічні стопопідйомники, при- +стрій для заміни ножа, система вилучення обрізків тощо. Також ви- +користовують велику кількість пристроїв для механізації допоміжних +операцій з підготовки стопи. +Фальцювання аркушів можливе вручну, однак найчастіше цю опе- +рацію виконують механізовано. Фальцювальні машини поділяються +на чотири групи: ножові, касетні, комбіновані, спеціальні. У касет- +них машинах фальцювання відбувається за допомогою касет з упо- +ром і рухомих валиків. Ножове фальцювання складається з чотирьох +етапів: попереднього рівняння, бічного рівняння, утворення петлі за +допомогою ножа, обтискання валиками місця згину. Ножові фальц- +апарати використовуються зазвичай в комбінованих фальцювальних +машинах. Комбіновані машини мають ножеві та касетні фальцапара- +ти: перший згин утворюється в касетній фальцсекції, а всі решта — в +ножевих. Спеціальні фальцмашини використовують для фальцюван- + +81 +ня стосу з 10–15 аркушів, при цьому весь папір згинається за один +удар. В цілому фальцмашини складаються з самонакладу, привода, +контрольно-блокувальної системи, пневматичної системи. +Пресування та пакування зошитів може здійснюватися за допомо- +гою пакувально-обтискних пресів, які можна поділити на такі групи: +пакувально-обтискні преси для обтискування та обв’язування сфаль- +цьованих аркушів, блокообтискні преси для обтискування книжкових +блоків та корінців, палітурно-обтискні преси для обтискування книг. +Для автоматизації приклеювання форзаців, ілюстрацій, дробових +частин зошита та інших додаткових елементів використовують при- +клеювальні автомати. Для обкантування зошита з приклеєними фор- +зацами — обкантовувальні автомати. Також автомати можуть бути +комбінованими: спочатку виконують приклеювання, а потім обкан- +товування. +Для комплектування блоків вкладанням використовуються вкла- +дально-швейні або вкладально-швейно-різальні автомати. Комплек- +тування блоків підбиранням здійснюється на аркушепідбиральних +машинах, які повинні забезпечувати послідовність, комплектність +зошитів і хороше зіштовхування [35; 75]. +Для шиття блоків дротом використовують дротошвейні машини: +операційні, вкладально-швейні, підбирально-швейні, а також дро- +тошвейні секції вкладально-швейно-різальних агрегатів. +Для шиття блоків нитками застосовують ниткошвейні машини, +які можуть бути автоматичними (усі операції виконуються без участі +обслуговуючого персоналу) та напівавтоматичними (зазвичай меха- +нізовані усі операції крім подачі та розкриття зошитів), універсальни- +ми (можуть виконувати брошурне і палітурне шиття різними видами +стібків на корінцевому матеріалі і без нього, призначені для видань +різних форматів) та спеціалізованими (розраховані на шиття простим +брошурним стібком без марлі видань обмеженого формату). +Залежно від технології, машини безшвейного скріплення можуть +включати такі основні вузли та пристрої: пристрій введення блока в +затискачі транспортера, вирівнювальний пристрій, фрезерна секція, +торшонувальна секція, клейовий апарат для нанесення клею на ко- +рінець книжкового блока, клейовий апарат для нанесення смужки +клею на бокові зошити блока, сушильний пристрій, охолоджуваль- +ний пристрій, секція подачі і приклеювання обкладинки, обканту- +вальна секція, обтискуючий пристрій, пристрій виведення блока з +машини, транспортувальний пристрій [75]. + +82 +Фальцювання і шиття термонитками відбувається на фальцюваль- +ному автоматі, який можна підключати до касетних і комбінованих +фальцмашин. +Заклеювання корінця книжкового блоку може проводитися на +різному обладнанні, наприклад, на блокозаклеювальному верстаті +неперервної дії [35; 76]. Сушіння корінців рекомендовано проводи- +ти в спеціалізованих сушильних пристроях, конвекційним способом +(повітря кімнатної температури або нагріте, що подається вентилято- +рами), радіаційно-конвекційним способом (теплоносієм є повітря та +електромагнітні хвилі інфрачервоного і видимого діапазонів), опро- +міненням. Після сушіння здійснюється обтискування корінців у пре- +сах з гідравлічним приводом пресувальної колодки [35]. +Обрізування книжкових блоків з трьох сторін зазвичай відбува- +ється на спеціальних різальних машинах, які можна поділити на такі +види: одноножеві з поворотним столом, триножеві однопозиційні, +для поштучного обрізування блоків. +Оздоблення корінця здійснюється на потокових лініях зі спеці- +альними секціями або на поопераційному обладнанні. Верстат для +зафарбовування обрізів зазвичай складається з самонакладу, секції +зволоження обрізів, секції зафарбовування обрізів, сушильного при- +строю, приймального транспортеру. Золочення обрізів проводиться +тисненням спеціальної фольги на обладнанні, у якому обріз блока +шліфують, полірують, при потребі ґрунтують і припресовують фольгу +за допомогою нагрітого валика з термостійкої гуми. +Закруглювання корінця блока здійснюється на закруглювальних +машинах, в секціях блокообробних агрегатів потокових ліній, на за- +округлювально-відгинальних автоматах. Після закруглювання корін- +ця блок передається на відгинання фальців [35; 76]. +Приклеювання лясе на великих підприємствах проводиться на +спеціалізованих автоматах, які можна підключати до потокової лінії, +призначеної для оброблення видань покращеного типу. Приклею- +вання капталів, паперової смужки і корінцевого матеріалу може від- +буватися вручну, на напівавтоматах, на блокообробних агрегатах і ав- +томатах [35]. +В цілому для заклеювання та сушіння, кругління корінців, відги- +нання фальців, приклеювання до корінця зміцнювальних елементів +можуть використовувати найрізноманітніше устаткування: опера- +ційні машини, що призначені для виконання лише однієї операції +(заклеювальний верстат, блокообтискний прес, закруглювальний + +83 +верстат тощо), машини для двох операцій (заклеювально-сушиль- +ні, закруглювально-каширувальні тощо), агрегати для трьох і більше +операцій, потокові лінії [76]. +Для розрізування задрукованої та незадрукованої аркушевої та +рулонної продукції, паперу, картону, палітурних та обкантувальних +матеріалів, марлі, полімерної плівки застосовують заготівельно-роз- +крійне устаткування: аркушерізальні, картонорізальні, картонороз- +крійні, бобінорізальні, тканинорозкрійні машини. +Палітурки можуть виготовляти вручну, напівмеханізованим і ме- +ханізованим способом на палітуркоробних машинах. Сучасні палі- +туркоробні машини є повністю автоматизованими і потребують втру- +чання оператора лише для нагляду за процесом, переналагодження +машини на новий тирах палітурок, подання заготовок або заміни +бобін відставу, прийняття готової продукції. Більшість машин при- +значені для виготовлення суцільнокритих палітурок. Палітуркороб- +ні машини класифікуються за напрямком технологічного процесу (з +вертикальним, горизонтальним, комбінованим і карусельним ходом +технологічного процесу), за характером руху напівфабрикату палі- +турки (з періодичним і неперервним рухом), за швидкістю (середньо- +швидкісні, швидкісні, високошвидкісні) [35; 76]. +Преси для тиснення на палітурках зазвичай будуються за тигель- +ним принципом: тиск створюється двома пресувальними плитами, +одна з яких нерухома, а інша має зворотно-поступальний рух. Преси +класифікуються за конструкцією (з горизонтальною і вертикальною +площиною тиснення), призначенням (для опрацювання великих +чи малих тиражів), ступенем механізації (автоматичні, напівавтома- +тичні), принципом будови (тигельні, плоскодрукарські, ротаційні), +технологічним призначенням (легкого і важкого типу). Усі преси, +як правило, складаються з механізму тиснення, станини, фольгопо- +давального механізму, пристрою підігріву штампу, пристрою розмі- +щення палітурки відносно штампу, пристрою регулювання глибини +тиснення, приводу. +Вставляння блока в палітурку відбувається за принципом вер- +тикального переміщення блока знизу вверх. Книговставні машини +складаються з таких механізмів та пристроїв: поштучної подачі бло- +ків, розкриття блока посередині і базування за товщиною і форма- +том, вертикального конвеєра з крилами для транспортування блоків, +клейових апаратів, самонакладу з пристроєм кругління корінця, ба- +зування палітурки перед вставлянням, суміщення блока з палітуркою + +84 +та їх обтиснення, знімання книги з крила і виведення на приймаль- +ний пристрій. Такі машини класифікують за швидкістю (тихохідні, +напівавтоматичні і автоматичні, високошвидкісні), ступенем агрега- +тування (операційні і агрегатовані), конструкцією (з одним і кількома +крилами) [76]. +Після вставляння блоків у палітурки здійснюється пресування і +сушіння книг, штрихування, обгортання суперобкладинкою, комп- +лектування стосів з книг, упаковування книжкової продукції. Пре- +сування книг здійснюється на палітурнообтискних пресах. Штриху- +вальне устаткування поділяється на операційне (використовується +невеликими і середніми підприємствами) і комбіноване. Зазначеного +поширення набули комбіновані пресувально-штрихувальні машини +неперервної і періодичної дії, які працюють разом з книговставни- +ми машинами. Обгортання книг суперобкладинкою здійснюється +вручну з використанням покривної машини або автоматизовано на +спеціальних машинах. Пакування книг буває ручним, механізованим +(із застосуванням комплектувальних, пакувальних і обв’язувальних +машин) і автоматизованим. +У палітурному виробництві також застосовують потокові техноло- +гічні лінії, які мають такі переваги: розташування устаткування по- +слідовно виконанню операцій, синхронізація операцій, оперативна +передача напівфабрикатів за допомогою транспортно-передавальних +пристроїв, періодичність запуску напівфабрикатів на потік, виконан- +ня операцій над ними і виведення з потоку. Потокові лінії класифіку- +ються за однорідністю продукції (сталого та змінного потоку), про- +дуктивністю (синхронного та несинхронного потоку), неперевністю +руху напівфабрикатів (неперервного та перервного потоку), ступенем +автоматизації та механізації (механізовані, комплексно-механізовані, +автоматизовані потокові лінії). +Для лакування можуть використовувати спеціалізовані машини +для лакування всієї поверхні, системи зволоження офсетних ма- +шин для лакування всієї поверхні або окремих ділянок, самостійні +лакувальні секції друкарських машин. Устаткування для припресо- +вування плівки до аркушевих матеріалів називають ламінаторами +[35; 76]. +Технологічні та економічні розрахунки. За відповідними формулами +визначаються необхідна кількість матеріалів, розмір деталей, термін +експлуатації та ін. Відповідно до економічних розрахунків здійсню- +ється вибір оптимального варіанту виготовлення видання [23, 35]. + +85 +Схема технологічного процесу відображає взаємопов’язану послі- +довність виконання технологічних операцій. Технологічна схема бро- +шурувально-палітурних процесів обирається залежно від технічних +характеристик видання (обсягу, формату, особливостей конструкції, +призначення видання), накладу, очікуваної собівартості та технічно- +го оснащення поліграфічного підприємства. Розрізняють типові та +індивідуальні технологічні схеми. Можлива також адаптація типових +схем, враховуючи конкретні умови проєктування та виготовлення +поліграфічної продукції [35; 56].Основною метою розроблення будь- +якої інформаційної технології є технологізація певного соціально +значимого процесу, тобто цілеспрямований вплив на його перебіг із +використанням комп’ютерно-обчислювальної техніки. Вихідними +даними при цьому є певна недостатньо систематизована інформація. +Високий рівень поділу процесів на етапи, системна повнота, регуляр- +ність та однозначність сприяють його раціоналізації, завершеності, +стандартизації й уніфікації, а, отже, плануванню й прогнозуванню. +Для формалізації наведених знань доцільно розробити онтологію +проєктування післядрукарських процесів. Структура онтології безпо- +середньо впливає на здатність встановлювати оптимальний розв’язок +основної чи побічних задач. Ітеративний підхід до створення полягає +у поетапному навчанні (наповненні) онтології. Можливе постійне +додавання нових класів та зв’язків між ними. У процесі збільшення +моделі виникає необхідність оптимізації шляхом видалення застарі- +лих класів. +Існують декілька основних типів онтологій: +– метаонтології: для опису загальних понять, що не належать до +предметної області; +– онтологія предметної області: формальний опис та визначення +термінологічної бази предметної області; +– онтологія конкретної задачі: визначення термінологічної бази +поставленої задачі; +– мережеві онтології: для опису результатів дії об’єктів предметної +області чи задачі. +Основними принципами побудови онтологій є: +– «формальна онтологія», запропонована Гуаріно, яка містить +теорії частин, цілісності, рівності, залежності, узагальнень та перед- +бачає такі принципи побудови: потреба у розумінні всієї предметної +області, чіткість ідентифікації, класифікація структури, встановлен- +ня ролей; + +86 +– скелетна методологія побудови онтології вручну, запропонована +Усолдом та Грунінґером, яка передбачає: встановлення мети та меж, +побудову онтології, оцінювання, документування, визначення прин- +ципів керування попередніми етапами; +– Ontological Design Patterns (ODPs): для визначення структур, +термінів, семантики. +В загальному побудова моделі складається з кількох етапів: +– нагромадження знань про предметну область; +– декомпозиція: розділення досліджуваного процесу на окремі +елементи, які стануть основою моделі; +– ідентифікація елементів; +– класифікація: визначення класів та елементів, що до них нале- +жать (ієрархія класів); +– опис властивостей; +– присвоєння значень властивостей; +– створення зв’язків; +– розширення та конкретизація онтології; +– перевірка; +– впровадження онтології [33]. +Опис предметної області здійснюється за допомогою класів — +основ них структурних одиниць онтологічної моделі, які можуть місти- +ти інші класи та/або екземпляри. Класи — це загальні поняття, колек- +ції, набори об’єктів. Екземпляри виступають суб’єктами. Зв’язок між +екземпляром і класом, до якого він належить, задається предикатом rdf: +type. Класи в онтології організовуються у таксономію (ієрархічну кла- +сифікацію). Так, для прикладу, Обкладинка та Палітурка є підкласами +класу Вид_покрівельного_матеріалу, який є підкласом Конструкційні_ +особливості: Вид_покрівельного_матеріалу SubClassOf Конструкцій- +ні_особливості, Конструкційні_особливості SubClassOf Проєктуван- +ня_післядрукарських_процесів. Властивості-відношення визначають +існуючі зв’язки між екземплярами. Наприклад: Значний_обсяг Ви- +значає Комплектування_підбиранням. Властивості-дані визначають +конкретні характеристики екземплярів певних класів. Наприклад, для +екземпляра Малий_обсяг класу Обсяг — Кількість_сторінок 64. +Не менш важливими для опису є глосарій та тезаурус. Оформлені +належним чином онтологічні словники сприяють полегшенню по- +дальшого процесу створення онтології [73]. +Для запису завжди істинних тверджень використовують аксіоми. +Редактор Protégé 5 дозволяє використання таких аксіом: аксіоми + +87 +класів (SubClassOf, EquivalentClasses, DisjointClasses та ін.), аксіоми +властивостей об’єкта (SubObjectPropertyOf, EquivalentObjectProper- +ties, InverseObjectProperties, FunctionalObjectProperty та ін.), аксіоми +властивостей даних (SubObjectPropertyOf, EquivalentDataProperties, +DisjointDataProperties та ін.), індивідуальні аксіоми (ClassAssertion, +ObjectPropertyAssertion, DataPropertyAssertion, NegativeObjectPro- +pertyAssertion та ін.), аксіоми анотації (AnnotationAssertion, SubAn- +notationPropertyOf, AnnotationPropertyDomain, AnnotationProper- +tyRange) [78]. +1.4. Функціональне моделювання проєктування післядрукарських +процесів +Проєктування +післядрукарських +процесів +Показники видання +Рівень якості +проєктування +післядрукарських +процесів +Апаратне та +програмне +забезпечення, інші +знаряддя праці +Особовий склад +працівників, експерти з +предметної області, +зацікавлені особи +Альтернативи +реалізації +Умови +експлуа- +таціїї +Нормативно-технічна +та технологічна +документація +Готовий проєкт +Рис. 2. Контекстна діаграма А-0 моделі IDEF0 проєктування +післядрукарських процесів +Використаємо методологію IDEF0 [40; 77] для функціонального +моделювання проєктування післядрукарських процесів. Контекстна +діаграма зображена на рис. 2. При цьому основною функцією сис- +теми є проєктування післядрукарських процесів, а зв’язок системи +із навколишнім середовищем зображується граничними стрілками: +I1 — показники видання, C1 — нормативно-технічна та технологічна +документація, C2 — умови експлуатації, C3 — альтернативи реалізації, + +01CCM1M,88 +O1 — рівень якості проєктування післядрукарських процесів, O2 — го- +товий проєкт, M1 — апаратне та програмне забезпечення, інші зна- +ряддя праці, M2 — особовий склад працівників, експерти з предмет- +ної області, зацікавлені особи. +Проаналізуємо інформаційне навантаження компонент множин +граничних стрілок IDEF0 моделі: +Граничні стрілки типу «Вхід» (Input): +– +1I (показники видання). Ключовими показниками книжкових +видань є вид, тип, формат та обсяг. +Граничні стрілки типу «Контроль» (Control): +– +1 +C (нормативно-технічна та технологічна документація). До +нормативно-технічної та технологічної документації належать: тех- +нічні вимоги та законодавчі положення, зокрема: закони, стандарти, +технічні умови, кодекси усталеної практики та ін. +– +2 +C (умови експлуатації). Умови експлуатації включають термін +та інтенсивність експлуатації готового видання. +– +3 +C (альтернативи реалізації). Парето-оптимальні альтернативи, +визначені оцінюванням нечітких відношень на множині альтернатив. +Граничні стрілки типу «Вихід» (Output): +– +1 +O (рівень якості проєктування післядрукарських процесів). Ре- +зультатом діяльності, спрямованої на створення проєкту, є відповід- +ний рівень якості. +– +2 +O (готовий проєкт). Визначає перебіг усіх технологічних дій, +направлених на реалізацію післядрукарських процесів. +Граничні стрілки типу «Механізми» (Mechanism): +– +1 +M (апаратне та програмне забезпечення, інші знаряддя праці). +Процес проєктування передбачає використання сучасних технічних +та програмних засобів, в тому числі специфічного, вузькопрофільно- +го програмного забезпечення. +– +2 +M (особовий склад працівників, експерти з предметної області, +зацікавлені особи). Проєктування післядрукарських процесів передба- +чає участь висококваліфікованих працівників, обізнаних із тонкощами +реалізації досліджуваних процесів, задля оцінювання вихідних даних +та прогнозування результату. Можливе залучення експертів, зокрема +науковців та зацікавлених осіб (замовників, маркетологів та ін.). +Діаграма першого рівня декомпозиції А0 моделі IDEF0 містить +такі блоки: +– ВКВ (визначення конструкції видання); + +89 +– ВВВ (визначення вимог до готового видання); +– ВПО (визначення послідовності технологічних операцій); +– ВРО (визначення режимів опрацювання). +Діаграма другого рівня декомпозиції А1 моделі IDEF0: +– ВСК (вибір способу комплектування); +– ВСС (вибір способу скріплення); +– ВПМ (вибір покривного матеріалу); +– ПДЕ (проєктування додаткових елементів). +Діаграма третього рівня декомпозиції А2 моделі IDEF0: +– ВВКБ (визначення вимог до книжкового блоку); +– ВВДЕ (визначення вимог до додаткових елементів); +– ВВПМ (визначення вимог до покривного матеріалу); +– ВВО (визначення вимог до оздоблення); +– ВВПБО (визначення вимог до покриття блоку обкладинкою); +– ВВВБП (визначення вимог до вставлення блоків у палітурку); +– ВВП (визначення вимог до пакування). +Діаграма третього рівня декомпозиції А3 моделі IDEF0: +– ВПОБП (визначення послідовності операцій брошурувальних +процесів); +– ВПОПП (визначення послідовності операцій палітурних про- +цесів). +Діаграма третього рівня декомпозиції А4 моделі IDEF0: +– ВРОБП (визначення режимів опрацювання брошурувальних +процесів); +– ВРОПП (визначення режимів опрацювання палітурних процесів). +Етап 2. Синтез моделей факторів проєктування післядрукарських +процесів +2.1. Розроблення семантичної мережі взаємозв’язків між фактора- +ми проєктування післядрукарських процесів +На основі експертних суджень формується деяка множина фак- +торів R={R1, R2, …, Rn}, що вміщає найбільш суттєві фактори. Для +ви окремлення характерних чинників процесу залучаються представ- +ники наукової спільноти та фахівці-практики. Використання екс- +пертного оцінювання дозволяє одержати кількісну оцінку ступеня +важливості кожного з факторів, що формують множину значень чин- +ників впливу на якість виконання процесу. +Зв’язки між визначеними факторами, необхідні для формування +підґрунтя подальшого опису предметної області, кількісного оціню- + +90 +вання їх вагових значень та, відповідно, встановлення домінантності, +визначаються та візуалізуються на основі теорії графів та семантич- +них мереж. Вузли семантичної мережі відображатимуть семантику +понять, тобто факторів, які згодом будуть представлені у вигляді аб- +страктних лінгвістичних змінних. Дуги відтворюють функціональні +(семантичні) відносини чи зв’язки між ними. Поєднання мовознав- +ства (семантика лінгвістичних змінних) та математики (мережі як ва- +ріант графа) забезпечує, з одного боку, використання звичайної мови +для опису бази знань досліджуваного процесу, з іншого — уможлив- +лює застосування формальних методів та нечіткої логіки для дослі- +дження, кінцевою метою якого є прогностичне оцінювання. Вузлами +семантичної мережі стають елементи множини R, а дугами — функці- +ональні зв’язки з певними смисловими навантаженнями (Ri, Rj). +Модель семантичної мережі створює базу для подальшого кон- +структивного опису предметної області, є наочною та інтуїтивно зро- +зумілою, адже є аналогом сучасних уявлень про фізіологічні механіз- +ми пам’яті людини [59]. +2.2. Формалізація з’язків між факторами за допомогою предикат- +них формул +Логіка предикатів є частиною математичної логіки, її формаль- +на мова представлена термами та взаємовідносинами між ними — +преди катами. До термів, як словотвірних елементів, відносять такі +конструкції мови предикатів: константи (конкретні реальні об’єкти), +змінні (узагальнені можливі об’єкти, у нашому випадку фактори), +функції (послідовність констант чи змінних, обмежених круглими +дужками), функтори (оператори перед функцією, що повертають +певне значення після впливу на об’єкт). Предикатом називають ло- +гічну функцію, яка приймає значення «істина», якщо відношення +між її аргументами мають смисл, або «фальш» у противному випадку. +Таким чином використання логіки предикатів полягає у виведенні +усіх зв’язків між факторами, враховуючи структуру семантичної ме- +режі [59; 61; 72]. +Означимо впливи кожного фактора проєктування післядрукар- +ських процесів: +1 +2 +– +R +R — визначає; +1 +3 +– +R +R — визначає; +1 +4 +– +R +R — ви- +значає; +1 +5 +– +R +R — обумовлює; +1 +6 +– +R +R — обумовлює; +1 +7 +– +R +R — фор- +мує; +1 +8 +– +R +R — обумовлює; +2 +5 +– +R +R — визначає; +2 +6 +– +R +R — впливає на +вибір; +2 +7 +– +R +R — формує; +2 +8 +– +R +R — обумовлює; +3 +5 +– +R +R — впливає на +вибір; +3 +8 +– +R +R — обумовлює; +4 +6 +– +R +R — визначає; +4 +7 +– +R +R — формує; + +91 +5 +6 +– +R +R — впливає на вибір; +5 +7 +– +R +R — формує; +6 +7 +– +R +R — формує; +8 +5 +– +R +R — обумовлює; +8 +6 +– +R +R — визначає; +8 +7 +– +R +R — формує. +Для формалізації опису відносин між термами семантичних ме- +реж використано предикатні формули, що включають такі конструк- +ції: ∧ — логічне «і»; ← — «якщо»; ∀ — квантор спільності (для всіх); +∃ — квантор існування (існує принаймні одне) [59]. +( ∀ +iR ) [ ∃ ( +1 +R , показники видання) ← визначає ( +1 +2 +, +R R ) ∧ ви- +значає ( +1 +3 +, +R R ) ∧ визначає ( +1 +4 +, +R R ) ∧ обумовлює ( +1 +5 +, +R R ) ∧ обумовлює +( +1 +6 +, +R R ) ∧ формує ( +1 +7 +, +R R ) ∧ обумовлює ( +1 +8 +, +R R )]; +( ∀ +iR ) [ ∃ ( +2 +R , конструкційні особливості) ← визначає ( +2 +5 +, +R R ) +∧ впливає на вибір ( +2 +6 +, +R R ) ∧ формує ( +2 +7 +, +R R ) ∧ обумовлює ( +2 +8 +, +R R ) +∧ визначається ( +2 +1 +, +R R ) ∧ обирається залежно від ( +2 +3 +, +R R )]; +( ∀ +iR ) [ ∃ ( +3 +R , умови експлуатації) ← впливає на вибір ( +3 +2 +, +R R ) +∧ впливає на вибір ( +3 +5 +, +R R ) ∧ обумовлює ( +3 +8 +, +R R )]; +( ∀ +iR ) [ ∃ ( +4 +R , тип виробництва) ← визначає ( +4 +6 +, +R R ) ∧ формує +( +4 +7 +, +R R ) ∧ визначається ( +4 +1 +, +R R )]; +( ∀ +iR ) [ ∃ ( +5 +R , матеріали) ← впливає на вибір ( +5 +6 +, +R R ) ∧ формує +( +5 +7 +, +R R ) ∧ обумовлюється ( +5 +1 +, +R R ) ∧ визначається ( +5 +2 +, +R R ) ∧ обира- +ється залежно від ( +5 +3 +, +R R ) ∧ обумовлюється ( +5 +8 +, +R R )]; +( ∀ +iR ) [ ∃ ( +6 +R , тип обладнання) ← формує ( +6 +7 +, +R R ) ∧ обумов- +люється ( +6 +1 +, +R R ) ∧ обирається залежно від ( +6 +2 +, +R R ) ∧ визначається +( +6 +4 +, +R R ) ∧ обирається залежно від ( +6 +5 +, +R R ) ∧ визначається ( +6 +8 +, +R R )]; +( ∀ +iR ) [ ∃ ( +7 +R , технологічні та економічні розрахунки) ← форму- +ється ( +7 +1 +, +R R ) ∧ формується ( +7 +2 +, +R R ) ∧ формується ( +7 +4 +, +R R ) ∧ форму- +ється ( +7 +5 +, +R R ) ∧ формується ( +7 +6 +, +R R ) ∧ формується ( +7 +8 +, +R R )]; +( ∀ +iR ) [ ∃ ( +8 +R , схема технологічного процесу) ← обумовлює ( +8, +R +5 +R ) ∧ визначає ( +8 +6 +, +R R ) ∧ формує ( +8 +7 +, +R R ) ∧ обумовлюється ( +8, +R +1 +R ) +∧ обумовлюється ( +8 +2 +, +R R ) ∧ обумовлюється ( +8 +3 +, +R R )] [61]. +2.3. Побудова моделі пріоритетного впливу факторів на якість про- +єктування післядрукарських процесів за методом математичного мо- +делювання ієрархій +Окрім виокремлення необхідних лінгвістичних змінних сучасні +умови виробництва вимагають чіткого розуміння їх пріоритетності. +Саме завдяки ієрархічному впорядкуванню досліджуваних факторів +можна сформувати цілісну картину необхідних технічних та інтелек- +туальних компонент. + +92 +Для встановлення рівнів пріоритетності факторів на основі семан- +тичної мережі використовуємо метод математичного моделювання +ієрархій. Для початку будується матриця досяжності А, бінарні еле- +менти якої визначаються за таким правилом: + +1, +0, +ij +якщо з вершини і можна попасти у вершину j +R +в іншому випадку + +=  + +. +(3) +Досяжність вершини Rj (j=1, 2, …, n) відносно вершини Ri (i=1, +2, …, n) обумовлюється наявністю зв’язку певного типу (прямого чи +опосередкованого). Позначимо підмножину досяжних вершин K(Ri). +При цьому вершина Ri, для якої можлива зворотня досяжність з вер- +шини Rj, буде її попередницею. Сукупність вершин попередниць +формує підмножину P(Ri). Перетин вершин сформованих підмножин +H(Ri)=K(Ri)∩P(Ri), за умови P(Ri)=H(Ri), визначає домінантність дії +факторів, що ототожнюються з цими вершинами та встановлюється +шляхом аналізу так званих ітераційних таблиць. Внаслідок виконан- +ня означених операцій над елементами семантичної мережі отриму- +ємо багаторівневу модель, що відображає домінантність дії факторів +на аналізований технологічний процес [58]. +На основі синтезованої семантичної мережі будується матриця +досяжності за принципом (3). Для зручності відображення матрицю +доцільно поміщати у таблицю, додавши позначення факторів. +Для подальшого встановлення пріоритетності факторів за ма- +трицею досяжності будуються ітераційні таблиці, що міститимуть +чотири колонки, де і — порядковий номер фактора у множині. +При цьому для формування стовпця K(Ri) ітераційних таблиць ви- +користовуємо дані, наведені у рядках матриці досяжності, а для +формування стовпця P(Ri) — дані, наведені у стовпцях цієї матри- +ці. У стовпці K(Ri)∩P(Ri) подамо спільні для K(Ri) та P(Ri) фактори +[58]. На основі отриманих даних синтезується модель пріоритет- +ного впливу факторів на якість проєктування післядрукарських + процесів. +Таким чином, найвищий пріоритет належить фактору R1 (показ- +ники видання), що є логічним з технологічної точки зору, адже вид +і тип видання, формат видання та його обсяг справді є визначаль- +ними при створенні проєкту реалізації післядрукарських процесів. +На другому рівні знаходяться фактори R3 (умови експлуатації) та R4 +(тип виробництва). Третім за пріоритетністю є фактор R2 (конструк- +ційні особливості), четвертим — R8 (схема технологічного процесу), + +93 +п’ятим — R5 (матеріали), шостим — R6 (тип обладнання). Найнижчий +рівень пріоритетності свідчить про підрядний характер фактора R7 +(технологічні та економічні розрахунки). +2.4. Побудова моделі пріоритетного впливу факторів на якість про- +єктування післядрукарських процесів за методом ранжування +Уточнення чи підтвердження пріоритетності факторів проєкту- +вання післядрукарських процесів здійснюється шляхом встановлен- +ня їх рангів за методом ранжування, який полягає у синтезуванні +деревовидних моделей на основі аналізу взаємозв’язків між виокрем- +леними факторами. Слід зазначити, що згадані зв’язки поділяються +на два типи: впливи та залежності, які передбачають прямі та опо- +середковані дії. Така методика дозволяє наблизити візуалізацію до +реальних умов перебігу досліджуваного процесу. При цьому кожному +типу присвоюються відповідні числові показники, що уможливлює +подальше математичне оцінювання. +У дослідженні доцільно враховувати такі означення і твердження. +Означення 1. Будь-який технологічний процес поліграфічного ви- +робництва містить деяку множину факторів, які здійснюють визна- +чальний вплив на якість його реалізації, відповідно й на якість дру- +кованої продукції. +З огляду на те, що кожен процес у поліграфії містить пев- +ну множину факторів, що впливають на його якість, нехай +{ +} +1 +2 +, +,..., +m +D +d d +d += + буде довільною множиною технологічних процесів, +а +{ +} +1 +2 +, +,..., +m +m +m +n +R +r +r +r += + — множиною факторів, що впливають на якість +конкретного процесу, де +m +n — це кількість факторів m -го техноло- +гічного процесу. При цьому: + +( +) +( +) ( +) +1 +, +1,2,..., +, +n +k +jk +j +С S +S +k +m += += +ω += + + +(4) +де ( +) +k +С S + — значення функції якості m -го процесу; ( +) +jk +S +ω + — ваговий +показник додаткової якості, принесеної j -м фактором у k -й техно- +логічний процес. Тоді подамо означення таким чином: + +( +) ( ) +( +) +; +; +. +k +p +r C r +d +D +r +R +∃ +∀ +∈ +∈ + +(5) +Означення 2. Ранг та пріоритет фактора визначається ваговим ко- +ефіцієнтом. Серед будь-якої множини факторів можна виокремити +хоча б один пріоритетний. + +94 +Тобто для множини ваг факторів +{ +} +1 +2 +, +,..., +m +m +m +n +W +w +w +w += +, якщо +( ) +{ +} +1 +2 +, +,..., +m +m +m +n +P w +max w +w +w += +, матимемо: + +( +)( +) ( ); +; +. +p +w P w +d +D w +W +∃ +∀ +∈ +∈ + +(6) +Твердження 1. Існування зв’язків між факторами є передумовою +для їх формалізованого відображення у вигляді графа. +Твердження 2. Облік та аналіз впливів та залежностей між факто- +рами у вихідній графічній моделі, побудованій на основі експертних +суджень, дозволяє визначити початкові ранги факторів. +Твердження 3. При порівнянні факторів у межах вихідного графа +синтезована багаторівнева модель показує лише переваги між ними. +Твердження 4. Виявлення кінцевих вагових значень, які визнача- +ють ранг та ступінь впливу факторів на m -й технологічний процес +поліграфічного виробництва, можливе шляхом створення та обробки +матриці попарних порівнянь і обчислення нормалізованих компо- +нент головного власного вектора матриці. +Означення 3. Множина факторів, упорядкованих за спаданням їх +нормалізованих вагових значень, не містить абсолютно ідентичних за +ступенем впливу на технологічний процес. +Якщо +( ) +1 +j +j +A w +w +w + +> += + для ( +) +1,2,... +1 +j +n += +− +, то вірним буде наступ- +ний запис: + +( +) ( ); +. +w A w +w +W +∀ +∈ + +(7) +Згідно з твердженнями 1–4, синтез моделі пріоритетного впливу +факторів на m -й технологічний процес поліграфічного виробництва +здійснюється шляхом виокремлення характерних для аналізованого +процесу факторів, створення, аналіз та обробку вихідної графічної +моделі, у якій на основі експертних суджень встановлено зв’язки між +факторами. +За основу методу ранжування взято числові показники, які сто- +суються кількостей впливів і залежностей між факторами та відпо- +відних їм вагових коефіцієнтів. При цьому розрізняємо прямі дії, +назвавши їх впливами 1-го порядку, та непрямі — 2-го порядку. За- +лежності також розрізнятимемо, встановивши для них аналогічно +1-й і 2-й порядки важливості. +Для розрахунку сумарних вагових значень прямого та опосеред- +кованого впливів факторів та їх інтегральної залежності від інших +факторів введемо відповідні позначення. Нехай +ijk — кількість впли- + +95 +вів чи залежностей для j -го фактора +1,..., ) +j +n += +; +iw — вага i -го типу. +Ідентифікуємо числові значення індексів наступним чином: +1 +i = для +впливів 1-го порядку, +2 +i = + для впливів 2-го порядку, +3 +i = + для залеж- +ностей 1-го порядку, +4 +i = + для залежностей 2-го порядку. Вважатиме- +мо, що для впливів обох типів ваги будуть додатними, тобто +1 +0 +w > +, +2 +1 / 2 +w +w += +, відповідно для залежностей — від’ємними, а саме: +3 +0 +w < +, +4 +3 / 2 +w +w += +. Нехай +ij +R — інтегральні вагові значення факторів за сума- +ми ваг усіх типів зв’язків. Тоді формула для розрахунків матиме вид: + +4 +1 +1 +, +n +ij +ij +i +i +j +R +q w += += +=∑∑ + +(8) +де n — номер фактора досліджуваного процесу. +Відповідно до початкових умов +3 +0 +w < + і +4 +0 +w < +, отже +3 +0 +j +R +< + і +4 +0 +j +R +< +. Щоб привести вагові значення «до початку координат», тоб- +то отримати додаткові величини, слід перемістити гістограму інте- +грального графічного відображення усіх типів зв’язків вверх за таким +співвідношенням: + +( +) +3 +4 , +1,2,..., +. +j +j +j +max R +max R +j +n +Δ = ++ += + +(9) +На основі заданих умов отримаємо формулу підсумкових вагових +значень факторів: + +( +) +4 +9 +1 +1 +, +Fj +ij +i +j +i +j +R +k w += += += ++ Δ +∑∑ + +(10) +де +( +) +3 +4 , +1,2,..., +j +j +j +max R +max R +j +n +Δ = ++ += + [30; 58]. +Величини +Fj +R служать підставою для ранжування ваг, тобто вста- +новлення рівнів факторів якості реалізації технологічного процесу. +За результатами ранжування здійснюється синтез графічної моделі за +отриманими ваговими значеннями, що відображають пріоритетність +впливу факторів на процес. +Для реалізації методу стосовно кожного з факторів проєктування +післядрукарських процесів на основі розробленої семантичної мере- +жі будуються ієрархічні дерева зв’язків з іншими факторами, врахо- +вуючи прямі та непрямі впливи і прямі та опосередковані залежності +[30; 58; 59]. +За допомогою методу ранжування встановлюються вагові значен- +ня факторів та уточнюється їх пріоритетність. Таким чином фактори +R3 (умови експлуатації) та R4 (тип виробництва), що знаходилися на +одному рівні, отримали відповідно другий та четвертий рівні пріори- + +96 +тетності. При цьому фактор R2 (конструкційні особливості) змістився +на третю позицію у моделі. Пріоритетність інших факторів лише під- +твердилася. +Етап 3. Оптимізація моделі пріоритетного впливу факторів на якість +проєктування післядрукарських процесів +3.1. Формування матриці попарних порівнянь факторів відповідно до +шкали відносної важливості об’єктів за Сааті +Оптимізація вагових значень факторів і синтез моделі здійсню- +ються за методами багатокритеріальної оптимізації та попарних по- +рівнянь. Первинне визначення вагових значень факторів техноло- +гічних процесів на основі методу ранжування передбачає отримання +укрупнених результатів, що потребують подальшого експертного +опрацювання. Метод аналізу ієрархій, реалізований на основі шкали +відносної важливості об’єктів за Сааті, дозволяє встановити уточнені +(оптимізовані) вагові значення та передбачає побудову матриці по- +парних порівнянь, обчислення компонент її головного власного век- +тора та їх нормалізацію, а також перевірку результатів за ключовими +критеріями. Унаслідок оптимізації здійснюється деталізація перебігу +досліджуваного процесу, що позитивно впливає на його подальшу ре- +алізацію. +З цією метою будуємо квадратну обернено-симетричну матри- +цю попарних порівнянь (МПП), порядок якої визначається числом +аналізованих факторів. Алгоритм її організації такий. Порівнюються +умовні міри впливу кожного із факторів першого стовпця матриці до- +сяжності та кожний із факторів верхнього рядка матриці. Додаткови- +ми умовами при порівнянні служать отримані при ранжуванні вагові +значення факторів. На перетині рядка і кожного зі стовпців МПП за- +носимо числове значення переваги фактора, використовуючи шкалу +відносної важливості об’єктів (табл. 5). Так, для двох факторів (напр., +ri і rj), які порівнюються між собою, в залежності від їх важливості та +міри впливу на проєктування післядрукарських процесів матимемо +пропоновані у таблиці значення відповідного елемента матриці по- +парних порівнянь у позиції (ri, rj). Зрозуміло, що при такому алгорит- +мі діагональні елементи МПП рівні одиниці. +Нижня частина матриці попарних порівнянь заповнюється обер- +неними значеннями. Так, у позицію (ri, rj) заносимо відповідно 1, 1/3, +1/5, 1/7, 1/9. При незначних відмінностях між вагами критеріїв ви- +користовують парні числа 2, 4, 6, 8 та їх обернені значення [58; 59; 68]. + +97 +Таблиця 5 +Шкала відносної важливості об’єктів +Оцінка +важливості +Критерії порівняння +Пояснення щодо +вибору критерію +1 +Об’єкти рівноцінні +Відсутність переваги ri над rj +3 +Один об’єкт дещо +переважає інший +Існує підстава наявності +слабкої переваги ri над rj +5 +Один об’єкт переважає +інший +Існує підстава наявності +cуттєвої переваги ri над rj +7 +Один об’єкт значно +переважає інший +Існує підстава присутності +явної переваги ri над rj +9 +Один об’єкт абсолютно +переважає інший +Абсолютна перевага ri над rj +не викликає сумніву +2, 4, 6, 8 +Компромісні проміжні +значення +Допоміжні порівняльні оцінки +3.2. Визначення компонент головного власного вектора матриці по- +парних порівнянь +Головний власний вектор +( +) +1 +2 +, ,..., n +R r r +r + МПП визначається як се- +реднє геометричне компонент кожного рядка матриці: + +1 +2 +1, , +n +i +i +i +in +R +a +a +a +i +n += +⋅ +⋅ += + +(11) +де n — кількість використаних факторів. +Для одержання головного власного вектора (тобто вектора пріори- +тетів) матриці попарних порівнянь використаємо метод, запропоно- +ваний Сааті [55]. Розрахунки за вказаним методом з використанням +ідей теорії імітаційного моделювання здійснюються за допомогою +програми «Імітаційне моделювання в системному аналізі методом +бінарних порівнянь» [57], розробленої на кафедрі комп’ютерних +наук та інформаційних технологій Української академії друкарства. +Після завантаження програми отримуємо інтерфейс у вигляді діало- +гового вікна. Опція «Введіть число критеріїв» обумовлює кількість +факторів, далі — кнопка «задати». «Введіть назви критеріїв» — вво- +димо цифрові номери факторів, кнопка «застосувати». Заповнюємо +таблицю вікна «Задання експертних оцінок переваг критеріїв» еле- +ментами матриці попарних порівнянь, після кнопка «застосувати». +Результати опрацювання — у вікні «Вивід проміжних результатів», +стовпець якого En відтворює компоненти нормалізованого вектора + +98 +R, що ідентифікують розраховані вагові значення факторів досліджу- +ваного процесу. +3.3. Визначення компонент нормалізованого вектора матриці по- +парних порівнянь +Нормалізуємо значення компонент головного власного вектора +n +R МПП [58; 59; 68], встановивши попередній результат розв’язання +задачі: + +1 +2 +1 +2 +1 +1, += +⋅ +⋅ += += +⋅ +⋅ +∑ +n +i +i +in +in +n +n +i +i +in +i +a +a +a +i +n +R +a +a +a +. +(12) +Для зручнішого подання вагових значень факторів множимо +оптимізовані компоненти вектора +n +R на довільний коефіцієнт k . +Нехай +500 +k = +. +Оцінка узгодженості вагових значень факторів обчислюється +шляхом множення матриці попарних порівнянь справа на вектор +n +R . +В результаті обчислення одержимо нормалізований вектор +1 +n +R . +Компоненти власного вектора +2 +n +R + матриці попарних порівнянь +отримаємо, поділивши компоненти вектора +1 +n +R на відповідні компо- +ненти вектора +n +R . +3.4. Аналіз результатів оптимізації за максимальним значенням +головного власного вектора матриці попарних порівнянь, індексом узго- +дженості та відношенням узгодженості +Максимальне власне значення +max +λ + додатної обернено-симетрич- +ної матриці A визначається як середнє арифметичне компонент век- +тора +2 +n +R +. +Оцінка одержаного рішення визначається індексом узгодженості +IU , який вираховується за формулою: + +max +1 +n +IU +n +λ +− += +− +. +(13) +Отримані значення порівнюють з еталонними значеннями по- +казника узгодженості — випадковим індексом RI . Результати можна +вважати задовільними, якщо отримане шляхом обрахунків значення +індекса узгодженості IU не перевищує 10 % еталонного значення +випадкового індекса RI , обраного з урахуванням кількості аналізо- + +99 +ваних факторів. Отже для підтвердження адекватності розв’язку по- +ставленої задачі повинна виконуватися нерівність +0,1 +IU +RI +< +× +. +Нижче наведена таблиця величин випадкового індекса для ма- +триць різного порядку, в якій порядок матриці відповідає кількості +аналізованих об’єктів (факторів) і вказується у першому рядку, а ета- +лонне значення показника узгодженості для кожного порядку вказу- +ється у другому рядку. +Таблиця 6 +Значення випадкового індекса для матриць різного порядку +Кількість +об’єктів +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +Еталонне +значення +індекса +0,58 0,90 1,12 1,24 1,32 1,41 1,45 1,49 1,51 1,54 1,56 1,57 +Додатково результати оцінюють відношенням узгодженості, вели- +чину якого отримують із виразу: RU +IU RI += +. Результати попарних +порівнянь можна вважати задовільними, якщо +0,1 +RU ≤ +. Це свідчи- +тиме про достатній рівень збіжності процесу та належну узгодженість +експертних суджень стосовно попарних порівнянь факторів, відобра- +жених у відповідній матриці. +При незадовільних значеннях індекса узгодженості та відношення +узгодженості треба переглянути вихідний граф зв’язків між фактора- +ми, уточнити значення величин відповідних їм попарних порівнянь, +тобто розв’язати деяку обернену задачу, достовірність розв’язку якої +перевіряється за наведеними вище критеріями. +Цікавими в цьому контексті можуть бути такі міркування. Якщо +максимальне значення власного вектора матриці попарних по- +рівнянь і величина відношення узгодженості не виходять за межі +допустимих значень, то їх можна вважати критеріями оптиміза- +ції одержаної ієрархічної моделі впливу факторів на ефективність +проєктування післядрукарських процесів. За цими значеннями +встановлюється адекватність ієрархічної моделі реальній ситуації +та її узгодженість з експертними оцінками важливості факторів +[68]. +Відповідно +max +8,483 +λ += +, +0,069 +IU = +. Еталонне значення індекса +RI для матриці 8-го порядку становить 1,41, що не перевищує 10 % +індекса узгодженості IU . Отже нерівність +0,1 +IU +RI +< +× +є вірною і + +100 +підтверджує адекватність розв’язку задачі. +0,049 +RU = +, тож результа- +ти попарних порівнянь можна вважати коректними. +3.5. Візуалізація співвідношень компонент вихідного та нормалізо- +ваного векторів. Побудова оптимізованої моделі пріоритетного впливу +факторів на якість проєктування післядрукарських процесів +Для одержання вагових значень факторів на основі отриманих +моделей їм присвоюється градація умовних числових позначень, від- +повідно до рівня домінантності факторів, починаючи відлік з най- +нижчого. Нехай вага найнижчого рівня буде рівною 20 умовним оди- +ницям, а вага кожного наступного збільшуватиметься на 20 умовних +одиниць відносно попереднього фактора. Отримані числові значення +факторів подаються у вигляді компонент вихідного вектора +0 +R згідно +з порядком їх розміщення у матриці. +На підставі отриманих вагових значень, представлених векторами +n +R та +0 +R , будуються гістограма і порівняльний графік. +Порівняльне графічне відображення дає підставу стверджувати, +що компоненти векторів, розрахованих за методом ранжування фак- +торів та отриманих у результаті застосування методу попарних по- +рівнянь, незважаючи на деяку різницю у вагових значеннях, по суті +відтворюють останній порядок і суть слідування факторів. Вказане +уможливлює використання вагових компонент нормалізованого век- +тора як основи для синтезування оптимізованої моделі пріоритетного +впливу виокремлених факторів на якість проєктування післядрукар- +ських процесів. +Оптимізація дозволила уточнити значення ваг факторів досліджу- +ваного процесу та деталізувати міру впливу кожного з них. Оптимі- +заційні результати підтвердили достовірність проведених досліджень, +не змінивши порядок пріоритетів факторів [68]. +Після детального аналізу та порівняння вихідного та нормалізова- +ного векторів синтезується оптимізована модель пріоритетного впли- +ву факторів на процес. Вона служить підставою для проєктування +альтернативних та розрахунку оптимальних варіантів реалізації тех- +нологічного процесу, його етапів чи окремих операцій, фактори яких +упорядковані за ваговими коефіцієнтами важливості. + +101 +Етап 4. Визначення оптимальних альтернатив реалізації проєктуван- +ня післядрукарських процесів +4.1. Багатофакторний вибір альтернативи на основі лінійного згор- +тання критеріїв +Залежно від глибини пізнання проблеми розділяють на три +класи: добре структуровані, неструктуровані та погано структуро- +вані. У добре структурованих проблемах існуючі залежності добре +з’ясовані, тому можуть бути виражені у символах і числах та в під- +сумку давати числеві оцінки. Неструктуровані проблеми містять +лише описи ресурсів, характеристик та ознак, причому кількісні +залежності між ними є невідомими. Погано структуровані пробле- +ми, у свою чергу, містять як якісні, так і кількісні елементи, а якіс- +ні невизначені та маловідомі сторони проблеми мають домінуючу +тенденцію. +Визначення класу сформульованої проблеми дозволяє обрати ме- +тодику її вирішення. Так, добре структуровані проблеми вирішуються +шляхом використання методології дослідження операцій, неструкту- +ровані — за допомогою евристичного методу, а погано структурова- +ні — використовуючи системний аналіз. +З огляду на вищенаведені факти можна зробити висновок, що +проблема встановлення оптимальної альтернативи проєктування +післядрукарського опрацювання книжкових видань є погано струк- +турованою. Таким чином, визначення альтернативних варіантів ви- +рішення проблеми реалізовується за допомогою системного аналізу. +Генерування множини альтернатив уможливлює подальший вибір +оптимальної альтернативи із цієї множини. Сформована множина +альтернатив відображає можливі способи досягнення поставлених +цілей. Вибір оптимальної альтернативи здійснюється із врахуванням +обмежень та критерію оптимальності [59]. +У ході дослідження були встановлені вагові значення факторів +аналізованих технологічних процесів та побудовані моделі їх пріо- +ритетного впливу. Отримана інформація є основою для планування +стратегії реалізації проєктування післядрукарських процесів, яка по- +лягає у виборі оптимального альтернативного варіанту. Це дасть нам +уявлення про необхідну затрату трудомісткості та міру важливості +факторів. +Розв’язок поставленого завдання здійснюється за допомогою бага- +токритеріальної (в нашому випадку в ролі критерію виступає фактор, +отже багатофакторної) оптимізації. При цьому є достатнім викорис- + +102 +тання лише домінуючих факторів, що обумовлено принципом Па- +рето [22], суть якого полягає у використанні взаємно недомінованих +факторів, які утворюють множину Парето +( ) +P D , де +n +D +R +⊂ + — мно- +жина допустимих розв’язків. Фактори із помітно нижчими ваговими +значеннями просто відкидаються. +Синтезована раніше семантична мережа є підставою для побудови +матриці попарних порівнянь, опрацювання якої приводить до отри- +мання умовних вагових значень, що визначають числові пріоритети +факторів — міри важливості їх для технологічного процесу. Далі — +розрахунок та визначення оптимального (серед альтернативних) ва- +ріанту реалізації проєктування післядрукарських процесів. +Багатокритеріальна оптимізація функцій ( ) +( ) +( ) +( +) +1 + +,..., n +r x +r x +r +x += +на +множині B полягає у виокремленні максимального значення функ- +цій корисності +( ) +max, +i +x B +r x +∈ +→ + +1, . +i +n += + Відповідно за методом лінійно- +го згортання критеріїв об’єднання часткових цільових функціоналів +1,... n +r +r здійснюється за формулою [25; 59]: + +( +) +( ) +1 +, +max; +, +n +i i +x D +i +R w x +w r x +w +W +∈ += += +→ +∉ +∑ + +(14) + +( +) +1 +1 +,..., +; +0; +1 , +n +T +n +j +i +i +W +w +w +w +w +w += + + += += +> += + + + + +∑ + +де +iw — ваги факторів множини Парето. +Для факторів незалежних за корисністю та перевагою існує така +функція корисності [25]: + +( ) +( +) +1 +, +n +i +i +i +i +U x +w u y += +=∑ + +(15) +де +( ) +U x — багатокритеріальна функція корисності +( ) +(0 +1) +U x +≤ +≤ + +певної альтернативи x ; +iw — встановлене вагове значення i -го кри- +терію, причому 0 +1, +iw +< +< + +( +) +1 +1; +n +i +i +i +i +w +u y += += +∑ + — функція корисності i -го +критерію +( +) +(0 +1) +i +i +u y +≤ +≤ +; +iy — значення альтернативи x за i-м крите- +рієм [18]. +Для реалізації сформованої задачі виконуються такі дії: +1. Формується множина Парето, взявши до уваги лише фактори +з найвищою пріоритетністю: +1 +R — показники видання (188 у. о.); +3 +R — умови експлуатації (105 у. о.); +2 +R — конструкційні особливості + +103 +(74 у. о.); +4 +R — тип виробництва (49,5 у. о.). Фактори з суттєво ниж- +чою пріоритетністю відкидаються [25; 54; 59]. +2. Задаються три альтернативні варіанти реалізації досліджувано- +го процесу, які позначаються як +1 +2 +3 +, +, +. +A A +A Формується таблиця оці- +нювання альтернатив на основі міри важливості кожного виокрем- +леного фактора. Міра важливості кожного аналізованого фактора +для заданих альтернативних варіантів виражається у відсотках. Існує +великий перелік можливих комбінацій (табл. 7). Реальні значення +залежать від конкретного виробничого завдання. При цьому загаль- +на сума усіх альтернатив одного фактора не повинна перевищувати +100 %. +Таблиця 7 +Комбінації значень факторів +Комбінації значень факторів у відсотках +10–10–80 +20–10–70 +30–10–60 +40–10–50 +10–20–70 +20–20–60 +30–20–50 +40–20–40 +10–30–60 +20–30–50 +30–30–40 +40–30–30 +10–40–50 +20–40–40 +30–40–30 +40–40–20 +10–50–40 +20–50–30 +30–50–20 +40–50–10 +10–60–30 +20–60–20 +30–60–10 +50–10–40 +10–70–20 +20–70–10 +60–10–30 +50–20–30 +10–80–10 +70–10–20 +60–20–20 +50–30–20 +80–10–10 +70–20–10 +60–30–10 +50–40–10 +3. Створюється матриця попарних порівнянь вагових значень +факторів, оцінених за шкалою відносної важливості об’єктів за Сааті. +4. Здійснюється нормалізація головного власного вектора матриці +попарних порівнянь у програмі «Імітаційне моделювання в систем- +ному аналізі методом бінарних порівнянь» [57]. Унаслідок нормаліза- +ції отримуються оптимізовані вагові значення факторів. Встановлю- +ються критерії нормалізації. +Перевірка правильності розв’язку задачі здійснюється шляхом ви- +конання нерівностей +0,1 +IU +RI +< +× + та +0,1 +RU ≤ +, де RI — випадковий +індекс для матриці 4-го порядку (табл. 6), +0,9. +RI = + +4. Визначаються функції корисності кожної запроєктованої аль- +тернативи за факторами множини Парето. +5. Визначаються багатокритеріальні оцінки корисності для трьох +запроєктованих альтернатив. + +104 +Підставивиши у формулу (15) значення R2: +( +) +4; +i +i +ij +n +u y +u += += + — ко- +рисність j-ї альтернативи ( +) +1,2,3 +j = + за i-м фактором ( +) +1,...,4 +i = +, отри- +маємо наступне: + +4 +1 +; +1,2,3, +j +i +ij +i +U +w u +j += += += +∑ + +(16) +де +j +U — багатофакторна оцінка корисності j-ї альтернативи. +На основі формули (16) формуються такі відношення: + +1 +1 +11 +2 +21 +3 +31 +4 +41; +U +w +u +w +u +w +u +w +u += +× ++ +× ++ +× ++ +× + + +2 +1 +12 +2 +22 +3 +32 +4 +42; +U +w +u +w +u +w +u +w +u += +× ++ +× ++ +× ++ +× + + +3 +1 +13 +2 +23 +3 +33 +4 +43 [25]. +U +w +u +w +u +w +u +w +u += +× ++ +× ++ +× ++ +× + +(17) +При цьому +1 +0,264; +U = +2 +0,322; +U = +3 +0,414. +U = +Найкраща альтерна- +тива реалізації проєктування післядрукарських процесів обирається +за максимальним значенням Uj, ( +1,2,3) +i = +. Відповідно альтернатива +A3 є оптимальною для досліджуваного процесу, а визначальним є фак- +тор «Показники видання» (R1). +4.2. Багатофакторний вибір альтернативи на основі нечіткого від- +ношення переваги +Прийняття управлінських рішень щодо альтернативних варіантів +реалізації технологічних процесів може ускладнюватися відсутністю +інформації про їхню пріоритетність та неможливістю кількісного +оцінювання переваг. Натомість, можливо здійснити попарне порів- +няння альтернатив на відрізку [0;1] та представити дані у числовому +вигляді. Оцінювання здійснюється на основі багатокритеріальної +оптимізації, де в ролі критеріїв виступають фактори технологічно- +го процесу. За принципом Парето [22], як і в методі встановлення +оптимальної альтернативи на основі лінійного згортання критеріїв, +достатнім вважається вибір лише домінуючих факторів із найвищи- +ми ваговими показниками, які формують множину Парето. Відпо- +відно при нечіткому відношенні переваги на множині альтернатив +прийняття рішень буде здійснюватися за Парето-оптимальними аль- +тернативами. +Введення чіткого відношення нестрогої переваги +iR на множи- +ні альтернатив +{ +} +1,..., +n +X +x +x += + дозволяє висловити одне з наведених +тверджень для будь-якої пари альтернатив ( , ) +x y : x не гірша y , тоб- + +105 +то +( +) +, +, +x +y +x y +R +≥ +∈ +; y не гірша x , що записується як +( +) +, +, +y +x +y x +R +≥ +∈ +, +x та y неможливо порівняти між собою, ( +) +( +) +, +, +, +. +x y +R +y x +R +∉ +∉ +Такий +підхід уможливлює звуження класу раціонального вибору. +Якщо існує строга перевага ( +) +, +z +x y +R +∈ +, альтернатива x переважає +y , тобто x +y +> +. За умови чітких функцій корисності +jr множини X +альтернатива x , що має вищу оцінку ( ) +jr +x за фактором ,j є кращою, +ніж альтернатива y , оцінка якої ( ) +jr +y . Подане твердження описуєть- +ся чітким відношенням переваги +j +R множини X : + +( +) +( ) +( ) +{ +} +, +: +, , +j +j +j +R +x y +r +x +r +y +x y +X += +≥ +∈ +. +(18) +Визначимо якість проєктування післядрукарських процесів шля- +хом оцінювання нечітких відношень переваги +iR на множині аль- +тернатив +{ +} +1 +2 +3 +, +, +X +x +x +x += +: +1 +R (Показники видання) — +1 +2 +2 +3 +, +x +x +x +x += +< +; +2 +R (Умови експлуатації) — +1 +3, +x +x +< + +2 +3 +x +x +> +; +3 +R (Конструкційні осо- +бливості) — +1 +2 +2 +3 +, +x +x +x +x +> += +; +4 +R (Тип виробництва) — +1 +2 +2 +3 +, +x +x +x +x +> += +. +Для виокремлення Парето-оптимальної альтернативи необхід- +но обрати альтернативу +0x +X +∈ + із найвищою оцінкою корисності на +множині усіх факторів: + +( +) +( ) +0 +, +1, ; +j +j +r +x +r +y +j +m +y +X +≥ +∀ = +∀ ∈ +. +(19) +Згортка усіх критеріїв сформованої множини Парето в єдиний +скалярний здійснюється за способом перетину [22; 59; 79]. +Позначимо +1 +1 +. +m +j +j +Q +R += += + Таким чином, множина альтернатив X = +{ +} +1,..., +n +x +x += +із відношенням переваги +1 +Q є відповідною до множини +альтернатив з функціями корисності +( ) +jr +x . Визначення недоміно- +ваних альтернатив за нечітким відношенням переваги +1 +Q полягає у +заміні кількох відношень +( +) +1, +j +R +j +m += + на перетин між ними. Вважати- +мемо, що +( +) +, +j x y +µ + є функцією належності чіткого відношення пере- +ваги +jr . Сформована умова матиме вид: + +( +) +( ) +( ) +( +) +( +) +1, +, +, +, +0, +, +j +j +j +j +якщо r +x +r +y +тобто x y +R +x y +якщо x y +R + +≥ +∈ + +µ +=  +∉ + +. +(20) +Відповідно функція належності згортки +1 +Q запишеться таким чи- +ном: + +( +) +( +) +( +) +( +) +{ +} +1 +1 +2 +, +min +, +, +, +,..., +, +Q +n +x y +x y +x y +x y +µ += +µ +µ +µ +. +(21) + +106 +Згортка критеріїв із врахуванням вагових значень факторів техно- +логічного процесу +jv та відповідних функцій корисності матиме ви- +гляд: + +( ) +( ) +min +j +j +j +Q x +v r +x += +. +(22) +Згортка вихідних відношень +2 +Q також формується ваговими зна- +ченнями аналізованих факторів +jv і відповідними функціями корис- +ності: + +� � +2 +1 +1 +, +1, +0 +m +m +j +j +j +j +j +j +Q +v r +x +äå +v +v +� +� +� +� +� +� +� +. +(23) +Їй відповідає така функція належності [58]: + +( +) +( +) +2 +1 +, +, +m +Q +j +j +j +x y +v +x y += +µ += +µ +∑ +. +(24) +У результаті обчислень отримаємо: + +( +) [ +] +2 +0,4; 0,74;1,26 . +нд +Q +ix +µ += + +За перетином множин +1 +нд +Q + та +2 +нд +Q + максимальне значення функції +належності +( +) +нд +Q +ix +µ + належить +3x , тобто оптимальним вважається тре- +тій варіант. +4.3. Перевірка результатів +Внаслідок проведення багатофакторного вибору оптимальної +альтернативи на основі лінійного згортання критеріїв визначено ба- +гатофакторні оцінки корисності: +1 +0,264; +U = +2 +0,322; +U = +3 +0,414. +U = +Максимальною оцінкою корисності є +3 +U , отже оптимальною є третя +альтернатива. +У результаті багатофакторного вибору альтернативи на основі +нечіткого відношення переваги одержано такі значення функції на- +лежності: +( +) +нд +Q +ix +µ +: +1 +0,4; +x = + +2 +0,74; +x = + +3 +1,26 +x = +. Таким чином, можна +стверджувати, що варіант +3x є оптимальною альтернативою проєкту- +вання післядрукарських процесів. +Результати, отримані внаслідок встановлення оптимальної аль- +тернативи за методом лінійного згортання критеріїв та за методом на +основі нечіткого відношення переваги, є тотожними, що свідчить про +достовірність проведеного дослідження [79]. + +107 +Етап 5. Визначення інтегрального показника якості проєктування +післядрукарських процесів +Остаточно моделювання системи прогностичного оцінювання +якості проєктування післядрукарських процесів на базі нечіткої логі- +ки зводиться до розв’язання таких завдань [15; 16; 44; 64]: +– встановлення універсальної терм-множини значень та відповідних +їй лінгвістичних термів виокремлених факторів (лінгвістичних змінних); +– побудова багаторівневої моделі логічного виведення, структура +якої відтворює ієрархію факторів та лінгвістичних термів, що впли- +вають на якість реалізації процесу. Компонента найвищого рівня +визначає вихідний прогнозований показник якості досліджуваного +процесу у вигляді нечіткої множини; +– побудова та опрацювання матриць попарних порівнянь для +множини лінгвістичних термів відносно квантів поділу інтервалів +значень універсальної множини та отримання для кожної з лінгвіс- +тичних змінних функцій належності; +– нормування значень функцій належності та співвіднесення їх із +квантами поділу універсальної множини; +– побудова суміщених графіків за нормованими значеннями +функцій належності для лінгвістичних змінних і відповідних їм лінг- +вістичних термів; +– розроблення нечіткої бази знань (або матриці знань) з викорис- +танням нечітких логічних висловлювань типу «якщо <умова>, тоді +<висновок (або дія)>», що відтворює алгоритм формування якості +проєктування післядрукарських процесів в залежності від рівня якос- +ті лінгвістичних термів; +– побудова нечітких логічних рівнянь на підставі матриці знань та +функцій належності, які визначають зв’язок між функціями належ- +ності вхідних та вихідних даних; +– побудова аналітичного виразу для формалізованої ідентифікації +прогнозованого результату у вигляді нечіткої множини, отриманої на під- +ставі багаторівневої моделі логічного виведення та нечіткої бази знань; +– дефазифікація нечіткої множини, суть якої полягає у розрахун- +ку числового показника прогнозованої якості за методом центра мас +або центра ваги плоскої фігури, обмеженої графіком функції належ- +ності і віссю абсцис. +При дефазифікації нечіткої множини використовуються значення +функцій належності лінгвістичних змінних, область існування яких +визначена універсальною множиною. + +108 +5.1. Фазифікація нечіткої множини +Проєктування післядрукарських процесів — це необхідна складо- +ва забезпечення якості готової книжкової продукції, яка включає ряд +послідовних операцій, спрямованих на досягнення поставленої мети. +Однак фактори, які здійснюють неопосередкований вплив на реалі- +зацію досліджуваного процесу, не завжди містять кількісну складову. +Натомість, значно інформативнішими стають певні лінгвістичні ха- +рактеристики. Виникає необхідність заміни понять чіткої множини +поняттями нечіткої множини. Саме тому для забезпечення точності +моделювання доцільно використовувати методи та засоби нечіткої +логіки. +Суттєвим елементом та перевагою нечіткої логіки є можливість +фазифікації, тобто заміни компонент чіткої множини відповід- +ними їм поняттями нечіткої множини. Відомо, що суть її полягає +у зіставленні терм-множини значень аналізованих факторів від- +повідника нечіткого формату змінних величин — функцій належ- +ності. Тобто змінні, які не можуть бути чітко вираженими за до- +помогою кількісних значень та які зручно описувати словами чи +словосполученнями, вважаються лінгвістичними змінними, таки- +ми як: «Показники видання», «Конструкційні особливості» чи ін. +При цьому значення кожної лінгвістичної змінної формуються у +певну сукупність — терм-множину, компоненти якої називаються +термами. Так, терм-множина лінгвістичної змінної «Показники +видання» складається з термів «просте», «ускладнене», «складне». +Лінгвістичною вважається змінна, значення якої виражено засоба- +ми звичайної мови — словами або словосполученнями. При цьому +множину можливих значень лінгвістичної змінної прийнято нази- +вати терм-множиною, а довільний її елемент — термом. Так, для +лінгвістичної змінної «Тип обладнання» термами будуть лінгвіс- +тичні оцінки «ручне», «механічне», «автоматизоване», що утворю- +ватимуть терм-множину значень. +Фазифікація забезпечує доволі високий рівень відповідності мо- +делі реальному об’єкту і служить, як буде показано пізніше, основою +для подальшого моделювання прогностичного оцінювання проєкту- +вання післядрукарських процесів. +У роботах основоположника нечіткої логіки Заде [20; 21] вводить- +ся поняття універсальної множини D , як такої, що стосується всієї +проблемної області. Тоді нечітку підмножину M множини D визна- +чають через шкалу D і функцію належності +( ) +M d +µ + [20], тобто + +109 + +( ) +( +) +{ +} +, +, +M +M +d +d +d +D += +µ +∈ +, +(25) +де +( ) +( +) +0 +1 +M d +≤ µ +≤ +. +Функція належності встановлює міру приналежності кожного +елемента нечіткої множини універсальній множині, тобто M +D +∈ +. За +умови дискретності і скінченності базової шкали (тобто поділеної на +кванти чи проміжки) нечітка множина + +( +) +( +) +( +) +( +) +( +) +1 +1 +2 +2 +1 +/ +, +/ +,..., +/ +/ +n +M +M +M +n +n +M +i +i +i +M +d +d +d +d +d +d +d +d += += µ +µ +µ += +µ +∑ +, (26) +або спрощено: +1 +/ +n +i +i +i +M +d += += +µ +∑ +. Запис означає «прикріплення» функції +належності +( +) +M +id +µ + до елемента +id . +Остаточно функції належності виступають ідентифікатором вхід- +них значень лінгвістичних змінних у нечіткому форматі, тобто множині +значень змінної d ставляться у відповідність функції належності ( ) +d +µ +. +Вважатимемо, що реалізація визначеного технологічного процесу +буде певною функцією G , у якості аргументів якої будуть виокремле- +ні фактори +m +m +1 +2 +, +,..., +m +n +r +r +r +, тоді: + +( +) +m +m +1 +2 +, +,..., +m +n +G +F r +r +r += +, +(27) +де +m +n — кількість факторів m -го технологічного процесу. +Отже досліджуваний процес є процедурою з множиною початко- +вих змінних ( +) +1, +ir +i +n += + та кінцевою змінною G . +Існування кількісних значень змінних уможливлює задання про- +міжку, що виражатиметься граничними значеннями цих змінних +[13; 14]: +, +, +1, ; +, +i +i +r r +i +n +G G += +. Зважаючи на те, що виокремлені фак- +тори є якісними змінними, постає потреба формування множини +та меж задання значень: +( ) +( ) +( ) +{ +} +1 +2 +, +,..., +, +j +D +d +d +d += + де +( ), +1, +k +d +k +j += + — мно- +жина кількісних чи якісних умовних одиниць, потужність якої +визначає індекс j . Тоді результуюча змінна G із граничними +межами також може подаватися в умовних одиницях множиною +( ) +( ) +( ) +{ +} +1 +2 +, +,..., +. +j +G +g +g +g += + Такі універсальні множини забезпечують вико- +нання залежності (27). В той же час доцільно оцінювати лінгвістичні +змінні засобами природної мови (наприклад: «просте», «ускладне- +не», «складне»), формуючи лінгвістичні терм-множини. +З огляду на наведені твердження побудова багаторівневої моделі +нечіткого логічного виведення встановлення інтегрального показ- + +110 +ника якості досліджуваного технологічного процесу передбачає фор- +мування часткових показників якості; виокремлення універсальної +множини значень та терм-множини кожної лінгвістичної змінної; +безпосередню візуалізацію ієрархічної залежності. +Вважатимемо процес проєктування післядрукарських процесів +функцією +( +) +1 +2 +3 +4 +5 +6 +7 +8 +, +, +, +, +, +, +, +, +G +F R R R R R R R R += + з такими аргументами: +1 +R — показники видання; +2 +R — конструкційні особливості; +3 +R — умо- +ви експлуатації; +4 +R — тип виробництва; +5 +R — матеріали; +6 +R — тип об- +ладнання; +7 +R — технологічні та економічні розрахунки; +8 +R — схема +технологічного процесу [27; 30]. Інтегральний показник якості про- +єктування післядрукарських процесів визначатиметься за принципом +ієрархізації структури процесу. Відповідно залежність якості проєкту- +вання видання може бути виражена через якість часткових показників: + +( +) +, , +G +G +F +M O P += +. +(28) +Аргумент M визначає якість формування видання: + +( +) +1 +2 +3 +, +, +, +M +M +F +m m m += + +(29) +де +1 +m — лінгвістична змінна «показники видання», +2 +m — лінгвістич- +на змінна «конструкційні особливості», +3 +m — лінгвістична змінна +«умови експлуатації». +Аргумент O визначає якість організації виробництва: + +( +) +1 +2 +3 +, +, +, +O +O +F +o o o += + +(30) +де +1o — лінгвістична змінна «тип виробництва»; +2o — лінгвістична +змінна «матеріали»; +3o — лінгвістична змінна «тип обладнання». +Аргумент P визначає якість опрацювання видання: + +( +) +1 +2 +, +, +P +P +F +p p += + +(31) +де +1p — лінгвістична змінна «редагування»; +2p — лінгвістична змінна +«коректура». +Сформуємо таблицю, вказавши лінгвістичну суть кожної змінної, +універсальні множини значень та відповідні лінгвістичні терми. +Значення умов експлуатації сформовано на основі груп довговіч- +ності користування книжковим виданням: 1-ша група — нетривалий +термін служби (до двох років) з малою інтенсивністю користування; та +2-га група — нетривалий термін служби (до двох років) з великою ін- +тенсивністю користування; 3-тя група — середній термін користування + +111 +(від 2 до 10 років) з малою інтенсивністю користування; 4-та група — +середній термін користування (від 2 до 10 років) з великою інтенсив- +ністю користування; 5-та та 6-та групи — тривалий термін (від 10 років +і більше) з малою чи високою інтенсивністю користування [27; 35; 70]. +Таблиця 8 +Терм-множини значень лінгвістичних змінних +Змін- +на +Лінгвістична суть +змінної +Універсальна +множина зна- +чень +(множина D) +Лінгвістичні терми +(множина L) +m1 +Показники видання +(1–5) у. о. +Просте видання, +ускладнене видання, +складне видання +m2 +Конструкційні особли- +вості +(1–5) у. о. +Проста конструкція, +ускладнена конструкція, +складна конструкція +m3 +Умови експлуатації (гру- +пи довговічності корис- +тування) +(1–5) кате- +горія +Нормальні умови, +робочі умови, граничні +умови +o1 +Тип виробництва +(1–5) у. о. +Одиничне виробництво, +серійне виробництво, +масове виробництво +o2 +Матеріали +(складність опрацюван- +ня) +(1–5) у. о. +Низька складність, +середня складність, ви- +сока складність +o3 +Тип обладнання +(1–5) у. о. +Ручне, механічне, авто- +матизоване +p1 +Технологічні та економіч- +ні розрахунки +(ефективність виробни- +цтва) +(10–90) % +Низька ефективність, +середня ефективність, +висока ефективність +p2 +Схема технологічного +процесу +(1–5) у. о. +Проста, ускладнена, +складна +Для візуалізації залежності якості проєктування післядрукарських +процесів від значення лінгвістичних термів виокремлених факторів +синтезується багаторівнева модель нечіткого логічного виведення +[27; 59]. Використання багаторівневої моделі нечіткого логічного ви- +ведення сприяє послідовному встановленню прогнозу якості реалі- +зації проєктування післядрукарських процесів шляхом накопичення +знань від найнижчого до найвищого її рівнів. Ця модель включає + +112 +підпорядковані моделі: модель якості формування видання, модель +якості організації виробництва, модель якості планування. +Рівень якості досліджуваного процесу позначено лінгвістичним +термом G . При цьому універсальна множина D ділиться на части- +ни (кванти). У точках поділу задаються означені нами лінгвістичні +змінні та ранги +( +) +g +i +r +d +, що ідентифікують лінгвістичні терми. Отже, +вихідною базою даних буде множина +{ +} +1 +2 +, +,... +n +D +d d +d += + і ранги +( +) +g +i +r +d +, +що встановлюють пріоритетність лінгвістичних термів у діапазонах +id ( +) +1,..., +. +i +n += + З урахуванням сказаного лінгвістичний терм «рівень +якості технологічного процесу» G подається у вигляді деякої нечіт- +кої множини, елементи якої утворюють сукупності пар [15; 28; 41]: + +( +) +( +) +( +) +1 +2 +1 +2 +, +,..., +g +g +g +n +n +d +d +d +G +d +d +d + + +µ +µ +µ + + +=  + + + + + +, +(32) +де G +D +⊂ +; +( +) +g +id +µ + — міра належності елемента +id +D +∈ + до множини G . +Міри або функції належності +( +) +g +id +µ + є базовими складовими ло- +гічних рівнянь, розв’язання яких забезпечує числове значення функ- +ції належності лінгвістичного терму G . Для функцій належності ви- +конується умова нормування: +1 +2 +... +1. +n +µ + µ + ++ µ = + +При цьому розподіл мір (функцій) належності відповідає таким +умовам: + +1 +2 +1 +2 +... +n +n +r +r +r +µ +µ +µ += += += +, +(33) +де +( +) +i +g +id +µ = µ +; +( +) +i +g +i +r +r +d += + для всіх +1,..., +i +n += +. +Числові значення функцій належності, що слугують для вста- +новлення рангів факторів проєктування післядрукарських процесів, +отримуються із співвідношень [28; 41; 43]: + +1 +2 +3 +1 +1 +1 +1 +1 +1 +3 +2 +2 +2 +2 +1 +1 +2 +3 +1 +... +1 +... +.......................................... +... 1 +n +n +n +n +n +n +r +r +r +r +r +r +r +r +r +r +r +r +r +r +r +r +r +r +− +− +− + + + + +µ = ++ ++ ++ ++ + + + + + + + + + +µ = ++ + ++ ++ + + + + + + + + + + + + +µ = ++ ++ ++ ++ + + + + + + +. +(34) + +113 +На основі наведеного теоретичного обґрунтування формуються +ключові задачі: + +( +) +( +) +, +, +max, +1,3; +1,3; +1,2 +0, +0, +0 +max, +, +, +1,3 +F +a +b +c +a +b +c +g +i +i +F +G +F m o +p +a +b +c +m +o +p +y +y +Y G +Y i + += +→ += += += + +> +> +> + + +µ +→ +∈ +⊂ += + +. +(35) +Для графічного відображення лінгвістичних термів діапазон зна- +чень лінгвістичних змінних ділиться на чотири частини, у результаті +чого виникає п’ять точок ( +) +1 +2 +3 +4 +5 +, +, +, +, +d d d d d + [52, 53]. +При відомих, або отриманих на основі матриць попарних порів- +няннях, рангах для кожного з лінгвістичних термів розраховуються +функції належності +iµ у результаті опрацювання матриці + +2 +3 +4 +5 +1 +1 +1 +1 +1 +3 +4 +5 +2 +2 +2 +2 +1 +2 +3 +4 +5 +5 +5 +5 +1 +1 +... ... ... ... ... +1 +r +r +r +r +r +r +r +r +r +r +r +r +r +r +r +r +A +r +r +r +r +r +r +r +r + + + + + + + + + + +=  + + + + + + + + + + + +. +(36) +Отримання підсумкового результату полягає у досягненні макси- +мального значення функції, що характеризує рівень якості процесу +при максимальних значеннях функцій належності термів оцінюван- +ня факторів — лінгвістичних змінних. +Внаслідок побудови матриць попарних порівнянь для кожного +терму аналізованих лінгвістичних змінних проєктування післядру- +карських процесів формується певне кількісне уявлення про взаємо- +відношення рангів у точках універсальної множини. Тобто викорис- +тання шкали відносної важливості об’єктів за Сааті та методології +створення квадратних обернено-симетричних матриць значно по- +легшує сприйняття якісних ознак. Однак порівняння відбувається +в межах рангів одного терму, що не дає уявлення про взаємозв’язок +термів лінгвістичної змінної. Опрацювання функцій належності, на +основі матриць попарних порівнянь, уможливлює перетворення екс- +пертної думки у кількісні показники [28; 29; 63]. + +114 +Будуємо матриці попарних порівнянь для лінгвістичної змінної +«показники видання» з терм-множиною значень +( +) +1 +L m += = <про- +сте, ускладнене, складне> та універсальною множиною значень +( +) [ +] +1 +1;2;3;4;5 +D m += + у. о., що характеризують кількісні ознаки. + +( +) +1 +1 +7 9 +5 9 +3 9 +1 9 +9 7 +1 +5 7 +3 7 +1 7 +9 5 +7 5 +1 +3 5 +1 5 +9 3 +7 3 +5 3 +1 +1 3 +9 +7 +5 +3 +1 +просте +S +m + + + + + + + + += + + + + + + + + +; + +( +) +1 +1 +5 +8 +3 +1 +1 +8 +3 +1 +1 +5 +5 +5 +5 +1 +5 +3 +1 +1 +8 +8 +8 +8 +1 +5 +8 +1 +1 +3 +3 +3 +3 +1 +5 +8 +3 +1 +ускладнене +S +m + + + + + + + + +=  + + + + + + + + + + + +; + +( +) +1 +1 +5 +7 +8 +9 +1 5 +1 +7 5 +8 5 +9 5 +1 7 +5 7 +1 +8 7 +9 7 +1 8 +5 8 +7 8 +1 +9 8 +1 9 +5 9 +7 9 +8 9 +1 +складне +S +m + + + + + + + + += + + + + + + + + +. +Внаслідок обчислення матриць значення функцій належності +для термів «просте», «ускладнене» та «складне» лінгвістичної змінної +1 +m «показники видання» будуть наступними: + +( +) +1 +0,36 +просте y +µ += +; +( +) +2 +0,28 +просте y +µ += +; +( +) +3 +0,2 +просте y +µ += +; + +( +) +4 +0,12 +просте y +µ += +; +( +) +5 +0,04 +просте y +µ += +; + +( +) +1 +0,055 +ускладнене y +µ += +; +( +) +2 +0,277 +ускладнене y +µ += +; +( +) +3 +0,444 +ускладнене y +µ += +; + +( +) +4 +0,166 +ускладнене y +µ += +; +( +) +5 +0,055 +ускладнене y +µ += +; + +( +) +1 +0,033 +складне y +µ += +; +( +) +2 +0,166 +складне y +µ += +; +( +) +3 +0,233 +складне y +µ += +; + +( +) +4 +0,266 +складне y +µ += +; +( +) +5 +0,3 +складне y +µ += +. + +115 +Пронормовані відносно одиниці значення функцій належностей +(коефіцієнт нормування +( +) ( +) +1 max +, +1,2,3 +е +е +i +k +y +i += +µ += +; +( +) +nе +i +е +y +k +µ += +× +( +) +е +iy +×µ +) матимуть вид: + +( +) +1 +1 +n +просте +y +µ += +; +( +) +2 +0,778 +n +просте +y +µ += +; +( +) +3 +0,556 +n +просте +y +µ += +; + +( +) +4 +0,333 +n +просте +y +µ += +; +( +) +5 +0,111 +n +просте +y +µ += +; + +( +) +1 +0,124 +n +ускладнене +y +µ += +; +( +) +2 +0,624 +n +ускладнене +y +µ += +; +( +) +3 +1 +n +ускладнене +y +µ += +; + +( +) +4 +0,374 +n +ускладнене +y +µ += +; +( +) +5 +0,124 +n +ускладнене +y +µ += +; + +( +) +1 +0,11 +n +складне +y +µ += +; +( +) +2 +0,553 +n +складне +y +µ += +; +( +) +3 +0,777 +n +складне +y +µ += +; + +( +) +4 +0,887 +n +складне +y +µ += +; +( +) +5 +1 +n +складне +y +µ += . +Утворимо нечіткі множини за формулою (32): + +1 0,778 0,556 0,333 0,111 += +; +; +; +; +1 +2 +3 +4 +5 +просте видання + + + + + + + у. о.; + +0,124 0,624 1 0,374 0,124 += +; +; ; +; +1 +2 +3 +4 +5 +ускладнене видання + + + + + + + у. о.; + +0,11 0,553 0,777 0,887 1 += +; +; +; +; +1 +2 +3 +4 +5 +складне видання + + + + + + + у. о. +За нечіткими множинами побудуємо графік функцій належності +термів «просте», «ускладнена», «складне». При цьому по осі абсцис +відобразимо універсальну множину значень, а по осі ординат — нор- +мовані значення функцій належності термів лінгвістичної змінної +«показники видання» [29; 69]. +Опускаючи подібні викладки для решти лінгвістичних змінних, +перейдемо до наступної компоненти нечіткої логіки. +База нечітких знань може бути представлена у вигляді матриці +знань, яка пов’язує вхідні змінні (фактори m -го технологічного про- +цесу) з вихідною змінною (результатом реалізації m -го технологічно- +го процесу). Для побудови матриці знань використовується система +висловлювань «якщо — і — тоді», «якщо — тоді — інакше», «якщо — +або — тоді — інакше». На основі матриці знань створюється система +нечітких логічних рівнянь, яка дозволяє отримати числові значення +функцій належності та інтегрального прогнозу якості m -го техноло- +гічного процесу [26; 42]. + +116 +0 +0,5 +1 +1,5 +1 +2 +3 +4 +5 +Значення функцій +належності +Значення універсальної множини +ПОКАЗНИКИ ВИДАННЯ +Просте видання +Ускладнене видання +Складне видання + +Рис. 3. Візуалізація функцій належності лінгвістичної +змінної «показники видання» +Наведемо комбінації отримання результату для двох значень +функцій належності +1 +µ та +2 +µ : + +( +) +1 +1 +2 +1 +2 +1 +2 +2 +1 +2 +, +, +max +, +, +, +якщо +якщо +µ +µ ≥ µ + +µ ∨ µ = +µ µ += µ +µ < µ + + +(37) + +( +) +1 +1 +2 +1 +2 +1 +2 +2 +1 +2 +, +, +min +, +, +, +якщо +якщо +µ +µ ≤ µ + +µ ∧ µ = +µ µ += µ +µ > µ + + +(38) +де операція ∨ у нечітких логічних рівняннях вказує на отримання +максимального значення, а операція ∧ — мінімального значення. +Нехай для лінгвістичних змінних M (якість формування видан- +ня), O (якість організації виробництва) та P (якість опрацювання +видання) термами будуть «низька», «середня», «висока». Відпо- +відно інтегральний показник G (якість проєктування післядру- +карських процесів) описуватиметься такими ж термами [27; 60; +64]. Тоді нечітка база знань для відношення +( +) +, , +G +G +F +M O P += + мати- +ме вид: + +ЯКЩО (M = низька) І (M = середня) І (M = висока); + +І (O = низька) І (O = середня) І (O = висока); + +І (P = низька) І (P = середня) І (P = висока); + +ТОДІ (G = низька) І (G = середня) І (G = висока). +Сформовані умови відображаються у матриці знань. + +117 +Таблиця 9 +Матриця знань для лінгвістичної змінної G +Якість вихідних +даних видання M +Якість +опрацювання +видання O +Якість +оформлення +видання P +Якість +проєктування +післядрукарських +процесів G +низька +низька +низька +низька +низька +середня +низька +середня +низька +середня +середня +висока +середня +середня +висока +висока +висока +висока +висока +середня +висока +Нечіткі логічні рівняння для термів «низька», «середня», «висока» +інтегрального показника G матимуть вид: + +( ) +( +) +( ) +( ) +( +) +( ) +( ) +( ) +( +) +( ) +( ) +( +) +( ) +( ) +( ) +( +) +( ) +( ) +( +) +( ) +( ) +; +; +. +низька +низька +низька +низька +низька +середня +низька +середня +середня +низька +середня +висока +середня +середня +висока +висока +висока +висока +висока +середня +висока +G +M +O +P +M +O +P +G +M +O +P +M +O +P +G +M +O +P +M +O +P +µ += µ +∧ µ +∧ µ +∨ +∨µ +∧ µ +∧ µ +µ += µ +∧ µ +∧ µ +∨ +∨µ +∧ µ +∧ µ +µ += µ +∧ µ +∧ µ +∨ +∨µ +∧ µ +∧ µ + +Зважаючи на те, що залежності якості формування видання, ор- +ганізації виробництва та опрацювання видання також можуть бути +виражені через якість часткових показників +( +) +1 +2 +3 +, +, +, +M +M +F +m m m += + +( +) +1 +2 +3 +, +, +, +O +O +F +o o o += +( +) +1 +2 +, +P +P +F +p p += +і на основі експертних суджень щодо +множин +1 +2 +3 +( +, +, +), +L m m m + +1 +2 +3 +( , +, +), +L o o o + +1 +2 +( +, +) +L p p + формуються нечіткі бази +знань, матриці знань і нечіткі логічні рівняння лінгвістичних змінних +проєктування післядрукарських процесів [59]. +Логічні висловлювання стосовно таких лінгвістичних змінних: +– «якість формування видання»; +– «якість організації виробництва»; +– «якість опрацювання видання». +ЯКЩО (m1) = (просте, ускладнене, складне), +І (m2) = (проста, ускладнена, складна); +І (m3) = (нормальні, робочі, граничні); +ТОДІ (M) = (низька, середня, висока); + +118 +ЯКЩО (o1) = (одиничне, серійне, масове), +І (o2) = (низька, середня, висока); +І (o3) = (ручне, механічне, автоматизоване); +ТОДІ (O) = (низька, середня, висока); +ЯКЩО (p1) = (низька, середня, висока), +І (p2) = (проста, ускладнена, складна); +ТОДІ (P) = (низька, середня, висока). +Далі будуються матриці знань для аналізованих лінгвістичних +змінних. Для зручності вони відображаються у табличній формі [50; +60; 64]. +Таблиця 10 +Матриця знань для лінгвістичної змінної M (якість формування видання) +Показники +видання m1 +Конструкційні +особливості +(складність +конструкції) m2 +Умови +експлуатації +m3 +Якість вихідних +даних видання +M +складне +складна +граничні +низька +складне +складна +робочі +складне +ускладнена +робочі +середня +ускладнене +ускладнена +нормальні +ускладнене +проста +нормальні +висока +просте +проста +нормальні +Таблиця 11 +Матриця знань для лінгвістичної змінної O (якість організації виробництва) +Тип виробництва +o1 +Матеріали +(складність +опрацювання) o2 +Тип +обладнання o3 +Якість організації +виробництва O +одиничне +висока +ручне +низька +серійне +висока +ручне +серійне +середня +механічне +середня +серійне +середня +автоматизоване +серійне +низька +автоматизоване +висока +масове +низька +автоматизоване + +119 +Таблиця 12 +Матриця знань для лінгвістичної змінної P (якість опрацювання видання) +Технологічні та економічні +розрахунки (ефективність +виробництва) p1 +Схема +технологічного +процесу p2 +Якість +опрацювання +видання P +низька +складна +низька +низька +ускладнена +середня +проста +середня +середня +ускладнена +висока +проста +висока +висока +ускладнена +Нечіткі логічні рівняння для визначених термів матимуть вид: +– для лінгвістичної змінної «якість формування видання» +( +) +( +) +( +) +( +) +( +) +( +) +( +) +1 +2 +3 +1 +2 +3 , +низька +складне +складна +граничні +складне +складна +робочі +M +m +m +m +m +m +m +µ += µ +∧ µ +∧ µ +∨ +∨µ +∧ µ +∧ µ + +( +) +( +) +( +) +( +) +( +) +( +) +( +) +( +) +( +) +( +) +( +) +( +) +( +) +( +) +1 +2 +3 +1 +2 +3 +1 +2 +3 +1 +2 +3 +, +; +середня +складне +ускладнена +робочі +ускладнене +ускладнена +нормальні +висока +ускладнене +проста +нормальні +просте +проста +нормальні +M +m +m +m +m +m +m +M +m +m +m +m +m +m +µ += µ +∧ µ +∧ µ +∨ +∨µ +∧ µ +∧ µ +µ += µ +∧ µ +∧ µ +∨ +∨µ +∧ µ +∧ µ + +– для лінгвістичної змінної «якість організації виробництва» +( ) +( ) +( +) +( +) +( ) +( +) +( +) +( ) +( ) +( +) +( +) +( ) +( +) +( +) +( ) +( ) +( +) +1 +2 +3 +1 +2 +3 +1 +2 +3 +1 +2 +3 +1 +2 +, +, +низька +одиничне +висока +ручне +серійне +висока +ручне +середня +серійне +середня +механічне +серійне +середня +автоматизоване +висока +серійне +низька +автоматизова +O +o +o +o +o +o +o +O +o +o +o +o +o +o +O +o +o +µ += µ +∧ µ +∧ µ +∨ +∨µ +∧ µ +∧ µ +µ += µ +∧ µ +∧ µ +∨ +∨µ +∧ µ +∧ µ +µ += µ +∧ µ +∧ µ +( +) +( ) +( +) +( +) +3 +1 +2 +3 ; +не +масове +низька +автоматизоване +o +o +o +o +∨ +∨µ +∧ µ +∧ µ + +– для лінгвістичної змінної «якість опрацювання видання» +( ) +( +) +( +) +( +) +( +) +( ) +( +) +( +) +( +) +( +) +( ) +( +) +( +) +( +) +( +) +1 +2 +1 +2 +1 +2 +1 +2 +1 +2 +1 +2 +, +, +. +низька +низька +складна +низька +ускладнена +середня +середня +проста +середня +ускладнена +висока +висока +проста +висока +ускладнена +P +p +p +p +p +P +p +p +p +p +P +p +p +p +p +µ += µ +∧ µ +∨ µ +∧ µ +µ += µ +∧ µ +∨ µ +∧ µ +µ += µ +∧ µ +∨ µ +∧ µ + + +120 +5.2. Дефазифікація нечіткої множини +Для встановлення інтегрального показника якості проєктуван- +ня післядрукарських процесів здійснюється процес дефазифіка- +ції, враховуючи розподілення якості за частковими показниками +( +) +, , +G +G +F +M O P += +. +Слід зазначити, що дефазифікація є одним з ключових процесів не- +чіткої логіки, який полягає у перетворенні значень нечіткої множини +у кількісний показник. Дефазифікація передбачає наявність сформо- +ваних нечітких баз знань та нечітких логічних рівнянь досліджуваного +технологічного процесу для подальшого формування таблиць на осно- +ві терм-множин з пронормованими значеннями функцій належності +у визначених точках поділу універсальної множини значень виокрем- +лених лінгвістичних змінних та підставлення значень термів у нечіткі +логічні рівняння. Для здійснення числових розрахунків у дослідженні +обрано метод центру ваги, згідно з яким кількісне значення початкової +змінної рівне абсцисі центру ваги площі, що обмежена графіком кри- +вої функції належності аналізованої змінної [22; 62; 69; 72]. +Відповідно до наведених тверджень формуються таблиці значень +функцій належності для кожної лінгвістичної змінної за точками по- +ділу універсальної множини значень та терм-множинами (табл. 6–13) +[22; 26; 62; 72]. +Як приклад наведемо таблицю значень терм-множини +( +) +1 +D m + +лінгвістичної змінної «Показники видання»: +Таблиця 13 +Функції належності терм-множини +( +) +1 +D m + (показники видання) +iy , умовні одиниці +1 +2 +3 +4 +5 +( +) +просте +iy +µ +1 +0,778 +0,556 +0,333 +0,111 +( +) +ускладнене +iy +µ +0,124 +0,624 +1 +0,374 +0,124 +( +) +складне +iy +µ +0,11 +0,553 +0,777 +0,887 +1 +Наведемо нечіткі логічні рівняння для термів «низька», «середня», +«висока» найвищого рівня G: +( ) +( ) +( ) +0,667 +0,443 +0,334 +0,667 +1 +0,334 +0,334, +0,777 +0,443 +1 +0,333 +1 +1 +0,443, +0,333 +0,375 +0,666 +0,333 +1 +0,666 +0,333. +низька +середня +висока +G +G +G +µ += +∧ +∧ +∨ +∧ ∧ += +µ += +∧ +∧ ∨ +∧ ∧ = +µ += +∧ +∧ +∨ +∧ ∧ += + + +121 +5.3. Визначення числового значення інтегрального показника якості +На основі отриманих даних виконується дефазифікація нечіткої +множини за формулою [22; 26; 62; 72]: + +( +) +( ) +( ) +1 +1 +1 +1 +m +i +i +m +i +i +G +G +G +i +G +m +G +G += += + + +− ++ +− +µ + + +− + + += +µ +∑ +∑ +, +(39) +де G — найменше значення показника якості; G — найбільше +значення показника якості; m — кількість нечітких термів [22; 26; +62; 72]. +Приймаються умовні межі для змінної G : +1% +G = +, +100% +G = +. Об- +числення виконується за трьома точками поділу: 1 %, 50 %, 100 %. +У результаті обчислення встановлюється числове значення інтеграль- +ного показника якості проєктування післядрукарських процесів: + +. +1 0,334 +50 0,443 100 0,333 +50,256%. +0,334 +0,443 +0,333 +прогноз +G +⋅ ++ +⋅ ++ +⋅ += += ++ ++ + +Опираючись на сформовану послідовність етапів дослідження, +наведемо синтезовану структурно-функціональну модель інформа- +ційної технології прогностичного оцінювання якості проєктування +післядрукарських процесів (рис. 4). +Таким чином, розроблена структурно-функціональна модель +складається з п’яти основних етапів, кожен з яких розділений на +відповідні підетапи, що визначають окрему дію з отримання, мо- +делювання, аналізу та синтезу інформації, задля визначення якості +досліджуваного процесу. Така деталізація, внаслідок впровадження +розробленої інформаційної технології в реальні виробничі умови +уможливлює обдумане, прогнозоване формування проєкту реалізації +післядрукарських процесів, підвищення економічної ефективності, +доцільності операцій, спрощення післядрукарського опрацювання +книжкової продукції. +Використаємо методологію IDEF0 для функціонального моде- +лювання інформаційної технології проєктування післядрукарських +процесів. Побудуємо контекстну діаграму А-0, діаграму першого рів- +ня декомпозиції А0, діаграми другого рівня декомпозиції А1, А2, А3, +А4, А5, діаграми третього рівня декомпозиції А23, А24, А41, А42, А51, +А52 [40; 77]. + +122 +ЕТАП 1 +Аналіз предметної області +1.1. Узагальнений опис операцій та +технологій післядрукарського +опрацювання книжкової продукції +1.2. Функціональне моделювання +післядрукарського опрацювання +книжкової продукції +1.3. Аналіз факторів впливу на якість +ППП. Розроблення онтології +1.4. Функціональне моделювання +ППП +ЕТАП 2 +Синтез моделей факторів ППП +2.1. Розроблення семантичної мережі +взаємозв’язків між факторами +проєктування післядрукарських +процесів +2.2. Формалізація з’язків між +факторами за допомогою предикатних +формул +2.3. Побудова моделі пріоритетного +впливу факторів ППП за методом +математичного моделювання ієрархій +2.4. Побудова моделі пріоритетного +впливу факторів ППП за методом +ранжування +ЕТАП 3 +Оптимізація моделі факторів ППП +3.1. Формування матриці попарних +порівнянь факторів +3.2. Визначення компонент головного +власного вектора МПП +3.3. Визначення компонент +нормалізованого вектора МПП +3.4. Аналіз результатів оптимізації за +максимальним значенням головного +власного вектора МПП, індексом +узгодженості та відношенням +узгодженості +3.5. Візуалізація співвідношень компо- +нент вихідного та нормалізованого +векторів. Побудова оптимізованої +моделі пріоритетного впливу факторів +на якість ППП +ЕТАП 4 +Визначення оптимальних +альтернатив реалізації ППП +4.1. Багатофакторний вибір +альтернативи на основі лінійного згор- +тання критеріїв +4.2. Багатофакторний вибір +альтернативи на основі нечіткого від- +ношення переваги +4.3. Перевірка результатів +ЕТАП 5 +Визначення інтегрального +показника якості ППП +5.1. Фазифікація нечіткої множини +5.2. Дефазифікація нечіткої множини +5.3. Визначення числового значення +інтегрального показника якості +Рис. 4. Структурно-функціональна модель інформаційної технології +прогностичного оцінювання якості проєктування +післядрукарських процесів +Контекстна діаграма зображена на рис. 5. При цьому основною +функцією системи є інформаційна технологія прогностичного оці- +нювання якості проєктування післядрукарських процесів, а зв’язок +системи із навколишнім середовищем зображується граничними +стрілками: I1 — потреба у розробленні інформаційної технології, I2 — + +ETAII5Il IlI. Po3po6JeHH 0HToJoril1.4. @yHKniOHaIHe MOeOBaHHIIIII.ETAII 2ETAII3ETAII4ETAIIAnals npedneot obndci1.1. YaraHeH ollc oepain TaTexHOIOri icJpyKapcEEorO1.2. DyHKnioHaIHe MOIeOBaHHLEHHKEOBoi poyEIii1.3. AHalis bakTopiB BIJIHBy Ha kicTE123 +погано структурована задача, C1 — нормативно-технічна та техноло- +гічна документація, C2 — теорії, методи, методики, принципи, O1 — +оптимальна альтернатива реалізації проєктування післядрукарських +процесів, O2 — інтегральний показник якості проєктування післядру- +карських процесів, M1 — апаратне та програмне забезпечення, M2 — +дослідники, експерти з предметної області, інші зацікавлені особи. +Інформаційна технологія +прогностичного +оцінювання якості +проєктування після- +друкарських +процесів +Потреба у +розробленні інфор- +маційної технології +Погано +структурована +задача +Оптимальна +альтернатива +реалізації ППП +Апаратне та +програмне +забезпечення +Дослідники, експерти з +предметної області, +зацікавлені особи +Теорії, +методи, +методики, +принципи +Нормативно-технічна +та технологічна +документація +Інтегральний +показник якості ППП +Рис. 5. Контекстна діаграма А-0 моделі IDEF0 інформаційної +технології прогностичного оцінювання якості проєктування +післядрукарських процесів +Опишемо кожну граничну стрілку, враховуючи поділ за типами. +Граничні стрілки типу «Вхід» (Input): +– +1I (потреба у розробленні інформаційної технології). Потреба +в організації інформаційних процесів з використанням засобів об- +числювальної техніки, що пришвидшує опрацювання даних, пошук +інформації та спрощує доступ до неї; +– +2I (погано структурована задача). За глибиною пізнання роз- +різняють три класи проблем: добре структуровані, неструктуровані та +погано структуровані. Останні характеризуються наявністю як якіс- +них, так і кількісних показників, з явною перевагою маловідомих, не- +достатньо досліджених якісних характеристик проблеми. До погано + +01120CM,M124 +структурованих проблем відносяться великомасштабні задачі, яким +притаманні значна кількість альтернатив, залежність від сучасних тех- +нологій, невизначеність щодо тривалості виконання, кількості фінан- +сових ресурсів та матеріалів, наявність ризиків. Проєктування після- +друкарських процесів належить до погано структурованих проблем. +Граничні стрілки типу «Контроль» (Control): +– +1 +C (нормативно-технічна та технологічна документація). До +нормативно-технічної документації належать технічні вимоги та за- +конодавчі положення, зокрема: закони, стандарти, технічні умови, +кодекси усталеної практики та ін.; +– +2 +C (теорії методи, методики, принципи). Кожен інформацій- +ний процес виконується на основі загальновідомих чи новітніх тео- +рій, методів, методик та принципів. Так, наприклад, виокремлення +та формалізація зв’язків між факторами проєктування післядрукар- +ських процесів здійснюється за методами системного та матричного +аналізу, теорією графів та семантичних мереж, логікою предикатів; +створення моделі пріоритетного впливу факторів відбувається за тео- +рією ієрархічних багаторівневих систем і т. д. [58; 59]. +Граничні стрілки типу «Вихід» (Output): +– +1 +O (оптимальна альтернатива реалізації проєктування післядру- +карських процесів). Виконання будь-якого технологічного завдання +передбачає наявність можливих альтернатив. Важливим етапом є вибір +найкращої альтернативи реалізації серед множини існуючих [25; 79]; +– +2 +O (інтегральний показник якості проєктування післядрукар- +ських процесів). Основною метою виконання будь-якого процесу +є отримання якісного результату. При цьому прогнозування якості +уможливлює досягнення мети. Встановлення кількісного показника +якості проєктування післядрукарських процесів здійснюється за до- +помогою методів та засобів нечіткої логіки [26; 42; 62]. +Граничні стрілки типу «Механізми» (Mechanism): +– +1 +M (апаратне та програмне забезпечення). Пошук, опрацюван- +ня, зберігання та передавання інформації передбачає використання +сучасних технічних та програмних засобів; +– +2 +M (дослідники, експерти з предметної області, зацікавлені +особи). Реалізація інформаційної технології прогностичного оціню- +вання якості проєктування післядрукарських процесів передбачає +проведення ряду досліджень із залученням фахових науковців, фор- +муванням експертних висновків, апробацією та консультуванням із +зацікавленими особами. + +125 +Діаграма першого рівня декомпозиції А0 моделі IDEF0 утворена +шляхом декомпозиції контекстної діаграми та містить такі функціо- +нальні блоки: +– АПО (аналіз предметної області). Здійснюється для означення +теоретичної складової досліджуваного процесу та виокремлення по- +слідовності операцій шляхом функціонального моделювання. При +цьому розглядається не лише створення проєкту, а й сам процес піс- +лядрукарського опрацювання книжкової продукції, адже важливо +розуміти особливості об’єкта проєктування; +– СМФ ППП (синтез моделей факторів проєктування після- +друкарських процесів). Полягає у розробленні семантичної мережі +та формалізації зв’язків між факторами, використовуючи елементи +логіки предикатів, а також у визначенні рівнів домінантності факто- +рів та побудові моделі пріоритетного впливу. Пріоритетність факто- +рів визначається за методом математичного моделювання ієрархій і +уточнюється за методом ранжування [58, 59]; +– ОМФ ППП (оптимізація моделі факторів проєктування піс- +лядрукарських процесів). Передбачає встановлення оптимізованих +вагових значень факторів досліджуваного процесу та побудову опти- +мізованої моделі. Цей етап дозволяє деталізувати пріоритетність фак- +торів і, за наявності, уникнути розміщення кількох факторів на одна- +ковому рівні [68]; +– ВОАР ППП (встановлення оптимальних альтернатив реалізації +проєктування післядрукарських процесів). Здійснюється проєктуван- +ня та дослідження можливих альтернатив реалізації аналізованого про- +цесу та обирається оптимальна. При цьому опрацювання здійснюється +за двома методами, а результати порівнюються. Збіжність отриманих +результатів свідчить про адекватність розв’язку задачі [25; 61]; +– ВІПЯ ППП (встановлення інтегрального показника якості про- +єктування післядрукарських процесів). На основі методів та засобів +нечіткої логіки встановлюються прогнозовані числові параметри до- +сліджуваного процесу та, відповідно до заданих умов, визначається +інтегральний показник якості [26; 42; 62]. +Наступним етапом є побудова діаграм другого рівня декомпозиції, +тобто декомпозиція діаграми першого рівня. Діаграма А1 складається +з чотирьох функціональних блоків: +– ООТ ПОКП (опис операцій та технологій післядрукарського +опрацювання книжкової продукції). Описуються можливі операції +та технології післярукарського опрацювання, умови їх вибору та реа- + +126 +лізації. Такий опис уможливлює подальше моделювання та проєкту- +вання; +– ФМ ПОКП (функціональне моделювання післядрукарського +опрацювання книжкової продукції). Функціональне моделювання +здійснюється за методологією IDEF0. Полягає у формуванні кон- +текстної діаграми, де основною функцією системи є післядрукарське +опрацювання книжкової продукції, декомпозиції контекстної діагра- +ми (створенні діаграми першого рівня декомпозиції) та декомпозиції +діаграми першого рівня (створенні діаграм другого рівня декомпози- +ції). Формується деревовидна ієрархічна модель післядрукарського +опрацювання книжкової продукції, яка ілюструє відношення між +батьківськими та дочірніми вузлами моделі IDEF0 [40; 77]; +– АФВ та РО ППП (аналіз факторів впливу та розроблення онто- +логії проєктування післядрукарських процесів). Означується інфор- +маційна складова факторів впливу на якість досліджуваного процесу. +Здійснюється деталізований опис виокремлених факторів: показни- +ки видання, конструкційні особливості, умови експлуатації, тип ви- +робництва, матеріали, тип обладнання, технологічні та економічні +розрахунки, схема технологічного процесу [30]. Розробляється онто- +логія [33]; +– ФМ ППП (функціональне моделювання проєктування піс- +лядрукарських процесів). Будується контекстна діаграма, діаграма +першого рівня декомпозиції та діаграми другого рівня декомпозиції. +Основною функцією системи є проєктування післядрукарських про- +цесів. Також формується деревовидна ієрархічна модель, вершиною +якої є контекстна діаграма [40; 77]. +Діаграма А2 містить такі функціональні блоки: +– РСМ (розроблення семантичної мережі). Модель семантичної +мережі є основою для подальшого дослідження. За структурою це +орієнтований граф, сукупність вузлів якого відповідає множині фак- +торів, а дуги — зв’язкам між ними [61]; +– ФЗФ (формалізація зв’язків між факторами). Формалізований +опис зв’язків між факторами здійснюється з використанням елемен- +тів логіки предикатів [59; 61]; +– ПМПВФ за МММІ (побудова моделі пріоритетного впливу +факторів за методом математичного моделювання ієрархій). Метод +математичного моделювання ієрархій полягає у встановленні рівнів +пріоритетності факторів шляхом побудови матриці досяжності та іте- +раційних таблиць [58]; + +127 +– ПМПВФ за МР (побудова моделі пріоритетного впливу факто- +рів за методом ранжування). Метод ранжування передбачає побудову +ієрархічних дерев, що ілюструють зв’язки між факторами і встанов- +лення пріоритетності факторів за ваговими значеннями [30]. +Для третього та четвертого функціональних блоків діаграми А2 до- +цільно продовжити декомпозицію. Діаграма А23 містить такі функці- +ональні блоки: +– СМД (створення матриці досяжності). Матриця досяжності для +зручності відображення даних будується у вигляді таблиці. Наявність +прямого чи опосередкованого впливу позначається одиницею, а від- +сутність — нулем; +– СІТ (створення ітераційних таблиць). Ітераційні таблиці містять +чотири колонки: порядковий номер фактора у множині; порядкові +номери факторів, на які впливає визначений фактор; порядкові номе- +ри факторів, від яких залежить визначений фактор; спільні порядкові +номери впливаючих та залежних факторів. Кожна ітерація полягає у +викресленні рядка (рядків) ітераційної таблиці, у якому співпали дані +у третьому та четвертому стовпцях. Фактор, що відповідає першому +викресленому рядку, має найвищий рівень пріоритетності, а фактор, +що відповідає останньому викресленому рядку, — найнижчий рівень +пріоритетності; +– МПФ (моделювання пріоритетності факторів). Дані, отримані +внаслідок ітерації, використовуються для побудови моделі пріоритет- +ного впливу факторів [58]. +Діаграма А24: +– СІД (створення ієрархічних дерев). Для кожного фактора мно- +жини будуються ієрархічні дерева, що ілюструють прямі та опосеред- +ковані впливи визначеного фактора на інші фактори та ієрархічні де- +рева, що ілюструють прямі та опосередковані залежності; +– ВВЗФ (встановлення вагових значень факторів). За ієрархіч- +ними деревами визначається кількість прямих та опосередкованих +впливів і залежностей. Приймаються умовні вагові коефіцієнти. Об- +числюються інтегральні вагові величини факторів за сумами ваг усіх +типів зв’язків; +– ВРФ (встановлення рангів факторів). Згідно з інтегральними +ваговими значеннями визначаються ранги факторів. При цьому фак- +тору із найменшим інтегральним значенням належить найнижчий +ранг — перший. Кільком факторам можуть бути присвоєні однакові +ранги; + +128 +– ВРПФ (встановлення рівня пріоритетності факторів). Рівень +пріоритетності встановлюється за рангом фактора. Фактору з найви- +щим рангом належить найвищий рівень пріоритетності — перший. +Кілька факторів можуть бути однаковими за пріоритетністю; +– МПФ (моделювання пріоритетності факторів). На основі вста- +новлених рівнів пріоритетності факторів, отриманих внаслідок іте- +раційних процесів та уточнених шляхом ранжування, синтезується +ієрархічна модель пріоритетного впливу факторів. При цьому найви- +щий рівень моделі відповідає фактору з найбільшим пріоритетом, а +найнижчий — з найменшим пріоритетом серед виокремленої множи- +ни [30; 59]. +Розглянемо функціональні блоки діаграми А3: +– ФМППФ (формування матриці попарних порівнянь факторів). +На основі шкали відносної важливості об’єктів за Сааті формується +матриця попарних порівнянь факторів. За критеріями порівняння +обирається необхідна оцінка корисності від 1 до 9. Якщо об’єкти рів- +ноцінні, оцінка корисності 1. Якщо один об’єкт абсолютно перева- +жає інший — 9. Для опису проміжних відношень слугують інші оцін- +ки в межах вказаної шкали [25; 68]; +– ВКГВВ (визначення компонент головного власного вектора). +Головний власний вектор визначається як середнє геометричне еле- +ментів кожного рядка матриці попарних порівнянь; +– ВКНВ (визначення компонент нормалізованого вектора). Ком- +поненти нормалізованого вектора визначають числові пріоритети +факторів та дозволяють уточнити їх вагові значення; +– АРО (аналіз результатів оптимізації). Здійснюється перевірка +отриманих результатів за нормативними значеннями індекса узго- +дженості, відношення узгодженості та максимальним значенням го- +ловного власного вектора матриці попарних порівнянь; +– ВСКВ (візуалізація співвідношень компонент векторів). Буду- +ються гістограма та порівняльний графік вагових значень компонент +вихідного та нормалізованого векторів. Вихідний вектор формується +на основі моделі пріоритетного впливу факторів за присвоєними ва- +говими значеннями. Для зручності візуалізації компоненти нормалі- +зованого вектора адаптуються за довільним коефіцієнтом; +– ПОМПВФ (побудова оптимізованої моделі пріоритетного впли- +ву факторів). За перевіреними результатами оптимізації синтезується +оптимізована модель пріоритетного впливу факторів на якість про- +єктування післядрукарських процесів. Найвищий рівень моделі від- + +129 +повідає фактору з найбільшим пріоритетом, а найнижчий — з най- +меншим. Отримана модель є основою подальшого прогностичного +оцінювання [68]. +Діаграма А4 містить такі блоки: +– БВА ЛЗК (багатофакторний вибір альтернатив на основі ліній- +ного згортання критеріїв). Встановлення оптимального варіанту ре- +алізації проєктування післядрукарських процесів за методом ліній- +ного згортання критеріїв полягає у лінійному об’єднанні часткових +цільових функціоналів в один, а задача багатокритеріальної (багато- +факторної) оптимізації — у знаходженні максимального значення +функцій корисності [25; 59]; +– БВА НВП (багатофакторний вибір альтернатив на основі нечіт- +кого відношення переваги). Багатофакторний вибір альтернатив на +основі нечіткого відношення переваги полягає у встановленні попар- +них переваг між запроєктованими альтернативами факторів проєк- +тування післядрукарських процесів та їх кількісному представленні; +– ПР (перевірка результатів). Порівнюється, чи однаковими є +встановлені оптимальні альтернативи за двома вищеописаними ме- +тодами. Тотожність результатів свідчить про адекватність розв’язку +задачі [59; 79]. +Для першого та другого функціональних блоків діаграми А4 до- +цільно продовжити декомпозицію. Діаграма А41 містить: +– ФМП (формування множини Парето). Множина Парето вклю- +чає тільки фактори з суттєво вищою пріоритетністю, фактори з низь- +кою пріоритетністю відкидаються; +– ПА (проєктування альтернатив). Проєктується необхідна кіль- +кість альтернативних варіантів реалізації проєктування післядрукар- +ських процесів; +– ОА (оцінювання альтернатив). Здійснюється відсоткове виражен- +ня міри впливу факторів множини Парето для кожної альтернативи; +– СМППФ (створення матриці попарних порівнянь факторів). +Згідно із ваговими даними факторів множини Парето та за шкалою від- +носної важливості об’єктів формується матриця попарних порівнянь; +– НГВВ (нормалізація головного власного вектора). Внаслідок +нормалізації головного власного вектора матриці попарних порів- +нянь факторів множини Парето встановлюються вагові значення, +необхідні для подальших обчислень; +– ВК та БОК (визначення корисності та багатокритеріальних оцінок +корисності). Формуються матриці попарних порівнянь альтернативних + +130 +варіантів реалізації щодо кожного фактора множини Парето, за якими +визначаються корисності альтернатив. Багатокритеріальні оцінки ко- +рисності кожної альтернативи обчислюються як суми добутків вагових +значень факторів та корисності відповідних альтернатив [25]; +– ВОА (вибір оптимальної альтернативи). Оптимальна альтернати- +ва реалізації проєктування післядрукарських процесів обирається за +максимальним значенням багатокритеріальної оцінки корисності [59]. +Діаграма А42: +– ОНВП на МА (оцінювання нечітких відношень переваги на +множині альтернатив). Формуються відношення нестрогої переваги +між альтернативами кожного фактора множини Парето; +– ФМВФ (формування матриць відношень для факторів). На +основі відношень переваги формуються матриці відношень. Причо- +му наявність переваги позначається одиницею, а непорівнюваність +альтернатив між собою — нулем; +– ПЗВ (побудова згорток відношень). Формується згортка від- +ношень за усіма факторами множини Парето, де одиницею позна- +чається наявність переваги між альтернативами для усіх факторів, а +нулем — непорівнюваність альтернатив хоча б за одним фактором. +Інший тип згортки відношень визначається за ваговими значеннями +факторів та відповідних функцій корисності; +– ВПНА (визначення підмножин недомінованих альтернатив). +Визначаються на основі згорток відношень та за відповідними фор- +мулами; +– ВФНСМ (визначення функцій належності спільної множини). +Визначається спільна множина недомінованих альтернатив та функ- +ції належності; +– ВОА (вибір оптимальної альтернативи). Оптимальною є альтер- +натива із максимальним значенням функції належності [25; 59]. +Діаграма А5 містить три функціональні блоки, а саме: +– Ф (фазифікація). Процес фазифікації полягає у зіставленні мно- +жини значень її функцій належності; +– Д (дефазифікація). Процес дефазифікації є зворотним до фази- +фікації. Дефазифікація нечіткої множини здійснюється за принци- +пом центра ваги; +– ВЧЗІПЯ (визначення числового значення інтегрального показ- +ника якості). Визначається для можливості прогностичного оціню- +вання якості проєктування післядрукарських процесів за певних ви- +значених умов. Виражається у відсотках [27–29; 60; 62]. + +131 +Подальшій декомпозиції підлягають перший та другий функціо- +нальні блоки діаграми А5. Відповідно діаграма А51 містить такі блоки: +– ФЧПЯ (формування часткових показників якості). Для вста- +новлення інтегрального показника якості проєктування післядру- +карських процесів доцільно сформувати часткові показники якості +лінгвістичних змінних та згрупувати її за спільними ознаками та при- +значенням; +– ВУМЗ та ТМАЗ (виокремлення універсальної множини значень +та терм-множини аналізованих змінних). Для кожної лінгвістичної +змінної формується універсальна множина значень зі встановленими +межами та одиницями вимірювання і терм-множина, яка словесно +описує градацію універсальної множини; +– ПБМНЛВ (побудова багаторівневої моделі нечіткого логічного +виводу). Багаторівнева модель нечіткого логічного виводу будується +для ієрархічного представлення залежності між якістю проєктування +післядрукарських процесів та значеннями лінгвістичних термів ви- +окремлених факторів [27]; +– ОФНЛЗ (опрацювання функцій належності лінгвістичних змін- +них). За відносними оцінками рангів лінгвістичних термів створю- +ються квадратні обернені симетричні матриці, внаслідок обчислення +яких встановлюються числові значення функцій належності у п’яти +точках поділу універсальної множини. Отримані нечіткі множини ві- +зуалізуються за допомогою графіків [28; 29]; +– ФБЗ (формування баз знань). Формується нечітка база знань +для інтегрального показника якості та для кожної лінгвістичної змін- +ної, враховуючи ієрархію, наведену у багаторівневій моделі нечіткого +логічного виводу; +– ФМЗ (формування матриць знань). За сформованими базами +знань синтезуються матриці знань для якості проєктування післядру- +карських процесів та для кожного часткового показника; +– ФНЛР (формування нечітких логічних рівнянь). За сформова- +ними матрицями знань будуються нечіткі логічні рівняння для кож- +ного терму часткових показників якості та для термів лінгвістичної +змінної «якість проєктування післядрукарських процесів» [50; 60; 64]. +Діаграма А52 включає: +– ФТЗФНЛЗ (формування таблиць значень функцій належності +лінгвістичних змінних). За терм-множинами з пронормованими зна- +ченнями функцій належності у п’яти точках поділу універсальної мно- +жини створюються таблиці значень для кожної лінгвістичної змінної; + +132 +– ФНЛР (формування нечітких логічних рівнянь). Здійснюється +підстановка значень з таблиць значень у нечіткі логічні рівняння для +термів «низька», «середня», «висока» кожної лінгвістичної змінної. +Відповідно проводяться обчислення підсумкових значень функцій +належності [22; 26; 62; 72]. +Для відображення ієрархічної залежності функцій використаємо +діаграму дерева вузлів, у якій верхній рівень відповідає контекстній +діаграмі (батьківському елементу), а нижні — декомпозиції потоків +(дочірнім елементам). При цьому взаємозв’язки між функціональ- +ними блоками не відображаються, лише ієрархічна впорядкованість. +Такий підхід уможливлює цілісний аналіз ієрархії функціональних +блоків моделі IDEF0 [77]. +Висновки. У дослідженні наведено розв’язання актуального науко- +во-прикладного завдання розроблення інформаційної технології про- +гностичного оцінювання якості проєктування післядрукарських про- +цесів на основі дослідження домінантності виокремлених факторів і +застосування нечіткої логіки для отримання інтегрального показника +якості. Виокремлено основні етапи інформаційної технології. +Наведено загальну характеристику реалізації та проєктування піс- +лядрукарського опрацювання книжкових видань. Виокремлено та +описано фактори впливу на якість проєктування післядрукарських +процесів. Здійснено моделювання функцій реалізації та проєктуван- +ня досліджуваного процесу. Створено IDEF0-моделі, які складаються +з сукупності ієрархічно впорядкованих та взаємопов’язаних діаграм: +контекстної діаграми, декомпозиції контекстної діаграми (діаграми +першого рівня декомпозиції) та декомпозиції функціональних блоків +діаграми першого та другого рівнів. Описано основні підходи до ство- +рення онтології та основні типи онтологій. +Подано методологію побудови семантичної мережі, що відтворює +зв’язки між факторами впливу на якість аналізованого процесу. За +допомогою логіки предикатів здійснено формалізоване відображен- +ня зв’язків між ними. +Наведено особливості синтезу та оптимізації моделі пріоритетного +впливу факторів на якість проєктування післядрукарських процесів. +Критерії оптимізації становлять: власне значення матриці +max +8,483 +λ += +, +індекс узгодженості +0,069 +IU = +, відношення узгодженості +0,049 +RU = +. +Критерії оптимізації знаходяться в допустимих межах. +Визначено оптимальні альтернативні варіанти реалізації проєкту- +вання післядрукарських процесів за методами багатофакторного ви- + +133 +бору альтернатив на основі лінійного згортання критеріїв та на основі +нечіткого відношення переваги. При цьому за методом багатофак- +торного вибору альтернатив на основі лінійного згортання критеріїв +максимальне значення отримала оцінка корисності +3 +0,414 +U = + аль- +тернативи А3. За методом багатофакторного вибору альтернатив на +основі нечіткого відношення переваги максимальне значення отри- +мала функція належності +( +) [ +] +3 +0,4; 0,74;1,26 +нд +Q +x +µ += +, тобто оптималь- +ним вважається третій варіант. Порівняно результати пошуку опти- +мальних альтернатив та встановлено тотожність варіантів. +Отримано значення функцій належності лінгвістичних змінних +аналізованого технологічного процесу шляхом обчислення матриць +попарних порівнянь для кожної лінгвістичної змінної та відповідної +їй терм-множини значень. Терми лінгвістичних змінних представле- +но нечіткими множинами. +Описано отримання значення оцінки якості проєктування піс- +лядрукарських процесів шляхом дефазифікації нечітких множин за +принципом центра ваги. Інтегральний показник якості за обраних +умов становить +. +50,256% +прогноз +G += + при максимальних значеннях 100%. +Розроблено структурно-функціональну модель інформаційної +технології прогностичного оцінювання якості проєктування після- +друкарських процесів, що враховує етапи дослідження та уможлив- +лює апріорне забезпечення якості друкованої продукції. Створено +IDEF0-моделі інформаційної технології: побудовано контекстну діа- +граму А-0, діаграму першого рівня декомпозиції А0, діаграми другого +рівня декомпозиції А1, А2, А3, А4, А5, діаграми третього рівня деком- +позиції А23, А24, А41, А42, А51, А52 та діаграму дерева вузлів. +СПИСОК ВИКОРИСТАНОЇ ЛІТЕРАТУРИ +1. ДСТУ 3017:2015. Видання. Основні види. Терміни та визначення понять. +Київ, 2016. 38 с. +2. ДСТУ 4489:2005. Видання книжкові та журнальні. Вимоги до форматів. +Київ, 2006. 10 с. +3. Антонова С. Г. Редакторская подготовка зданий: учебник. Москва: Изда- +тельство МГУП, 2002. 468 с. +4. Барановський І. В., Яхимович Ю. П. 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Models of +Postpress Processes Designing. 1st International Workshop on Digital Content +& Smart Multimedia, DCSMart 2019, Lviv, Ukraine, December 23–25, 2019. +P. 259–270. + +139 +THERMALLY STIMULATED PROCESSES +AND PYROELECTRICITY IN FERROELECTRIC POLYMERS +Sergeeva A. E. +Стаття присвячена експериментальному дослідженню тонких плі- +вок полівініліденфториду (ПВДФ), його сополімеру з тетрафторетиле- +ном П(ВДФ-ТФЄ), а також композитів на основі ПВДФ та неорганічних +керамічних матеріалів титанату барію BaTiO3 та титанату циркона- +ту свинцю (ЦТС). Всі ці матеріали є сегнетоелектриками. Вивчено їхню +поведінку при різних температурних впливах, зокрема струми термо- +стимульованої поляризації (ТСП) та деполяризації (ТСД), а також піро- +електричний ефект у цих матеріалах. Встановлено, що термічний вплив є +важливим при формуванні сегнетоелектричної поляризації та забезпечен- +ня її стабільності. +Встановлено важливу роль об’ємного заряду в сегнетоелектричних полі- +мерах на величину та стабільність залишкової поляризації. Запропоновано +методи поділу гомозаряду та гетерозаряду у полімерних плівках. +Отримані результати мають як наукове, так і практичне значення, +оскільки сегнетоелектричні полімери широко використовуються для виго- +товлення різних сенсорів і датчиків. +This article is devoted to the experimental study of polyvinylidene fluoride +(PVDF) thin films, its copolymer with tetrafluoroethylene P(VDF-TFE), as well as +composites based on PVDF and inorganic ceramic materials of barium titanate Ba- +TiO3 and lead zirconate titanate (PZT). All of these materials are ferroelectrics. +Their behavior was studied under different temperature influences, in particular, +currents of thermally stimulated polarization (TSP) and depolarization (TSD), as +well as the pyroelectric effect in these materials. +It was found that thermal action affects the formation of ferroelectric polariza- +tion and its stability. The important role of the space charge in ferroelectric polymers +on the magnitude and stability of polarization has been established. Methods for +separating homocharge and heterocharge in polymer films were proposed. +The results obtained are of both scientific and practical importance, since fer- +roelectric polymers are widely used in the manufacture of various kinds of sensors +and transducers. +1. Introduction +To measure the thermal relaxation of the residual polarization, the mea- +surement of the thermally stimulated depolarization currents (TSD) is the +most appropriate. Despite numerous experimental studies, there is still no +theory of the TSD current method for the case of poled ferroelectric poly- +mers like polyvinylidene fluoride (PVDF). Therefore, the description and + +140 +interpretation of measured current peaks are usually qualitative and hypo- +thetical. +To detect the nature of the TSD current peaks, their connection with po- +larization and pyroelectricity must be taken into account, as well as processes +occurring in the amorphous and crystalline phases. Such an attempt was made +[1; 2] by considering individual contributions to TSD currents of pyroelectric +processes, polarization in the amorphous phase, “charge-induced interphase +polarization” (called the Maxwell-Wagner effect) and the ferroelectric po- +larization in the crystalline phase. In qualitative description of the predicted +processes, in addition to compensating charges, “injected surplus charges” +were taken into account, that is, space charges. Often it is considered as a +self-evident that there is polarization in PVDF, compensating charges, and +space charges. While there is no doubt about the existence of polarization, the +existence of the space charge in addition to compensating charges is question- +able, since PVDF has a sufficiently high specific conductivity about g = 10–11 +Sm/m at room temperature [3; 4] and the dielectric permittivity ε = 10–20. +Therefore, any surplus charges will be neutralized with the Maxwell re- +laxation time of approximately + +0 +13s +g +ε ε +τ = +≈ +. +(1) +This indicates that in the short-circuited sample, after about 40 seconds, +any electric field caused by charges (other than compensating charges and +polarization charges of the ferroelectric crystals) will disappear. +Homogeneously polarized two-phase materials, like PVDF, consist of +ferroelectric crystallites scattered in the amorphous matrix. Compensation +of the depolarizing field in the ferroelectric crystallites is possible only due +to the charges localized at two sides of the crystallites. Full compensation by +the electrode charges, as in the case of single crystals or 100 % crystalline +materials, is not possible. In PVDF and other biphasic ferroelectric poly- +mers, the accumulation of charge at the boundaries between the crystalline +and amorphous phases only occurs to a small extent due to the difference in +dielectric constant, and is the most likely due to presence of the ferroelec- +tric polarization. von Seggern and Fedosov proposed a model of a layered +structure with alternating ferroelectric and non-ferroelectric layers for the +description of initial poling [3, 4], switching of polarization [5], short circu- +iting and the back switching [6] in PVDF. +The theory of the TSD method [7] was developed only for electrets with +dipole and/or space charge polarization. It is assumed that polarization or + +141 +space charge is initially thermally frozen, and then it defrosts under linear +heating. For application the TSD method to ferroelectric polymers, the the- +oretical basis has not yet been constructed, since polarization in PVDF is not +thermally frozen, but has the ferroelectric nature and can occur in high fields +without heating during poling. In addition to the irreversible relaxation cur- +rents, in the TSD experiments on ferroelectric polymers, there are reversible +pyroelectric currents, and the separation of these components is not an easy +task. However, the TSD method, due to its informative and versatile nature, +has been widely used for studying the polymer ferroelectric as well. +The TSD current peak at 50–60 °C has been observed by many research- +ers in the non-ferroelectric α-PVDF and the ferroelectric β-PVDF poled in +a wide range of temperatures, electric fields and times. The only common +feature of all PVDF samples on which these experiments were carried out +was the presence of the amorphous phase. Thus, this TSD current peak with +high probability can be associated with processes occurring in the amor- +phous phase of PVDF. +In many cases, it was assumed that the TSD current peak near 50–60 °C +is associated with the so-called αc-process [8]. However, data on the nature +of the αc-process are still controversial. Moreover, an interrelation between +structural transformations and TSD currents should be established, since +the TSD currents are the result of electrical, but not always structural pro- +cesses. Making assumptions about the nature of the TSD currents peaks, it +is necessary to take into account not only structural transformations, but +also fundamental electrical principles and laws. Otherwise, a qualitative ex- +planation without the corresponding formulas and equations may be false. +Two high-temperature peaks, in addition to the usual α- and β-processes in +PVDF, were found by the TSD method. One of the processes was attribut- +ed to charges trapped on the boundary between the nonpolar crystalline +α-phase and the amorphous region. The other was assumed to be related +to charges on polar β-crystallites. The authors believe that both peaks are +due to the positive homocharge injected from the anode, although it is quite +probable that they are related to the poling temperature. +Eliasson [9], studying the influence of the polarizing field, temperature, +and electrode material on TSD currents, believed that the formation of a +bulk charge was influenced by injection, although her results did not match +with the position and magnitude of peaks in the data of Ieda and others +[10]. The picture becomes even more complicated if we compare the data +on the TSD obtained by different researchers. The variety of relaxation pro- +cesses determined by the TSD method is due to the lack of clear methods + +142 +for identifying peaks (sometimes they take for relaxation peaks the smallest +bends at the TSD current curve). Neagu and others [11] believe that the +high influence on the TSD currents has the material of electrodes and the +uncontrolled composition of the atmosphere, in particular presence of oxy- +gen, nitrogen and water vapors. +It follows from the theory of the TSD currents [12] that in a one-com- +ponent homogeneously polarized dipolar sample, the measured current is +equal to the displacement current dP/dt, so that the integral of the TSD +current is equal to the value of the initial polarization. As shown by von +Seggern and Fedosov [5], the integral of the TSD current is smaller than the +residual polarization in the case of a two-phase system. +Possibilities of thermally stimulated research methods are extremely +wide, since most relaxation processes are thermally activated. At the same +time, these possibilities in the study of ferroelectric polymers have not yet +been detected and have not been used. This relates to the study of the ef- +fective conductivity dynamics in the process of the thermoelectret poling +(TEP), the comparison of TEP and TSD currents, the separation of homo- +charge and heterocharge contribution in the ferroelectric polymers to the +relaxation current, the use of fractional TSD methods for separation of the +pyroelectric and the relaxation components of the total current. +The aim of the present article was to obtain additional experimental re- +sults by using above mentioned methods for clarifying physical processes +responsible for formation of the residual polarization in PVDF films, being +a typical representative of the ferroelectric polymers. Another part of inves- +tigation is related to finding interrelation between TSD currents and the py- +roelectricity in this class of materials. We also performed some experiments +on P(VDF-TFE) copolymer and composites of PVDF with the inorganic +crystals like barium titanate (BaTiO3) and lead zircanate titanate (PZT) in +order to make the research more generalizing. +2. The features of the Thermally Stimulated Depolarization Current +method +In the case of thermoelectret poling (TEP), unlike isothermal poling, +the sample was initially kept at room temperature at constant voltage for +some time necessary to decrease the absorption current to values of the or- +der of 10–11 A, and then the temperature was linearly increased to 150 °C at +a constant rate (0.5–4 °C/min) with continuous measuring of the poling +current. After completion of poling, the samples were quickly cooled down +without switching off the applied voltage. + +143 +Since many relaxation processes have the thermally activating nature, +the TSD method [12] was used to predict the space charge and the residual +polarization stability and to study the mechanism of their formation. The +sample electrodes were connected with each other through the electrometer +having a sensitivity of 10–14–10–16 A by current and the current recording +device. The temperature was raised at a constant rate in the range of 15–150 +°C and measured by a chromel-copel thermocouple. The principle of the +current TSD method is shown in Fig. 1. +We measured the thermally stimulated decrease in the electret potential +by the vibration electrode method (Kelvin’s method). Measurements in the +range from -100 °С to +180 °С was carried out by using the relaxation spec- +trometer Solomat-91000. Studies in the field of low temperatures from -170 +to + 40 °C were performed by using the Kithley-6100 electrometer on the +samples that were originally cooled in liquid nitrogen. +3. Relaxation of homocharge and heterocharge during the TSD currents +measurement +A number of properties of the ferroelectric polymers can be explained +within the framework of the modern theory of polar electrets [13] consid- +ering relaxation of the homocharge and the heterocharge in a self-consis- +tent regime without taking into account the ferroelectricity in the crystalline +phase. We consider the interrelation between the homocharge and the het- +erocharge taking into account experimental data on thermally stimulated +and isothermal relaxation of PVDF films poled in the corona discharge. +Four types of depolarization varieties were used to study the relaxation +processes, namely thermally stimulated (T) and isothermal (I) depolariza- +tion of short-circuited samples (S) and depolarization in the open circuit +mode (O). The modes were denoted as TS, TO, ISO, and IO, where the +first letter indicated the temperature mode (thermally stimulated or iso- +thermal), and the second was related to the electrical state (short-circuit or +open circuit). Additional experiments on the thermally stimulated electret +potential (TP) kinetics were also performed after 24 hours of keeping in the +open circuit configuration. A film of polytetrafluoroethylene (PTFE) with +a thickness of 10 μm was used as a dielectric gap in TO and IO modes. All +thermally stimulated experiments were performed at a constant heating rate +of 3 °C/min. In isothermal experiments, the temperature was maintained +constant after the required temperature value was achieved by rapid heating. +The electret potential in the TP method was measured by the Kelvin meth- +od and was continuously recorded. + +144 +Time +External field +Temperature +TSD current +Charging current +Fig. 1. The principle of the thermoelectret poling (1) and depolarization (2) methods +During poling in a corona discharge, the excess charge is localized on +the surface of the sample forming a homogeneous charge σ, which creates +a homogeneous field in the sample volume, in which the internal dipolar +polarization (heterocharge) is formed characterized by the surface density +of the bound charge P. In the case of the sample short-circuiting without a +gap, only the heterocharge relaxes [12], and the equality σ = P and the zero +internal field (E = 0) is supported due to the current redistribution in the +external circuit. In the presence of a dielectric gap and in the open circuit +mode, the relaxation currents of the homocharge and the heterocharge flow +in opposite directions. +In order to find separately components corresponding to the decay of +the homocharge σ and the heterocharge P of the full depolarization current +in the open circuit mode, we present the current density i(t) and the surface +potential V(t) as + +( ) +( ) +( ) +dP t +d +t +i t +s +dt +dt +σ + + += +− + + + + +, +(2) + +[ +] +1 +0 +1 +( ) +( ) +( ) +sx +V t +t +P t += +σ +− +ε ε +, +(3) + +0 +1 +1 +( ) +( ) +dV t +i t +x +dt +ε ε += − +⋅ +, +(4) + +E +T +TSDC145 +where, t is time, ε and xo are the dielectric constant and the thickness of the +sample; ε1 and x1 are similar parameters of the dielectric gap. For the con- +ductivity current density, it is possible to write down + +0 +( ) +( ) +( ) +C +g +d +t +i +t +V t +x +dt +σ += += − +, +(5) +where +0 exp( +/ +) +g +g +Q +kT += +− + is the specific conductivity, k is Boltzmann’s +constant, T is temperature, Q is the activation energy of the intrinsic con- +ductivity, go is a pre-exponential factor. Integrating (4) over time and replac- +ing the variable t by T taking into account the linear heating +0 +T +T +t += ++β⋅ +where β is the heating rate, То is the initial temperature of the experiment, +we obtain from (5) the temperature dependences of the depolarization cur- +rents and the electret potential + +1 +0 +1 +0 +0 +0 +1 +( ) +exp +( ) +T +x g +d +Q +i T +i T dT +dt +bT x +kT +∞ +σ + + +′ += += − +− + + +ε ε + +∫ +, +(6) + +2 +( ) +( ) +dP +i T +d +i T +dt +s +dt +σ += += ++ +, +(7) + +1 +0 +0 +1 +( ) +( ) +T +x +V T +i T dT +bT +∞ +′ += +ε ε ∫ +. +(8) +All values in the right-hand sides of the equations (6–8) are known from +the experiment. Thus, this technique allows to differentiate processes of ho- +mocharge and heterocharge relaxation in different modes of TSD by using +experimental i(T) curves. +4. Application of thermoelectret poling of PVDF films +The thermoelectret poling method (TEP) has several advantages over +isothermal poling, because it allows to obtain additional data on the mech- +anism of the polarization formation. It is also possible to determine the op- +timal temperature of poling, as well as to find the temperature, at which the +ohmic conductivity becomes significant. +From Fig. 2 and Table 1 one can distinguish the following features: +1) The TEP curves contain three characteristic areas: a) the growth of +the current irrespective of the corona discharge polarity; b) decrease of the +current (negative temperature coefficient of conduction); c) increase of the +current at high temperatures. + +146 +25 +50 +75 +0 +250 +500 +750 +1000 +2 +1 +Current density, A/m +2 +Temperature, +oС +Fig. 2. Dependence of current on temperature during thermally stimulated poling in +positive (1) and negative (2) corona discharge. Heating rate is 2 °C/min +Table 1 +Effective activation energy during TEP in different temperature ranges +(from the inclination of linear parts in lni-1/T curves) [9] +Charge +Polarity +Heating +Cooling +Activation energy, eV +Temperature range, °C +Activation energy, eV +Temperature range, °C ++ +0.87 +20–40 +0.82 +40–50 +0.82 +50–65 +0.92 +60–45 +1.06 +45–25 +– +0.87 +20–35 +1.1 +35–45 +1.12 +65–80 +1.19 +70–55 +0.83 +55–35 +2) With negative corona discharge polarity, the second region is more +pronounced than with positive polarity, and the decrease in conductivity +begins at lower temperatures. The difference in the currents of the TB pos- +itively and negatively poled samples indicates different injection levels. In +a positive corona, it is likely that both positive charges and negative ones +(from the rear electrode) are injected. In the case of a negative corona, pos- +itive charge carriers from the metal electrode are not injected. +3) When thermoelectret poling of PVDF films occurs, the irreversible de- +crease in the effective conductivity is due to the fact that the value of the ther- +mal current when cooled is much smaller than the current during heating. +In PVDF, the current peak during TEP (Fig. 2) cannot be considered to +be due to polarization, as in the case of linear polar polymers, because its + +147 +integration gives an unrealistically great value of the polarization. Probably, +the conductivity current in TEP ferroelectric polymers is much larger than +the polarization component of the current, therefore the graphs in Fig. 2 +reflect the nature of changing in the films effective conductivity. +The mechanism and nature of conductivity in PVDF are unknown, but +presence of the negative temperature coefficient of conductivity sections in +curves Fig. 2 suggests that, along with the thermally activated increase in the +number of moving carriers, there is also likely to be a trapping by deep traps, +and with certain ratios of field strength and temperature the second process +prevails over the first process. The trapped charges play an important role by +neutralizing the depolarizing field and contributing to the preservation of +the residual polarization. +High polarization in a poled film and a sharp decrease in conductivity (the +current passes through the maximum) are probably interconnected. The fer- +roelectric polarization in crystallites creates conditions for trapping of charges +at their boundaries. The field of the trapped charges screens the polarization +and contribute to its stabilization. Thus, the processes of the polarization de- +velopment and the charge trapping are interconnected and interdependent. +At the current curve of TEP from room temperature to 30–40 °С, the +dependence i(T) is exponential regardless of the corona polarity. This can be +related to the thermal generation of charge carriers in the volume. The fur- +ther course of the current graphs corresponds to the proposed model for the +polarization formation and the charge trapping. There is again increase of +the current in the third section that may be due to the internal thermoelec- +tric detrapping of the previously trapped charges with partial destruction +of the already formed polarization. If this assumption is valid, then it is an +important for practice conclusion that it is impractical to heat PVDF during +TEP above the minimum temperature on the current-temperature curve. +Decrease of the current and the effective conductivity in the second sec- +tion of the TEP curve may be due to the following reasons: +1) Depletion of the stock of own carriers due to their migration in the +external field and trapping near the electrodes (electrode polarization); +2) Irreversible changes at the electrodes or near to them leading to lim- +iting of the charge injection; +3) Generation of regions in the volume that do not conduct current, for +example, polarized crystallites with layers of the trapped charges; +4) Changing the equilibrium between free and trapped charges due to +the formation of new traps at the boundaries of the polarized crystallites and +macroscopic polarized regions. + +148 +The difference between TEP currents in positively and negatively charged +samples is against the migration mechanism causing the reduction in con- +ductivity. The second reason is also unlikely, because due to ionic impurities +the field on the electrodes should increase, which together with the effect of +the temperature would lead to increase in the injection level. The third reason +is more probable, because the ordering in the crystalline phase of the poly- +mers leads to decrease in localized states the density and decrease in conduc- +tivity (the band gap width is of the order of 6–9 eV). However, the ordering of +the preferred orientation of dipoles in crystallites in the external field cannot +substantially change their conductivity, because they already have the spon- +taneous polarization as the higher degree of the internal ordering. +Most likely, the conductivity of PVDF decreases as a result of the inten- +sive trapping of carriers at the boundaries of polarized crystals and macro- +scopic polarized regions, which create favorable conditions for localization +of the charges. We have found that similar processes at low temperatures and +high fields lead to appearance of areas of negative dynamic resistance on +volt-ampere characteristics. +If the proposed hypothesis is correct, then there the relationship between +the temperature and the field strength must be observed, in which high po- +larization is formed and the irreversible decrease in conductivity appears. +Dependence of the effective conductivity on temperature in TEP mode at +different constant voltages is shown in Fig. 3, from which it is seen that the +beginning of the negative temperature conductivity section moves to lower +temperatures with increasing the polarizing voltage. It is known that the high +polarization in ferroelectrics occurs in fields above the coercive one. From +the data of Fig. 3 it follows that the value of the coercive field decreases with +increasing temperature. From Fig. 3 and Table 1 it is evident that the acti- +vation energy that provides the effective conductivity in not polarized and +polarized samples is practically the same. At the same time, the conductivity +of the polarized films, and hence the concentration of free carriers in them +is almost 100 times smaller than in not polarized films. Consequently, in the +process of poling, there are redistribution of carriers and their additional +trapping at the newly created traps. +Let us analyze the shape of the TEP current curve taking into account +that the conductivity current IS is proportional to the concentration of free +charge carriers + +0 +c +c +U +i +n e x += µ⋅ +, +(9) + +149 +where μ is the mobility; U is the applied voltage; xo is thickness of the sample. +In the presence of localized states in the forbidden zone, the concentration +of trapped charges is determined by the Fermi-Dirac formula + +1 +{1 +(1/ +/ exp[ ( +) / +])} +t +t +t +n +N +g +F +E +kT +− += ++ +− +− +, +(10) +where Nt is the density of localized states; g is their statistical weight; Et is the +localized state energy; F is a quasi-level Fermi based on its own and injected +carriers. We assume that the total concentration of carriers and the Fermi +level remain constant. +2,9 +3,0 +3,1 +3,2 +3,3 +3,4 +-2 +-1 +0 +1 +2 +3 +Q = 0.8 eV +Q = 0.8 eV +Q = 0.8 eV +2 kV +1.4 kV +1 kV +ln[g(pSm/m)] +1000/T(K) +Fig. 3. Temperature dependence of the effective conductivity during thermally stim- +ulated poling in a corona discharge under different voltages at a control grid (electret +potential) +Increase in the density of the localized states with increasing polariza- +tion can be represented as a linear function where the polarization P is a +function of the field strength E. For ferroelectrics, the function P(E) can be +approximated by three rectilinear sections + +0, +, +( ) +( +) +/ ( +), +, +, +, +c +c +s +s +c +c +s +s +s +E +E +P E +E +E P +E +E +E +E +E +P E +E +< + + += +− +− +< +< + + +< + + +(11) +where Ec is the coercive field; Es is the field strength at which polarization +reaches saturation. Consider the decrease of the coercive field with +increasing temperature + +150 + +0 +c +E +E +T += +− γ ⋅ +. +(12) +We will assume that the dynamic permittivity at Ec < E < Еs does not de- +pend on T, that is equivalent to the constancy of the difference ΔЕ = Еs – Ес. +From (10)–(15), taking into account the made assumptions, we obtain the +dependence of the conductivity current on the temperature + +1 +0 +0 +( +/ +) +{1 +(1/ )exp[ ( +) / +]} +c +t +t +i +e V +x +n +N +g +F +E +kT +− += µ⋅ ⋅ +− ++ +− +− +, +(13) +where + +0 +1 +0 +0 +0 +2 +0 +0 +0 +0 +0 +2 +1 +; +( +/ +) / , +; +( +/ +) / , +( +/ +)[( +/ +) +( +)], +t +c +t +s +c +t +s +c +N +N T +T +E +V +x +N +N +P T +T +E +E +V +x +N +N +P +E +V +x +E +T +T +T +T += +< += +− +γ += ++ α +> += Δ ++ +− +γ += ++ α +Δ +− +− γ +> +> +. +(14) +It follows from expressions (13) and (14) that with increasing tempera- +ture in the range T < T1 the current ic increases. Nt begins to increase at T > +T1 provided + +2 +/ +( +/ +)exp( +/ +) +sP +E +Q +gkT +Q +kT +α +γ +Δ +> +− +, +(15) +where Q = F – Et. +There is a decrease in current ic despite the increase in temperature. The +current increases again, if the saturation of polarization is reached, or if the +condition (15) is violated. +Reducing of the effective conductivity during TEP indicates the impor- +tance of volume-charge processes, since the charge trapped on the bound- +aries of the polarized regions compensates the depolarizing field and con- +tributes to the long-term preservation of the residual polarization. A similar +relation was established during isothermal poling in high fields [14]. +Thus, the increase of temperature and the field strength equally influ- +ences on the generation and injection of moving charges, the large con- +centration of which is a prerequisite for the emergence and development of +the high local polarization. As the polarization is formed, the conductivity +of ferroelectric polymers is irreversibly reduced due to the trapping of the +injected charge carriers at deep traps formed by the polarization of crys- +tallites. These trapped charge carriers stabilize the residual polarization by +compensating local depolarizing fields. +5. Thermally stimulated depolarization currents in PVDF +Measurement of TSD currents is a powerful tool for studying relaxation +processes [12]. Although the theory of TSD currents was developed only for +the thermally frozen dipole polarization, this method is widely used to study + +151 +the ferroelectric polymers as well. In PVDF, two peaks are the most import- +ant. One of them, related to the glass transition in the amorphous phase, +is always observed at a temperature of about -45 °C and it is well-studied. +The nature of the second peak in the range of 50–80 °C (Fig. 4) is not fully +understood, although it is clear that several processes, such as the reorien- +tation of dipoles in the amorphous phase, the relaxation of the ferroelectric +polarization, the displacement of the space charge, as well as interphase and +piezoelectrode processes can be responsible for this peak. It is established +that the temperature of about 60 °C is characteristic for PVDF, but its nature +is not completely clear. Many researchers associate a peak at this tempera- +ture with so called αc relaxation. Lacabane et. al. [15] explain the appear- +ance of the peak by shrinkage, that is, by a partial restoration after stretching +carried out for obtaining the ferroelectric β-phase in PVDF. We believe that +this peak is associated with polarization in the amorphous phase. +Ferroelectric polymers have the properties of ordinary polar electrets in +addition to the ferroelectricity. Therefore, one can expect the presence of +two components of the residual polarization: one associated with the fer- +roelectricity in the crystalline phase, and another related to the amorphous +phase, although there is currently no direct experimental confirmation of +this phenomenon. +Analysis of the relationship between TSD currents in PVDF and pyro- +electricity was carried out in the work of von Seggern and Fedosov [5]. They +have found that the residual polarization decreases after heating to 60 °C, +while the pyrocoefficient remains unchanged. They concluded that the fer- +roelectric polarization in the crystalline phase is partially offset by localized +charges and partly by polarization in the amorphous phase. Therefore, in the +formation of the TSD peak in the ferroelectric polymers, several currents +are involved caused by relaxation of the electret and the ferroelectric com- +ponents of the residual polarization, and associated with the space charge. +We investigated polarized specimens subjected to TSD either in short-cir- +cuit mode or in open-loop with PTFE film as a dielectric gap between the +free surface of the sample and one of the electrodes [149–16]. The period of +time after poling to the TSD measurement was either one day or 16 months. +The samples were named “fresh” and “old” accordingly. Similarly to the +data reported in other papers, we observed one broad peak in the mode of +the short circuit on fresh samples (Fig. 4). +The direction of current at this peak corresponded to the residual po- +larization relaxation. Because the crystallinity of PVDF is about 50 % and +most of the molecular dipoles in the crystalline regions are in the ferroelec- + +152 +tric β-phase, the contributions of the electret and the ferroelectric compo- +nents to the formation of this peak in fresh samples can be compared. As for +the bulk charging component, it is known that it either does not contribute +to the TSD current in the mode of the short circuit, or its direction coin- +cides with the depolarization current component. +20 +40 +60 +80 +100 +120 +-0,4 +-0,2 +0,0 +0,2 +0,4 +0,6 +0,8 +Current density nA/cm +2 +Ioc(T) +Temperature, +oC +0 +2 +4 +6 +8 +Current density nA/cm +2 +Ic(T) +Isc(T) +Fig. 4. TSD currents Іsc(T) and Іoc(T) measured on fresh polarized samples in +short-circuit and open circuit modes. The curve Ic(T) corresponds to the vol- +ume-charge current +0 +20 +40 +60 +80 +100 +120 +-0,2 +0,0 +0,2 +0,4 +0,6 +0,8 +Current density nA/cm2 +Current density nA/cm2 + +Ioc(T) +Temperature, +oC +0 +1 +2 +3 +4 +Ic(T) +Isc(T) +Fig. 5 TSD currents Іsc(T) and Іoc(T) measured in polarized samples in short-circuit- +ed and open circuited modes after exposure for 16 months. The curve Ic(T) corre- +sponds to the volume-charge current + +153 +Comparing the TSD currents of fresh and aged polarized samples, we +observed a new phenomenon. One broad TSD current peak in the mode of +the short circuit was divided during the aging in two narrow peaks complete- +ly separated from each other. At the same time, two pairs of the oppositely +directed peaks appeared in old samples instead of one pair of peaks typical +for fresh samples (Fig. 5). This feature is likely to be common to all ferroelec- +tric polymers and does not depend on the polarization conditions, because +similar results were also obtained by us on samples poled by a non-focused +electron beam at the accelerating voltage of 20 kV and in P(VDF-TFE) and +PVDF films poled through a lime glass at the voltage of 7 kV. +The depolarization current in the open circuit mode remains unchanged, +while the TSD current due to the charge changes the direction to the op- +posite. Therefore, the two peaks shown in Fig. 4 can be explained as the +result of two partially overlapping and oppositely directed currents arising as +a result of the relaxation of polarization and space charge. +In order to separate the depolarization current IP(T) from the space +charge current Ic(T), it is reasonable to assume that the polarization is +homogeneous in the direction of the thickness. Since the compensating +charges trapped near the surface do not generate any current in the short +circuit mode, then Isc(T) = IP(T), where Isc(T) is the experimentally mea- +sured TSD current in the short circuit mode. The current Ic(T) can be cal- +culated from the experimental curves Isc(T) and Ioc(T) shown in Fig. 4 + +1 +2 +0 +2 +1 +( ) +1 ( ) 1 +( ) +c +c +sc +x +I T +T +I +T +x + + +ε += ++ +− + + +ε + + +, +(16) +where ε1, x1, ε2 and x2 are dielectric permittivity and thickness of the sample +and the dielectric gap, respectively. In our calculations, we used ε1 = 12, +ε2 = 2.1, x1 = 20 μm, x2 = 25 μm. It is noteworthy that the peak Ic(T) is at +the higher temperature than the peak of the depolarization, indicating that +the trapped charges are more stable than the residual polarization. +The obtained results can be explained qualitatively taking into account +the different nature of the three components of the TSD current. The elec- +tret polarization accounting for almost 50 % of the residual polarization in +fresh samples decays in time faster than the ferroelectric component. That is +why the two peaks are overlapped in fresh samples, become completely sep- +arated in the old films, as if the slow redistribution of residual polarization is +going on for a long time after the completion of poling. +Observed and calculated peaks are difficult to process quantitatively, +since there is no TSD currents theory in ferroelectric polymers. However, + +154 +as evident from the shape of the peaks, all three relaxation processes differ +significantly from the ideal Debye case, corresponding to the absence of the +relationship between the relaxing dipoles. This feature can be taken into +account considering that the polarization relaxes over time in accordance +with the law of the expanded exponent + +0 +( ) +exp + 1 +0 +t +P t +P +α + + += +− +≥ α ≥ + + +τ + + +, +(17) +where τ is a time constant, Po is the initial polarization. If the sample is lin- +early heated at the rate β = dT/dt, then + +0 +0 +1 +1 +( ) +exp +( +) +T +T +P T +P +dT +T +α + + + + + +  + + + +′ += +− + + + + +  + +′ +β +τ + + + + + + + + + + + + +∫ +, +(18) +where To is the initial temperature. It is reasonable to assume that the tem- +perature dependence of τ corresponds to the Arrhenius law + +0 +( ) +exp +A +T +kT + + +τ += τ + + + + +, +(19) +where A is the activation energy, k is the Boltzmann constant, τo is the char- +acteristic time. The expression for the TSD current density is derived from +the equations (17)–(19) + +[ +] +[ +] +{ +} +1 +0 +0 +( ) +exp +( ) +exp +( ) +P +A +i T +s T +s T +kT +α− +α + + +α + + += − +− +− + + + + +τ + + + + +, +(20) +where + +0 +0 +1 +( ) +exp +T +T +A +s T +dT +kT + + + + +′ += +− + + + + +βτ + + + +∫ +. +The results of computer fitting of the experimentally observed and cal- +culated TSD peaks in equation (20) confirmed our assumptions about the +nature and the thermal stability of the relaxation processes. They showed +that the depolarization peak in fresh samples where the electret and the +ferroelectric components are mixed, is wide (α = 0.24), because the two +relaxation processes responsible for its formation are very different. The +ferroelectric polarization is quite stable (A = 2.7 eV), and the TSD peak +due to its relaxation is relatively narrow (α = 0.52). The parameters of the +space charge peaks in the fresh and old samples are completely different, as +if there are two types of the space charges, one probably associated with the +ferroelectric polarization, and the other one with the electret component. It + +155 +is also likely that the small peak that occurs near the electret depolarization +peak in open mode (Fig. 5) is due only to the electret component of the vol- +ume charge. Since the glass transition temperature is -45 °C in PVDF, the +ordering of the dipoles in the amorphous phase is not thermally frozen, as +in the ordinary polar electrets. The dominant orientation of dipoles in these +conditions may be supported by the field of the trapped charges. +Thus, it has been shown that in corona poled films of the ferroelectric +polymers, there are two components of polarization, and both components +are accompanied by corresponding space charges. The electret-type ther- +modynamically unstable component relaxes as long as the broad TSD peak +observed in fresh polarized samples is not transformed into two completely +separated narrow peaks. +The unstable electret component of the residual polarization can be re- +moved by heating the poled sample to a specific temperature (about 60 °C in +the case of PVDF). Apparently, the trapped charges always accompany the +dipolar polarization regardless of its nature. +6.1. Pyroelectric effect in ferroelectric polymers and its nature +Pyroelectric effect in PVDF films was discovered more than 40 years +ago. However, despite the large number of works, the nature of pyroelec- +tricity in PVDF still remains unclear. A series of papers was devoted to the +pyroelectric properties of the ferroelectric polymers. It is assumed in the +first of the three most popular models that pyroelectricity results from the +contribution of electrostriction, dipole fluctuations and changes in the size +with temperature. In the second model, only the change in the dimensions +of the sample is considered and the crystals, while in the third model, the +pyroelectricity is attributed to electrostrictions and to the change in size +when temperature changes. +Under the pyroelectric effect, one means the range of phenomena as- +sociated with reversible changes in the electric displacement vector (induc- +tion) when the temperature changes. In the case of a free sample, the pyro- +coefficient is determined by the following expression [13] + +, +, +, +, +, +i j +i +i +i +i +i j +H E +U E +H E +U +D +D +D +p +T +T +U +T + + ∂ + + +∂ +∂ +∂ + + + + += += ++  + + + + + + + + +∂ +∂ +∂ +∂ + + + + + + + + +, +(21) +where Di is the component of the induction vector; Ui,j is the deformation +tensor; H is the mechanical stress; E is the field strength, +, +i +i j +D +U + + +∂ + + + + +∂ + + + is the + +156 +piezo modulus; +,i j +U +T +∂ + + + + +∂ + + + is the thermal expansion coefficient. The first term +in (21) corresponds to the primary or true pyroelectric effect measured on +the compressed sample, and the second term characterizes the secondary +pyroelectric effect being the result of the piezoelectric induction changes +due to the thermal expansion. +Since the pyroelectric effect depends both on the internal polarization +and on the space charge, in principle, it can be caused by the temperature +dependence of both quantities. If we neglect the influence of the space +charge, then for the case of a flat short-circuited sample with homogeneous +polarization P we obtain + +0 +( / +) +D +P +q +S +p +T +T +T +T +∂ +∂ +∂σ +∂ += += += += +∂ +∂ +∂ +∂ +, +(22) +where q and σ are magnitude and density of the bound surface charge; S is +the surface area. +In the experimental conditions, the current ( ) +dq +I T +dt += + occurring when +the temperature change (dT/dt) is measured, and the pyrocoefficient is con- +sidered to have the following value + +1 +1 +( ) +/ +dq +I T +p +S dT +S dT +dt += += +. +(23) +Because ро ≠ р there are differences in the values of the theoretically cal- +culated and experimentally measured pyrocoefficients. It has been proved +that the pyroelectric effect can only be caused by a nonuniform distribution +of the space charge (without taking into account polarization). +Investigating the pyroelectric effect in PVDF, Lines and Glass [17] came +to the conclusion that this is a real pyroelectricity, but not a depolariza- +tion effect observed in many polar electrets, because the crystalline phase of +PVDF completely corresponds to the definition of a ferroelectric, as a py- +roelectric with reversible spontaneous polarization under application of the +electric field. A fundamental question was posed that has not been solved +for the time being: is the pyroelectricity an equilibrium property of PVDF +or a result of non-equilibrium polarization, that is, in some way it is a fixed +orientation of dipoles? +In early works on PVDF, the effect of volume charge on the pyroelectric +effect was considered decisive, but after the proof of the ferroelectric na- + +157 +ture of PVDF crystallites, the pyroelectric was more often associated with +the spontaneous polarization. So, in the model of Broadhurst and Davies +[18] the behavior of rigid dipoles in thin crystalline plates (lamellae) dis- +tributed in the amorphous phase is considered. In the model of Wada and +Hayakawa [19], the presence of spherical ferroelectric particles scattered +in the amorphous phase is assumed. Both models predict the influence of +thermal expansion (dimensional effect) on the pyroelectric effect, as well +as temperature dependence of the dielectric constant and the spontaneous +polarization Psc(T). +At the same time, there is no satisfactory correspondence between cal- +culated and experimental data. drew Attention was attracted to the fact that +the models of Broadhurst [18] and Wada and Hayakawa [19] ignored the +contribution of the volume charge to the pyroelectric effect. An attempt to +take into account the volume charge led to contradiction with the obtained +data [13]. Estimated calculation of Lines and Glass [17] showed that the +theoretical pyrocoefficient even at 100 % orientation of dipoles in PVDF is +several times lower than the value measured in the experiment. +We believe that not only the crystalline, but also the amorphous phase +contributes the pyroelectricity. Elling et al [20] found that the pyrocoefficient +value is affected not only by the residual polarization, but also by the supra- +molecular structure on which the mechanical properties of PVDF depend. +It is shown in the work of Fedosov and Sergeeva [21] that one of the +components of the pyroelectric effect in the ferroelectric polymers is the +electret component, that is, the pyroactivity of PVDF is due to the reversible +temperature changes of the residual polarization closely related to those in +equilibrium with trapped charges. +Fedosov and von Seggern [3, 4, 6] proved that compensating charges +localized on the surface of crystallites are very important in two-compo- +nent ferroelectric polymers of the PVDF type for obtaining high and stable +polarization. With periodic increase and decrease of temperature [21], the +pyrocoefficient irreversibly decreases at temperatures much lower than the +Curie point indicating the possible effect of charges. +It is generally accepted that the pyrocoefficient in PVDF is directly pro- +portional to the value of the residual polarization. However, this relationship +is more complicated, because the pyrocoefficient usually increases nonlin- +early with increasing temperature, while there is no increase in polarization +occurs in this case. +Summarizing the above data, we can conclude that the pyroelectricity +in PVDF is usually considered in isolation from other processes. However, + +158 +to understand the nature of this phenomenon, it is of interest to experi- +mentally study the dynamics of its formation and changes simultaneously +with other isothermal and thermally simulated processes, such as mea- +surement of volt-ampere characteristics, thermoelectret poling and de- +polarization. +6.2. Measuring the pyroelectric coefficient in poled PVDF films +The pyroelectric effect is usually investigated in quasi-static or dynamic +mode. In the first case, the pyroelectric current is measured during the slow +heating of the short-circuited sample, while in the second case, the variable +component of the current is studied during a rapid change of temperature. +The main difficulties of the quasi-static method are the separation of the py- +roelectric (reversible) component of the thermal shock from the relaxation +(irreversible) component in the TSD current. +We measured the pyroelectric dynamic coefficient by the thermal pulse +method developed by Collins [22] and used in a number of other papers. +The light pulse of 50 μs duration was generated using the Metz 45 CT-3 +flashlight and was used as a reproduced heat source that penetrates the sur- +face of the poled films. The pyroelectric signal was recorded using a broad- +band oscilloscope. This method is the dynamic one. +With the help of a highly sensitive pyroelectric sensor it was established +that light pulses are characterized by a rather high reproducibility. The av- +erage energy scatter in measuring of 200 consecutive pulses was 2.4 %. The +magnitude of the pyroelectric coefficient was judged by the maximum value +of the electric signal; thus the results were obtained in relative units. +Measurement of the pyrocoefficient by a quasi-static method was car- +ried out by linear heating and cooling of polarized samples. Dependence of +the pyrocoefficient on temperature was calculated by the following formula + +( ) +( ) +p +c +I T +p T +A += +β +, +(24) +where IP(T) is the pyroelectric current measured during cooling, βc is the +cooling rate, which is a derivative of the temperature over time, A is the sam- +ple surface area. The heating rate was maintained constant 3 K/min, while +the cooling rate depended on time and temperature. +6.3 Switching of polarization and pyroelectric activity of PVDF films +Pyroelectric studies of PVDF films have an independent value, since +PVDF is widely used in pyroelectric sensors. However, it is interesting to +study pyroactivity in conjunction with the residual ferroelectric polar- + +159 +ization, because it will allow to clarify the nature of the pyroelectricity in +PVDF, and to ensure its stability. +Measurement of the pyroactivity by the Collins method was carried out +immediately after the polarization switching. Fig. 6 shows how the pyro- +electric signal changes when the polarization is fully switched from a fully +polarized state. Although the value of the pyrocoefficient can only be judged +in relative units, it is evident that the sensitivity of the method is rather high +and the signal a completely symmetric after the full switching. It appeared +that full switching occurs only if the voltage pulse duration exceeds 100 s. +At a shorter duration of the voltage pulse, there is only a partial switching of +polarization judging from the data of Fig. 7. +0 +1 +2 +3 +4 +5 +-120 +-80 +-40 +0 +40 +80 +120 +Direction of switching +Initial state +Pyrosignal voltage, mV +Time, ms +Fig. 6. The pyroelectric signal after the polarization switching of PVDF film by ap- +plying 2 kV voltage for 50 seconds. Pyroelectricity was measured after 1.5 min after +the voltage switching off +Fig. 7 shows the results of four series of experiments, in which the polar- +ization switching was performed at different durations of the voltage pulse, +but with the same magnitude in each series. At a voltage of 0.5 kV (Fig. 7) +that provides a field strength of about 40 MV/m, being in the same order +as the coercive field, even with a pulse duration of 50 s, only 6.4 % of the +polarization is switched, which in principle can be switched, and if the pulse +duration is shorter than 50 ms, no switching is practically happening. +At a voltage of 1 kV applied for 50 s, 44.4 % of the residual polarization is +switched, that is, the sample is almost converted to the state with zero mean +polarization. At this voltage, the 2.2 % polarization is switched even within +50 μs of the switching voltage application. Increasing the voltage to 1.5 kV + +160 +leads to the switching of 79.4 % of the residual polarization by a 50 s appli- +cation of voltage. At a voltage of 2 kV for 50 s, the polarization is completely +switched. +10 +-6 +10 +-4 +10 +-2 +10 +0 +10 +2 +0 +20 +40 +60 +80 +100 +120 +Pyrosignal voltage, mV +Pulse duration, s +0 +1 +2 +3 +4 +5 +6 +0 +40 +80 +120 +50 s +5 s +0,5 s +Initial state +Pyroelectric voltage, mV +Time, ms +Fig. 7 Dependence of the pyroelectric signal on the duration of the polarizing pulse +in the range from 10 μs to 100 s during initial poling of the PVDF film by 2.5 kV +voltage +It is interesting to note the specific shape of the pyroelectric signal when +switched polarization is more than 50 %, that is, when the direction of the +average predominant orientation of the dipoles changes to the opposite di- +rection. +In the electrode zone, which the thermal pulse passes during to = 0.2 ms, +when the polarity direction changes to the opposite, a non-symmetric in +shape pyroelectric signal is formed in relation to the initial one. In the vi- +cinity of the electrode, the direction of the pyro-signal change is maintained +during the switching polarization indicating the existence of a near-to-elec- +trode layer of thickness about +0 +x +t += +λ + where λ is the thermal conductivity +of PVDF. +According to the literature, the coefficient of thermal conductivity of +PVDF is λ = 6∙10–8 m2/s, thus the thickness of the electrode layer is of the +order of 3 μm. We believe that the feature revealed by us is due to the fact +that the originally formed polarization in this layer does not switch even in +high fields. +It is natural to assume that polarization near the electrode does not in- +crease sharply, but there is some transition layer in which the polarization + +161 +grows from zero at the electrode to a maximum uniform value in the volume +of the film. According to the Poisson equation, inhomogeneous polariza- +tion in any layer can be stable only with the presence of a compensating +charge in this layer. Apparently, this charge was trapped by deep traps and +not released during the polarization switching. The revealed phenomenon is +similar to the established by us feature about impossibility of improving the +polarization uniformity if its initial formation took place in weak or medium +fields. +10 +-6 +10 +-4 +10 +-2 +10 +0 +10 +2 +0 +20 +40 +60 +80 +100 +120 +Pyrosignal voltage, mV +Pulse duration, s +0 +1 +2 +3 +4 +5 +6 +0 +40 +80 +120 +50 s +5 s +0,5 s +Initial state +Pyroelectric voltage, mV +Time, ms +Fig. 8. Pyroelectric signal at sequential polarization switching in PVDF films +by pulses of 0.5 kV voltage with duration from 5 ms to 50 s. The duration of the volt- +age pulse is indicated near the curves +It was found that polarization switched under the action of several suc- +cessive short voltage pulses is much smaller than the polarization switched +by one pulse of the duration equal to the total time of several short pulses. +This indicates that there is some distribution of switching times, i.e. some +dipoles are easily switched, while others require more time to be switched. +Under the influence of short voltage pulses, only «fast» dipoles are switched, +while during the continuous voltage application both «fast» and «slow» di- +poles are switched, so the total switched polarization significantly increases. +In conclusion, polarization switching at different time and field strength +is compared with the values of the pyrosignal under the same switching con- +ditions (Fig. 9). The absolute similarity of the above experimental graphs +indicates that there is a direct proportional relationship between the residual + +162 +ferroelectric polarization and the value of the pyroelectric coefficient. This +provision makes it possible to use the technically simple pyrocoefficient +measurement to evaluate the polarized state of poled PVDF films, that is, to +estimate the magnitude and the direction of the residual polarization. +10 +-7 +10 +-4 +10 +-1 +10 +2 +0,0 +0,1 +0,2 +40 +80 +40 +80 +120 +160 +200 +200 +160 +120 +Time, s +Pyroelectric signal, V +Time, s +10 +-7 +10 +-4 +10 +-1 +10 +2 +0 +2 +4 +6 +8 +10 +Polarization, C/cm +2 + +Fig. 9. Evolution of pyroelectric activity and stable ferroelectric part of polarization +obtained by sequential application of switching voltage pulses with increasing dura- +tion from 0.5 μs to 50 s and at different field strength +7. Separation of TSD current components in PVDF +Despite the fact that PVDF is considered as a ferroelectric polymer, +some of its electrical properties can be explained within the framework of +the theory of polar electrets. The phenomenological model of Gross-Swan- +Gubkin [23] suggests the presence of two types of charges in the electret, +namely, the homocharge σ(t), whose sign coincides with the polarity of the +electrodes during poling, and the heterocharge P(t) (internal polarization), +which is the result of the micro — and macro- displacements of own charges +in the dielectric under the field action. In the case of PVDF, the heteroch- +arge is the dipole polarization, and the homocharge is formed by charges +trapped on or near the surface [4]. +Stability of the electret state in a polar dielectric depends on the mutual +relaxation of the homocharge and the heterocharge. +Since the heterocharge (polarization) is usually the most important in +PVDF, the role of the homocharge has not paid enough attention to the + +163 +present, although the stabilizing effect of the space charge on the residual +polarization has already been discussed [4, 6]. +Thermally stimulated depolarization (TSD) is a method used to identi- +fy relaxation processes in polymer electrets. However, it is very difficult to +divide the effect of the homocharge and the heterocharge on TSD currents +especially if the corresponding peaks are superimposed on each other in a +wide range of temperatures. +We have developed a method for separating homocharge and heteroch- +arge currents [24] by solving the inverse problem. In addition, it has been +shown that the application of various modifications of the TSD method, +complemented by isothermal depolarization currents allows us to find such +important parameters of relaxation processes as the activation energy, char- +acteristic frequencies and the time constant. +The uniaxially oriented 25 μm thick PVDF films metallized on one side +were poled in corona triode at the control grid voltage of 3 kV at room tem- +perature and constant poling current density of 90 μA/m2 for 30 min and +then shortened and held at room temperature for 24 h (except for specimens +for measuring the electret potential kinetics). +Four modifications of the TSD method were used, namely thermally +stimulated (T) and isothermal (I) depolarization of short-circuited (S) and +open circuit (O) samples. Thus, the modifications are named TS, TO, IS +and IO where the first letter indicates the temperature mode (thermally +stimulated or isothermal), and the second indicates the electric state of the +sample (short-circuit or open circuit). +Additional experiments on the thermally stimulated electret potential (TP) +kinetics were performed after 24 h of being in the open circuit state. As a dielec- +tric layer in TO and IO modifications, PTFE film of 10 μm thickness was used. +Thermally stimulated experiments were performed at a heating rate +of 3 K/min. In isothermal experiments, the temperature was maintained +constant after its required value was achieved by rapid heating. The electret +potential in TP modifications was measured by the Kelvin method and con- +tinuously recorded. +The main features of the experimental curves shown in Fig. 10 and 11 +are as follows: +– The depolarization current in the TS modification forms a broad +«non-classical» peak with a maximum of 65 °C; +– There is an inversion of the TSD current in the TO modification, +while the current direction coincides with the direction of the current in the +TS modification in the initial heating stage; + +164 +20 +40 +60 +80 +100 +120 +-0.3 +-0.2 +-0.1 +0.0 +0.1 +0.2 +0.3 +1 +Current density, A/m +2 +Temperature, +oC +3 +1 +2 +0 +100 +200 +300 +3 +2 +Voltage, V +0 +5 +10 +15 +0 +2 +4 +6 +0 +5 +10 +15 +-0.1 +0.0 +0.1 +0.2 +0.3 +Current density, A/m +2 +Time, min +(a) +3 +2 +1 +Current density, A/m +2 +Time, min +(b) +3 +2 +1 + + +Fig. 10. Thermally stimulated currents in the TS modification (1) and in the TO +modification (2), as well as the electret potential in the TP modification +20 +40 +60 +80 +100 +120 +-0.3 +-0.2 +-0.1 +0.0 +0.1 +0.2 +0.3 +1 +Current density, A/m +2 +Temperature, +oC +3 +1 +2 +0 +100 +200 +300 +3 +2 +Voltage, V +0 +5 +10 +15 +0 +2 +4 +6 +0 +5 +10 +15 +-0.1 +0.0 +0.1 +0.2 +0.3 +Current density, A/m +2 +Time, min +(a) +3 +2 +1 +Current density, A/m +2 +Time, min +(b) +3 +2 +1 + + +Fig. 11. Isothermal transient currents at different temperatures in the IS mode (a) +and in the IO mode (b); 1–45 °C, 2–55 °C, and 3–70 °C. +– The electret potential in TP modification has a maximum at 40 °C. +– The current slowly decreases over time in the IS modification at all +temperatures, while the isothermal current changes the direction in IO +mode at elevated temperature. + +165 +These features can be explained within the framework of the model, +which implies existence in the samples of the homocharge and the hetero- +charge. First, consider the processes of poling and relaxation qualitatively. It +is reasonable to assume that negatively charged particles (ions and/or elec- +trons) generated by corona discharge are adsorbed and thermalized on the +surface of the sample due to their low (thermal) energy. Excessive charge in +the near-to-surface layer or on the surface forms a homocharge that has a +certain superficial density σ and creates a homogeneous field E in the vol- +ume of the sample. The high electron affinity of fluorine atoms facilitates +the trapping of charges at traps and formation of the stable homocharge. +Homogeneous internal polarization P (heterocharge) is formed as a +result of dipoles -CH2-CF2- orientation in the field created by a homo- +charge. The formation of polarization is equivalent to the formation of a +bound surface charge P, which has a sign opposite to the sign of the homo- +charge σ. Of all the polarization processes in PVDF, the orientation of the +-CH2-CF2- dipoles is the most significant due to their large dipole moment +of 2.1 Debye [13]. +If the polarization P is zero, then the field is created by a complete su- +perficial charge σ. When P begins to grow, the depolarizing field appears +which is “neutralized” by a part of the surface charge. Thus, the field in +volume is created by the difference (σ — P) between the surface charge and +the polarization. Consequently, the surface charge σ consists of two parts +σ = σ1 + σ2, the first of which is a charge that provides compensation of the +depolarizing field (σ1 = P), and the second σ2 = σ – P creates the electric +field in the volume of the sample. +After the short circuiting of the poled samples (in TS and IS modes), the +“excess” charge σ2 disappears. +The equilibrium between the homocharge and heterocharge (σ = σ1 = P), +as well as the zero internal field (E = 0) are supported by the current in the +external circuit, so that the measured current corresponds to the relaxation +of the heterocharge. +However, if after the short circuiting and the formation of equilibrium +σ = σ1 = P, a non-conductive dielectric insert (in TO and IO modes) is +introduced between one of the electrodes and the surface of the sample, +then one can observe the relaxation currents both the heterocharge and the +homocharge flowing in the opposite directions. The field in the volume is +no longer zero, so that the surface charge (homocharge) drifts in its own +field through the entire thickness of the sample, or it is slowly neutralized by +charge carriers responsible for its own conductivity. + +166 +In any case, the relaxation of the heterocharge occurs in a field other +than zero and caused by thermal disordering of oriented dipoles [12, 13]. +We will show that both components of the depolarization current can be +found from the dependence of i(T) in the TO mode (Fig. 10, curve 2). It is +known [12, 13] that the TSD current i(t) and the electret potential V(t) in +experiments with nonconductive insertion between the surface of the sam- +ple and the electrode, depend not only on the relationship between the ho- +mocharge and the heterocharge, but also on their derivatives, so + +( ) +( ) +( ) +dP t +d +t +i t +s +dt +dt +σ + + += +− + + + + +, +(25) + +1 +0 +1 +( ) +[ (t) +P(t)] +sx +V t = +σ +− +ε ε +, +(26) + +0 +1 +1 +( ) +( ) +dV t +i t +x +dt +ε ε += − +⋅ +, +(27) +where +0 +1 +1 +0 +1 +/ ( +) +s +x +x +x += +ε +ε + +ε +, t is time, ε and xo are the dielectric constant +and the thickness of the sample, ε1 and x1 are corresponding values of the +dielectric gap, εo is the permittivity of a vacuum. +The full component ic(t) can be represented as + +0 +( ) +( ) +( ) +C +g +d +t +i +t +V t +x +dt +σ += += − +, +(28) +where +0 exp( +/ +) +g +g +Q +kT += +− + is the own conductivity, k is the Boltzmann con- +stant, T is temperature, Q is the activating energy of its own conductivi- +ty, go is a pre-exponential factor. Integrating (27) and replacing the time t +with temperature T in (25)–(28) according to +0(1 +) +T +T +bt += ++ +, where b is the +heating rate, То is the initial temperature, we obtain the expressions for the +temperature dependences of the homocharge current i1(T) and the hetero- +charge current i2(T), as well as the voltage on the sample (potential) V(T) + +1 +0 +1 +0 +0 +0 +1 +( ) +exp +( +) +T +x g +d +Q +i T +i T dT +dt +bT x +kT +∞ +σ + + +′ +′ += += − +− + + +ε ε + +∫ +, +(29) + +2 +( ) +( ) +dP +i T +d +i T +dt +s +dt +σ += += ++ +, +(30) + +1 +0 +0 +1 +( ) +( +) +T +x +V T +i T dT +bT +∞ +′ +′ += +ε ε ∫ +. +(31) + +167 +20 +40 +60 +80 +100 +120 +0 +2 +4 +6 +8 +0 +10 +20 +30 +40 +2 +Voltage, V +3 +2 +1 +Current density, A/m +2 +Temperature, +oC + +Fig. 12. Temperature dependences of the homocharge (1) and heterocharge (2) re- +laxation currents, as well as of the voltage on the sample (3) calculated according to +the model +All quantities at the right side of the equations (29)–(31) are known, or +can be obtained experimentally. The results of calculations according to the +equations (29)–(31) based on the data of Fig. 10, are shown in Fig. 12. The +values of the activation energy Q = 0.76 eV and the factor go = 0.18 Sm/m +were obtained from constant values of the isothermal poling current and +voltage. +As one can see in Fig. 12, the homocharge and the heterocharge form +two broad peaks with almost identical maxima. The heterocharge relaxes +faster in the low-temperature region where the homocharge is relatively +stable. This is probably the reason for the initial increase of the thermally +stimulated potential (see curve 3 in Fig. 10 and curve 3 in Fig. 12). The +current inversion in TO and IO modes is caused by a change in the ratio be- +tween homocharge and heterocharge at high temperatures (curves 1 and 2 +in Fig. 12). +It is known that the inversion of the TSD current can be caused by the +re-polarization, that is, it arises as a result of the appearance of an addition- +al heterocharge in the field of a homocharge, and the voltage in this case +should decrease [12]. +However, this was not observed in our case (Fig. 10). On the other hand, +the initial growth of the electret potential during heating cannot be caused +by increase of the surface charge density σ, since charges in this case would + +168 +have to move against the electric field created by these charges, which is +impossible. Therefore, the first peak of the TSD current and the increase +of the electret potential (Fig. 10) are due to the faster disintegration of the +heterocharge (polarization) compared with the homocharge. It is possible +that in PVDF in the first stage of heating, not all polarization is destroyed, +but only its least stable part. +Thus, the long-term conservation of the heterocharge in PVDF films is +possible only in presence of the stabilizing field created by homocharge. We +believe that many special properties of PVDF are associated with successful +combination of a large dipole moment of -CH2-CF2- (2.1 D) that contrib- +utes to formation of heterocharge, and the high electron affinity of fluorine +atoms (3.37 eV) that contributes to the creation of the stable homocharge. +Although the electret state in the PVDF is unstable, the self-balanced re- +laxation of the homocharge and the heterocharge is slowed down due to the +stabilizing effect of the homocharge. +In the theory of electrets [23], it is assumed that homocharge and het- +erocharge decay by the exponential law with the temperature dependent +time constants. Therefore, such expressions should be valid for IO and IS +modes + +0 +1 +1 +1 +( ) +exp +s +t +i t + + +σ += − +− + + +τ +τ + + +, +(32) + +0 +2 +2 +2 +( ) +exp +P +t +i t + + += − +− + + +τ +τ + + +, +(33) + +0 +1 +0 +( ) +exp +Q +T +g +kT +ε ε + + +τ += + + + + +, +(34) + +2 +0 +( ) +exp W +T +kT + + +τ += τ + + + + +, +(35) +where W is the activation energy of the heterocharge relaxation, τ1 and τ2 are +the corresponding time constants. +Applying the equations (32)–(35) to the experimental curve in Fig. 11, +we calculated the following relaxation parameters for homocharge and het- +erocharge: activation energies (Q = 0.76 eV and W = 0.54 eV), characteristic +frequencies (f2 = 1/τo = 7.4 MHz and f1 = (go/εoε) = 1.7 GHz, time constants +at 20 °C (τ1 = 31000 s and τ2 = 2800 s). The results indicate that the homo- +charge is more stable than the heterocharge. + +169 +Thus, we have developed a method for separating the depolarization +currents of the homocharge and the heterocharge from the measured TSD +current, and revealed the relaxation behavior of the both components. +Application of various TSD modifications complemented with isother- +mal depolarization currents allowed to find the most important parameters +of the relaxation processes. +The developed method allows us to analyze the relationship between the +homocharge and the heterocharge not only in PVDF but also in other polar +dielectrics. The introduction of polar groups with the simultaneous creation +of deep traps could contribute to increasing of the residual polarization sta- +bility in polar polymer dielectrics. Therefore, if there are appropriate con- +ditions for creating a homocharge, then a high level of the residual polariza- +tion can also be provided for a long time. +8. Thermally stimulated and isothermal processes in composites +Composite materials based on polymers with impurities of ferroelectric ce- +ramics have a number of significant advantages over conventional ferroelectric +ceramics, but the possibilities of using composite materials as active elements +of piezoelectric and pyroelectric converters are not fully implemented. +It is known that most of the polarization in ferroelectric ceramics im- +mediately switches back to its original state after switching off the applied +voltage, and only 25–30 % of the domains remain oriented if no special +actions are taken. Therefore, the dominant orientation of domains should +be somehow fixed. A similar problem exists in ferroelectric polymers, in +which ferroelectric crystallites are distributed in the amorphous phase. This +structural similarity between composites and ferroelectric polymers can also +determine the similarity of the electrical relaxation processes in these two +classes of materials. +PVDF data to verify the applicability of the concepts already proven for +the case of the ferroelectric polymers. In addition, concrete data on the pa- +rameters of the electrical relaxation in the specified composites were obtained. +We considered the PVDF-BaTiO3 composite as a model material. The +obtained results were compared with ыamples of PVDF-BaTiO3 composites +with a thickness of 300 μm containing 0 %, 40 %, 50 % and 70 % of Ba- +TiO3 were produced by hot pressing of a mixture consisting of PVDF powder +and BaTiO3 particles with an average size of 10 μm. The composites were +annealed at 140 °C and examined using a Solomat 91000 spectrometer for +obtaining the general spectrum of TSD currents in the range from -80 °C to ++180 °C (Fig. 13). + +170 +-80 +-60 +-40 +-20 +0 +2 +4 +6 +8 +40 +60 +80 +100 +120 +Temperature, +оC + + +4 +3 +2 +1 +Current, 10 +-11A + +4 +3 +2 +1 +(x50) +Temperature, +оC +0 +40 +80 +120 +1,0 +1,2 +1,4 +1,6 +3 +2 +1 + +Activation energy, eV +Temperature, +оC +Fig. 13. TSD current curves of poled PVDF-BaTiO3 composites with different con- +tent of BaTiO3: 0 % (1), 40 % (2), 50 % (3) and 70 % (4) +-80 +-60 +-40 +-20 +0 +2 +4 +6 +8 +40 +60 +80 +100 +120 +Temperature, +оC + + +4 +3 +2 +1 +Current, 10 +-11A + +4 +3 +2 +1 +(x50) +Temperature, +оC +0 +40 +80 +120 +1,0 +1,2 +1,4 +1,6 +3 +2 +1 + +Activation energy, eV +Temperature, +оC +Fig. 14. The activation energy of relaxation processes in PVDF-BaTiO3 composites +containing 40 % (1), 50 % (2) and 70 % (3) of BaTiO3 + +171 +The samples were prepoled at 150 °C in the electric field of 1.25 MV/m +for 15 min, and then cooled to –100 °C without disconnecting the electric +field. The samples were then depolarized by heating in a short-circuit mode +at the rate of 7 °C/min. +The fractional analysis of relaxation processes was carried out by the +method of thermal windows. The polarization temperature increased every +time for 5 °C from 20 °C to 150 °C. The equivalent frequency of experiments +was about 2·10–4 Hz. From these experiments, the activation energy of the +relaxation processes was calculated (Fig. 14). +It was found that thermal activation of the polarization process is nec- +essary, since polarization is not formed at room temperature even in high +electric fields of about 20 MV/m. This fact is confirmed by the lack of the +TSD current after poling of specimens at room temperature. In addition, +the VAC at 20 °C was superficial and typical for the space charge limited +currents, but not N-shaped, as in the case of PVDF. +In all samples, including PVDF without ceramic additives, well-expressed +low-temperature peaks near -40 °C can be seen on TSD curves (Fig. 13). +This peak is near the glass transition temperature of the amorphous phase in +PVDF and is usually attributed to the β-relaxation associated with the micro +Brownian motion of molecular chains in amorphous regions. Neither the +peak nor its magnitude correlates with the amount of the filler in the com- +posite, which indicates that this peak is associated with the properties of the +polymer. The peak in the range 80–120 °C is structurally good only in the +case of PVDF, but suppressed in composites by the exponentially increasing +leakage current of unknown nature. To eliminate the parasitic currents, we +periodically included a capacitor in series with the sample. But even in this +case, the unambiguous interpretation of the peaks was difficult, because the +theory of TSD currents in composites has not yet been developed. +It is assumed that in the thermal windows method each individual peak +corresponds to a single Debye relaxation process. Then the peak analysis +gives the temperature-dependent relaxation time τ(T), which can be ap- +proximated by the Arrhenius equation + +0 +( ) +exp( +/ +) +T +Q +kT +τ += τ ⋅ +, +(36) +where τо is the pre-exponential factor; Q is the activation energy; k is Boltz- +mann’s constant. +As can be seen from Fig. 14, the activation energy slightly decreases in +the range of 20–80 °C from 1.17 eV to 1.09 eV regardless of the samples +composition. Then it sharply increases reaching the maximum values of + +172 +1.23–1.55 eV at 105–110 °С. The amount of the activation energy cor- +relates with the concentration of the ceramic filler and equals 1.23 eV at +40 %, 1.4 eV at 50 % and 1.55 eV at 70 % of BaTiO3 in the composite. In +addition, the peak temperature in the Fig. 5.10 is very close to Curie point +of BaTiO3 confirming the fact that relaxation behavior of the composite near +this temperature is determined by ceramics. +It was found that the maximum temperature of the thermal window peak +was about 15 °C above the polarization temperature for all fractions, regard- +less of the composition of the sample. +The dielectric constant of the composites increased with temperature +and was in a certain ratio with the percentage content of the filler equaling +20–250 at 40 %, 30–400 at 50 % and 40–1100 at 70 % of BaTiO3 in the +composite. It is known that the dielectric constant of pure PVDF was about +10–12, and in BaTiO3 it was equal to 1500–7000. The polarization field +applied to the composites in the experiments (1.25 MV/m) was higher than +the coercive field of pure BaTiO3 estimated as 0.3 MV/m, but it is unclear +whether the ferroelectric polarization occurs, because the resistance the +polymer matrix is much higher than that of ceramics. +Thus, it was established that the processes of the polarization formation +and electrical relaxation in PVDF-BaTiO3 composites are similar to similar +processes in the ferroelectric polymers. This can serve as a prerequisite for +the creation of a generalized model that not only explains, but also predicts +the electrical behavior of polymer-ceramic composites. +We have established the influence of the polymer matrix conductivity +and poling regime on the effective conductivity of the PVDF-PZT compos- +ites. The research was carried out on flat plates of PVDF-PZT composite, +made by hot pressing of a mixture of PVDF powders and PZT ceramics +taken in a volume ratio of 60:40. Two types of the PVDF powder differing +in concentration of ionogenic end groups that contribute to dissociation of +impurities, and therefore have a specific resistance at room temperature 1010 +Ω·m and 1012 Ω·m, were used to study the influence of the properties of +polymer matrix. Specific resistance of the PZT had an order of 1010 Ω·m. +Poling of the samples was carried out by the thermoelectret method. +The samples were kept for 50 min at high temperature in the outer field, +and then cooled without removal of the field. As changing parameters, we +used the poling temperature (70–130 °C) and the conductivity of the poly- +mer component. It was assumed that there are different conductivities and +dielectric permittivities in the layers. In real ferroelectrics polymers the +phenomenon of percolation and injection of carriers in volume should be + +173 +taken into account. From the theory of percolation, it is known that for +three-dimensional two-phase systems the leakage threshold depending on +the structural features of the phases is in the range of 0.05–0.6. In the case +of conventional ferroelectric polymers with the concentrations of the fill- +er or crystalline ferroelectric phase of the order of 0.4–0.5 it is very like- +ly to find the mixture either in the critical region or in the region where +the infinite cluster is formed. Therefore, known formulas for generalized +electrical characteristics of mixtures exopessed by formulae of Lichteneker, +Landauer-Brugemann, Odelevsky and others are unsuitable for ferroelec- +tric polymers and composites because they assume relative proximity of the +components properties and the small volume fraction of one of them. +It is obvious that in the presence of contacts between particles of crystal- +lites or ceramics, equivalent circuit diagrams should take into account not +only sequential combinations of layers, but also parallel ones. Consideration +of the injection based on the Poisson equation should lead to the field het- +erogeneity in the thickness of the sample. The mentioned effects in ferro- +electric polymers and composites have not yet been studied and the theory +of these phenomena is absent. +As can be seen from Fig. 15, change in the poling temperature affects the +temperature dependence of the conductivity. The activation energy increas- +es with increasing temperature both in low-conductive and high-conductive +composites, and the value of the conductivity decreases. This corresponds +to the proposed hypothesis that explains decrease of the conductivity by +trapping a part of the carriers at the boundaries of the polarized crystallites. +Indeed, residual polarization increases with increasing temperature and the +specific conductivity decreases. +The degree of the residual polarization and its stability in a ferroelectric +ceramic essentially depend on the magnitude of the injected space charge +that apparently compensates the depolarizing field occurring when dipoles +in crystallites are oriented. Similar processes occur in the ferroelectric poly- +mers. However, in view of the morphological features, the conditions for +maintaining the stable polarization in ferroelectric polymers are better than +in ferroelectric composites where the incomplete polarization occurs due to +boundaries scarcity, mechanical stress and restriction in free volume. There- +fore, some of the residual polarization immediately relaxes after removing +the external field. In the ferroelectric polymer, the ferroelectric particles are +free that creates favorable conditions for trapping the charge at their bor- +ders. Although the particles are in contact with each other, they do not form +a rigid grid and easily allow for volume changes during poling Large-scale + +174 +potential changes during poling contribute to deep trapping of charges, as +well as to reduced molecular mobility in the interphase layer That is why +the piezoactivity of polymer in ferroelectric polymers is higher than that of +ceramics used as a filler. +2,2 +2,4 +2,6 +2,8 +3,0 +-1 +0 +1 +2 +3 +6 +5 +4 +3 +2 +1 +ln g (10 +-9 Ом +-1.м +-1) +1000/Т +Fig. 15. Temperature dependence of the specific conductivity of PVDF-PZT sam- +ples poled at 70 °C (1.4), 100 °C (2.5) and 130 °C (3.6). Specific resistance of the +polymer is 1010 Ω·m (1, 2, 3) and 1012 Ω·m (4, 5, 6) +In «polymer-ferroceramics» composites as in the ferroelectric polymers, +one should not contradict the role of space charge and polarization in the +appearance of high pyroactivity, but consider them in a relationship. In the +composites like as in PVDF, irreversible relaxation processes and reversible +(pyroelectric) are interconnected. +It is known that pyroelectric currents are reversible, that is when switch- +ing from heating to cooling they must change the direction to the opposite. +However, as can be seen from Fig. 16, this is not always observed. +The imbalance of direct and reciprocal current is due to the influence +of the relaxation component, which does not diminish instantaneously to +zero with the termination of heating, but it relaxes with the time constant +of order of tens and hundreds of seconds. As a result, there is a delay in the +pyroelectric current, which is observed in Fig. 16. +With repeated heating and cooling of the samples, along with decrease +of the current in the forward direction as a result of the relaxation processes +annealing, the symmetry of the direct and the reverse current appears for the +same reason (Fig. 17) indicating predominance of the pyroelectric compo- +nent over the relaxation component. + +175 +0 +30 +60 +90 +120 +150 +180 +0 +4 +8 +12 +3 +2 +1 +Current density, A/m +2 +Temperature, +оС +0 +30 +60 +90 +120 +150 +180 +-2 +0 +2 +4 +6 +8 +3 +2 +1 +Current density, A/m +2 +Temperature, +оС +Fig. 16. Thermal currents during primary (1) and repeated (2) heating of poled +PVDF-PZT composites samples, and also cooling after the reheating (3). The heat- +ing rate is 3.5 °C/min. The thickness of the samples is 280 μm. Piezo modulus is +8 pC/N +0 +30 +60 +90 +120 +150 +180 +0 +4 +8 +12 +3 +2 +1 +Current density, A/m +2 +Temperature, +оС +0 +30 +60 +90 +120 +150 +180 +-2 +0 +2 +4 +6 +8 +3 +2 +1 +Current density, A/m +2 +Temperature, +оС +Fig. 17. Thermal currents when heated for the first (1) and the third (2) times, and +also after cooling after the third heating (3) of PVDF-PZT samples poled by the +thermoelectret method. The heating rate is 3.5 °C min. The thickness of the samples +is 240 μm, the poling temperature is 100 °C + +176 +It is interesting to note that in the polymer-ceramic composite, as in +PVDF, the maximum of pyroactivity coincides with the position of the TSD +current peak indicating the interrelation of these processes, and possibly +also their general nature. +Conclusions +Application of the corona triode in most of our studies allowed to make +the poling process fully controlled, to optimize the magnitude of the result- +ing polarization and to perform a virtual short circuiting after the comple- +tion of poling. Based on the multifactorial experiment, the best correlations +of parameters such as temperature and time of poling, as well as the poten- +tials of the corona electrode and the grid are established. A new technique +for studying the relaxation of homocharge and heterocharge processes in the +ferroelectric polymers was developed. The technique is developed for sep- +aration of the complete electrical displacement components during PVDF +films poling by voltage pulses for allocation and analysis of the polarization +components and kinetics of their formation. +The commonality and similarity of electrophysical and polarization pro- +cesses in ferroelectric polymers and composites have been experimentally +proved considering their two-phase structure and the need to neutralize the +depolarizing field by trapped charges at the interphase boundaries. +Phenomenological models of the polarized state formation and relax- +ation processes under different conditions were proposed and calculated +taking into account and explaining polarization heterogeneity, nonlin- +ear dependence of polarization on the field and trapping of carriers at the +boundaries of polarized regions. +A phenomenological model for the polarized state formation a ferroelec- +tric polymer subjected to constant current poling was developed and ana- +lyzed, in which an important role is assigned to injection of charges, which +create a heterogeneous distribution of the space charge, the field strength +and the residual polarization. Three-stage nature of the poling process of the +ferroelectric polymer films is explained. Comparison of experimental and +calculated kinetics of the electret potential showed their high degree of con- +formity that allowed considering the reasonable assumption about deeply +trapped injected charges, on the basis of which the model was constructed. +A model of the polarization switching in PVDF in the mode of the con- +stant applied voltage has been developed that took into account the follow- +ing features: +– Two-phase structure of the polymer, + +177 +– Presence of the intrinsic conductivity and injection of charges from +the electrodes, +– Trapping of charges at the boundaries of polarized crystallites and +their release depending on the stage of the process, +– Partial recombination of the released charges and their secondary +trapping, +– Dependence of the polarization switching time on the field strength, +– Nonlinear dependence of quasi-stationary polarization in crystallites +on the field strength. +A system of differential equations describing the process of the polariza- +tion switching was formulated and solved in which the following parameters +were used as alternating variables: +– Field strength in amorphous and crystalline phases, +– Polarization in crystallites, +– The effective conductivity and the surface charge density at the inter- +phase boundaries. +From comparison of the experimental polarization switching curve with +the calculated curve, such parameters as the effective mobility, the charac- +teristic polarization switching time and the activation field are found. Based +on the model, the difference between the initial polarization formation in +a two-phase polymer ferroelectric and the polarization switching was ex- +plained. +A model for explaining polarization profiles in PVDF films in the +mode of the constant voltage creating either the middle field close to the +coercive field, or the high field substantially exceeding the coercive field +was developed and analyzed. The model took into account the monopolar +injection of charges from a negative electrode, the nonlinear dependence +of the quasi-stationary ferroelectric polarization on the field strength, +the Poisson equation on interrelation between charges and the gradient +of the field strength. The character of the injected charges front motion +was calculated, as well as the time dependence of the field strength in the +zone adjacent to the positive electrode. Formation of the inhomogeneous +polarization in the case of the middle fields was explained, as well as for- +mation of the deeply trapped charge layer at the boundary of the polarized +region. This layer is stable even when the polarization is switched lead- +ing to distortion of the polarization uniformity profile and impossibility +of its improvement by application of very high fields. It is shown why the +uniform residual polarization is formed in the case of high applied fields +during initial poling. + +178 +On the basis of the conducted research, practical recommendations for +the modes of ferroelectric polymers and composites poling are developed, +which provide high and stable residual polarization. +REFERENCES +1. Rollik D., Bauer S., Gerhard-Multhaupt R., J. Appl. Phys. 85, 3282 (1999). +2. Rollik D., Kunstler W. et al., Proc. 10th Int. Symp. Electrets, 51 (1999). +3. von Seggern H. and Fedosov S., IEEE Trans. Diel. Elect. Insul. 11, 232 (2004). +4. von Seggern H. Fedosov S. N. Appl. Phys. Lett. 81, 2830 (2002). +5. von Seggern H. and Fedosov S. N., Appl. Physics Letters, 91, 62914 (2007). +6. Fedosov S. N. von Seggern H., J. Appl. Phys. 96, 2173 (2004). +7. Das-Gupta D. K. (ed.), Ferroelectric polymers and composites — Trans. Publ. +332 p. (2004). +8. Teyssedre G., et al., Proc. 8th Int. Symp. Electrets. 650 (1994). +9. Eliasson S., J. Phys. D.: Appl.Phys.19, 1965 (1986). +10. Ieda M., Mizutani Т., Nagata T., Annu. Rept. CEIDP. 399 (1994). +11. Neagu E. R. et al., J. Phys. D: Appl. Phys. 35, 1229 (2002). +12. Turnhout van J., TSD of polymer electrets. Elsevier, 327 p. (1995). +13. Sessler G. M. (еd.), Electrets — v.1, 3rd ed., Morgan Hill: 437 p. (1999). +14. Sessler G. M., Das-Gupta D. K. et al., IEEE Trans. Electr. Insul. 27, 872 (1992). +15. Teyssedre G. and Lacabanne C., Ferroelecfrics. 171, 125 (1995). +16. Sergeeva A. E., Fedosov S. N. et al., Phys. & Technol. Thin Films, 1, 382 (2005). +17. Lines M. E., Glass A. M., Principles and Applications of Ferroelectrics, Oxford, +680 p. (2001). +18. Broadhurst M. G., Davies G. T., Ferroelectrics. 82, 177 (1987). +19. Wada Y., Hayakawa R., Ferroelectrics. 32, 115 (1981). +20. Elling В., Danz R., Weigel P., Ferroelectrics. 56, 179 (1984). +21. Fedosov S. N., Sergeeva A. E., Solid State Physics. 31, 270 (1989). +22. Collins R. E., J. Appl. Phys. 51, 2973 (1980). +23. Gross B., J. Chem. Phys. 17, 866 (1949). +24. Fedosov S. N., Sergeeva A. E. et al., arXiv:0704.3993 5 p. (2007). + +179 +DISTRIBUTION OF FERROELECTRIC POLARIZATION IN POLED +PVDF AND P(VDF-TFE) FILMS +Fedosov S. N. +У статті наведено результати експериментального дослідження рівно- +мірності розподілу поляризації у сегнетоелектричних полімерних плівках за +товщиною зразків. Об’єктами дослідження обрані типові полімерні сегне- +тоелектрики — полівініліденфторид (ПВДФ) та його сополімер з трифтор- +етиленом П(ВДФ-ТФЕ). Вимірювання виконані сучасним чутливим мето- +дом п’єзоелектрично генерованої сходинки тиску. +Встановлено, що розподіл поляризації істотно залежить від величини +прикладеної напруги у процесі первинної електризації плівок. У разі слабких +та середніх полів, близьких до коерцитивного, розподіл є неоднорідним з мак- +симумом поблизу позитивного електрода. При цьому рівномірність поляриза- +ції не можна поліпшити шляхом подальшого застосування дуже сильних полів. +Якщо первинна електризація проводиться у сильних полях, то розподіл +поляризації однорідний. Досліджено особливості сополімера, електризова- +ного в коронному розряді. Розроблено феноменологічні моделі процесів, що +відбуваються при формуванні поляризації в сегнетоелектричних плівках та +сформульовані практичні рекомендації. +This article presents the results of experimental study of the polarization distri- +bution uniformity in ferroelectric polymer films over the thickness of the samples. +Typical polymeric ferroelectrics — polyvinylidene fluoride (PVDF) and its copoly- +mer with trifluoroethylene P(VDF-TFE) were selected as objects of research. The +measurements were carried out by a modern sensitive piezoelectric generated pres- +sure step method. +It was found that the distribution of polarization substantially depends on the +value of the applied voltage during the primary electrification of the films. In the +case of weak and medium fields close to coercive, the distribution is inhomogeneous +with a maximum near the positive electrode. However, the uniformity of polarization +cannot be improved even by the subsequent application of very strong fields. +If the primary electrification is carried out in strong fields, then the polarization +distribution is uniform. The features of the copolymer electrified in corona discharge +have been investigated. Phenomenological models of the processes occurring during +the formation of polarization in ferroelectric films have been developed and practical +recommendations have been formulated. +1. Introduction. State of the problem +Spatial distribution of polarization in PVDF films is extremely import- +ant both from scientific and practical points of view. Even in earlier works +[1; 2] it was noted that the piezoelectricity and pyroactivity in PVDF films + +180 +near the positive electrode are higher than near the negative one that was +erroneously associated with injection of holes and the formation of a non- +uniformly distributed positive space charge. Further studies [3–5] showed +that in some cases not only the space charge, but also the polarization are +distributed non-uniformly in the thickness direction. +For the first time, heterogeneity of polarization in PVDF was detect- +ed by Day et al. [1] by different values of the pyroelectric activity near two +sides of polarized films. Sassner [2] found that from tightly pressed to each +other three films only the film adjacent to the positive electrode was highly +polarized It was found [6] that in the high field (E > 150 MV/m), the po- +larization is almost homogeneous, while in the middle fields the maximum +of polarization is either in the center of oriented films, or near the anode in +the unoriented ones. +Gerhard-Multhaupt et al. [7] investigating the distribution of piezoac- +tivity by the method of a pressure pulse generated by a powerful laser con- +firmed that during thermoelectret poling in the middle fields, the maximum +polarization is near the anode, as in the case of poling in a corona discharge. +Authors of [8] believe that because of the high conductivity of PVDF, +areas of excess charge cannot exist, and charge-compensated polar- +ization zones are formed. At the same time, we have calculated Debye’s +length of screening LD for the following PVDF characteristics: temperature +T =300 K, the dielectric permittivity ε = 10, the mobility of charge carriers +μ = 10–12 m2/(V∙s), the specific conductivity g = 10–12 Sm/m. +We obtained LD = 170 μm that is much larger than the typical thickness +of the films (10–50 μm). Therefore, the effect of screening by the space +charge should be weakly expressed in PVDF. +Mopsik and de Reggi [9] found an increased value of the coercive field +strength near the surface of the PVDF, and de Reggi and Brodhard [10] +found that, in spite of the displacement of polarization to the anode, it is +zero near the electrode. Sessler and Berraissoul [11] found that the piezo- +activity near the electrodes and, consequently the polarization is very small. +The weakening of the field, in our opinion, is an indication of the injec- +tion of charge carriers and, on the contrary, the field and polarization near +the blocking electrode are increased. +In [4], the maximum polarization near the anode is reported after poling +of PVDF in a positive corona discharge, although in the other work of the +same authors it is indicated that the polarization in this case is concentrated in +the central zone [6]. Bichler et al [3] found that the position of the maximum +polarization depends on the mode of thermal and mechanical processing of + +181 +PVDF. The authors of the paper [3] concluded that the polarization in the +PVDF containing the α-phase was shifted to the anode, while the polarization +was uniform in the presence of the β-phase although the heat-treatment and +stretching changed both the crystalline structure of the films and their other +properties. In [12], the polarization attenuation near the anode is reported in +corona poled PVDF films. Such contradictory data are explained by the fact +that the selection of films for the study was random (various thicknesses, re- +gimes of poling, annealing, and mechanical pre-treatment). In addition, the +research methodology was imperfect in some cases, so that there was a sub- +jective factor in interpreting the measurement results. Direct measurements +of the polarization profile are possible only by the method of the pressure step, +while all other methods should be considered as non-direct ones. +The dynamics of the polarization profile in PVDF was studied only in +a few works. Thus, it was established [13] that polarization develops in the +central zone in biaxially oriented PVDF films containing 70 % β-phase in +the case of middle field (60 MV/m). However, when changing the polarity +of the voltage, the complete switching near the anode does not occur and a +bimorph structure is formed. +Fedosov and Sergeeva, investigating the distribution of polarization in +films electrically charged in a corona discharge [5; 14–16], found that the +maximum polarization is near a positive electrode with a negative polarity +of the corona discharge. +This indicates that injection of negative carriers takes place, while the +positive electrode is blocking. When charged in a positive corona there is +a double injection: positive charges from the corona and negative charges +from the electrode. It was found that the free surface of the film exposed to +the corona discharge can be regarded as a virtual injection electrode. +In a number of studies, the thermal stability of polarization and its dis- +tribution in the thickness direction in PVDF and P(VDF-TrFE) [10], as +well as in P(VDF-TFE) [16] were investigated. The charge and polarization +distribution in PVDF films poled by the electron-beam method [17] was +studied by the laser induced pressure pulse (LIPP) method. +Fedosov and Sergeeva found that the trapped electrons in the volume are +not concentrated in a thin layer at a certain depth, but are distributed with +uneven density in a zone of the finite thickness [18]. +These electrons form a virtual negative electrode, from which injection +of charges in a non-irradiated region takes place leading to increase in the +imaginary penetration depth of the electrons and to inhomogeneity of po- +larization in the non-irradiated region. + +182 +The importance of the injection processes, but not the distribution of +intrinsic charges in volume was evidenced by Mitsutani and Ieda [19]. They +found that the poling current increases in 200 times, if a corona discharge +is used instead of a metal electrode. The experimental results in papers [19; +20] have been explained by the injection of charge carriers. At the same +time, some authors believe that the corona discharge forms an ideal block- +ing contact with any dielectric [21]. Thus, the question of the injection of +charge carriers and their role in the formation of polarization remains open +and controversial. +The reasons of the fragmentary and contradictory nature of the literature +data on the polarization profiles in PVDF are the complexity of experimen- +tal methods and ambiguity in interpretation of the results. +The aim of this study is to clarify the situation with importance of the +uniformity of the polarization distribution in polymer ferroelectrics by per- +forming additions experiments and developing the corresponding phenom- +enological models. +2. Methods for studying polarization profiles in ferroelectric polymers +Profile of polarization and space charge in thin polymer films is studied +by one of the following three methods is used: +1) The method of the piezoelectrically generated pressure step (PPS); +2) The method of the thermal wave induced by a modulated laser +(LIMM); +3) The method of the laser induced pulse pressure (LIPP). +The analysis of the efficiency, sensitivity and resolution of these meth- +ods showed that the measured current in the PPS method is proportional +to the polarization or gradient of the space charge, whereas in the LIPP +method the measured signal is proportional to the charge (if any) and +the gradient of polarization. Given the features of the LIPP method, +only zones where polarization changes in thickness direction is detect- +ed. Therefore, a high homogeneous polarization and complete absence of +the polarization give the same signal. Despite the resolution of the LIPP +method is practically the same as the resolution of the PPS method, it +should be recognized that the method of the pressure step (PPS) is more +reliable and informative. +In the LIMM method, the depth of the thermal wave penetration de- +creases with the increase of the modulating frequency, so at very high mod- +ulation frequencies above 10 MHz it is possible to investigate very thin near- +to-electrode layers of less than 1 μm in thickness. + +183 +However, the resolution of the LIMM method drastically decreases with +increasing the distance from the surface to the depth of the sample, and this +is a significant disadvantage of the LIMM. +Taking into account the results of the analysis, we have chosen the PPS +method, which provides a fairly high resolution of about 2–4 μm and the +possibility of observing the real-time polarization profile on oscilloscope’s +screen. It does not require complex calculations, assumptions, and solu- +tions of incorrect inverse tasks as in the case of the LIMM method. The +colossal advantage of the PPS method is the ability to study the dynamics of +the polarization profile “in situ” directly in the process of poling, polariza- +tion switching, and short-circuiting of the samples. +Most methods for measuring polarization and space charge profiles in +dielectrics are applied to already polarized samples providing the informa- +tion about the final state, while the process of the polarization development +and its profile remained inaccessible for a direct experimental study. In this +sense, a unique possibility is provided by the piezoelectrically generated +pressure step (PPS) method, in one of the modifications of which there +is the ability to measure the profile “in situ” directly when the polarizing +voltage is applied or the specimen is short-circuited. Such measurements of +the dynamics of the polarization profile are extremely important for under- +standing the physical processes occurring in ferroelectric polymers during +their poling and switching of polarization. +The PPS method developed by Eisenmenger et al. [6] was applied by us, +and all measurements were performed in the laboratory of Prof. W. Eisen- +menger at the Department of Physics of the Stuttgart University. The meth- +od is based on the generation of an electric signal (a current pulse) when a +pressure step generated by a piezoelectric crystal passes through the sam- +ple. The piezoelectric pressure step results from a voltage step with a very +steep front. The front of the pressure wave extends with the sound speed of +2250 m/s creating a current pulse in the short-circuited sample. It has been +proved that the shape of the current pulse repeats the profile of the polariza- +tion distribution in the thickness of the film. +The block diagram of the installation using the PPS method is shown +in Fig. 1. The voltage step is formed by means of a constant voltage source +(500 V) loaded with connected in series a resistance and a capacitor. This +chain with a frequency of about 100 Hz is locked to a resistor of 50 Ω, in +parallel with which a quartz crystal is connected. A sample is pressed to the +back side of the piezoelectric crystal, to which a grounded copper electrode +is connected. + +184 +Silicon oil +Pressure step +1 +50 Ω +50 Ω +Conducting rubber +Sample +Signal +І(t) +Piezocrystal +2 +Voltage step U(t) +Fig. 1. Schematic diagram of the polarization profile measurement by the piezoelec- +trically induced pressure step (PPS) method +For better transferring of the pressure wave from quartz to the specimen, +a thin layer of silicone oil is applied between them. The electric signal is tak- +en from the rear side of the sample with the help of a clamping conductive +rubber electrode. The load is a 50 Ω resistor, the signal from which is fed to +the broadband amplifier and then either to the spectrum analyzer, or to the +oscilloscope. In the case of thin specimens, a 23-μm thick polypropylene +gasket was used to reduce the capacity. +Measurements have shown that the steepness of the pressure step front +is of the order of 0.4 ns, while the sound speed in PVDF at room tem- +perature is about 2250 m/s. Thus, the time of the pressure wave passage +through the sample at its thickness of 20 μm is of the order of 10 ns. The +duration of one voltage pulse was 100 ns, that is, a step-by-step mode was +implemented. +All used devices (amplifier, spectrum analyzer, and oscilloscope) had a +bandwidth of more than 1 GHz. The sensitivity of the PPS method was +about 2 μm and was limited by the steepness of the pressure step. An electri- +cal signal in the spectrum analyzer was converted into a digital code to allow +computer processing of the data. +To investigate the polarization profile, several series of experiments were +performed on PVDF films. Aluminum electrodes of 5 mm in diameter on +both sides were pre-deposited at the samples by vacuum evaporation. Initial +poling and the polarization switching were carried out at room temperature +by applying a constant voltage of certain magnitude and polarity. + +M185 +The magnitude of the voltage was chosen so that average field was 60 +MV/m in a series of polarizing and switching, which is slightly higher than +the coercive field of PVDF according to the literature data [12]. Such a +mode was named as «middle fields». +In another series, the polarizing field strength was 160 MV/m being +much higher than the coercive value. Such regimes were classified as «high +fields». At the middle fields and at the high fields, full polarization cycles +were investigated. After each phase of polarization or switching, the speci- +men was short-circuited for a time sufficient to establish a quasi-stationary +state (from 200 to 2000 s). +The polarization profiles were measured about 100 times per second and +recorded from the oscilloscope screen. Then the analog information of se- +lected frames was converted into digital and entered into the computer for +further processing. All results are presented in the form of graphs of depen- +dence of polarization on the distance in the sample from its surface. +3. Distribution of polarization in thin PVDF films +Polarization profiles and the space charge give important information +about their interrelation in the process of the polarized state formation and +in ensuring of its stability. This allows us to move from hypotheses and as- +sumptions to concrete experimental facts, the analysis of which contributes +to the deeper understanding of the ferroelectric polymers characteristics. +That is why special attention was paid to the dynamics of polarization +profiles in PVDF films not only during the process of poling but also during +the polarization switching and short-circuiting both in the middle fields +close to the coercive (50–60 MV/m) and in high fields with a strength of +about 160 MV/m. +The obtained results allowed constructing models, which take into ac- +count the relation between injection and separation of charges, presence +of deep charge trapping zones and its interrelation with the residual polar- +ization. The impossibility of a complete switching of an inhomogeneously +polarized ferroelectric polymer [22] discovered by us is of great practical +importance for the choice of poling modes and shows how strong is relation +between the ferroelectric polarization and the surface charge. +3.1. Poling field near the coercive value +From Fig. 2 it can be seen that, with the average field strength close to +the coercive value Ec = 50 MV/m [23], the dynamics of the polarization +profile is characterized by the following: At the initial stage of poling, af- + +186 +ter 8 seconds after the voltage application, the polarization distribution is +uniform, but its value is very low (0.5 μC/cm2). Over time, the distribution +of polarization in in the thickness direction becomes non-uniform with the +maximum near a positive electrode. After poling of PVDF in the average +field for 2000 s, a sharply heterogeneous asymmetric distribution of the re- +sidual ferroelectric polarization appears with a layer of about 5 μm thickness +near the negative electrode, in which the residual polarization is zero. When +the voltage is disconnected and the sample is short-circuited, the character +of the polarization distribution does not change and the polarization re- +mains heterogeneous, but its magnitude decreases from 3.31 to 1.71 μC/cm2 +in the region of the maximum. +0 +5 +10 +15 +20 +0 +1 +2 +3 +4 +2 +4 +6 +8 +10 +Polarization, C/cm +2 +Stage +Depth, m +Fig. 2. Distribution of polarization in P(VDF-TFE) film during its poling in the field +of 60 MV/m. The stage number corresponds to different times after the starting +of poling: 1–8 s, 2–70 s, 3–100 s, 4–150 s, 5–250 s, 6–350 s, 7–450 s, 8–750 s, +9–1000 s, 10–1510 s, 11–2000 s +The resolution of the method for measuring the polarization profile is +of the order of 2–3 μm, which leads to appearance of smooth polarization +profiles in near-to-electrode regions and in other places of the virtually sharp +polarization change. For example, it was shown [5] by measuring the polar- +ization profile near the electrode by the LIMM method having the resolu- +tion near the electrodes of the order of 0.1 μm that the polarization changes + +187 +sharply from the maximum value to zero within about 1 μm in the vicinity +of the positive electrode. In the vicinity of the negative electrode where po- +larization is absent, distortion of the profile due to the finite resolution does +not occur. +The effect of resolution, probably, also affects the boundary between the +first and the second zones where the polarization changes more sharply than +it follows from the curves in Fig. 2. +0 +5 +10 +15 +20 +-2 +-1 +0 +1 +2 +3 +4 +0 +2 +4 +6 +8 +10 +Polarization, C/cm +2 +Stage +Depth, m +Fig. 3. Polarization profiles in the P(VDF-TFE) film during the polarization switch- +ing in the field 60 MV/m after initial poling and the short-circuiting. The stage +corresponds to different times from the starting of the switching: 1–0 s, 2–0.2 s, +3–0.5 s, 4–1 s, 5–5 s, 6 –50 s, 7–200 s, 8–500 s, 9–1000 s, 10–1500 s, 11–2000 s +After changing the voltage polarity (Fig. 3) a minimum is formed in the +place of the former maximum at a depth of about 16 μm, because the po- +larization in this place is not completely switched, but even does not reach +zero. At the same time, the oppositely directed polarization is formed to the +right and to the left of this intersection. +High polarization is formed again only near the positive electrode now +connected to the opposite side of the film. It should be noted that the polar- +ization switching is faster than initial poling, and the residual polarization in +the peak area is almost 1.5 times greater than after initial poling. + +188 +Comparison of polarization profiles after several switchings showed that +with even number of switchings, practically identical profiles are appeared. +In the case of odd number of switchings, the profiles are also the same, ex- +cept for the profile after the first charging when there is no reverse polariza- +tion near the negative electrode. +Thus, the profile is determined by whether the number of switchings is +either even, or odd. In both cases, the distribution of polarization is sharply +heterogeneous and asymmetrical with respect to the center of the sample. +The main polarization maximum, regardless of the parity of the phases, is +always near the electrode, which was positive in the last previous experi- +ment, and the magnitude of this maximum is almost 1.5 times greater than +in the case of an odd number of switchings than with the even number. +The time for quasi-stationary state formation decreases with increase in +the number of voltage switchings from 2000 s during initial poling to 250– +500 s during the subsequent transitions. +In some studies, for example [10, 24], the information that the coercive +field near the surface is greater than that in the volume are incorrect, in our +opinion, because the incomplete switching is, most likely due to heteroge- +neity of the field. Due to injection of charge carriers, the field near the sur- +face is smaller than in the volume, and therefore the polarization is poorly +switched there. +3.2. Attempts to improve properties of non-uniformly polarized films +It is seen from Fig. 2 and Fig. 3 that in the middle fields (60 MV/m) po- +larization is heterogeneous at any polarity of the voltage, and the complete +switching does not occur in any section of the sample. The formed bimorph +structure is stored regardless of the direction of the external switching field. +At the same time, as will be shown below, homogeneous polarization is +formed in high fields (160 MV/m), which then remains homogeneous with +any changes in the magnitude and sign of the applied voltage up to complete +depolarization. In this regard, it was interesting to investigate behavior of the +polymer ferroelectric films in high fields, originally poled in middle fields. +If the initial polarization inhomogeneity is due to the fact that the field +is not high enough, homogeneity should increase after applying a high field, +due to expansion of the polarized region. However, we have found that the +polarization does not become homogeneous, and the polarized region does +not expand under the action of a high field. +Experiments were carried out as follows. PVDF films were placed in a +field of 60 MV/m and polarization profiles were measured. As can be seen + +189 +from Fig. 2 and 3, the spatial distribution of polarization was sharply het- +erogeneous. Further, without interrupting the measurements of the polar- +ization profile we increased the voltage to 3.2 kV by steps of 200 V. The field +strength at 3.2 kV is several times greater than the coercive value. +0 +5 +10 +15 +20 +0 +1 +2 +3 +4 +5 +6 +7 +2 +4 +6 +8 +10 +Polarization, C/cm +2 +Stage +Depth, m +Fig. 4. Polarization profiles in the P(VDF-TFE) film during the stepped voltage in- +crease from 1.2 kV (primary poling) to 3.2 kV. The value of the voltage step is 0.2 kV, +the exposure time at each voltage is 50 s +However, as it follows from the graphs in Fig. 4, the increase in the +field strength did not lead to the expected improvement of the polariza- +tion uniformity. Only the magnitude of the maximum increased, while +the non-uniform character of the polarization distribution remained un- +changed. +Thus, in order to obtain the high and homogeneous residual polar- +ization, it is not enough to apply a high field. It is necessary to take into +account the conditions in which the sample was poled for the first time. +If initial poling was carried out in the high field, then the residual polar- +ization will be homogeneous at any applied forward poling or switching +voltage. +If initial poling was carried out in medium or weak fields, then the het- +erogeneity of the residual polarization cannot be corrected or eliminated by + +190 +applying the high field. In this case, for obtaining the uniform profile of the +residual polarization, we recommend a complete thermal depolarization of +the sample and its annealing in the short-circuited condition at about 160 +°C for several hours, so that the trapped charges in the volume will be com- +pletely dissipated. After cooling the sample, it is necessary to re-pole it, but +necessarily in the high field. +3.3. Poling and switching of polarization in high fields +In the case of high fields (160 MV/m), (Fig. 5), polarization is much +more uniform than in the case of middle fields, and the polarization uni- +formity appears even after initial poling. When polarity of the polarizing +voltage changes, the symmetric switching of polarization occurs. By apply- +ing the voltage of the opposite polarity, and by increasing it in small steps, +it is possible to almost completely depolarize the sample. The field strength +at which this occurs corresponds to a value of 60 MV/m. Namely this value +can be considered as a real coercive field. +It is interesting to note that the subsequent application of an external +field of 60 MV/m of any polarity provides homogeneous residual polariza- +tion, which cannot be obtained after initial poling in such a field. The com- +plete depolarization of a highly polarized sample irrespective of the polarity +of the external field occurs at field strength of 60 MV/m, which indicates +the symmetry of the hysteresis loop if initial poling was carried out in high +fields. +Thus, the main features of poling and switching in high fields are as fol- +lows: +1. Polarization in the sample volume is homogeneous and symmetric +with respect to the central section; +2. There is no difference in the shape of the profile and the magnitude of +polarization at different polarizing voltages; +3. Polarization is easily switched over the entire volume, and full depo- +larization is possible; +Homogeneity of polarization is stored not only in high but also in middle +fields. +Of great importance to practice, we have the effect of “formatting” or +“conditioning” in a high field, after which homogeneous polarization is +provided at any field strength, including the coercive field. +This enables, if necessary, to change the magnitude and sign of the re- +sidual polarization in a wide range from zero to saturation that cannot be +achieved without this formatting. + +191 +4. Phenomenological model of polarization profile formation at constant +poling field +It follows from Fig. 2 that in the initial stage of poling at 8 seconds after +the application of a constant voltage creating average field strength of 60 +MV/m the polarization is uniform and corresponds to about 0.5 μC/cm2. +0 +5 +10 +15 +20 +25 +-4 +-2 +0 +2 +4 +6 +2 +4 +6 +8 +Polarization, C/cm +2 +Stage +Depth, m +Fig. 5. Polarization profiles in the P(VDF-TFE) film initially poled at 3 kV after +applying the opposite polarity voltage of different values. Stages: 1 — initial state, +2 — 1.2 kV, 3 — 1.6 kV, 4 — 2.,0 kV, 5 — 2.4 kV, 6 — 2.8 kV, 7 — 3.2 kV +This indicates a uniform distribution of the field strength and absence of +injected charges [25]. At the same time, the stationary value of polarization, +can be calculated by the formula corresponding to initial poling [26] taking +into account its non-linear dependence on the field strength, the presence +of the coercive value Ec and at 50 % crystallinity + +( +) +2 ( +) +r +st +c +s +c +P +P +E +E +E +E += +− +⋅ +− +. +(1) +Substituting in (1) the value of Pr = 13 μC/cm2 [27], Es = 200 MV/m +[23], Ec = 50 MV/m, E = 60 MV/m, we obtain Pst = 0.43 μC/cm2. The re- +versible polarization component Pcap is proportional to the field strength and +the dielectric permittivity + +Рcap= εо(ε–1)Е. +(2) + +192 +Assuming ε = 10 [21] and taking into account that εо = 8.85∙10–12 F/m +and E = 60 MV/m, we obtain Pcap = 0.3 μC/cm2. From the graph of the po- +larization profile dynamics, it is seen that the value of polarization after 8 s +of the voltage action is about 0.5 μC/cm2. Thus, all polarization is reversible, +that is, the ferroelectric component during this time is not yet formed. +With further application of the field, the polarization becomes non-uni- +form (Fig. 2) indicating appearance of inhomogeneous distribution of the +field strength with its weakening near the negative electrode and the increas- +ing near the positive electrode. According to the Poisson equation, inhomo- +geneous polarization of this kind is possible only in the presence of excessive +negative charge in the place of the field heterogeneity + +0 +( , ) +( , ) +E x t +x t +x +∂ +ε ε += ρ +∂ +. +(3) +This charge is likely to be injected from a negative electrode and is pres- +ent near this electrode extending with time to the sample depth. Without +taking into account the formation of the ferroelectric polarization, it can be +assumed that the charge distribution is close to the rectangular [13], and the +speed of the charge front motion is determined by mobility μ and the field +strength E1 at the boundary x1 between the zone with the space charge and +the zone free of excess volume charge + +[ +] +1 +1 +( ) +( ), +v t +E +x t t += µ +. +(4) +Since the applied voltage remains constant (Uo = const), the normaliza- +tion condition is fulfilled + +0 +0 +0 +( , ) +x +E x t dx +U += +∫ +. +(5) +The expression (5) is simplified when the rectangular distribution of the +injected charge is assumed, since in the region from 0 to x1, the field accord- +ing to the Poisson equation (3) depends linearly on the coordinate, while in +the other part of the sample it is constant and equal to E1. Thus, for finding +the x1(t) function and the field strength E1(t) we have the following system +of equations + +1 +1 +(t) +( ) +dx +E t +dt += µ +, +(6) + +1 +0 +1 +0 +1 +( ) +( ) +2 +E t +x +x t +U + + +− += + + + + +. +(7) + +193 +0 +200 +400 +600 +800 +1000 +0 +5 +10 +15 +20 +25 +60 +80 +100 +120 +Depth, m +1 +2 + +Field strength, MV/m +Fig. 6. Estimated graph of the front of injected charges motion after application of a +constant voltage to a PVDF film under the charge mobility of 3⋅10–16 m2/V·s (1) and +the time dependence of the field strength at the boundary, to which the front of the +injected negative charges reached (2) +The equations (6) and (7) were solved by numerical methods, and the +graphs x1(t) and E1(t) are shown in Fig. 6 at xo = 23 μm, μ = 3·10–16 m2/V·s, +Uo = 1380 V. +From the above graphs it follows that there is some acceleration of the +motion of the injected charges front in time. At the same time, the field +strength in the part of the sample which the injected charges have not yet +reached increases with time exceeding the initial strength more than 2 times +after 1000 s of poling. +The polarization switching time depends on the field. Let us explain this +in more detail. If we consider that the switching time of the ferroelectric +polarization in PVDF is about 5 μs at E = 200 MV/m, and the dependence +of the switching rate on the field strength is of the following form + +0 exp +A +E +E + + +τ = τ + + + + +, +(8) +where τo has an order of 20 ns, then for the activation field EA we will get the +following value: + +0 +ln +1.1 +A +E +E +τ += += +τ +GV/m. +(9) + +194 +The polarization switching time in the field of 60 and 120 MV/m should +be τ60 ≈ 2 s, τ120 ≈ 2·10–4 s in accordance with the formula (8). +Thus, the increase of the field strength by 2 times leads to decrease of the +switching time by 4 orders of magnitude, but both values are small compar- +ing to the time scale of the experiments. This allows assuming that the pro- +cess of the ferroelectric polarization formation is quasi-stationary. In this +case, we can disregard the dependence of the switching time on the field +strength, but use the field dependence of the ferroelectric polarization (1) +assuming that at any given time Pfe = Pst. +It was shown [16] that in the PVDF, in addition to the capacitive Pcap +and the ferroelectric Pfe component of polarization, there is also a revers- +ible component Prev of the definitely not established nature, the presence +of which is associated with dipole polarization in the amorphous phase of +the polymer. The correlation between the components of polarization can +be established by analyzing the evolution of the polarization profile after +the voltage is switched off and the sample is short-circuited. In the process +of poling, when the voltage is applied, there are all three components of +polarization + +Р1 = Рcap+Рfе+Рrev, +(10) +where P1 = 3.31 μC/cm2 at the point of maximum polarization. In the case +of the shortening, the components of Pcap and Prev disappear and only the +ferroelectric component remains, that is, P2 = Pfe with P2 = 1.71 μC/cm2. +Since the polarization formation process is rather slow, the experiment time +is much greater than the Maxwell relaxation time + +0 +3 +M +s +g +ε ε +τ += +≈ +. +(11) +At own conductivity of PVDF g = 3∙10–11 Sm/m [16], there is no reason +to assume that there is a partial back switching of the ferroelectric polariza- +tion due to insufficient compensation of the depolarizing field. Therefore, +Pfe does not change with the short-circuiting. By the formula (1) we can find +the corresponding polarization maximum of (Pst = 1.71 μC/cm2) and the +field strength E = 89.5 MV/m. The capacitive component of the polariza- +tion Pcap = 0.79 μC/cm2 according to the formula (2). Then the reversible +component of the polarization will be equal to Prev = P1 — Pcap — Pfe = 0.81 +μC/cm2. +Since the reversible polarization most likely, is due to the dipole struc- +ture of the amorphous phase, it can be taken into account by introducing + +195 +the effective dielectric permittivity of the amorphous phase, which includes +all the reversible processes. +The obtained value of the same order (19.6) was used in the works of +von Seggern and Fedosov [15; 28] in calculations of the two-stage forma- +tion of the ferroelectric polarization in PVDF. The dynamics of polariza- +tion in four cross sections (Fig. 7) shows that the degree of heterogeneity +increases, because the polarization of about 0.5 μC/cm2 near the negative +electrode at the depth of about 5–6 μm does not increase in time, as it does +in the second part of the sample, but it gradually decreases to zero (Fig. 7). +At the same time, the maximum near the positive electrode located initially +at a depth of 17.5 μm, and then shifted to a coordinate of 15.4 μm increases +with time. +0 +1000 +2000 +0 +1 +2 +3 +Polarization, C/cm +2 +Time, s +5 +10 +15 +20 + +Е +Р +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +0 +х +х +х +2 +х +х +х +о +Е +Е +Fig. 7. Dynamics of polarization in the P(VDF-TFE) during initial poling in the field +of 60 МV/м at different distances from the film surface (depth): 5, 10, 15 and 20 μm. +This suggests that the ferroelectric polarization is not formed near the +negative electrode, but there is a decrease of the field and polarization to +zero. It is known from the theory of injection currents [25] that the field +strength at the injecting electrode is very small or equal to zero, but near the +electrode where excessive charge is located, the field is non-zero increasing +linearly in the case of the homogeneous charge distribution, as follows from +the formula (6). If the charge density decreases in the direction of depth, +the graph of the E(x) dependence will be convex. That is, only injection +of charges cannot explain the presence of a zone in the thickness of about + +196 +5–6 μm, in which the field and polarization are almost zero. Obviously, +there is another phenomenon that leads to decrease of the field strength and +polarization near the negative electrode. + +0 +( +) / +20.2 +a +cap +rev +P +P +E +ε = ++ +ε += +. +(12) +0 +1000 +2000 +0 +1 +2 +3 +Polarization, C/cm +2 +Time, s +5 +10 +15 +20 + +Е +Р +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +0 +х +х +х +2 +х +х +х +о +Е +Е +Fig. 8. Scheme of processes occuring during poling of PVDF films in middle fields +and leading to formation of a heterogeneous three-layer structure. Also the distribu- +tion of the injected charge along the thickness, the field strength and polarization +are shown +It is known that the effective conductivity decreases sharply during +formation of the ferroelectric polarization in PVDF [17], that is, it can be +assumed that the conductivity of the polarized part of the sample is much +smaller than that of the not polarized part. In this case, the distribution of +the total applied voltage Uo between the not polarized and polarized parts +occurs as between two connected in series resistors of different values. +The voltage, and hence the field strength, is small in the not polarized +part, it is higher in the polarized part. This distribution of voltages con- +tributes to the formation of even greater heterogeneity of the residuals +polarization. +Thus, equations (6) and (7), which do not take into account the depen- +dence of the effective conductivity on the ferroelectric polarization Pfe, only +valid until the beginning of the Pfe formation. After this, the uniform motion + +197 +of the injected charge is stopped, because its localization on the boundary of +the polarized and not polarized regions occurs in accordance with the Pois- +son equation (3). Chargers only partially penetrate into the polarized region +or do not penetrate at all, that is, the effective conductivity of the polarized +region decreases. There is a redistribution of the applied voltage, so that it +decreases at the not polarized part, and increases at the polarized part. As a +result, the field strength and reversible polarization decrease in the adjacent +to the injection electrode region, while they increase in the polarized region. +Exactly this is observed on the experimental curves of the polarization pro- +file evolution (Fig. 2). +This phenomenon leads to the formation of a three-layer structure, +schematically shown in Fig. 9. +0 +х2 +х1 +хо +Е2 +Е1 +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +х +Е +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +- +Е1=0 +Е2=0 +(а) +(b) +(c) +Fig. 9. Scheme of processes occurring in PVDF poled in middle fields at the mo- +ment of the short-circuiting (a), distribution of the field strength at the moment of +cut-off (b), and state of the sample after aging in the short-circuited condition +In the area adjacent to the negative electrode, there is a high concentra- +tion of injected charges, high conductivity, low field strength and very low +reversible polarization. At the boundary of the not polarized and polarized +regions, a layer of localized negative charges is formed. Within this layer, the +field is heterogeneous and polarization sharply increases from zero to the + +198 +maximum value. In the third zone, there is the homogeneous field and the +homogeneous polarization. +When the sample is short-circuited after the completion of poling, the +average field strength becomes zero. At the same time, the direction of the +field strength vector in the not polarized part of the sample E1 (Fig. 9) be- +comes such that excess free injected charges from the first zone are “blown” +through an electrode that was negative during poling. The reversible com- +ponents of polarization in all zones are reduced to zero, the excess non-lo- +calized charges are dispersed due to their own conductivity, and the field +strength at all points of the sample becomes zero with a time constant equal +to the Maxwell’s relaxation time (11), as shown in Fig. 9. +According to the experimental data of Fig. 2, the first zone occu- +pies an area from x= 0 to x1 = 6 μm, the second zone is from x1 = 6 μm to +x2 = 14 μm, and the third zone is from x2 = 14 μm to xo = 23 μm. As it follows +from the experimental polarization profiles, the boundaries of the zones do +not change with time. In the second zone, the excess negative charge is dis- +tributed almost uniformly. This is confirmed by the presence of practically +linear sections of the polarization profile in this zone. +It is essential that the polarization profile changes with time at a constant +voltage. This indicates that slow processes of transfer and redistribution of +the space charge are involved in formation of the polarization and in its +switching. In the general case, as follows from our data, the polarization is +a complex function of the field, coordinates in the volume of the dielectric +and time. +The obtained results correspond to the model, which provides an im- +portant role of the volume charge in the formation of the polarized zones +in PVDF and the injection of charge carriers from electrodes. Experimental +data indicate that the level of injection of negative charges from the met- +al electrode is higher than from the positive electrode. It is also possible +that the mobility of injected negative charges is much higher than positive +charges. Intrinsic free carriers play a minor role in this case. +Thus, in the case of initial poling, the homogeneity of the field is dis- +turbed by injection of negative charges. In a large part of the sample near +the injectable electrode, the field is attenuated and smaller than the coercive +field, so the ferroelectric polarization is not formed there and the residual +polarization is zero. At the same time, the field exceeds the coercive val- +ue near the positive electrode, and the high residual polarization is formed +there. The polarization heterogeneity is fixed by negative charges trapped in +the region where the gradient of polarization exists. The depolarizing field + +199 +on the opposite side is compensated by positive charges located either at the +electrode or in the near-to-surface layer. +After poling and short circuiting, the field in the peak area supports po- +larization. There is also a redistribution of moving charges: in the vicinity of +the negative electrode, they move in the opposite direction to the injection +until the field at all points of the volume becomes zero (Fig. 9). Uncom- +pensated trapped charges remain only at the slopes of the polarization peak. +The massive trapping of injected charges at the boundary of the polar- +ized region begins immediately as soon as a zone of the high polarization +appears. This charged layer divides the volume into two parts. In the first +part, adjacent to the negative electrode, there is no high polarization, and +the concentration of free injected carriers is rather high. This results in a +high apparent conductivity and, accordingly, in a weakened field in this +zone in the process of poling. At the same time, the polarized region ap- +pears separated from the injection electrode by a layer of the trapped charge +carriers, and its apparent conductivity becomes considerably smaller than in +the first zone. This phenomenon can be considered as the Maxwell-Wagner +effect induced by the non-homogeneous polarization, which leads to in- +creasing field in the polarized region. That is why, with the passage of time, +the polarized region does not expand, and the value of polarization increas- +es. Phenomenologically, trapping of charges and division into two zones is +manifested in reducing the charging current at constant voltage, that is, in +reducing the effective conductivity. +When polarity of the applied voltage is changed, the preferred injection +of negative charge carriers is again takes place, but they are injected from the +opposite electrode. As a result, the region of the high field appears where the +residual polarization was zero. This leads to the high polarization formation +in new direction in this zone. In the area where residual polarization was +strong, the field is weakened due to the injection of negative charges and +presence of the negative bulk charge. Therefore, switching of polarization +does not occur here, but a part of the residual polarization of the former +direction remains. +In the zone of the negative space charge localization (8–15 μm), the +direction and value of the polarization gradient do not change. This indi- +cates that the negative charges trapped during initial poling are still in place, +despite the fact that the polarization direction in the zone where they are +located changes to the opposite direction. This unusual phenomenon is +completely consistent with the Poisson equation for the case of a zero field. +It is also possible that there is a delocalization of previously trapped carriers + +200 +and their re-trapping without a significant change in the spatial position of +localization. +Thus, after the switching, an asymmetric bimorph structure is formed, +which is stored at subsequent transitions. The negative charge layer, judging +by the polarization gradient in the region of 8–15 μm, is preserved as if it +is fixed in the sample volume during all its transitions. The presence of this +layer explains the faster formation of the polarization profile during switch- +ing compared to initial poling when this layer is not yet present. This same +layer prevents formation of the homogeneous polarization even in the case +of high applied fields. +The effect of impossibility to improve the profile of polarization by in- +creasing the applied voltage to the films initially poled in the middle fields +can be explained by the influence of the injected and trapped charges. From +Fig. 7 it is seen that the polarization gradient at the boundary of the polar- +ized region in the sample volume does not change the sign when the polarity +of the switching external voltage changes. This indicates that in the volume +there is a layer of deeply trapped negative charges, which plays the role of a +barrier preventing the expansion of the polarized region. This layer is stable +because it compensates for the depolarizing field in the regions lying at one +and the other side of it (at different polarities of the external field). Since +this layer obstructs the free motion of injected negative charges, their con- +centration in the region between this layer and the cathode is much greater +than between the charged layer and the anode. Accordingly, the effective +conductivities of these regions are different, and the applied voltage is dis- +tributed unevenly, so that a significant part of the voltage is applied to the +already polarized region. +Thus, increase in voltage cannot widen the polarized region because of +the blocking layer, that is, it does not improve polarization homogeneity. +So, the initial inhomogeneous polarization remains inhomogeneous in high +fields of any magnitude and polarity. +The phenomenon discovered by us is of fundamental importance from +scientific, methodological and practical points of view. First, it further clar- +ifies the mechanism of interrelation of the polarization with the trapped +space charge. It would seem that a high field 3 times higher than the coercive +field, should provide uniform polarization regardless of the initial condi- +tions. However, this is not the case. +The influence of the trapped charge is so significant that even high fields +cannot suppress it. Secondly, in the study of switching and hysteresis phe- +nomena in ferroelectric polymers, it seemed self-evident to start electrifying + +201 +from a weak field gradually increasing the applied field. That is how the hys- +teresis measurements are performed “at the infra-low frequencies”. Taking +into account our data it turns out that such measurements are incorrect, +because the magnitude and, most importantly, the profile of polarization, +depends not only on the field strength, but also on the pre-history of the +sample. +It was established by studying poling and switching in high fields that po- +larization is homogeneous in this case and it is easily switchable over the en- +tire volume. In the case of high field initial poling, a complete depolarization +is possible, and the polarization homogeneity persists not only in high but +also in middle fields. These features can be explained by the fact that, given +the presence of a high field, the polarized region quickly occupies almost the +entire volume, which leads to blocking the movement of charges and a sharp +weakening of the injection of charges role. The processes of compensation +and neutralization of the depolarizing field occur in this case, either on the +electrodes, or near the surface, so that the entire main volume remains free +of injected and trapped charges, which could disrupt the field’s uniformity +and polarization. The change of the polarization gradient near the electrodes +during the polarization switching indicates that the sign of the trapped com- +pensating charges also changes. This is only possible if these charges are not +trapped too deep, so they can be “shaken” from their traps under action of a +high field with the subsequent localization in the same region. +5. Uniformity of polarization in corona poled P(VDF-TFE) copolymer +Polarization profiles in P(VDF-TFE) have not been studied before, and +the data obtained on other corona-charged ferroelectric polymers are rather +fragmentary. For example, it was found that polarization occupies the cen- +tral zone of a positively charged PVDF [29]. In another sample of PVDF, +which was in similar conditions, the peak of polarization was found near +the positive surface, while the biaxially stretched PVDF showed more or +less uniform polarization [30]. The polarization profiles in polarized PVDF +films that were poled in a negative corona turned out to be bell-shaped [31], +while a significant decrease in polarization was observed near the positive +side of a biaxially stretched PVDF poled in a positive corona [32]. Distor- +tion of polarization homogeneity is usually considered as a consequence of +the injected charge presence [29–32], but the details of this mechanism are +still only partially clear. +In [5], we report on measurements of polarization profiles obtained by +applying a piezoelectrically generated pressure step (PPS) method to films + +202 +P(VDF-TFE) that were charged in a negative corona discharge under dif- +ferent conditions. +The samples were films from experimental batches of 20 μm thick +P(VDF-TFE) consisting of 95 % VDF and 5 % TFE. The films were extrud- +ed from the melt and stretched unilaterally by the supplier (Plastpolymer, +Russia) and contained approximately 90 % of the ferroelectric β-phase crys- +tals according to the IR spectroscopy measurements. Aluminum electrodes +with a diameter of 20 mm and a thickness of 150 nm were deposited at one +surface of the samples by thermal evaporation in vacuum. Non-metallised +films were also sometimes used. +Poling was carried out in a corona triode [33] with a bare surface of the +sample subjected to a negative corona discharge initiated by a sharpened +tungsten electrode. The ions and electrons passed through a control grid, +which was held at a constant negative potential in relation to the grounded +rear electrode. The polarization field was generated by charges adsorbed on +the surface of the sample. The grid was made vibrating to allow simultane- +ous measurement of the surface potential by the Kelvin method and the DC +poling current. +Six combinations with three poling parameters were investigated by +maintaining the field strength at two levels (50 MV/m and 100 MV/m), +temperatures (25 °C and 85 °C), and electrical mode (constant current and +constant voltage). Moreover, we conducted experiments with a multi-lay- +ered sample formed from identical films, in which only the lowest film was +metallized that was in contact with a positive electrode. Immediately after +completion of poling all samples were short-circuited for 15 minutes. The +short circuiting was carried out by the non-electrode grounding of the bare +sample surface. To do this, polarity of the corona was changed from negative +to positive with the simultaneous grounding of the control grid. Thus, the +sample was short-circuited, because its upper surface, now bombarded with +positive corona discharge ions, received a grid potential equal to the poten- +tial of the rear electrode. The duration of the short circuit was long enough +to provide a zero field everywhere in the main part of the sample. After the +short circuiting, the samples were stored in an open circuit conditions. +Polarization profiles were measured at room temperature using a piezo- +electric-induced pressure step (PPS) method. The full description of the +method is given elsewhere [29], and only its basic principle is described +here. The pressure step is generated by an electrically controlled quartz +crystal connected to the sample. Pressure waves propagate at a sound speed +(~ 2000 m / s) through a sample in the direction of the thickness causing an + +203 +electrical signal measured by an oscilloscope with a bandwidth of 1 GHz +and then digitized for further processing. It was shown [30; 34] that the +reaction of the short-circuit current to the pressure step provides a direct +image of the spatial distribution of the piezoelectricity in the sample. It is +also known [26] that piezoelectric coefficients in ferroelectric polymers are +proportional to the level of the residual polarization. Thus, the magnitude +of the current at any time was proportional to the residual polarization in +the corresponding point of the sample. Therefore, the measured signal was +calibrated directly in polarization units. A 23 μm polypropylene film was in- +serted between the sample and the measuring electrode to reduce the input +capacitance. To obtain reliable data, we measured the polarization profiles +twice on each sample. +We found that the residual polarization is distributed non-uniformly in +P(VDF-TFE) films under constant current conditions, regardless of tem- +perature, as can be seen from Fig. 10 and 11. The polarization peaks in the +samples poled at room temperature are shifted to the positive side leaving +almost half of the thickness not polarized (Fig. 10). In samples heated to +85 °C, the peak is higher and closer to the positive surface than at room +temperatures (Fig. 11). Another small peak is observed near the surface +bombarded with corona discharge ions in all samples poled by the constant +current, as shown in Fig. 10 and 11. +0 +4 +8 +12 +16 +20 +0 +2 +4 +6 +8 +10 +P, C/cm +2 +x, m +0 +4 +8 +12 +16 +20 +0 +2 +4 +6 +8 +10 +P (C cm +-2) +x (m) +0 +4 +8 +12 +16 +20 +0 +2 +4 +6 +8 +10 +(a) +x (m) +P (C cm +-2) +x (m) +0 +4 +8 +12 +16 +20 +0 +2 +4 +6 +8 +10 +(b) +0 +4 +8 +12 +16 +20 +0 +2 +4 +6 +8 +10 +P (C cm +-2) +x (m) +Fig. 10. Distribution of polarization in P(VDF-TFE) films after poling at 25 °C +and the DC current density of 80 μA/m2 for 15 min. The field at the end of poling +was 100 MV/m. The coordinate x = 0 corresponds to the sample surface bombarded +by negative corona ions + +204 +0 +4 +8 +12 +16 +20 +0 +2 +4 +6 +8 +10 +P, C/cm +2 +x, m +0 +4 +8 +12 +16 +20 +0 +2 +4 +6 +8 +10 +P (C cm +-2) +x (m) +0 +4 +8 +12 +16 +20 +0 +2 +4 +6 +8 +10 +(a) +x (m) +P (C cm +-2) +x (m) +0 +4 +8 +12 +16 +20 +0 +2 +4 +6 +8 +10 +(b) +0 +4 +8 +12 +16 +20 +0 +2 +4 +6 +8 +10 +P (C cm +-2) +x (m) +Fig. 11. Distribution of polarization in P(VDF-TFE) films after poling at 85 °C and +the DC current density of 160 μA/m2 for 15 minutes and cooled to 25 °C in the ap- +plied field of 100 MV/m. The x = 0 coordinate corresponds to the negative side of +the sample +Multilayer samples were poled at constant voltage. The field strength +was either moderate (50 MV/m) or high (100 MV/m). The first value was +close to the coercive field of PVDF. The polarizing field in the multilayered +samples was not the same in two-layer films from which the sample was +composed. At the average field of 50 MV/m, only the film having direct +contact with the positive rear electrode had residual polarization (Fig. 12). +The upper film did not show any residual polarization indicating that the +voltage was applied mainly to the lower film. +However, both films are polarized in the case of a high field, as can +be seen from Fig. 13 The distribution of polarization in the lower («pos- +itive») film is rather uniform (Fig. 13 (b)), whereas in the upper film +there are two asymmetric peaks with the higher one located near the +surface that was bombarded by the corona ions (Fig. 13 (a)). Three-lay- +er and four-layer specimens were poled in the average nominal field of +50 MV/m. The results shown in Fig. 14 and 15 differ significantly from +the results obtained on the two-layered samples (Fig. 12 and 13). Of the +three films in the sample, the upper film, which was subjected to the ac- +tion of ions, was not polarized at all. The distribution of polarization in + +205 +the film attached to the positive electrode is not uniform and similar to +that in the case of constant current poling (Fig. 10 and 11), while in the +middle film there are two symmetric peaks separated by a saddle (Fig. +14 (a)) In the case of four films, only two films at the positive side of the +sample are polarized, but not uniformly (Fig. 15). Polarization peaks in +both films are shifted to the positive side, and the magnitude of the po- +larization is much higher in the film, which contacts the electrode (Fig. +15 (a) and (b)). +0 +4 +8 +12 +16 +20 +0 +2 +4 +6 +8 +10 +P, C/cm +2 +x, m +0 +4 +8 +12 +16 +20 +0 +2 +4 +6 +8 +10 +P (C cm +-2) +x (m) +0 +4 +8 +12 +16 +20 +0 +2 +4 +6 +8 +10 +(a) +x (m) +P (C cm +-2) +x (m) +0 +4 +8 +12 +16 +20 +0 +2 +4 +6 +8 +10 +(b) +0 +4 +8 +12 +16 +20 +0 +2 +4 +6 +8 +10 +P (C cm +-2) +x (m) +Fig. 12. Distribution of polarization in the lower film of a two-layered sample poled +at 85 °C in the constant field with the average intensity of 50 MV/m for 15 minutes +and cooled to 25 °C in the applied field. Coordinate x = 0 corresponds to the neg- +ative side of the film. The upper film bombarded by corona discharge ions did not +have any residual polarization +Distribution of polarization in the middle and the lowest films of a +three-layer sample poled at 85 °C in the average field of 50 MV/m and +cooled to 25 °C in the applied field have shown the similar results. Coor- +dinate x = 0 corresponded to the negative side of each film. The upper film +that was bombarded with corona discharge ions did not have any residual +polarization. +From our experiments on multilayer samples, it should also be antici- +pated that the polarization peak near the positive electrode with a large de- +pleted polarization region near the negative electrode occurs in the case of +one thick film. A similar phenomenon was observed in corona poled PVDF +films with a thickness of 120 μm [30]. + +206 +0 +4 +8 +12 +16 +20 +0 +2 +4 +6 +8 +10 +x (m) +P (C cm +-2) +x (m) +0 +4 +8 +12 +16 +20 +(b) +(a) +Fig. 13. Distribution of polarization in (a) upper and (b) lower films of a two-layer +sample poled at 85 °C with the constant average field of 100 MV/m for 15 minutes +and cooled to 25 °C in the applied field. Coordinate x = 0 corresponds to the nega- +tive side of each film +Polarization and injection of charges +The heterogeneity of polarization in the direction of thickness in homo- +geneous specimens may obviously be due to the non-uniform distribution +of the applied field. According to the Poisson equation, the inhomogeneity +of the field strength E(x,t) is due to the presence of either a real uncompen- +sated charge ρ(x,t) or the polarization charge dP(x,t)/dx: + +[ +] +0 +( , ) / +( , ) +( , ) / +E x t +x +x t +P x t +x +ε ε ∂ +∂ += ρ +− ∂ +∂ , +(13) +where ε is the dielectric constant, εо is the permittivity of a vacuum, P is +the ferroelectric polarization, x is the coordinate in the direction of the +film thickness, t is time. Since the polarization P itself depends on the field +strength E, the initial heterogeneity of the poling field should be attributed +only to the effect of real charges. +There are two main sources of the space charge in a dielectric. It can +be caused by the spatial separation of already existing intrinsic positive and +negative charge carriers, or by injection of charges to the volume from the +outside. To show how to use equation (13) to distinguish the effects of in- +jected and internal carriers, we first assume that the external voltage V is + +207 +applied to a sample of thickness xo, when the density of the injected charges +is much lower than that of the intrinsic carriers. +From equation (13) it follows that the field increases near both surfaces +of the sample and accordingly decreases in the central region. If the applied +field Ep = V/xo is equal to or close to the coercive value Ec, then two peaks +of the ferroelectric polarization will appear in front of the electrode sections +separated by a non-polarized zone, as shown schematically in Fig. 16 (b). +Now suppose that the same voltage V is applied to another sample where +monopolar injection of negative carriers takes place, and their density is +much higher than that of the intrinsic charges. The injection charge does not +affect the average Ep field, but creates heterogeneity of the field, as shown +schematically in Figure 16 (a). The field at the injecting electrode is almost +zero, but it increases in the direction of x in accordance with equation (13) +until it reaches the Ec value at a certain depth. It is clear that the peak of the +residual polarization will be shifted to a positive electrode. +Thus, one can determine the dominant phenomenon from the position +of polarization peaks. For example, profiles in Fig. 13 (a) and 14 (a) indicate +that the level of injection was low in these samples. However, injection of +negative charges in many cases is more important than the separation of the +intrinsic carriers. The consequence is visible, for example, in Fig. 10, 11, +14 (b), 15 (a) and 16 (b), in which polarization peaks in all these cases are +observed near the positive electrode. +Spatial neutrality inside the sample will be distorted due to the predom- +inant movement of positive charges. The charges injected during poling do +not remain there after a short circuiting. They form a spatial charge that cor- +responds to the slope of the residual polarization profile, since dP(x)/dx = += ρ (x). E(x) = 0 under short circuit conditions. +The contribution of the space charge to the measured signal cannot be +experimentally separated from the residual polarization, but it can be con- +sidered as insignificant, since the piezoelectricity in ferroelectric polymers, +to which the PPS method is sensitive [30; 34] is caused by the residual po- +larization, but not by the space charge. +Our results obtained for P(VDF-TFE) films are consistent with the data +on the polarization profiles observed in the case of other ferroelectric poly- +mers that have been poled in a corona discharge. The depletion of polariza- +tion near the negative side due to the charge injection was detected in PVDF +and P(VDF-TrFE) [30–32]. Moreover, a similar phenomenon was observed +in ferroelectric polymers, poled by the thermoelectret method [29; 30], by +direct application of a high field and the electron-beam polarization. + +208 +0 +4 +8 +12 +16 +20 +0 +2 +4 +6 +8 +10 +x (m) +P (C cm +-2) +x (m) +0 +4 +8 +12 +16 +20 +0 +2 +4 +6 +8 +10 +(b) +(a) +Fig. 15. Distribution of polarization in (a) penultimate lowest and (b) the last lowest +film of a four-layer sample that was poled at 85 °C in the average field of 50 MV/m +for 15 minutes +The charge injection is most likely appears from a virtual electrode +formed on a surface bombarded by electrons and ions. Our results show that +homogeneity of polarization is more severely distorted by injection, if low +or moderate fields are used. For example, the field in the case of a constant +voltage gradually increases from zero to about 100 MV/m, and the resulting +polarization distribution is highly heterogeneous (Figs 10 and 11). Almost a +quarter of the sample thickness is not polarized, since the field in this area +is too low for the formation of the ferroelectric polarization. In the case of +two-layer samples poled in the average field of 50 MV/m, charges are main- +ly injected into the film under action of the corona that causes increase of +the film conductivity. We assume that the conductivity corresponds to the +following equation + +[ +] +( +) +n +n +g +e n ++ +− ++ ++ +− +− +′ +′ += +µ + µ ++ +µ + +µ +, +(14) +where e is the elementary charge, n is the density of the carriers, n+ and n- +are injected charge densities, μ+, μ-, μ’+ and μ’- are mobilities of intrinsic +and injected carriers (they may be different). This expression implies that +the conductivity increases if injection takes place. As a result, the applied + +209 +voltage is redistributed, so that its main part is applied to a film attached to +the positive electrode. The distribution of polarization in such a film is quite +homogeneous (Fig. 12), although the effect of the negative charge injec- +tion is still considered as a thin non-polar layer near the negative side of the +sample. The top film was completely not polarized because there was a very +low field. Similarly, one film in a three layer and two films in four-layered +experiments are also not polarized. +a) +Polarization +Charge +Ec +Field +Charge +After short-circuiting +b) +Charge +Charge +After short-circuiting +Ec +Field +Polarization +Polarization +Fig. 16. Schematic diagram showing distribution of volume charge, field strength +and ferroelectric polarization during corona poling in the case of (a) monopolar in- +jection of negative charges and (b) separation of internal positive and negative charge +carriers. The average field strength is equal to the coercive field Ec. Also shown is the +distribution of localized charge after completion of poling and short circuiting of +the sample +The results of our measurements on P(VDF-TFE) films coincide with +the results obtained from multilayered experiments on PVDF films poled by +the thermoelectret method [35], but the explanation of this phenomenon is + +210 +different. The increase of the pyroelectric and piezoelectric activities near +the positive electrode was attributed [35] to the effect of the positive charge +injection. We believe that, according to the theory of injection currents [25], +the heterogeneity of the field and hence polarization is due to injection of +the negative charges, but not the positive ones, as previously thought [35]. +This is considered normal if the charge is injected either from a real met- +al electrode, or from a virtual electrode formed on the surface of the sam- +ple bombarded by electrons and ions. However, our results indicate that the +virtual injecting electrode can also be formed on a surface that was neither +metallized nor bombarded by ions. Exhaustion of polarization at the nega- +tive side of the samples shown in Fig. 12, 14 (b), and 15 (b) proves that in all +these cases, a negative charge is injected. +Transition zones +It is worth analyzing the behavior of the space charge after the com- +pletion of poling. Immediately after a short circuiting, the average field in +the sample becomes zero, but the local field still exists. Therefore, mobile +charges are redistributed under the action of this field until the field be- +comes zero at any point of the sample. The characteristic Maxwell relax- +ation time for this process is given as + +0 / g +τ = ε ε +, +(15) +where g is the explicit conductivity. Considering the typical values of +g = (10–11–10–12 Sm/m [12]) for PVDF and its copolymers, we obtain +τ ≈ 10–100 s. The real value of τ is even lower, since additional carriers are +introduced during poling, and the apparent conductivity increases accord- +ingly, as can be seen from equation (14). +From equation (13) it follows that under conditions of equilibrium +(E(x) = 0), the spatial charge ρ(x) can be localized only at the boundaries of +the polarized zones where the derivative dP/dx ≠ 0. + +( ) +( ) / + (t +) +x +dP x +dx +ρ += +> τ . +(16) +It is clear from equation (16) that thickness of the transition zone where +the polarization decreases from its maximum value to zero, depends on the +density of the charge, therefore, the higher the density of the charge, the +narrower the transition zone. +The thickness of the transition zone cannot be measured with a high pre- +cision by the PPS method, since its resolution (2 μm) is comparable to the +thickness of the zones. However, these values can be estimated by compar- + +211 +ing the growth time of the measured electrical signal and the pressure step. +The first in all cases was longer than the last, indicating that the transition +zones are thicker than 2 microns. For example, the most delicate transition +zones (4–5 μm) are shown in Fig. 12 and 13 (b). The corresponding times +of the electrical signal grows and the pressure step are 2–3 ns and 1 ns, re- +spectively. +It is known that any polarization heterogeneity creates a polarization +charge with the density of dP(x)/dx. This charge creates a depolarizing field, +which tends to switch the ferroelectric polarization back to its original state +after the completion of poling. The residual polarization can be stable only +if the depolarization field is compensated or neutralized. We believe that in +the case of the ferroelectric polymers, the compensation is carried out by the +spatial charge ρ(x) trapped in the transition zones, by which the polarized +part of the sample is separated from the not polarized part. Since the po- +larization charge dP(x)/dx and the real charge ρ(x) are equal to each other +(according to equation (16)), the depolarizing field is completely compen- +sated, so that E(x) = 0 everywhere in the sample. We consider the existence +of the transition zones in conjunction with compensating spatial charges as +a general feature of poled P(VDF-TFE) and, probably, of all other ferro- +electric polymers. Presence of the spatial charge in the transition zones is a +guarantee of a high stability of the residual polarization. +Near-to surface regions +We observed two types of polarization profiles in near-to-surface zones +of P(VDF-TFE). The residual polarization was zero to a certain depth, as +can be seen in Fig. 10, 11, 14 (b), 15 (a) and 15 (b) near the negative sur- +face. In other cases, Pr = 0 near the positive surface, as shown in Fig. 10, +11, 12, 13 (b), 14 (b), 15 (b) or near the negative surface in Fig. 12, 13 (a), +13 (b). It is clear that zones of the first type are created due to the massive +injection of negative charges during poling, because the field near the injec- +tion surface is reduced and the ferroelectric polarization is not formed. The +thickness of the not polarized zone depends on the depth of the injected car- +riers’ penetration. The zones are particularly wide in the case of moderate +poling fields, as can be seen from Fig. 10, 11, 15 (a) and 15 (b). On the other +hand, if the polarizing field strength is high, the near-to-surface zones are +very narrow if the negative charges are not injected deeply into the volume +(Fig. 12, 13 (a), 13 (b), 14 (a)). +In some cases, the separation of the intrinsic charge carriers dominates +over the external injection. Then there are two polarization peaks at the two + +212 +sample surfaces. Not polarized near-to-surface zones are either very narrow +or not observed at all (Fig. 13 (a) and 14 (a)). According to our results, it can +be concluded that a certain time is required for the injected charge for deep +penetration into the bulk. This can only be done if the pre-poled regions +are not polarized, for example in the case of low or moderate electric fields. +However, if the ferroelectric polarization is already formed near the surface, +as in the case of a high field, the injected charge cannot easily pass through +a polarized region. It seems that the effective conductivity of the polarized +regions is much lower than that of not polarized ones. The second type of +near-to-surface zones with rather high polarization can be seen near a met- +allized surface attached to a positive electrode during poling. The role of a +positive electrode in the accumulation and distribution of polarization has +been widely discussed since the discovery of the inhomogeneous distribution +of piezoelectricity and pyroelectricity in PVDF [35], and many contradic- +tory explanations of this phenomenon were proposed. Our measurements +show that the maximum polarization appears in all metallized samples near +the positive electrode. This means that the conditions are favorable both for +the rapid development of ferroelectric polarization, and for its stabilization. +Positive charges are either not injected or deeply trapped very closely to the +surface creating good conditions for compensating the depolarizing field. At +the same time, the trapped charges do not allow the attachment of a highly +polarized zone directly to the electrode. +The PPS method with a resolution of about 2 μm cannot provide more +information about the fine structure of near-to-surface zones, but this can +be achieved by using the LIMM method [36]. Polarization profiles in uni- +formly electrified P(VDF-TFE), measured by this method, are present- +ed in Fig. 17. We used the same specimens as those for which the results +obtained by the PPS method are shown in Fig. 13 (b). It is known that +the resolution of the LIMM method is about 0.1 μm near the illuminated +electrode [37]. +As can be seen from Fig. 17, the polarized zones are not directly at- +tached to the positive and negative surfaces. The transition zones consist +of thin layers where the polarization drops from maximum to zero and is +supplemented by a completely not polarized layer of about 0.5 μm thick- +ness. +The applied voltage is distributed non-uniformly between layers in +the case of multilayered samples poling. Only the film near the positive +electrode shows a high and fairly uniform polarization, while the upper +films remain not polarized indicating that the injected charge permeates + +213 +the entire thickness of the film. Therefore, to obtain a uniformly polarized +P(VDF-TFE) copolymer film in a moderate field, it would be advisable +to cover the main sample during poling with another auxiliary film. In +the case of high poling fields, the residual polarization is homogeneous, +since injections of charges are suppressed. But even in this case, the po- +larized part of the volume is separated from the sample surfaces by transi- +tion zones where compensating charges are trapped. A thin layer of about +0.5 μm thickness always remains completely not polarized near the sample +surfaces. +Fig. 17. Distribution of polarization measured by the method of the modulated +intensity of laser radiation in near-to-surface regions of a nominally well-poled +P(VDF-TFE) film. The conditions for poling were the same as for the sample shown +in Fig. 5. Coordinate x = 0 corresponds to the negative side of the film +6. Effect of temperature on distribution of ferroelectric polarization +Recently, it has been shown that a high stability of the residual polariza- +tion in PVDF and P(VDF-TrFE) is due to interaction of the polarization +with the injected charge trapped at the boundaries of crystallites or macro- +scopic polarized regions [26]. +In both cases the polarization and the space charge form a stable and +a self-consistent system in which the latter plays a decisive role. Assum- +ing Debye’s approximation for relaxation and the continuous distribution + +(arb. units) +12 +16 +20 +x (μm)214 +of activation energies for the charge trapping, Eisenmenger et al. received +such a distribution for PVDF and P(VDF-TrFE) [38]. +Our purpose was to find out how the bulk charge affects the thermal +stability of the residual polarization in P(VDF-TFE) copolymer which also +belongs to the class of the ferroelectric polymers, but is much less studied +than PVDF and P(VDF-TrFE). +To do this, we measured the polarization profiles in P(VDF-TFE) sam- +ples as a function of temperature by performing the linear heating from +20 °C to the melting point of crystallites. The activation energy was calcu- +lated by applying our experimental data and the theoretical model proposed +in [38]. The obtained results were compared with those that are known for +PVDF and P(VDF-TrFE) copolymer. +The samples were cut from experimental batches of P(VDF-TFE) +20 μm thick copolymer films containing more than 90 % of the ferroelec- +tric β-forms in the crystalline phase. Aluminum electrodes with a diameter +of 5 mm and a thickness of 0.15 μm were deposited on both sides of the +samples by thermal evaporation in vacuum. Poling was carried out either by +direct application of high voltage (3.2 kV at 20 °C for 2 min) or by thermo- +electret method (2.5 kV at 85 °C for 10 min and fast cooling to 20 °C under +the applied voltage). +The polarization of the field in both cases was three to four times greater +than the coercive field, which is 35–40 MV/m in P(VDF-TFE). The resid- +ual polarization profiles in the direction of the sample thickness were mea- +sured with a repetition rate of about 100 Hz using the PPS method, while +the temperature was linearly increased at a rate of 3 K/min from 20 °C to the +melting point of the crystallites, which turned out to be 134 ± 2 °C. +It is established that the distribution of polarization in the thickness +direction is rather uniform, except for areas close to the electrode zones, +where the polarization decreases from the maximum to the low value (Fig. +18). The profiles of polarization at all temperatures were slightly asymmet- +ric, with a maximum located near the positive electrode, similarly to that +observed in other ferroelectric polymers. We used these maximum values +for evaluating the thermal stability of the residual polarization. From the +data presented in Fig. 19, it is clear that the polarization in P(VDF-TFE) +breaks down with the temperature throughout the studied range almost lin- +early decreasing from the maximum at room temperature to zero at a melt- +ing point (134 ° C). This behavior is significantly different from PVDF and +P(VDF-TrFE) where the polarization decreases only when the temperature +exceeds 90 °C. + +215 +0 +5 +10 +15 +20 +25 +0 +1 +2 +3 +4 +5 +(a) +136 +119 +98 +81 +63 +47 +32 +18 +Pr (C cm +-2) +x (m) +0 +5 +10 +15 +20 +25 +0 +2 +4 +6 +8 +10 +(b) +134 +126 +113 +101 +84 +72 +61 +49 +37 +18 +Pr (C cm +-2) +x (m) +Fig. 18. Spatial distribution of polarization at different temperatures in P(VDF-TFE) +films poled (a) by direct application of the high field and (b) by the thermoelectret +method. Zero on the axis of the thickness corresponds to the negative surface of the +sample during processing +It is advisable to use the Debye approximation for the relaxation of po- +larization with the temperature dependence of the decay constant corre- +sponding to the Arrhenius law. Then, the current of depolarization ia(T) in +the case of one activation energy is [38]: + +[ +] +0 +0 +0 +0 +( ) +/ +exp( +/ +) +exp +exp( +/ +) +a +T +T +i T +dP +dT +h f +a T +P +h f +a T dT += − += + + += +⋅ +− +⋅ +− ⋅ +− + + + + +∫ +, +(17) +where h is the heating rate, fo is the proper frequency, Po is the initial value of +polarization at To, a = A k, where A is the activation energy, k is Boltzmann’s +constant. Taking into account that energy is continuously distributed on the +surface of the polarized crystallites surrounded by a disordered amorphous +phase, one can conclude that the energy spectrum of traps is, most likely, +continuous, rather than discrete. +Therefore, the total depolarization current i(T) is a superposition of all +relaxation components: + +0 +( ) +( ) ( ) +a +i T +g a i T da +∞ += ∫ +, +(18) + +216 +where g(a) is the distribution function of activation energies. It was shown +that the depolarization current i(T) calculated from the experimental curve +P(T) is an image of the distribution function g(a): +0 +40 +80 +120 +160 +0 +2 +4 +6 +8 +10 +(b) +(a) +Pr (C cm +-2) +T ( +0C) +Fig. 19. The value of residual polarization in P(VDF-TFE) obtained experimentally +(points) and theoretically (solid lines) depending on (a) poling in a high field and (b) +b the thermoelectret method +The results of calculations based on experimental data of Fig. 19 are shown +in Fig. 20. It is clear that the high-temperature behavior of the P(VDF-TFE) +copolymer is regulated by two relaxation processes characterized by signifi- +cantly expanded energy levels. The low-temperature peak in thermoelectret +samples is slightly shifted to lower energy, whereas the high-temperature peak +does not affect by the heat treatment. The relationship between the values of +the two peaks in P(VDF-TFE) differs from PVDF [38] where the second peak +is more advanced than the first one. Comparing the curves in Fig. 20 (a) and +20b, one can see that there is no significant difference in values and distribu- +tion of the activation energies in the samples polarized in a high field strength +and by the thermoelectret method. This indicates that the residual polariza- +tion in P(VDF-TFE) is not thermally frozen, as in the case of ordinary polar + +217 +thermoelectrets, but it is stabilized, most likely, by the field of the trapped +charges. P(VDF-TFE) has two components of polarization, namely: a ferro- +electric component and an electret component. The first one is concentrated +in the crystalline phase, and the second is localized in the amorphous phase. +Therefore, the two peaks shown in Fig. 20 can be related to the relaxation of +these polarization components. A similar behavior was observed in PVDF and +P(VDF-TrFE) copolymer [38] indicating that this phenomenon is likely to be +common in the whole class of the ferroelectric polymers. + +( ) +( +) +i T +g mT +∝ +, +(19) +where m is a constant value. +It is known that the ferroelectric polarization is stable only when the de- +polarizing field is somehow neutralized or compensated. In the ferroelectric +polymers, this compensation is performed by trapped charges [38]. +0 +30 +60 +90 +120 150 +0.00 +0.02 +0.04 +0.06 +2.4 +2.0 +1.5 +1.0 +0.5 +2.2 +2.0 +1.8 +1.6 +g(A) (x10 +-3) +(a) +A (eV) +-dP/dT (nC cm +-2 K +-1) +T ( +0C) +0 +30 +60 +90 +120 150 +0 +40 +80 +120 +2.0 +1.5 +1.0 +0.5 +2.4 +2.2 +2.0 +1.8 +1.6 +g(A) (x10 +-3) +A(eV) +(b) +-dP/dT (nC cm +-2 K +-1) +T ( +0C) +Fig. 20. The temperature dependence of the depolarization current i (T) = dP / dT +and the distribution function of the activation energy in P(VDF-TFE) calculated +depending on (a) poling in a high field and (b) +Since the charge is deeply trapped and the binding energy is in the range +of 1.65–2.35 eV, as can be seen from Fig. 20, the spatial charge effectively +compensates the depolarizing field in the crystals. This explains the high +polarization stability at room temperature. According to our calculations, +based on the data of Fig. 20, polarization is expected to decrease to 90 % of +its initial value for about one year. + +218 +The model of the continuous distribution of activation energies was ver- +ified by calculating the dependence P(T) by using the data given in Fig. 20. +The results of the calculations shown in Fig. 19 by solid lines agree with the +experimental data indicating that the thermal stability of the residual polar- +ization in P(VDF-TFE) and, probably, in other ferroelectric polymers, is +indeed controlled by the trapped volume charge. +Conclusion +Results of experimental study of the polarization distribution uniformity +in ferroelectric polymer films over the thickness of the samples are presented +in this article presents. We selected typical polymeric ferroelectrics, namely, +polyvinylidene fluoride (PVDF) and its copolymer with trifluoroethylene +P(VDF-TFE) as objects of the study. The measurements were carried out by +a modern sensitive piezoelectric generated pressure step method. +It has been found that the polarization uniformity substantially depends +on the value of the applied electric filed during initial poling of the films. +the distribution of polarization was inhomogeneous with a maximum near +the positive electrode in the case of weak and medium applied fields close to +coercive value of the field. +A very important feature has been discovered. It appeared that the uni- +formity of polarization cannot be improved even by the subsequent applica- +tion of very strong fields. +However, if the initial poling of a fresh sample has been carried out in +strong fields, then the uniform polarization distribution has been formed. +The features of the P(VDF-TFE) copolymer electrified in corona discharge +have been investigated as well. Phenomenological models of the process- +es occurring during the formation of polarization in ferroelectric polymer +films have been developed for clarifying physical processes responsible for +the formation of the polarization distribution. +REFERENCES +1. Day G. W., Hamilton C. A., Peterson R. L., Appl. Phys. Lett. 24, 456 (1974). +2. Sussner H., Dransfeld K., J. Polym. Sci.: Polym. Phys. 26, 529 (1988). +3. Bihler E., Neunann G., Eberle G. et al., Annu. Rep. CEIDP. 140 (1990). +4. Eisenmenger W., Schmidt H., Proc. Int. Symp. Electrets, 635 (1999). +5. Fedosov S. N., Sergeeva A. E. et al., J. Phys. D: Appl. Phys. 29, 3122 (1996). +6. Eisenmenger W., Schmidt H., Dehlen B., Brazilian J. of Physics, 29, 295 (1999). +7. Gerhard-Multhaupt R., Gross В., Sessler G. M., in Electrets, 383 (1988). +8. Fedosov S. N., von Seggern H. J., Appl. Phys. 103, 014105 (2008). + +219 +9. Mopsik F. J., De Reggi A. S., Appl. Phys. Lett. 44, 65 (1984). +10. De Reggi A. S., Broadhurst M. 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Phys. 16, 529 (1978). +36. Lang S. B. and Das-Gupta D. K., J. Appl. Phys. 59, 2151 (1986). +37. Ploss B., Bianzano O., Proc. 8th Intern. Symp. Electrets. 211 (1994). +38. Kussner B. et al., Proc. 8th Int. Symp. Electrets, 594 (1994). + +220 +Розділ ІІ +АВТОМАТИЗАЦІЯ ТА УПРАВЛІННЯ +ТЕХНОЛОГІЧНИМИ ПРОЦЕСАМИ +ТЕХНОЛОГІЧНИЙ РОЗВИТОК СУДНОПЛАВСТВА, СИСТЕМ +ШВАРТУВАННЯ СУДНОПЛАВСТВА МАЙБУТНЬОГО +Пунченко Н. О., Цира О. В. +Водний транспорт був і існує як провідний елемент системи світової еко- +номки. Існує постійне збільшення морського та річкового перевезення, а та- +кож вимоги до якості вантажного перевезення шляхом водного транспорту +(своєчасність, безпека, надійність), які змінюються у напрямку поліпшення. +Розвиток відбувається з метою використання автономних систем, які є од- +нією з найбільш вагомих змін, що спостерігаються в морській промисловості. +У роботі наведено огляд систем управління безекіпажними суднами (кора- +блями), де людський фактор не впливає на рішення, що приймаються. Пред- +ставлені переважаючі складові інтелектуальної системи. Наведено види ав- +томатизованих систем швартування: лазерні, вакуумні, магнітні. Системи +швартування знижують ризик перевищення швидкості судна за рахунок зни- +ження впливу людського чинника при швартуванні, знижують вплив оцінки +поточної ситуації зближення судна з причалом, обирають режими і наочно +відображають робочий процес за визначеною ситуацією, підвищуючи тим +самим ефективність системи в цілому. +В результаті огляду зрозуміло, що у світі немає галузі економіки, яка в +останні роки не вплинула б на цифрову трансформацію, а телекомунікаційні +компанії зробили достатньо, щоб розширити цей спектр послуг. Тим часом у +морській промисловості у світі цифрова трансформація робить лише перші +кроки. Основою для цього є канали зв’язку, без яких передача даних у принципі +неможлива. На воді це завдання є найбільш складним, оскільки волоконно- +оптичний кабель не може бути підведений до судна. Тому на річці та морі є +необхідним супутниковий зв’язок, існує суттєва потреба його використання +не тільки для комунікацій та цифрових розваг на борту, а й для моніторингу +стану судна та вантажу, можливості дистанційного управління, контролю +бункерних суден, питання безпеки. Звідси випливає, що безекіпажний флот +буде використовувати інтегровані автономні системи управління, які мо- +жуть керуватися оператором на березі. +Water transport has been and exists as a leading element of the world economy. +There is a constant increase in sea and river transport, as well as requirements for + +221 +the quality of freight transport by water transport (timeliness, safety, reliability), +which are changing in the direction of improvement. The development is taking +place with the aim of using autonomous systems, which is one of the most signif- +icant changes observed in the maritime industry. The paper provides an overview +of control systems for unmanned vessels (ships), where the human factor does not +affect the decisions made. The predominant components of the intellectual system +are presented. The types of automated mooring systems are given: laser, vacuum, +magnetic. Mooring systems reduce the risk of over-speeding of the vessel by reduc- +ing the influence of the human factor during mooring, reduce the impact of assessing +the current situation of the ship’s approach to the berth, select modes and visually +reflect the working process according to the current situation, thereby increasing the +efficiency of the system. +As a result of the review, there is no industry in the world that has not affect- +ed digital transformation in recent years, and telecommunications companies have +done enough to expand this range of services. Meanwhile, in the marine industry, +in the world, digital transformation is only taking its first steps. The basis for this is +communication channels, without which data transmission is, in principle, impos- +sible. On the water, this task is most difficult because the fiber-optic cable cannot be +connected to the vessel. Therefore, on the river and sea, satellite communication is +necessary, its use not only for communications and digital entertainment on board, +but also for monitoring the condition of the vessel and cargo, remote control capa- +bilities, control of bunker vessels, security issues. It follows that the unmanned fleet +will use built-in autonomous control systems that can be operated by the operator +ashore. +Для програми розвитку перспективних шляхів підвищення за- +гальної безпеки мореплавання, в умовах зростання інтенсивності +морського судноплавства спостерігаються тенденції збільшення кіль- +кості смертельних випадків від морських аварій [2]. Однією з причин +цього є людський чинник. Оскільки в інноваційному суспільстві така +галузь як судноводіння при зародженні визначила себе як інновацій- +на. Такому визначенню є підтвердження, а саме група MariNet, яка +створена в рамках Національної технологічної ініціативи. Група змо- +гла об’єднати великі компанії і невеликі стартапи у галузі морських +високих технологій, наукові центри, офіційні органи і внз [3], що +представлені соціуму як інтелектуальні автономні системи, які є ра- +дикальними змінами в судноплавній індустрії. Це інтелектуальні сис- +теми, які приймають рішення без втручання ззовні. Інтелектуальні +системи стали базисом для створення такого напрямку як безекіпаж- +не судноводіння, де використовується комбінація дистанційного й +автономного управління, яке зводить до мінімуму людський чинник +у безпеці судноводіння. + +222 +Основи теоретичних та практичних наукових досліджень у галузі +інформаційних технологій та систем судноплавства дуже детально +представлені в роботах таких вчених: A. E. Сазонова (математич- +не та програмне забезпечення автоматизованих систем управління +суднами), С. В. Смоленцева (основи будівельних систем інтелек- +туального управління), С. В. Руда (системи моніторингу та управ- +ління суднами технічного та допоміжного флоту), I. Г. Малюгіна, +В. І. Комашинського (питання будівництва транспортних сис- +тем), Д. А. Скорошодова (інтегровані системи управління судном), +A. A. Сикарева (стійкі системи радіозв’язку), A. A. Диди (складні +системи), а також іноземних вчених, таких як Ch. Liu (автоматизо- +вані системи управління кораблем), М. Хойхтяя (автономні системи +управління, супутникові зв’язки), Е. Топп (дистанційне управлін- +ня системами), Р. Польвара (системи технічного бачення) та інші. +У своїх роботах автори заклали теоретичну та практичну базу, яка +сприяє підвищенню ефективності функціонування та розвитку вод- +ного транспорту. +Вважається, що судна без екіпажу будуть дешевшими, безпечні- +шими і будуть менше забруднювати навколишнє середовище. А ідея +і обґрунтування ідей їх створення базується на кількох основних по- +ложеннях: +Положення 1 — за відсутності екіпажу вартість підтримки судна +може бути зменшена на 30–40 %; +Положення 2 — за відсутності екіпажу макет і архітектура судна +значно спрощуються, що тягне за собою зменшення вартості будів- +ництва та обслуговування судна; +Положення 3 — вартість підготовки фахівців судна може бути зна- +чно зменшена; +Положення 4 — досягнення науки та технологій свідчать, що з тех- +нічної точки зору фундаментальних обмежень завдання не має; +Положення 5 — розробка та реалізація забезпечення кораблів на- +лежить до нового напрямку науки і техніки, який об’єднує та сприяє +зростанню творчої діяльності наукових, дизайнерських, освітніх та +промислових організацій галузі; +Положення 6 — будівництво та реалізація військових суден, зда- +ється, є довгим багатоступеневим процесом, що включає поступову +зміну структури флоту, яка складається з традиційних суден, що об- +слуговуються екіпажами, і що є контрольованими віддалено або по- +вністю автономно заданою програмою. + +223 +Перевага — це давня професія, яка має багато століть. Зрештою, +в доісторичні часи люди подорожували до інших берегів на човнах, +таким чином поступово зміцнюючись на землі. Основи доставки +стародавніх артефактів були на практиці, тому що у них не було +сучасної теоретичної бази, підручників та карт. Першими людьми- +навігаторами були фінікійці, знання яких починають свій шлях +з 15 століття, наприклад, лоцманом Васко да Гамы Ибн Маджид +був накопичений досвід: кожен, хто хоче впоратися з елементами +моря, повинен розбиратися в румбах та фазі місяця, відстанях та +напрямках. +Величезна частина нашої планети покрита водою. Тому можна +впевнено сказати, що морський транспорт ніколи не стане застарі- +лим, незалежно від того, як розвивається наземне та повітряне облад- +нання. Щоб подолати моря та океани, потрібні грамотні судноводії, +яким добре відомі пристрої їхнього судна, а також характер нестійко- +го елемента води. +В даний час безпілотні судна відповідно до міжнародних конвен- +цій є незаконними. Щоб підтвердити таке твердження, ми дамо неве- +лику оцінку міжнародно-правовим актам, які встановлюють вимоги +до стану транспорту та флоту, а також його експлуатації. +Найбільші зусилля в цьому напрямку були зроблені Міжнародною +морською організацією та Міжнародною організацією праці. Почи- +наючи з сорокових років, ці організації розробили цілий ряд міжна- +родних конвенцій безпеки. При розробці і застосуванні зазначених +конвенцій функції управління залежать від двох відповідних вимог. +Перш за все, це стан плавання судна в залежності від прапора. Другий +координуючий орган повинен бути спеціалізованою організацією — +класифікаційним товариством. Відповідальність за виконання вимог +конвенції покладається на власника судна. Однак практика пока- +зала, що всі суворі вимоги до суден були розроблені міжнародними +організаціями, ці вимоги не були виконані. Держава прапора з одно- +го боку, зацікавлена особа і намагається забезпечити судновласників +найбільш сприятливими умовами праці з економічної точки зору, +з іншого боку, держава прапора не завжди має можливість здійсню- +вати ефективний контроль стану її судна і його роботи. Відповідно +до вищесказаного був введений нагляд з боку класифікаційних това- +риств різних країн. Для цієї мети був розроблений Міжнародний ко- +декс з управління безпекою (ISM-Code). Його головна мета полягає в +тому, щоб забезпечити безпеку на воді. + +224 +Міжнародні організації, що регулюють безпеку судноплавства +Після Другої світової війни і створення ООН суспільство прийшло +до висновку про необхідність впровадження авторитетної міжнарод- +ної організації в області безпеки судноплавства. І саме такою органі- +зацією в 1948 році стала Міжнародна морська консультативна органі- +зація. У 1973 році організація отримала назву Міжнародної морської +організації (ІМО). Вона функціонує в рамках ООН. Її штаб-квартира +знаходиться в Лондоні. +Міжнародні організації безпеки судноплавства: +ILO — Міжнародна організація праці; +ICF — Міжнародна палата доставки; +ISF — Міжнародна федерація судновласників; +INSA — Міжнародна асоціація судновласників; +МАК — Міжнародна асоціація класифікаційних товариств; +IALA — Міжнародна асоціація маячних служб; +IPH — Міжнародна асоціація портів та гаваней; +МСЕ — Міжнародний телекомунікаційний союз; +CIRM — Міжнародний комітет морського радіозв’язку; +IMPA — Міжнародна асоціація морських лоцманів; +IFSMA — Міжнародна федерація асоціацій морських капітанів; +ICFTU — Міжнародна конфедерація профспілок вільної торгівлі; +WMO — Всесвітня метеорологічна організація; +ISO — Міжнародна організація стандартизації; +ICAO — Міжнародна організація цивільної авіації; +ІМО — Міжнародна морська організація. +Верховний орган Міжнародної морської організації — Асамблея, +яка регулярно відбувається кожні два роки і в якій беруть участь всі чле- +ни організації. Рада проходить між зборами. Виконує функції Асамблеї +та має право надавати урядам рекомендації щодо безпеки доставки та +запобігання забрудненню. Крім того, Рада організації має такі функції: +1) координація всіх органів організації; +2) надання робочих програм та бюджету для затвердження Асамб- +леєю; +3) приймає і удосконалює обов’язкові до виконання і рекоменда- +ційні міжнародні конвенції, кодекси, резолюції, протоколи, цирку- +ляри і рекомендації; +4) звернення Генерального секретаря до Асамблеї; +5) запрошення та організація зустрічі з представниками інших ор- +ганізацій для участі в Асамблеї. + +225 +Призначення до Ради Міжнародної морської організації відбува- +ється відповідно до правил: +а) десять країн, що мають найбільший інтерес до міжнародної на- +вігації; +б) десять країн, що демонструють найбільший інтерес до міжна- +родної морської торгівлі; +в) двадцять країн, які не включені до категорій а) та б), і ті, хто за- +цікавлені морським транспортом або навігацією та представляють всі +географічні райони світу. +Комітети Міжнародної морської організації. +На постійній основі працюють такі комітети: +1-й Комітет з питань безпеки (MSC — Maritime Safety Committee) +є найважливішим у Міжнародній морській організації, він включає +всіх членів організації. +2-й Комітет з охорони навколишнього природного середовища +(MEPC — The maritime Environment Protection Committee) включає +всіх членів організації. Він був організований як збори, а в 1985 році +отримав повний правовий статус незалежного. +Ці два комітети допомагають у роботі 9 підкомітетів: +– BLG — транспортування рідини та газів; +– DSC — перевезення небезпечних та загальних вантажів та кон- +тейнерів; +– FP — захист від пожежі; +– COMSAR — радіозв’язок, пошук та порятунок; +– Nav — безпечна навігація; +– модернізація та обладнання кораблів; +– SLF — стабільність, вантажний бренд, безпека риболовних су- +ден; +– STW — стандарти навчання та навігаційні вимоги; +– FSI — впровадження держави. +3-й Юридичний комітет (Legal Committee) включає всі країни- +члени Міжнародної морської організації. +4-й Комітет з технічного співробітництва (Technical Co-operation +Committee) — включає всі країни-члени Міжнародної морської ор- +ганізації. +5-й Комітет формальностей (Facilitation Committee) — відкритий +для всіх країн-членів Міжнародної морської організації. +Організовано в 1972 році як дочірнє відділення Ради з полегшення +формальностей у міжнародній навігації. У 1991 році видав Додаток до + +226 +Конвенції Міжнародної морської організації як стандартного коміте- +ту. Однак додаток ще не набув чинності. +Секретаріат Міжнародної морської організації — складається з зо- +внішніх співробітників та 300 співробітників головного офісу в Лон- +доні. +2. IACS Міжнародна асоціація класифікаційних суспільств. +Міжнародну асоціацію класифікаційних суспільств організовано +за рекомендацією Конвенції про вантажні морської конвенції 1930 +року. У 1968 році вона отримала консультативний статус у Міжнарод- +ній морській організації як неурядової організації. +Члени Міжнародної асоціації класифікаційних товариств: +ABS — Американське бюро доставки; +BV — Бюро Верітас (Франція); +CCS — Китайська спілка класифікації; +DNV — Det Norske Veritas (Норвегія); +GL — Німецький Ллойд; +KR — Корейський реєстр суден; +LR — Регістр судноплавства Ллойда (Англія); +NK — Ніппон Кайджи Кіокай (Японія); +RINA — Італійський морський регістр; +RS — Російський морський реєстр судноплавства. +Асоційовані члени: +CRS — Хорватське судноплавства; +IRS — Індійський реєстр судноплавства. +Основні цілі: +– забезпечення безпеки людського життя в морі; +– забезпечення плавання в безпеці; +– забезпечення надійного перевезення вантажів морем та вну- +трішніми водними шляхами; +– запобігання забруднення навколишнього середовища. +Для досягнення цих цілей правила, засновані на наукових дослі- +дженнях, розробляють та вдосконалюють вимоги міжнародних кон- +венцій та кодів. +3. ITU — Міжнародний телекомунікаційний союз. 24 травня 1844 р. +Самуїл Морзе надіслав перше повідомлення телеграфною лінією між +Вашингтоном та Балтімором. 17 травня 1865 р. Перша Міжнародна +телеграфна конвенція була підписана в Парижі між 20 країнами. На +підставі цієї Конвенції було створено Міжнародний телеграфний +союз. Через заснування союзу ця конвенція зазнала знач них змін — в + +227 +1876 році увійшов телефон, у 1896 р. — радіолокація. Зміни включе- +ні до Конвенції 1903 року. У 1906 р. Перша радіотелеграфна конвен- +ція була підписана в Берліні на першій конференції з радіотехніки. +У Додатку до цієї Конвенції прийняті перші правила для радіозв’язку, +які пізніше були оновлені і тепер відомі як «Правила переміщення». +У 1920 році почалися перші радіопередачі, а в 1927 році міжнародні +радіослужби схвалили розподіл частот та правил між різними країна- +ми та користувачами радіозв’язку. У 1932 році на Мадридській кон- +ференції були поєднані міжнародні конвенти. Об’єднана конвенція +була названа міжнародною конвенцією телекомунікацій. Також з +1 січня 1934 року союз був перейменований на Міжнародний теле- +комунікаційний союз (МСЕ). У 1947 році на МСЕ (ІТU) вступив до +Егіди ООН, а головний офіс організації був переведений з Берна до +Женеви. +У 1963 році був запущений перший супутник Synk-1, і почалася +епоха супутникового зв’язку. На позачерговій конференції в Же- +неві було представлено комунікацію з космічного спілкування, де +було передбачено не тільки частоти супутникового зв’язку, а й ор- +біти супутників зв’язку. У 1992 році ця комунікація була доповнена +у зв’язку з новими особливостями цифрового зв’язку та викорис- +танням негеостаційних супутників. На пленарному засіданні додат- +кової конференції ITU була реорганізована. Тут трьома секторами +стали: — телекомунікаційна стандартизація (ITU-T), — радіозв’язок +(ITU-R), — розробка телекомунікацій (ITU-D). На Кіотській конфе- +ренції 1994 року був затверджений перший стратегічний план розви- +тку союзу та комунікації у світі. Крім того, на цій конференції орга- +нізовано глобальний телекомунікаційний політичний форум (WTPF) +для вирішення політичних питань між країнами зв’язку. Перший +WTPF пройшов у Женеві у 1996 році з питань глобальних мобільних +супутникових комунікацій, а другий — у 1998 році для надання теле- +комунікаційного обслуговування. +4. ILO — Міжнародна організація праці. +Міжнародна організація праці була заснована в 1919 році на базі +Версальського договору в інтересах соціальної справедливості. Ця +організація має структуру тризіркової моделі, яку представляють уря- +ди, роботодавці та працівники (профспілки). Цілі та завдання Між- +народної організації праці були підтверджені в Декларації у Філадель- +фії, прийнятій Конференцією Міжнародної організації праці в 1944 +році. Декларація містить принципи: + +228 +– робота не є товар; +– свобода думки та право Асоціації є важливим елементом для +підтримки процесу; +– бідність в будь-якому місці створює небезпеку для загального +процвітання; +– всі люди незалежно від раси, переконань та статі мають право шу- +кати матеріального добробуту та духовного розвитку в контексті поваги +до свободи та гідності, економічної підтримки та рівних можливостей. +У 1946 р. Міжнародна організація праці стала першою спеціалізо- +ваною організацією, яка взаємодіє з ООН. У 1969 р. Міжнародна орга- +нізація праці була нагороджена Нобелівською премією миру. Перша +конференція Міжнародної організації праці відбулася у жовтні–лис- +топаді 1919 року у Вашингтоні. Вона прийняла шість рекомендацій та +8 конвенцій, включаючи № 1 про 8-годинний робочий день. +Спочатку організація включала 42 держави, зараз — 175. Конференції +проводяться щорічно. Кожні два роки конференція приймає дворічну +програму та бюджет. Між конференціями адміністративна рада включає +28 представників урядів, 14 від працівників та роботодавців. Секретаріат +та штаб-квартира розташовані в Женеві. Основні стратегічні цілі: +– розробка та впровадження норм та фундаментальних принципів +та трудових прав; +– створення більш широких можливостей для жінок та чоловіків, +щоб забезпечити гідну зайнятість; +– розширення охоплення та підвищення ефективності соціально- +го захисту для всіх; +– зміцнення тристоронньої структури та підтримки соціального +діалогу. +Способи досягнення цілей: +– розробка міжнародних заходів та програм для полегшення ре- +алізації фундаментальних прав людини, вдосконалення роботи та +життя, розширення можливостей зайнятості; +– розробка міжнародних стандартів праці (підтримка унікальної +системи контролю за їх застосуванням), яка служить керівним прин- +ципом національних органів у здійсненні цих заходів; +– комплексна програма міжнародного технічного співробітни- +цтва, розроблена та впроваджена з активним партнерством із засно- +вниками, щоб допомогти країнам у здійсненні цих заходів; +– підготовча, освітня та видавнича діяльність, сприяння реалізації +всіх цих зусиль. + +229 +З 1919 р. Міжнародна організація праці прийняла 184 Конвенції та +194 рекомендації. +Основні міжнародні конвенції безпеки судноплавства. +Перший досвід у створенні міжнародних домовленостей виник +на підставі правил запобігання зіткненням, що з’явилися на почат- +ку XIX століття. Пізніше, з розвитком флоту та глобальними пере- +везеннями, вони неодноразово переглядалися. Остання конвенція +MPPSS-72, затверджена 20 жовтня 1972 року, набрала чинності лише +15 липня 1977 року. +Після трагічної смерті пасажирського лайнера «Титанік» була при- +йнята перша міжнародна конвенція про захист людського життя на +морі 1914 року, потім 2-га конвенція про захист людського життя на +морі — була прийнята в 1929 році, 3-тя у 1948 році, 4-ту прийнято +17 червня 1960 року — набрала чинності 26 травня 1965 року. Тепер +чинна Конвенція Solas-74/78. +Вперше про забруднення навколишнього середовища світо- +ва спільнота підіймає це питання у другій половині ХХ століття. +У 1954 р. з ініціативи Великобританії була проведена конференція +з нафтового забруднення. Вона прийняла Конвенцію OILPOL-54, +яка вступила в дію 26 липня 1958 року. Ця конвенція охоплювала +два основних напрямки світового судноплавства, стосується тільки +забруднення наф тою та її компонентами, корекція пройшла в 1962, +1969 і 1971 роках. +Після катастрофи танкера «Торрі Каньйон» в Ла-Манші в 1967 +році світове співтовариство, оцінюючи суму збитку (попадання +близько 120 000 тонн нафти в море), прийнли ряд різних міжнарод- +них конвенцій: +Основні міжнародні конвенції з безпеки і запобігання забруднен- +ня навколишнього середовища: +СОЛАС-74/88; +SOLAS-74/88. +Міжнародна конвенція з охорони людського життя на морі 1974 +з додатковим Протоколом 1988 року: +МАРПОЛ-73/78; +MARPOL-73/78. +Міжнародна конвенція з запобігання забруднення з суден 1973 +року з додатковим Протоколом 1978 року: +ПДНВ-78/95; +STCW-95. + +230 +Міжнародна конвенція про підготовку і дипломування моряків та +несення вахти 1978 року з Кодексом 1995 року: +МППСС-72; +COLREG-72. +Міжнародні правила запобігання зіткнення суден на морі — +1972 року: +САР-79; +SAR-79. +Міжнародна конвенція для збереження і порятунку — 1979 року: +КГМ-66/88; +LL-66/88. +Міжнародна конвенція про вантажну марку — 1966 року зі зміна- +ми 1988 року: +ФАЛ -65; +FAL-65. +Конвенція про формальності в Міжнародних морських переве- +зеннях вантажу — 1965 року: +КНА-88; +SUA-88. +Конвенція про боротьбу з незаконними актами, спрямованими +проти безпеки морського судноплавства — 1988 року: +КСИ-89; +SALVAGE-89. +Міжнародна Конвенція про порятунок майна — 1989 року: +КГО -69; +CLC-69. +Міжнародна конвенція про цивільну відповідальність за шкоду, +заподіяну забрудненням нафтою — 1974 року. +Конвенція СОЛАС-74/88 (SOLAS-74/88). +Конвенція була прийнята 1 листопада 1974 року на Міжнародній +конференції з охорони людського життя на морі, а протокол до неї +10 листопада 1988 року на міжнародній конференції з гармонізованої +системи експертизи та сертифікатів. Також 11 листопада 1988 року +було прийнято низку виправлень до SOLAS -74. +Комітет з питань безпеки на морі постійно працює над покращен- +ням та вдосконаленням SOLAS-74/78, внесення змін до неї. +Конвенція СОЛАС (SOLAS) та протокол 1988 року до неї були +підписані англійською, іспанською, китайською, російською та +французькою мовами, а всі тексти рівноцінні. Офіційною мовою за- + +231 +лишається англійська, отже з розбіжностями англійська версія при- +ймається як основа. +Конвенція СОЛАС (SOLAS) спочатку мала 8 розділів: +I — загальні положення +II-1 — конструкція — поділ на відсіки та стійкість, механічні та +електричні установки +II-2 — конструкція — захист від вогню, виявлення та пожежога- +сіння. Нове видання було прийнято у грудні 2000 року, набрало чин- +ності 1 липня 2002 року. +III — рятувальні інструменти та пристрої. Нове видання в 1996 +році набрало чинності з 1 липня 1998 року. +IV — радіозв’язок. Нове видання затверджено в 1988 році. Введен- +ня чинності через запровадження ГМССБ з 1 лютого 1992 по 1 лютого +1999 року. +V — безпека мореплавання. Нове видання було затверджено в груд- +ні 2000 року, набрало чинності 1 липня 2002 року (стосується АІС). +VI — перевезення вантажів. +VII — перевезення небезпечних вантажів. Затверджено Міжна- +родною морською організацією у 2002 році, набрала чинності з 1 січ- +ня 2004 року (була підсумована Кодексом перевезення небезпечних +вантажів морем — UMDG-code). +VIII — ядерні судна — затверджені Асамблеєю Міжнародної мор- +ської організації в 1981 році. +Наступні глави були додані пізніше: +IX — управління безпечною експлуатацією суден. Затверджено в +травні 1994 року, набуло чинності 1 липня 1998 року. +X — заходи безпеки для високошвидкісних суден. Затверджено в +травні 1994 року, набуло чинності 1 січня 1996 року. +XI — спеціальні заходи щодо підвищення безпеки на морі. Затвер- +джено в травні 1994 року, набуло чинності 1 січня 1996 року. +XII — додаткові заходи безпеки для навалочних суден. За- +тверджена в листопаді 1997 року, набуло чинності 1 липня 1999 +року. +Основна мета конвенції SOLAS полягає в об’єднанні і зменшен- +ні кількості стандартів для будівництва, обладнання та безпечного +управління морських суден. Головне управління з виконання вимог +Конвенції лежить на урядах країн, під прапором яких кораблі пла- +вають. Конвенція СОЛАС також зобов’язує держави контролювати +судна в портах навігації (Правило 4 глави XI). + +232 +MARPOL-73 / +78. +Міжнародна конференція з запобігання забруднення моря, склика- +на Міжнародною морською організацією в 1973 році, прийняла кон- +венцію з запобігання забруднення з суден, яку в 1978 році було змінено +відповідно до Протоколу на Міжнародній конференції з питань безпе- +ки та запобігання забрудненню танкерами. В результаті вона була на- +звана: «Міжнародна конвенція з запобігання забруднення з суден 1973 +року, змінений в 1978 році протокол» або скорочено МАРПОЛ-73/78. +Конвенція набула чинності 2 жовтня 1983 (Додатки I і II). +Правила, що охоплюють різні джерела забруднення з суден, ви- +кладені в шести додатках до MARPOL -73/78: +I Правила для запобігання забруднення нафтою. Чинні з 2 жовтня +1983 року. +II Правила для запобігання забруднення шкідливими рідкими ре- +човинами. Вступ в силу з додаванням 1985 на 6 квітня 1987. +III Правила запобігання забруднення шкідливими речовинами, +що перевозяться морем в упаковці, вантажних контейнерах, знімних +танках, автомобільних і залізничних цистернах. Чинні з 1 липня 1992. +IV Правила запобігання забруднення стічними водами із суден. +Чинні з 27 вересня 2003 року. +V Правила для запобігання забруднення сміттям з суден. Чинні +з 31 грудня 1988 року. +VI Правила запобігання забруднення атмосфери з суден. Затвер- +джена в вересні 1997 року, але в силу ще не вступила. +Деякі важливі правила та положення Додатку І MARPOL (правила +запобігання забруднення нафтою). +У правилі 1 надано визначення: +– «Нафта» означає мастило у будь-якій формі, включаючи сиру +нафту, рідке паливо, мастило, що містить осади, масляні залишки та +очищені нафтопродукти; +– «Нафто-вмісна суміш» означає суміш з будь-яким вмістом мас- +тила; +– «Нафтове паливо» означає будь-яке мастило, що використо- +вується як паливо для основних двигунів та допоміжних механізмів +судна; +– Танкер нафти «означає судно, побудоване або адаптоване для +транспортування нафти оптом у вантажних приміщеннях; +– «Комбінований вантажний корабель» означає судно, призна- +чене для транспортування нафти оптом або твердого вантажу оптом; + +233 +– «Спеціальний округ» означає морську зону, де відповідно до ви- +знаних технічних причин, що належать до його океанографічних та +екологічних умов, специфіка доставки на ній вимагає прийняття спе- +ціальних обов’язкових методів запобігання забруднення моря з мас- +тилом. Спеціальні райони — це райони, перелічені у правилі 10 цього +Додатку; +– «Інтенсивність миттєвого розливу» означає інтенсивність роз- +ливу нафти в літрах на годину в будь-який час, поділена на швидкість +судна в вузлах; +– «Танк» означає закрите приміщення, призначене для транспор- +тування рідин; +– «Бортовий танк» означає будь-який резервуар, що прилягає до +бортової обрізки судна; +– «Центральний танк» означає будь-який резервуар, розташова- +ний всередині судна з поздовжнім пересуванням; +– «Стійкий грязьовий танк» означає будь-який резервуар, спеці- +ально розроблений для збору залишків з танків, промивання води та +інших масляних сумішей; +– «Чистий баласт» означає баласт у танку, який після останньо- +го перевезення в ньому був очищений таким чином, що стік з цього +танка, з нерухомого судна в чисту, спокійну воду в ясний день, не ви- +кликає видимих слідів нафти на поверхні води; +– «Ізольований баласт» означає водяний баласт, прийнятий у тан- +ку, який повністю відокремлений від вантажу або паливної системи; +– «Проникність приміщення» означає співвідношення об’єму +приміщення, який може бути заповнений водою до загального обся- +гу приміщення. +Правило 9 показує обмеження для скидання нафти: +1. З урахуванням положень відповідно до правил 10 і 11 цього До- +датка і пункту 2 цієї статті, заборонити скидання в море нафти або +нафто-вмісних сумішей з суден, до яких цей додаток застосовується, +за винятком випадків: а) з нафтового танкера, за винятком випадків, +передбачених у підпункті (б) цього пункту: — танкер знаходиться за +межами особливого району; — танкер знаходиться на відстані біль- +ше 50 морських миль від найближчого берега; — танкер на своєму +шляху; — миттєва швидкість скидання нафти не перевищує 30 літрів +на морську милю; б) з судна валовою місткістю 400 рег. т або більше +тонн валової місткості, крім нафтових танкерів, а також від машин- +них приміщень нафтового танкера, відділень вантажного насоса, за + +234 +винятком тих пір, поки вміст нафти в стоці не змішується з мастилом +та залишками вантажу нафти: +– судно знаходиться за межами особливого району; +– судно знаходиться в дорозі; +– вміст нафти в стоці без розведення не перевищує 15 частин на +мільйон; +– на борту експлуатується устаткування для фільтрування нафти, +що задовольняє пункт 17 правила 16 цього Додатку. +2. Стосовно судна валової місткості менше 400 рег. т, крім нафто- +вих танкерів, якщо судно знаходиться в особливому районі, адміні- +страція повинна забезпечити, щоб воно було обладнане, наскільки це +доцільно і практично можливо, пристроєм для зберігання залишків +нафтопродуктів на борту і їх скидання в приймальні споруди або в +море відповідно до вимог пункту I (б) цього правила. +3. У всіх випадках, коли в безпосередній близькості від судна +або його сліду на поверхні води виявлено видимі ознаки нафти, +уряди Сторін Конвенції повинні без зволікання розслідувати цей +факт. +6. Вуглеводневі радикали, які не можуть бути скинуті в море відпо- +відно до пунктів 1 і 2 цього правила, зберігаються на борту і виванта- +жують в прийомні об’єкти. +У правилі 10 Додатку I наведені методи запобігання забруднення +нафтою з суден при плаванні в особливих районах: +1. Це райони Середземного моря, Балтійського моря, Чорного +моря, Червоного моря, район Затоки, Антарктична область і Аден- +ська затока. +2. У спеціальній зоні забороняється викид в море нафти або сумі- +ші, що містить нафту, з будь-якого нафтового танкера або судна. +Додаток V конвенції MARPOL (правила запобігання забрудненню +сміттям з суден). +У правилі 1 визначено: +– «сміття» означає всі види харчових, побутових та операційних +відходів (усунення свіжої риби та її залишків), які утворюються в +процесі нормальної роботи судна та підлягають постійному або пері- +одичному видаленню, за винятком речовин, визначення або список +яких наведено в інших додатках до цієї Конвенції. +– «найближчий пляж». Вираз «від найближчого берега» означає +оригінальну лінію, з якої, за даними міжнародного права, відрахо- +вуються територіальні води відповідної території, за винятком пів- + +235 +нічно-східного узбережжя Австралії, де початкова лінія наведена в +Конвенції. +– «спеціальний округ» означає морську зону, де відповідно до ви- +знаних технічних причин, що стосуються його океанографічних та +екологічних умов, специфіка доставки на ній вимагає прийняття спе- +ціальних обов’язкових методів запобігання забрудненню моря сміт- +тям. Спеціальні райони — це райони, перелічені у правилі 5. +У правилі 3 додатку V MARPOL наводяться умови для видалення +сміття за межами спеціальних територій: +а) заборонено викид у море всіх видів пластмас, включаючи син- +тетичні кабелі, синтетичні риболовецькі мережі та пластикові пакети +для сміття, але не обмежуючись ними; +б) жодна шкідлива речовина, що перевозиться в упаковці, не +може бути скинута за борт за жодних умов. +I. 25 морських миль від берегу для плаваючих і пакувальних мате- +ріалів; +II. 12 морських миль для харчових відходів та іншого сміт- +тя, включаючи паперові вироби, ганчірки, скло, метал, пляшки, +осколки та аналогічне сміття; в) кидати в море сміття, зазначене +в підпункті (b) (ii) цього правила, може бути дозволено, якщо таке +сміття проходить через подрібнювач, і це зроблено до меж від най- +ближчого берега, але в будь-якому випадку заборонено, якщо від- +стань до найближчого берега становить менше 3 морських миль. +Таке подрібнене сміття повинне проходити через поверхню з отво- +рами не більше 25 мм. +Відповідно до пункту 1 правила 4, забороняється використовува- +ти будь-які матеріали, які підлягають застосуванню зі стаціонарними +або плавучими платформами, розробкою та пов’язаних з ними про- +цесами обробки в морі морських притулків мінеральних ресурсів, а +також від всіх інших суден, зв’язаних з такими платформами або зна- +ходиться в межах 500 м від них. +Якщо сміття змішане з іншими відходами, видалення або скидан- +ня яких підпадає під інші вимоги, то жорсткіші вимоги. Скидання +в море пластику й зол із пластику заборонене всюди. +У правилі 5, додаток V MARPOL наведені спеціальні зони для за- +побігання забруднення сміттям: 1. Для цілей цієї заявки спеціальні +зони є областю Середземного моря, в районі Балтійського моря, ак- +ваторії Чорного, району Червоного моря і райони Затоки, морські ра- +йони Північного моря і Антарктична територія, басейн Карибського + +236 +моря, в тому числі в Мексиканській затоці і Карибському морі, ви- +значення якого дано нижче: +a) район Середземноморського моря означає Середземне море +із затоками і морями, розташованими в ньому, обмежено з Чорно- +го моря з паралельним 41º північної широти, а на Заході — Meridian +5º36’ Західної довготи перетину Гібралтарської протоки; +b) район Балтійського моря означає Балтійське море саме по собі +з Botnik і фінських бухт і з проходом в Балтійське море, обмеже- +не паралельно 57° 44,8’ північної широти мису Скаген в Скагеррак +протока; +с) район Чорного моря означає саме Чорне море, межує з Серед- +земним морем з паралельно 41º північної широти; +d) район Червоного моря означає фактичне Червоне море з Су- +ецьким, обмежене з півдня прямою лінією, що проходить між Рас- +SI-ANS (12° 8,5’ північної широти, 43° 19,6’ східної довготи) і Husner +Murad (12° 40,4’ ’північної широти, 43° 30,2’ східної довготи); (Е) +Район затоки означає морський район, розташований на північний +захід від прямої лінії, що проходить між Рас-Ель-Хадда (22°30’ пів- +нічної широти, 59°48’ східної Lension) і Рас-Ель-Fast (25°04’ північної +широти, 61° 25’ східної довготи). +e) район зони Північного моря: в Північному морі обмежено: (I) +від Північного моря на південь — паралелі 62° північної широти, а +на сході — Meridian 4° західної довготи; (Ii) протоку Скагеррак, пів- +денна межа якого визначається паралельно 57° 44,8 північної широти +на схід від мису Скаген; і (W) Манш і підходи на схід від меридіана 5° +західної довготи і на північ від Parallel 48° 30’ північної широти; +g) Антарктичний район означає морський район, розташований +на південь від паралельної 60’ південної широти; +h) район Карибського басейну, як визначено в параграфі I статті 2 +Конвенції про захист та розвиток морського середовища Карибсько- +го басейну (Картахена та Індіас, 1998), означає Мексиканську затоку +та Карибський басейн з бухтами та морями в них. +Перегляд, зміну та доповнення MARPOL-73/78 доручено Коміте- +ту захисту морського середовища. +STCW-78/95. +Конвенція STCW стала першим міжнародним документом з осно- +вних правил про підготовку та дипломування моряків та несення вах- +ти. Вона була прийнята 7 липня 1978 року, набрала чинності 28 квітня +1984 року. + +237 +Стаття II STCW-78 містить визначення, головні з яких: +– «Партія» означає державу, за яку набрала чинності Конвенція; +– «Адміністрація» означає уряд, під прапором якого корабель має +право плавання; +– «Диплом» означає дійсний документ, незалежно від того, як це +було названо, виданий адміністрацією або її повноваженними, або +визнаний адміністрацією на право його власника займати позицію, +зазначену в цьому документі або дозволену національними прави- +лами; +– «Власник диплому» означає особу, яка володіє дипломом на +правовій основі; +– «Організація» означає міжнародну морську організацію; +– «Морське судно» означає судно, відмінне від тих, що плавають +виключно у внутрішніх водах у межах захищених вод або в безпосе- +редній близькості від них, або в межах правил порту; +– «Риболовецьке судно» означає судно, що використовується для +риболовлі, китів або інших живих ресурсів моря. +Правило I/1 Додаток до Конвенції 1978 року містить наступні +визначення: «Капітан», «Старший помічник капітана», «Поміч- +ник капітана», «Механік», «Старший механік», «Другий механік», +«Механік-статер», «Радіооператор», «Особа звичайного складу». Це +правило повинно бути виключено для безекіпажних суден. +Меморандуми про взаєморозуміння. +Інститут контролю іноземних судів у портах, з метою встановлен- +ня дотримання цими судами до звичайних вимог, виник на початку +80-х років у формі регіональної угоди ряду країн (Паризький Мемо- +рандум взаєморозуміння щодо контролю суден державного порту). +Світ підписав та експлуатує наступні регіональні угоди про управ- +ління портом: +– Паризький меморандум — 01.07.82 у Парижі; +– Латиноамериканська угода — 5.11.92 у Vina Del Mar (Чилі) +(Винья-дель-Мар); +– Меморандум Токіо — 01.12.93 в Токіо; +– Карибський меморандум — 09.02.96 в Крісчех (Барбадос); +– Середземноморський меморандум — 11.07.97 у Валетті (Мальта); +– Меморандум Індійського океану — 05.07.98 у Преторії (Півден- +на Африка); +– Меморандум Центральної та Західної Африки — 22.10.99 в Абу- +джа (Нігерія); + +238 +– Чорноморський меморандум — 07.04.2000 в Стамбулі. +Регіональні угоди порту: +– перевірка іноземних суден у портах; +– використання ідентичних засобів керування; +– застосування узгоджених процедур контролю; +– застосування домовленостей; +– взаємний обмін інформацією. +Основні засоби контролю: +– SOLAS 74/88; +– MARPOL 73/78; +– STCW 78/95; +– COLREG-72; +– LL-66/88; +– CLC-69; +– Конвенція ILO. +Особлива увага приділяється наступним кораблям: +– пасажир, bulk; +– кораблі для перевезення небезпечних вантажів та забруднюю- +чих речовин; +– відвідування порту вперше, або через 12 місяців та більшу пере- +рву; +– прийшов з іншого порту з зауваженнями PSC; +– під прапором країн, що належать до «чорного списку». +«Чорний список» — це список країн, судна яких після перевірки +PSC були затримані в портах, що дозволяє адміністрації порту не об- +тяжувати суда надмірними інспекціями. У той же час таки суди бу- +дуть перебувати під пильним контролем для запобігання можливим +порушенням. +Постанова Міжнародної морської організації A.787 (19) «Проце- +дури контролю судів державою порту» була прийнята 23 листопада +1995 року, і є основним документом, що регулює процедуру перевірки +суден у портах. +Глава 1, Визначення, глава 2 регулює перевірки судових інспекцій +у портах, глава 3 забезпечує процедури для більш детальної перевір- +ки, глава 4 — арешти кораблів у порту навігації. +Міжнародна конвенція для пошуку та порятунку. SAR-79 +Міжнародна система пошуку та рятування. Спочатку захоплене +морем судно ставало видобутком прибережних мешканців і безжа- +лісно грабувалося. Світова спільнота вперше прийняла міжнародну + +239 +угоду про надання порятунку людям у морі в 1914 році в Конвенції +про захист людського життя на морі, після катастрофи «Титаніка». +Ця Конвенція була довірена судам, що знаходяться поруч. Тому +частота 500 кГц та сигнал SOS були прийняті. Окрім того, 3 хвилини +мовчання були встановлені кожні 30 хвилин у радіо, а світовий оке- +ан поділяється на 13 зон, через прослуховування ефіру в будь-який +момент є безперервним. Наприкінці ХХ століття така система за- +старіла, крім того на кораблях та літаках з’явилося нове радіооблад- +нання, набравши чинності ГМССБ. Тому постанова Міжнародної +морської організації A.406 (X) від 17 листопада 1977 року рекоме- +дувала скликати конференцію для прийняття рятувальної конвен- +ції. Конференція відбулася в Гамбурзі з 9 по 27 квітня 1979 року, де +світова спільнота прийняла пошукові та рятувальні конвенції про +море (SAR-79). За рішенням 69-го засідання КБМ у травні 1998 +року було прийнято нову заяву до Конвенції САР-79, яка набрала +чинності з 1 січня 2000 року. За даними Конвенції SAR-79 голо- +вна роль у пошуку та порятунку приділяється прибережним послу- +гам — центрам рятувальних координацій (RCC), які повинні бути +організовані в кожній країні. +Терміни, що використовуються в SAR-79: пошук, пошукові та +рятувальні зони, центр порятунку, рятувальні підцентри, продукт та +рятувальний інструмент, аварійний етап, стагінальна невизначеність, +стадія тривоги, стадія катастрофи, координатор у пункті дії. +Глава 2 Додатків до Конвенції SAR-79 регулюються міжнародни- +ми стандартами для координаційних пошукових послуг та порятунку. +При отриманні інформації про будь-яку особу, що страждає на ка- +тастрофу у морі, або, страждає на морі, влада повинна вживати тер- +мінових заходів для забезпечення необхідної допомоги. На підставі +цієї допомоги вона зобов’язана самостійно організувати або разом з +іншими державами пошукові та рятувальні послуги, які повинні мати +наступні основні елементи: +1. Правова база; +2. Призначення відповідального органу; +3. Організація наявних коштів; +4. Засоби зв’язку; +5. Координаційні та виконавчі функції; +6. Процеси покращення послуг, включаючи планування, відноси- +ни на національному та міжнародному рівнях; +7. Підготовка персоналу. + +240 +Пошукові послуги та рятувальні роботи в рамках пошукового та +рятувального майданчика, межі яких узгоджуються між зацікавле- +ними сторонами. Сторони надають допомогу будь-якій людині, що +потерпає від катастрофи у морі. Вони виконують це незалежно від +національної приналежності або статусу такої особи або обставин, +в яких ця особа знаходиться. Генеральний секретар надсилає інфор- +мацію про рятувальну службу, яка повинна бути своєчасно скори- +гована: +1. Інформація про національні органи, відповідальні за пошукові +та рятувальні послуги на морі; +2. Розташування CRS або інших центрів для забезпечення координа- +ції пошукових та рятувальних операцій та засобів спілкування з ними; +3. Інформація про межі пошукової та рятувальної зони та прибе- +режних комунікацій у катастрофі та безпеки; +4. Введення основних пошукових та рятувальних методів. +Для забезпечення ефективності сторони забезпечують найбільш +повну координацію з повітряними послугами. Там, де можна створи- +ти RCC та JSC для цілей навігації та літака. Сторони забезпечують ви- +користання єдиних процедур для цілей як морського та повітряного +пошуку, так і порятунку. +Координація в пункті дії, коли виникає інцидент: призначається +координатор пошукових та рятувальних дій (SMC), який, як прави- +ло, діє з RCC Rescue Center або Центр RSC RSC, який забезпечує ко- +ординацію. Обов’язки координатора (OSC): +– координує дії всіх пошукових та рятувальних інструментів у +пункті дії; +– планує пошукові та рятувальні операції, якщо план не був отри- +маний від координатора дій (SMC); +– змінює план пошукових та рятувальних операцій відповідно до +ситуації, інформує SMC; +– координує зв’язок у пункті дії; +– моніторинг виконання дій іншими засобами; +– забезпечує повне виконання операцій, приділяючи особливу +увагу поділу всіх фондів як в ефірі, так і в морі; +– періодично передає повідомлення SMC, відповідно до стан- +дартної форми SITREP: +– проводить детальний запис операції; +– інформує координатора дій (SMC) про можливість появи ко- +штів, що більше не потрібні; + +241 +– повідомляє координатору дій (SMC) кількість збережених; +– надає координатору дій (SMC) імен та точок призначення ко- +штів по збереженню людей; +– звіт, який зберігається по кожному крокові; +– запитує додаткову інформацію з (SMC). Відповідальність ко- +ординатора на місці дії (OSC). Координатор на сайті Action (OSC) +повинен отримати план дій якомога швидше від SMC. Тим не мен- +ше, ОСС може розвивати свій власний план (залежно від обста- +вин). Виконавці також повинні змінити план пошуку відповідно +до екологічно змінної атмосфери, зокрема, коли вони виникають: +прибуття додаткових засобів допомоги; отримання додаткової ін- +формації; зміни погодних умов, видимості, умов освітлення тощо. +Пошукові операції повинні починатися відразу після прибуття до +місця порятунку. +У разі виникнення мовних труднощів слід використовувати +міжнародні сигнали та стандартні фрази Міжнародної морської +організації для спілкування на морі. Запитуючи обов’язки, ОСВ +повинен інформувати відповідну прибережну радіостанцію (CRS) +або службу управління повітряним рухом (ATS), а також коорди- +натора дій (SMC) з регулярними інтервалами або коли змінюється +ситуація. +Національні пошукові послуги та рятувальні послуги. Кожна сто- +рона розробляє відповідні процедури для загальної організації, ко- +ординації та вдосконалення пошукових та рятувальних послуг. Для +забезпечення ефективності пошукових та рятувальних операцій сто- +рони повинні: +1. Забезпечити координацію використання наявних засобів; +2. Встановити тісну співпрацю між організаціями в таких сферах, +як операції, планування та підготовка персоналу, навчання та дослі- +дження. +Співпраця між державами. Сторони повинні координувати робо- +ту своїх координаційних центрів, а також їх пошукові та рятувальні +операції з сусідніми державами. При необхідності, координувати на- +ціональні закони, сторони зобов’язані визнати їх територіальні води, +територію та повітряний простір над ними для пошуку та порятунку +людей. Сторонам, особливо якщо їх пошукові та рятувальні ділянки +перекривають одна одну, необхідно укласти угоди про прийом ряту- +вальних підрозділів на їх території або повітряному просторі. Якщо +не існує ніякої угоди між сторонами, якщо це необхідно, надається + +242 +запит, до якого сторони, відповідальні органи зобов’язані якомога +швидше відповісти: +– Негайно підтвердити отримання запиту; +– Вказати умови, якщо такі є, згідно з якими рятувальні одиниці +допускаються до території держави. Кожна сторона повинна автори- +зувати свої процедури пошуку: +– Просити допомогу з інших центрів координації, включаючи суд- +на, авіацію, персонал, постачання тощо, які можуть знадобитися; +– Дати будь-який дозвіл на доступ до своєї території або повітря- +ного простору таких суден, авіації, персоналу або пропозиції; +– Координувати з митними, імміграційними, санітарними та ін- +шими органами влади необхідні заходи для прискорення рятування. +Кожна сторона гарантує, що такі центри координації забезпечують +негайну допомогу іншим центрам, включаючи допомогу авіаційних +суден, персоналу, постачання тощо. +Системи суден для повідомлень. Сторони надають на цілодобовій +основі швидке та надійне отримання сповіщень про лиха в межах по- +шуку та рятувальних районів. Будь-яка країна або декілька країн, що +отримують повідомлення про страждання, зобов’язані: +– негайно транслювати повідомлення відповідному центру ряту- +вальної координації або рятувального підключення, а потім, наскіль- +ки це можливо, допомагати забезпечити зв’язок у пошуках та поря- +тунку; +– підтвердити сповіщення, якщо це необхідно. Для полегшення +операцій пошуку та порятунку сторони можуть створювати систему +суден, бажано на основі рекомендацій Міжнародної морської органі- +зації. Система повинна надавати користувачам інформацію про рух +кораблів: +– план переходу; +– розташування судна; +– кінцеве повідомлення. +У випадку катастрофи: +– скоротити час між моментом втрати зв’язку з судном та почат- +ком пошуку та порятунку, без сигналу катастрофи; +– швидко визначити судна, які можуть бути залучені до допомоги; +– вміти встановити меншу область пошуку; +– сприяти наданню термінової медичної допомоги або консуль- +тації. Система суден повідомлень повинна задовольнити положення: +– надавати інформацію про місцезнаходження, плани переходу; + +243 +– дозволити відправити рух суден; +– отримувати повідомлення від учасників за певними інтерва- +лами; +– бути простим у намірах і в операційних відносинах; +– дозволити стандартні формати, загальноприйняті на міжнарод- +ному рівні та стандартному порядку повідомлення. +Список національних контактних адрес. Контактні адреси наці- +ональних центрів, відповідальних за безпеку моря та запобігання за- +брудненню від кораблів, публікуються Міжнародною морською орга- +нізацією та оновлюються щорічно. Нова версія та адрес, як правило, +затверджується на засіданнях Комітету з питань безпеки та Комітету з +охорони морського середовища та поширюється циркулярно. Зазви- +чай список складається з двох частин: +1. Короткий список національних органів влади (раніше MSC/ +CHERC.630), місцеві підрозділи національних інспекційних послуг, +офіційні послуги, що працюють від імені держави, а також органів, +відповідальних за розслідування аварій (раніше MSC/Цик542), та +секретаріату Меморандумів про взаєморозуміння щодо контролю су- +ден державою порту. +2. Перелік контактних адрес існуючих національних центрів, від- +повідальних за прийом, передачу та обробку термінових повідомлень +від кораблів зі шкідливими речовинами, включаючи мастило. +Список 1 повинен бути на кожному судні та в компанії в докумен- +тації СУБ (план дій у надзвичайних ситуаціях). Список 2 має бути +на кожному судні в аварійних засобах, щоб запобігти забруднення +мастилом. Коректування контролюється реєстром з річним обсте- +женням. +Форма аварійного повідомлення про аварійні події в плані дій су- +ден про надзвичайні ситуації: +План дій судна в надзвичайних ситуаціях. +Форма початкового повідомлення. +SS (координати, широта, довгота) / DD (відстань до прибережно- +го знаку). +N С. град. хв. E W град. хв. / град. мор. мілі. +EE курс град. / FF (швидкість, вузли) 1/10. +L L (передбачуваний шлях). +ММ (слухаюча радіостанція). +NN (дата та час наступного повідомлення, UTC). День. Години. хв. +PP (вид та кількість вантажу/палива на борту). + +244 +QQ (коротка інформація про недоліки/пошкодження). +RR (коротка інформація про забруднення, включаючи оцінку +втраченої кількості). +SS (коротка інформація про погоду та морський стан). +Напрямок, вітер швидкість (на масштабі Бофорта) / напрямок, +висота хвиль (м). +ТТ (дані для зв’язку з судновласником / оператором / агентом). +UU (розмір і тип корабля). +Довжина: (м) / ширина: (м) / осад: (м) / тип. +X X (додаткова інформація). +Коротка інформація про інцидент. +Необхідність допомогти ззовні. +Дії вжиті. +Кількість екіпажу та інформація про будь-які тілесні ушкодження. +Інформація про страхову компанію. +Інша інформація. +Коли можуть виникнути труднощі та обмеження, що обумовлені +нерозумінням мови, повинні включати англійську мову з викорис- +танням, коли це можливо, стандартних фраз міжнародної морської +організації морських перевезень на морі. Для того, щоб передавати +детальну інформацію, англійська мова може бути використана на +свій розсуд, а також використані міжнародні сигнали. При їх вико- +ристанні в тексті повідомлення відразу після літерного індексу необ- +хідно внести відповідні вказівки про це. +Нижче наведені додаткові дані для заповнення спеціальної таблиці. +AA — назва судна, позивний або ідентифікаційні дані суднової ра- +діостанції і прапор судна. +ВВ — група з 6 цифр, яка вказує день (перші дві цифри), години і +хвилини (останні чотири цифри). +СС представляє собою групу з чотирьох цифр, що вказує на ши- +роту в градусах і хвилинах, а також знаки N (північ) або з S (південь), +і групу з 5 цифр, яка вказує довготу в градусах і хвилинах, а також зна- +ки Е (схід) або W (захід). +DD є істинний пеленг (перші 3 цифри) і відстань в морських милях +від чітко визначеної прибережної позначки (вказати берегову позначку). +EE — істинний курс. +FF — швидкість у вузлах і десятих вузла. +LL є оцінений шлях. При описі шляху необхідно давати ши- +роту і довготу кожної поворотної точки, як і в СС із зазначенням + +245 +типу передбачуваного шляху між цими точками, наприклад, RL (по +Loccodromia), ГК (на великій дузі окружності) або уздовж берегової +лінії в разі прибережного плавання, очікуваної дати і часу характер- +них точок у вигляді групи з шести цифр, як у ВВ. +ММ — повністю вказати назви прослуховування станцій / частота. +NN — група із зазначенням дати і часу, як і в ВВ. +PP — найменування і кількість вантажу (бункер) на борту судна. +QQ — резюме несправностей / недоліків / пошкоджень. Короткі +звіти про стан судна та можливості концентрації палива. +RR — коротка інформація про забруднення навколишнього се- +редовища. Назва мастила або палива витоку в море; оцінка величини; +оцінка руху скидання мастила / палива; Якщо це можливо, оцінити +поверхню області розливу. Місце дається як в СС або DD. +SS є короткий опис переважаючих погодних і морських умов. +TT — ім’я, адреса, номер telemet і телефон судновласника і пред- +ставника (фрахтувальник, власник або оператор судна або їх агент). +UU — інформація про довжину, ширину, осадку і тип судна. +XX — додаткова інформація: +короткий опис інциденту; +необхідність допомоги ззовні, допомога, яка була запрошена або +була надана іншими суднами; +вжиті заходи щодо скидання і руху судна; +кількість членів екіпажу та відомості про будь-які тілесні ушко- +дження; +інформація про страхову компанію: +інша інформація. +Після передачі вихідного повідомлення в обсязі таблиці, додатко- +ве повідомлення повинно бути передано так, що воно містить інфор- +мацію, важливу для безпеки судна і захисту морського середовища. +Наступна додаткова інформація повинна бути спрямована на +судновласника або оператора в можливо короткий час після перших +внесень інформації: +– додаткові деталі пошкодження судна і обладнання; +– вказується існуючий збиток; +– оцінка пожежної небезпеки і попереджувальних заходів, що +вживаються; +– розміщення вантажу на борту і його номер; +– число нещасних випадків; +– пошкодження та збитки, завдані іншим суднам; + +246 +– час (GMT), коли була запрошена допомога, і час, протягом яко- +го очікується допомога; +– ім’я рятувальника і тип аварійно-рятувального обладнання; +– чи було прохання про додаткову допомогу; +– вимоги до запасних частин та інших матеріалів; +– будь-яка інша важлива інформація. +Зв’язок в точці дії. Сигнал лиха: +– MAYDAY використовується для вказівки того, що судно знахо- +диться в стані загрози безпосередньої небезпеки і вимагає негайної +допомоги; +– має перевагу перед усіма іншими повідомленнями. +Терміновий сигнал. +– PAN-PAN використовується, коли безпека мобільних засобів +знаходиться під загрозою; +– терміногенний сигнал PAN-PAN повинен бути використаний, +коли існує небезпечна ситуація, яка, в кінцевому підсумку, може +спричинити необхідність залучення допомоги; +– має перевагу над усіма повідомленнями, за винятком сигналу +катастрофи. +Сигнал безпеки. +– SECURITE використовується для повідомлень, пов’язаних з +безпекою судоводіння або передачею важливих метеорологічних по- +переджень. +Будь-які повідомлення, передані після цих сигналів, мають прі- +оритет перед звичайними повідомленнями. Як правило, сигнал по- +вторюється тричі на початку повідомлення. Командир літака або +капітан визначеного корабля повинен оголосити стан катастрофи +за допомогою сигналу MAYDAY. Основні слова для радіопроцедур, +пошуку, які рятувальні співробітники повинні використовувати та +розуміти: +AFFIRMATIVE означає, що те, що передається, є правильним; +BREAK використовується для відокремлення частини повідо- +млення або одного повідомлення від іншого; +FIGURES вимовляються безпосередньо перед номерами в пові- +домленні; +I SPELL використовується для вимовляння слів по буквам; +NEGATIVE засобів немає; +OUT кінець передачі, коли відповідь не очікується або не по- +трібна; + +247 +OVER кінець передачі, коли очікується негайна відповідь; +ROGER означає, що прийняте повідомлення задовільне; +SILENCE вимовляється тричі і означає «зупинити негайно всі +програми»; +SILENCE FINI означає скасування тиші, використовується для +позначення кінця надзвичайної ситуації та відновлення нормального +радіообміну; +THIS IS вимовляється до назви станції або позивного сигналу; +WAIT означає, що «я повинен призупинитися на кілька секунд, +очікую подальшу передачу». +Більш детальний перелік процедурних слів наведено в «стан- +дартних фразах міжнародної морської організації для спілкування +на морі» та MCC. Передача повідомлення катастрофи від морського +судна: +– 156,8 МГц (УКВ, канал 16); +– 156,525 МГц (УКВ ЦИВ 70 канал); +– 2182 кГц (радіотелефонія); +– ПВ/КВ ЦИВ (2187,55 кГц, 8414,5 кГц вахта несеться обов’яз- +ково) та ще на одній з частот 4207,5 кГц, 6312 кГц, 12577 кГц, +16804,5 кГц; +– Інмарсат 1644.3–1644,5 МГц (АРБ); +– Інмарсат 1626,5–1646,5 МГц — АРБ 406–406,1 МГц. +Якщо існують сумніви щодо прийому невідповідності повідо- +млення, його слід надсилати на будь-яку існуючу частоту, яку можна +використовувати в місцевих районах, і на яких увага може бути отри- +мана негайно. З метою створення сигналів катастрофи можна ви- +користовувати рятувальне радіо. Передача сигналів тривоги з літака +здійснюється: +– зазвичай літак повідомляє блок керування рухом (АТС), який +повинен повідомити RCC; +– 121,5 МГц; +– 4125 кГц (радіотелефонія); +– радар-респондент встановлюється при 7700 МГц; +– літак під час невизначеної катастрофи може використовувати +будь-які засоби у своєму розпорядженні, щоб привернути увагу, по- +відомляти про своє місцезнаходження та допомогу. +Додаткове радіотехнічне обладнання, встановлене на морських та +літальних апаратах відповідно до вимог Конвенції SOLAS-74/88 і з +яким можна відправити невідповідність повідомлення: + +248 +– аварійний радіобуй (EPIRB), який, якщо вводиться або коли +вмикається вручну, надсилає закодований сигнал, індивідуальний +для кожного буя, на прибережні станції; +– радар-респондент (SART), після включення вручну, діє автома- +тично, приймаючи радіолокаційні імпульси РЛС. +Надсилає імпульси, які видно на екрані РЛС, як групу розшире- +них точок, як сигнали респондентських маяків. Зазвичай на екрані +РЛС респондент бачиться на 6–8 миль — на переносних УКВ-радіо- +станціях VHF. Повідомлення з судна про лихо повинно включати такі +важливі компоненти: +– Ідентифікація та координати судна; +– Тип природної катастрофи та тип допомоги; +– Погода в безпосередній близькості, напрямок вітру, хвилі, ви- +димість; +– Час залишення судна та кількість екіпажу, що залишився на +борту; +– Кількість і тип рятувальних засобів; +– Надзвичайні інструменти для розміщення на рятувальному +агенті або в морі; +– Кількість серйозно поранених. +У початковому повідомленні стільки інформації включено як +практично доречну, але цілий ряд коротких повідомлень більш до- +цільніший, ніж одне довге. Сигнали візуальної катастрофи наведені +в МППСС-72. Скасування повідомлення стихійного лиха повинно +бути зроблено, як тільки буде надана допомога, або якщо допомога +не треба. Будь-яке помилкове сповіщення слід скасувати, щоб не ви- +користовувати марно сили рятувальних послуг. +ISM-code. Світові стандарти. Незважаючи на покращений тех- +нічний стан флоту та сучасного навігаційного та радіотехнічного +обладнання, відділ надзвичайних ситуацій світового флоту залиша- +ється на тому ж рівні. Вина покладається в основному на некомпе- +тентність або непідготовленість екіпажів кораблів. За результатами +розслідування надзвичайних справ на морі людство зазначило, що +нещодавно «людський чинник» відіграє вирішальну роль. Тому було +вирішено регулювати та стандартизувати людські відносини на бор- +ту суден. +Вимоги до безпечної експлуатації кораблів наведено в міжнарод- +ному кодексі з питань управління безпекою та забрудненням (ISM- +code), який був прийнятий Міжнародною постановою Міжнародної + +249 +морської організації A.741 (18) 4 листопада 1993 року. Вона включає в +себе такі пункти: +1. Загальні положення; +2. Політика у сфері безпеки та охорони навколишнього середовища; +3. Відповідальність та повноваження компанії; +4. Призначена особа (особи); +5. Відповідальність та повноваження капітана; +6. Ресурси та персонал; +7. Розвиток планів проведення операцій на кораблях; +8. Готовність до надзвичайної ситуації; +9. Звіти про невідповідності, аварії, небезпечні ситуації та їх +аналіз; +10. Технічне обслуговування та ремонт судна; +11. Документація; +12. Перевірка, огляд та оцінка, зроблена компанією; +13. Експертиза, перевірка та контроль. +Конвенція SOLAS-74/78. +Комітет з безпеки на морі в 1994 році прийняв постанову IX до- +давання до конвенції SOLAS-74/88. +Правило 1 «Визначення»: +1. ISM-code — означає Міжнародний код для управління безпеч- +ною експлуатацією суден та запобігання забрудненню, прийнятий +Організацією А.741 (18) Постановою (18), з поправками, які можуть +бути зроблені Організацією; +2. Компанія означає власника судна або будь-якої іншої органі- +зації, або людину, таку як менеджер, який взяв на себе відповідаль- +ність за роботу судна від власника судна, погодившись прийняти всі +обов’язки та всю відповідальність, встановлену міжнародним кодом +управління безпекою. +3. Обладнання — це судно, конструкція якого включає в себе один +корпус, бортові шлери та бортові танки в вантажних приміщеннях і +призначені переважно для транспортування насипних вантажів або +рудозних або комбіновані судна. +4. Море-мобільна бурова установка — це судно, здатне виробляти +бурові операції для розвідки або розвитку ресурсів, таких як рідкі або +газоподібні вуглеводні, сірка або сіль. +5. Нафтовий танкер означає судно, побудоване або адаптоване, +головним чином, для перевезення нафти оптом у своїх вантажних +приміщеннях, і включає в себе комбіновані вантажні судна та будь- + +250 +який танкер-хімічний транспорт, якщо він транспортує нафту оптом +як вантаж або частину вантажів. +6. Швидкий корабель — це судно, здатне розвивати максимальну +швидкість в метрах за секунду, рівну або більше: 3,7 V0,1667, де V 7 — +розрахункове зміщення, м3. +7. Танкер Himovo — означає вантажне судно, побудоване або при- +стосоване і використовуване для транспортування оптом будь-якого +рідкого продукту, зазначеного в Міжнародному кодексі Хемноса. +8. Банзор — означає вантажний корабель, побудований або адап- +тований та використовуваний для транспортування оптом будь-якого +скрапленого газу або іншого продукту, зазначеного в Міжнародному +кодексі для газових транспортних засобів. +9. Риболовецьке судно — означає судно, що використовується для +риболовлі, ловлі морських тварин та морепродуктів, рибного госпо- +дарства. +10. DSC (доступний документ) — означає документ, виданий ком- +панією, адміністрацією прапора, що підтверджує, що судно відпові- +дає вимогам Кодексу. +11. SVUB (свідоцтво про управління безпекою) — це документ, +виданий адміністрацією компанії, після генерації служби управління +судном та підтверджуючий, що служба управління безпекою корабля +відповідає вимогам правила 2 «Кодексу» — MCUB є Введено для всіх +судновласників та кораблів, незалежно від дати будівництва, вчасно: +– 01.07.98 — швидкісні, масляні танкери, хімічні носії, газові но- +сії, масові та вантажні високошвидкісні кораблі з валовою місткістю +500 або більше тонн; +– 01.07.02 — інші вантажні судна та морські бурові установки ва- +ловою потужністю 500 або більше тонн. +Ця глава не застосовується до державних суден, які працюють +у некомерційних цілях. +Постанова Міжнародної морської організації A.787 (19) «Проце- +дури контролю над кораблями держави порту». Судно повинно мати +непрострочений сертифікат управління, виданий адміністрацією +порту прапора судна. Якщо є підстави для більш детальної перевірки, +зареєстровані наступні запитання ISM-code (посилання на елемент +ISM-code). +ISM-code. Загальні положення (ISM-code). Основна ланка сис- +теми управління безпекою, відповідно до стандартів Міжнародної +морської організації та Кодексу, є власником або оператором судна + +251 +(компанії). Система управління безпекою (SUB) повинна бути реалі- +зована у діяльності компанії для ефективних та професійних дій з ін- +формацією судового управління та є невід’ємною частиною основної +системи управління виробничою компанією. Код вимоги до системи +управління безпекою компанії: +А) Стандарти якості безпеки та запобігання забрудненню: +– дотримання системи обов’язкових правил та стандартів; +– гарантії впевненості в тому, що система приймає кодекси, керів- +ні принципи та стандарти, рекомендовані Міжнародною морською +організацією та організаціями морської промисловості; +Б) Загальні цілі компанії: +– забезпечення якості наданих послуг; +– забезпечення безпечної експлуатації суден та безпечних умов +роботи та навколишнього середовища; +– організація захисту від усіх виявлених ризиків; +– постійне вдосконалення навичок управління безпекою та суд- +ном, включаючи надзвичайну готовність, пов’язану з запобіжним за- +собами запобігання небезпеки і ризиків, пов’язаних із забрудненням. +В) Функціональні вимоги до системи управління безпекою: +– політика безпеки та екології; +– інструкції та процедури для забезпечення якості наданих по- +слуг, безпечної експлуатації судна та охорони навколишнього серед- +овища; +– кількість повноважень та зв’язків між узбережжям та персоналом +судна, а також внутрішніми лініями спілкування на березі та з суднами; +– забезпечення взаємодії з радіостанціями та портів для організа- +ції надійних щоденних обліків кораблів компанії; +– процедури при аваріях та випадках невідповідності вимогам Ко- +дексу; +– процедури підготовки до надзвичайних ситуацій та дій щодо їх- +нього усунення; +– процедури проведення внутрішніх аудитів та процедур розгляду +керівництва. 17.ISM-code. Інститут у сфері безпеки та охорони на- +вколишнього середовища (пункт 2 ISM-коду). +Кожна компанія повинна мати політику у сфері безпеки та охоро- +ни навколишнього середовища, яка полягає в: +– досягненні загальних цілей, передбачених Кодексом; +– забезпеченні безпечної експлуатації суден на рівні міжнародних +та національних стандартів (правил та норм); + +252 +– підвищенні, на цій основі конкурентоспроможності своїх суден +на світовому ринку. +У той самий час компанія проголошує свою прихильність і дає +пріоритет, насамперед, забезпечуючи безпеку та запобігання забруд- +ненню та повинна забезпечити основну мету політики. +Безпека на морі, запобігання смерті та травм людей, пошкоджен- +ня навколишнього середовища, особливо морського середовища та +майна, а також дотримання правил проведення комерційних опера- +цій. Це досягається: +– дотриманням міжнародних та національних стандартів (правил +та норм) щодо безпеки запобігання навігації та забруднення; +– стійким та надійним двостороннім спілкуванням кораблів з бе- +регом; +– звітами капітанів за станами кораблів, проблем на борту та за- +ходів для їх вирішення, необхідну підтримку узбережжя; +– наявністями взаємопов’язаних планів дій у надзвичайних ситу- +аціях та розробкою цих планів; +– здатністю компанії швидко і адекватно реагувати на небезпеку, +яка може виникнути на кораблі; +– забороною приносити, зберігати та використовувати алкогольні +напої та наркотики на борт суден; +– дослідженням аварій та надзвичайних ситуацій на кораблі та +вживанням заходів щодо їх запобігання. +На підставі вищесказаного компанія здійснює: +– кадрову політику — збирання кваліфікованого персоналу; +– технічну політику — забезпечення проектно-технічної, техно- +логічної та екологічної безпеки суден; +– соціальну політику — створення умов в інтересах персоналу для +забезпечення безпечної експлуатації кораблів. +Політика затверджується підписом Генерального директора. Ко- +пія політики компанії, підписана Генеральним директором, викладе- +на на визначеному місці в кожному підрозділі компанії, на судні — +на місці, найбільш відвідуваному екіпажем, та в кабіні капітана. Всі +співробітники компанії повинні бути знайомі з політикою компанії +для її виконання. +Політика компанії складається з трьох рівнів документації. +Політика — цілі та завдання. +Загальна структура системи управління: +– опис стратегій системи управління та цілей; + +253 +– визначення діапазону системи управління; +– опис організаційної структури; +– визначення відповідальності потужних повноважень ключових +працівників системи управління; +– перехресні посилання елементів посібника, використовуючи +використані стандарти. +Процедури — що робити: +– метод управління системою; +– процедури, що описують перелік різних заходів щодо системи +управління; +Інструкції — як це зробити: +– задокументовані завдання; +– опис робіт (інструкції з роботи); +– форми звітів та шаблонів, які використовуються в системі +управління безпекою. +ISM-code. Відповідальність та повноваження компанії (пункт 3 +ISM-коду). Стандартна структура СУБ будь-якої компанії повинна +включати: +– Вище керівництво; +– Загальні збори акціонерів / засновників; +– Рада директорів; +– Генеральний директор; +– Рада, яку очолює Генеральний директор та включає всіх сво- +їх депутатів та інших працівників, визначених зборами акціонерів. +Прибережні одиниці: +– служба безпеки (СБМ); +– технічна експлуатаційна служба (корабель або MCC); +– відділ персоналу (OK) або служба управління персоналом; +– видобуток; +– виробнича служба; +– комерційний відділ; +– юридичний відділ; +– служба зв’язку; +– департамент експлуатації; +– департамент логістики (ОМТС). +Мінімальні вимоги до структури компаній відповідно до рекомен- +дацій галузевого стандарту є такими: +Маленька: +– Генеральний директор; + +254 +– призначена особа, за умови її заміни під час відсутності відпо- +відного спеціаліста, прийнятого за угодою про зайнятість; +– технічний спеціаліст (механік, електромеханік), за умови +її заміни на період відсутності фахівцем, прийнятим тимчасово. +Примітка: договір для забезпечення системи управління безпекою +невеликої компанії не звільняється від зобов’язання призначати +осіб. +Середня: +– Генеральний директор; +– призначена особа; +– технічний фахівець: +– служба безпеки (один капітан-наставник для шести суден, +включаючи призначену особу, та один фахівець з комунікацій та SPI +на 12 суден); +– механік та судноплавна служба (1 менторний механік для шести +суден, включаючи технічного спеціаліста). +Велика: +– Генеральний директор; +– призначена особа; +– головний інженер; +– служба безпеки (1 наставник для 6 кораблів); +– механік та судноплавна служба (1 наставник для 6 кораблів); +– радіотехнічне обслуговування (може бути частиною СБМ — +1 наставник для 12 кораблів); +– всі інші прибережні одиниці, наведені вище. Склад та кіль- +кість працівників кожного відділу визначаються керівництвом +компанії. +ISM-code. Призначена особа. (Пункт 4 ISM-code). Безпека суден +та якість послуг повинна бути під постійним контролем керівництва +компанії. Для цих цілей керівник компанії встановлює призначену +людину. Згідно з офіційною посадою, призначена особа будь-якої +компанії може працювати в компанії на постійній основі або заступ- +ником керівника морської безпеки. +Під час відсутності призначеної особи обов’язки виконуються за- +ступником. Призначена особа повинна бути затверджена: +– у великій компанії — у Державному комітеті; +– у середній та невеликій компанії — у ГА порту реєстру. +Призначена особа будь-якої компанії може бути фахівцем, який +має морську базову освіту, диплом та всі сертифікати, включаючи + +255 +ISM-код, що і дозволяють капітану працювати на найбільшому кора- +блі компанії, щонайменше 3 роки. +Призначена особа виступає від імені керівника компанії її ін- +струкцій щодо безпеки навігації та запобігання забрудненню, що є +обов’язковими для всіх працівників компанії. +Щоб виконати це як частину системи управління безпекою, при- +значена особа: +– організовує та координує діяльність системи управління безпе- +кою; +– підтримує цю систему, включаючи нормативні документи; +– підтримує постійне спілкування з суднами, контролює їхню +безпеку та забезпечує їх прибережну підтримку, необхідну для вико- +ристання безпечної експлуатації; +– має прямий доступ до ресурсів та управління компанією; +– забезпечує контроль за дотриманням стандартів (правил та +норм) безпеки та ефективності системи управління безпекою; +– забезпечує судна та прибережні ресурси, що виділяються на без- +пеку; +– своєчасно і негайно реагує на повідомлення про невідповіднос- +ті, небезпечні ситуації та аварії; +– організовує систематичні внутрішні та зовнішні перевірки сис- +теми управління безпекою, виправлення невідповідностей та вико- +нання коригувальних дій; +– призводить до нормативно-правової документації (розповсю- +дження, налагодження, бюлетень тощо); +– проводить навчання для систематичних оглядів (аналізів) стату- +су безпеки в компанії та розробляє основні пропозиції щодо системи +регулювання політики та системи управління безпекою. +ISM-code. Ресурси та персонал (пункт 6 ISM-code). До ресурсів +безпечної роботи належать: +– Нормативні документи; +– Матеріальні ресурси; +– Довкілля; +– Фінанси; +– Підготовлений персонал. +Центральною ланкою системи управління безпекою є персонал, +який має кваліфікований, компетентний та професійно підготов- +лений рівень. Весь прибережний персонал, що забезпечує систему +управління безпекою, повинен мати морські назви та досвід роботи + +256 +з командними позиціями не менше 3 років. Вимоги до персоналу пе- +редбачає посадовий опис, з якими вони знайомі до початку роботи +ISM-code). +Готовність до надзвичайної ситуації (пункт 8 ISM-коду). Підготу- +вати та забезпечити постійну готовність компанії та суден до надзви- +чайних ситуацій. +Компанія є операційним штабом з надзвичайних ситуацій, затвер- +джених Генеральним директором, та на чолі з призначеною особою. +Склад аварійної штаб-квартири компанії узгоджується з ГА портом +реєстру. +ISM-код. Звіти про невідповідності, нещасні випадки, аварії, не- +безпечні ситуації та їх аналіз (параграф 9 МКУБ). СУБ компанії по- +винні забезпечити систему негайних звітів про всі інциденти, прямо +або опосередковано впливати на безпеку навігації — звіти про не- +відповідності. Форму звіту про невідповідності наведено у докумен- +тації суб’єкта. Звіти про невідповідності складають команду верфі +з підписом капітана або головою прибережної одиниці у таких ви- +падках: +– відбулися аварії, нещасні випадки; +– створені небезпечні, ризиковані та непередбачені ситуації; +– претензії, що виникли для рибного господарства, органів нагля- +ду, портових органів; +– невідповідності (невідповідність вимогам) у системі управління +безпекою; +– претензії та відгуки вимог до підсвічування; +– немає жодних пропозицій щодо модернізації та вдосконален- +ня підтвердження: якщо невідповідність усунута самостійно, і допо- +мога компанії не потрібна, звіт про невідповідність не складається. +Звіт про невідповідність складається в 2 примірниках. 1-й направ- +ляється на ім’я призначеної особи відповідно до схеми суб’єкта, на- +веденої у документації, а другий залишається на кораблі / підрозділі +компанії, яка написала звіт. Після отримання звіту про невідповід- +ність служба безпеки морського моря назначає призначену особу, +що повинна: +– зареєструвати доповідь, включаючи число на класифікацію до- +кументації суб’єкта; +– організувати дослідження та аналіз звіту; +– розробити рішення про це; +– моніторинг виконання коригувальних дій; + +257 +– проводити постійний рух доповіді та контролювати виконання +коригувальних дій; +– встановити період для виконання коригувальних дій; +– призначити відповідальну особу за виконання коригувальних та +профілактичних заходів. +Коригувальні дії зроблено у формі рішення про звіт про невід- +повідність, одна копія надсилається на адресу пристрою / судна, +який написав звіт, а 2-га копія людині, відповідальній за виконання +коригувальних дій. СБМ (призначена особа) контролює виконан- +ня цього рішення. Коригувальні та запобіжні заходи повинні бути +спрямовані на забезпечення безпеки навігації та охорони навко- +лишнього середовища, а ні в якому разі не зменшують рівень без- +пеки. Коригувальні дії: +– виправлення відповідних процедур та інструкцій; +– розробка нових процедур та інструкцій; +– розподілення досвіду серед суден та прибережного персо- +налу. +Звіт про невідповідність буде закрито після отримання призна- +ченою особою інформації від голови підрозділу, який написав звіт, +звітував про усунення невідповідностей у формі суб’єкта, наведеної +у документації. +ISM-code. Документація (Пункт 11 МКУБ). Система управління +безпекою будь-якої компанії регулюється безліччю документації. Її +склад та порядок відліку кожна компанія встановлює самостійно, але +це повинно охоплювати всі сфери компанії та кораблі. Кожне судно +повинно мати повний пов’язаний з ним набір документації. За при- +значенням документація поділяється: +1) Розтягнутий — поставляється з суднобудівельного заводу. Міні- +мальна композиція безпеки Marigold включає: +– Технічний паспорт судна (vessel information book), що містить +основні ТТД (основні зменшення, призначення, танкова ємність, +кількість вантажів, ваги та інше). +– Інформація за стабільністю та схемами розрахунку (stability and +trim book) — містить початкові дані для розрахунку стабільності та +діаграм статичної та динамічної стабільності при різних завантажу- +вальних діаграмах. +– Рисунки суднових конструкцій, механізмів та систем (draw- +ings) є життєво важливими для забезпечення безпечної експлуатації +судна. + +258 +2) Регуляторно-правова — це ключова документація. Це набір +обов’яз кових стандартів (правил та норм) для безпечної експлуатації +судна. +19.0.МКУБ (ISM-code). Пункти 4–6 та 8 Кодексу. ISM-код. При- +значена особа (особи) (Пункт 4 МКУБ). Безпека суден та якість по- +слуг мають бути під постійним контролем керівництва компанії. Для +цього керівник компанії своїм наказом засновує призначену особу. +За службовим положенням, призначеною особою будь-якої ком- +панії може бути людина, що працює в компанії на постійній осно- +ві, заступник керівника з безпеки мореплавання. Під час відсутності +призначеної особи обов’язки виконує її заступник. Призначена особа +має бути затверджена: +– у великій компанії — у Державному комітеті з рибальства; +– у середній та малій компанії — у ГА порту приписки. +Призначеною особою будь-якої компанії може бути фахівець, +який має морську базову освіту, диплом та всі відповідні свідоцтва, +включаючи МКУБ, які дозволяють працювати капітаном на най- +більшому судні компанії, досвід роботи капітаном найбільшого судна +компанії не менше трьох років. +Призначена особа діє від імені керівника компанії та її вказівки +щодо безпеки мореплавства та запобігання забруднення обов’язкові +для всіх працівників компанії. +Для виконання цього в рамках СУБ призначена особа: +– організує та координує діяльність системи управління безпекою; +– здійснює ведення цієї системи, зокрема нормативно-правових +документів; +– підтримує постійний зв’язок із суднами, контролює їхню безпе- +ку та надає їм берегову підтримку, необхідну для забезпечення без- +печної експлуатації; +– має прямий доступ до ресурсів та керівництва компанії. +– забезпечує контроль за дотриманням стандартів (правил і норм) +безпеки та ефективності системи управління безпекою; +– надає суднам та береговим підрозділам ресурси, виділені на за- +безпечення безпеки; +– своєчасно та оперативно реагує на доповіді про невідповідності, +небезпечні ситуації та нещасні випадки; +– організовує проведення планомірних внутрішніх та зовнішніх +аудиторських перевірок системи управління безпекою, виправлення +невідповідностей та виконання коригуючих дій; + +259 +– веде нормативно-правову документацію (розподіл, коригуван- +ня, розсилку тощо); +– проводить підготовку систематичних оглядів (аналізів) стану +безпеки в компанії та розробку на їх підставі пропозицій щодо кори- +гування політики та системи управління безпекою. +20.0. Відповідальність та повноваження капітана (Пункт 5 +МКУБ). Відповідно до вимог МКУБ, КТМ та Статуту служби на +суднах капітан є вищою посадовою та довіреною особою компанії +на судні. Капітан керує судном на основі єдиноначальності, підпо- +рядковується Генеральному директору та призначеній особі. Ніх- +то, ні суднова рада, ні судновий комітет, ні партійна організація, +ні комітет з безпеки, ні будь-який працівник компанії, включаючи +Генерального директора та призначену особу, не мають права ска- +сувати рішення капітана з будь-якого питання виробничої та по- +бутової діяльності судна. Усі члени екіпажу призначаються лише +за згодою капітана. Капітан видає накази по судну та має право +усунути будь-якого члена екіпажу від виконання його обов’язків +або списати з судна, вказавши підстави у наказі. Капітан несе від- +повідальність за: +– підтримання та підвищення престижу та авторитету компанії; +– проведення на судні політики безпеки та розуміння її судновим +персоналом; +– ефективне функціонування суднової СУБ; +– створення в судновому колективі моральних та матеріальних +передумов для підвищення суднової СУБ; +– наявність та своєчасне підтвердження всіх суднових свідоцтв та +документів суднового персоналу; +– організацію служби на судні, розподіл обов’язків, відповідаль- +ності та повноважень екіпажу, включаючи аварійні ситуації; +– складання та затвердження посадових інструкцій суднового +персоналу, причому в праві відступити від статутних вимог підпри- +ємства; +– організацію зв’язку з компанією та внутрішньобортового +зв’язку; +– передачу в компанію повідомлень про аварійні заходи та недо- +тримання положень Кодексу; +– контроль за дотриманням персоналом судна міжнародних та на- +ціональних стандартів, включаючи стандарти компанії, для забезпе- +чення безпечної експлуатації судна; + +260 +– проведення занять, навчання та тренувань з відпрацювання суд- +новим персоналом дій в аварійних ситуаціях, включаючи забруднен- +ня довкілля; +– ведення суднової документації та суднових журналів; +– надання до компанії оглядів (аналізів) щодо ефективності судно- +вих СУБ та пропозицій щодо її вдосконалення. Капітан має виняткові +повноваження в прийнятті рішень щодо забезпечення безпечної екс- +плуатації судна та звернення до компанії за допомогою. Він не обме- +жений у праві прийняття рішень щодо забезпечення безпеки судна та +суднового персоналу, запобігання забрудненню навколишнього серед- +овища, збереження вантажу та майна і компанія підтримує його в цьому. +21.0.ISM-код. Ресурси та персонал (Пункт 6 МКУБ). До ресурсів +для забезпечення безпечного ведення робіт належать: +– нормативні документи; +– матеріальні ресурси; +– довкілля; +– фінанси; +– підготовлений персонал. +Центральною ланкою СУБ є персонал, який має бути кваліфіко- +ваним, компетентним та професійно підготовленим. Весь береговий +персонал, що забезпечує СУБ компанії, повинен мати морські зван- +ня та досвід роботи на командних посадах не менше трьох років. Ви- +моги до персоналу викладаються у посадових інструкціях, із якими +вони знайомляться під розпис на початок роботи. Комплектування +суднового персоналу здійснюється відповідно до чинного законодав- +ства, з обов’язковим узгодженням із призначеною особою. Капітан +зобов’язаний знати: +– національне та міжнародне законодавство та нормативно-пра- +вові документи; +– параметри непотоплюваності, міцності, стійкості, живучості +судна та його особливості; +– міжнародні угоди щодо безпеки мореплавства; +– морське право, закони, правила та звичаї портів заходу; +– правила класифікаційного суспільства; +– правила, норми, рекомендації, інструкції компанії в частині +експлуатації судна. +Судновий персонал повинен: +– мати морську базову освіту, дипломи, сертифікати та свідоцтва, +що засвідчують його кваліфікацію; + +261 +– знати структуру судна та її особливості; +– мати достатній досвід роботи (при призначенні вперше на ко- +мандні посади пройти відповідне стажування); +– вміти орієнтуватися в будь-яких умовах експлуатації, включаю- +чи аварійні; +– знати умови експлуатації та галузь діяльності судна; +– знати режим роботи, робочі навантаження, розпорядок на судні; +– виконувати правила техніки безпеки; +– знати свої посадові обов’язки та суднову систему управління +безпекою. +Береговий персонал повинен: +– мати спеціальну базову освіту, що відповідає призначенню; +– мати відповідні дипломи та свідоцтва, що підтверджують квалі- +фікацію; +– знати сферу діяльності підприємства та її СУБ; +– мати достатній досвід практичної діяльності; +– знати міжнародне морське право, відповідні міжнародні догово- +ри, національне морське законодавство; +– знати міжнародні та національні нормативно-правові стандарти +з безпеки мореплавання та ПЗМ; +– знати міжнародні та національні правила ведення фінансових +операцій; +– знати правила класифікаційних товариств. +Для підтримки кваліфікації персоналу на належному рівні +компанія повинна здійснювати його планомірне навчання. Осно- +вними видами навчання суднового персоналу, передбаченими +ПДМНВ-78/95, є: +1. Експлуатаційне навчання (in-service training) — проводиться на +судні з виконання суднових операцій, але на березі перед призначен- +ням на судно для підготовки та перевірки знань, майстерності, квалі- +фікації, компетентності та професійної підготовленості. +2. Сертифікаційне навчання (training for certification) — прово- +диться для підготовки та сертифікації командного складу за відпо- +відними міжнародно визнаними стандартами, кваліфікованими ін- +структорами. +3. Виробничо-ознайомче навчання (shipboard familiarization) — +проводиться з персоналом, який призначається на судно, з озна- +йомленням зі своїми обов’язками, влаштуванням судна та суднових +приміщень, входів та виходів, включаючи аварійні, судновими при- + +262 +строями, системами та обладнанням для нормальних та аварійних +умов експлуатації. +4. Інше навчання (other training requirement applicable to all ships) — +проводиться на всіх суднах з основним та тимчасовим судновим пер- +соналом за способами та технікою виживання в аварійних ситуаціях, +порядком залишення судна в кризових ситуаціях, а також методами +індивідуального захисту (протипожежна безпека, техніка безпеки, +перша невідкладна допомога тощо). +5. Спеціальне навчання (ship type specific training) — проводиться +з судновим персоналом специфічних типів суден (добувні, обробні, +приймальні, з небезпечними вантажами тощо). +6. Загальноосвітнє навчання — проводиться із судновим та бе- +реговим персоналом. Навчання проводиться на березі та на судні у +вигляді лекцій, курсів підвищення кваліфікації, тренувань на трена- +жерах, стажувань як дублери тощо. Програми навчання на березі та +на суднах узгоджуються та коригуються за результатами аварійних +випадків, виявлених невідповідностей СУБ, зовнішніх та внутрішніх +аудиторських перевірок. Відділ кадрів веде облік навчання кожного +працівника. На судні навчання відображається в судновій документа- +ції та пред’являється наглядовим органам на їхню вимогу. +26.0. Готовність до аварійної ситуації (Пункт 8 МКУБ). Для під- +готовки та забезпечення постійної готовності компанії та суден до +аварійних ситуацій створюються: у компанії — оперативний штаб з +аварійних ситуацій, затверджений наказом Генерального директора +та очолюваний призначеною особою. Склад аварійного штабу ком- +панії узгоджується з ГА порту приписки. На судні — судновий комітет +із безпеки (мінімальний склад капітан, старпом, стармех). Порядок +дій аварійного штабу та суднового комітету з безпеки наводяться у +взаємопов’язаних береговому (shore based emergency plan) та судново- +му планах дій в аварійних ситуаціях. Компанія має проводити підго- +товку до дій у потенційно можливих аварійних ситуаціях. Мета такої +підготовки — постійна готовність компанії швидко та ефективно ре- +агувати на аварійні ситуації, які можуть виникати на суднах. Відпові- +дальним за готовність суден та їх екіпажів до дій у аварійних ситуаціях +є призначена особа. Підготовка повинна передбачати: +– ідентифікацію та опис аварійних ситуацій, що можуть виникну- +ти на суднах; +– розробку планів дій берегового та суднового персоналів у потен- +ційно можливих аварійних ситуаціях; + +263 +– складання програм навчання та тренувань з відпрацювання бе- +реговим та судновим персоналом дій в аварійних ситуаціях, запобі- +гання аваріям, локалізацією та зведенням до мінімуму наслідків (ма- +ють наводитися в положенні з тренувань та навчання). +– методи та підтримання контактів та зв’язку між судном та +берегом, переданих в аварійних ситуаціях. Бажано використову- +вати рекомендації ІМВ (Резолюція А. 648(16) «Про основні за- +сади системи суднових повідомлень та вимоги, що висуваються +до них»). Плани дій у аварійних ситуаціях. Береговий повинен +відображати: +– склад, посади, службові та домашні телефони основного персо- +налу штабу; +– порядок та місце збору штабу; +– обов’язки штабу та його взаємодію із зацікавленими партнера- +ми, порядок запиту допомоги; +– методи та порядок повідомлень з судна на берег і назад; +– чек-листи, що ідентифікують аварійні ситуації, та буклети про- +цедур для дій суднового персоналу у цих ситуаціях; +– взаємодія з оперативним штабом ГА порту; +– довідкова інформація про аварійно-рятувальні організації та +центри в районах плавання суден компанії; +– порядок прийняття та виконання рішень та контроль їх вико- +нання. +Суднові вимоги повинні додатково включати: +– склад, посади, телефони суднового комітету з безпеки; +– взаємодію та зв’язок із зацікавленими партнерами та суднами, +що знаходяться в районі. +Відповідно до конвенції МАРПОЛ-73/78 на судні має бути «Суд- +новий план надзвичайних заходів щодо боротьби із забрудненням на- +фтою (shipboard oil pollution emergency plan)». За структурою та побу- +довою він аналогічний до плану дій в аварійних ситуаціях. Компанія +повинна проводити регулярні тренування та навчання суднового та +берегового персоналу за вказаними вище планами. До програм під- +готовки повинні включатися: +– індивідуальні інструкції та навчання суднового персоналу щодо +використання рятувальних та протипожежних засобів; +– заняття, тренування та навчання суднового персоналу щодо бо- +ротьби за живучість та дій у потенційно небезпечних аварійних ситу- +аціях; + +264 +– перевірки стану, надійності та готовності до дії суднового ава- +рійного майна та обладнання, включаючи радіообладнання. +23.0. ISM-код. Доповіді про невідповідності, аварії, нещасні ви- +падки, небезпечні ситуації та їх аналіз. (Пункт 9 МКУБ). СУБ ком- +панії повинна передбачати систему негайних доповідей про всі події, +що прямо чи опосередковано зачіпають безпеку мореплавства, — до- +повіді про невідповідності. Форма доповіді про невідповідність на- +водиться у документації СУБ компанії. Доповіді про невідповідності +складаються судновим командним складом (обов’язково підписує +капітан) або керівником берегового підрозділу у таких випадках: +– нещасних випадках, аваріях, аварійних пригодах; +– створених небезпечних, ризикованих та непередбачених ситу- +аціях; +– претензій рибоохорони, наглядових органів, влади портів; +– невідповідності (недотримання вимог) у системі управління +безпекою; +– претензій клієнтури та зворотних претензій до субпостачальни- +ків; +– пропозицій щодо модернізації та вдосконалення СУБ, що +з’яви лися: якщо невідповідність усунена самотужки і допомоги +компанії не вимагає, доповідь про невідповідність не складається. +Доповідь про невідповідність складається у двох примірниках. 1-й +прямує на ім’я призначеної особи за схемою, наведеною в докумен- +тації СУБ компанії, а 2-й залишається на судні/підрозділі компанії, +що написали доповідь. Після отримання доповіді про невідповід- +ність служба безпеки мореплавства, а де її немає, призначена особа +повинна: +– зареєструвати доповідь, надавши їй номер за класифікацією до- +кументації СУБ компанії; +– організувати вивчення та аналіз доповіді; +– виробити рішення щодо неї; +– проконтролювати здійснення коригувальних дій; +– вести постійний рух доповіді та контроль виконання коригу- +вальних дій; +– встановити термін виконання коригувальної дії; +– призначити відповідальну особу за виконання коригувальних +та запобіжних дій. Коригувальна дія оформляється у вигляді рішення +за доповіддю про невідповідність і один примірник надсилається на +адресу підрозділу/судна, що написав доповідь, а другий примірник + +265 +особі відповідальній за виконання дії, що коригує. СБМ (призначена +особа) контролює виконання цього рішення. Коригувальна та запо- +бігаюча дія повинна бути спрямована на забезпечення безпеки море- +плавства та захисту навколишнього середовища, та жодним чином не +знижувати рівень безпеки. Коригувальні дії здійснюються шляхом: +– виправлення відповідних процедур та інструкцій; +– розробки нових процедур та інструкцій; +– поширення досвіду серед суднового та берегового персоналу. +Доповідь про невідповідність закривається після отримання призна- +ченою особою від керівника підрозділу, який написав доповідь. До- +несення про усунення невідповідності за формою, наведеною в до- +кументації СУБ компанії. +24.0 МКУБ (ISM-code). Розробка планів проведення операцій на +суднах. Пункт 7 Кодексу. +Основна відповідальність за розробку планів суднових операцій +покладається на організацію. Керівництво компанії має визначити, +які суднові операції найбільш важливі для функціонування її суден. +Плани компанії: +– річний план, що передбачає огляд (аналіз) пропозицій промис- +лової (судноплавної) діяльності; +– підготовчий план, який передбачає підготовку суден до рейсу, +відповідно до завдання; +– експлуатаційний план, що передбачає здійснення промислу/ +вантажоперевезень, відповідно до рейсового завдання. Річний план +виробничої діяльності, та аналіз його виконання здійснюється бе- +реговими службами підприємств. Підготовчий план здійснюється +береговими службами підприємств, разом із судновим. Компанія +розглядає та виконує різні договори/контракти (ремонт, сервісне об- +слуговування суднового обладнання, зв’язок, постачання, портові +формальності та багато іншого), необхідні для успішної роботи судна +в морі. На основі договірних (контрактних) умов основними видами +підготовки судів є: +– Навігаційна — здійснюється службою безпеки щодо гаранту- +вання безпечного промислу (прогноз гідрометеобставин, забезпечен- +ня морськими картами, укомплектованість судна аварійним та ряту- +вальним обладнанням, наявність планів дій в аварійних ситуаціях та +підготовка екіпажів до дій в аварійних ситуаціях); +– Технічна — здійснюється механіко-судновою (технічною) служ- +бою (виконання планового технічного обслуговування, ремонту та + +266 +докування, забезпечення технічної та технологічної готовності до +промислу, перевірка строків дії суднових документів, проведення +чергових оглядів, організація бункерування суден, перевірка якості +палива, організація матеріально-технічного постачання); +– Кадрова — здійснюється відділом кадрів (комплектація судно- +вого персоналу, перевірка медичної придатності, перевірка дипломів +та сертифікатів, організація заміни суднового персоналу); +– Експлуатаційна (промислова) — здійснюється службою мо- +реплавства та відділом видобутку/комерційним/експлуатаційним +(планування роботи в промислових районах, призначення агентів, +забезпечення суден вантажною та експлуатаційною інформацією, за- +безпечення документами за правилами ведення промислу, організа- +ція зв’язку та диспетчерських зведень, перевірка знарядь постачання +необхідного промислового постачання); +– Фінансова — здійснюється комерційним відділом та бухгалте- +рією, з виділенням повноважень капітана (забезпечення суден не- +обхідними засобами, оплата експлуатаційних послуг, встановлення +порядку використання виділених коштів, контроль фінансових опе- +рацій, дотримання комерційної таємниці підприємства, контроль +руху готівки та майна); +– Страхування — здійснюється юридичним відділом (забезпе- +чення всіх видів страхування, встановлення порядку надання допо- +відей про нещасні випадки та аварії, за результатами яких можливі +ризики, статистичний облік збитків від виплат за претензіями та по- +зовами). +– Суднові операції — під час експлуатації суден компанія здій- +снює розробку планів суднових операцій відповідно до ISM-code, +враховуючи рекомендації ІМО та ґрунтуючись на національній сис- +темі організації суднової служби багатьох країн. Суднові операції, за +можливими наслідками, поділяються на: +– спеціальні — помилки у виконанні яких призводять до небез- +печних ситуацій або виявляються після того, як аварія сталася; +– критичні — помилки у виконанні яких одразу породжують +аварію або створюють загрозу для суднового персоналу, судна +чи забруднення (наприклад: аварійні постановка та підйом зна- +рядь лову, портові операції (лоцман, швартовка, якір та ін.), ван- +тажні операції в морі та портах, бункерувальні операції, аварійні +тощо). Критичні суднові операції мають виконуватися під суво- +рим контролем. При цьому має бути повна переконаність у квалі- + +267 +фікації, компетентності та практичній підготовленості суднового +персоналу. +Суднові операції об’єднуються у послідовності процесу промислу +та/або вантажоперевезень у такому порядку: +1. Загальні суднові операції: організація служби на судні — по- +садові обов’язки суднового персоналу — доповіді/рапорти судново- +го персоналу за підпорядкованістю — зв’язок судна з компанією — +інспекції та контроль, що здійснюються капітаном та командним +складом — суднова документація (склад, утримання, реєстрація) — +медичне обслуговування — придатність до виконання посадових +обов’язків та уникнення перевантажень суднового персоналу — ал- +коголь, медикаменти, наркотики (судова політика, контроль вико- +ристання та обстеження) — організація технічного обслуговування +та ремонту — інструкції з експлуатації та обслуговування суднового +обладнання — охорона праці та техніка безпеки — запобігання за- +бруднення навколишнього середовища — перевірочні листи — про- +мисловий розклад. +2. Операції під час перебування судна у порту: судова вахтова +служба (стоянкова) — взаємодія з владою порту — перевірка, випро- +бування та підготовка до дії протипожежних засобів — навантаження +та вивантаження — контроль розміщення вантажу, міцності та стій- +кості — вивантаження нафтовмісних вод та шкідливих речовин на +берег — організація здачі харчових відходів, сміття та стічних вод — +ремонтні роботи в порту — випадкові розливи рідких вантажів із +суднового бункера — відповідальність за випадки забруднення — дії, +якщо судно тимчасово затримується в порту — отримання промисло- +вого та виробничого спорядження. +3. Операції з підготовки судна до рейсу: перевірка та реєстрація +судна — перевірка міцності та стійкості — перевірка надійності за- +криття всіх люків та отворів у корпусі — перевірка надійності крі- +плення промислового устаткування — визначення/прогноз гідроме- +теообставин — підготовка навігаційних карт та планування переходу +до підготовки документації — перевірка, коректура карт та посібни- +ків — бункерування судна — отримання продуктів, води та запасних +частин — завершення ремонту та перевірка виконання — перевірка та +підготовка ГД та механічного обладнання судна — перевірка та підго- +товка систем управління судном — перевірка та підготовка систем та +механізмів забезпечення безпеки (засоби навігації, якір, навігаційні +вогні та ін.) — перевірка та підготовка засобів зв’язку — перевірка та + +268 +підготовка обладнання та пристроїв ПЗМ — перевірка та підготовка +промислового та виробничого обладнання та пристроїв. +4. Операції при знаходженні судна в морі та на промислі: суд- +нова ходова навігаційна вахта — спеціальні вимоги при плаванні в +складних умовах — радіозв’язок — спостереження за навколишнім +середовищем — спостереження за станом та режимами експлуатації +судна та основного обладнання — готовність судна до маневруван- +ня — постановка знарядь лову — ведення промислових операцій — +виробнича діяльність рибцехів та обробка риби — швартові операції +(бункерування, розвантаження) — готовність до непередбачених/ +екстремальних ситуацій. +5. Операції з підготовки судна до приходу в порт: перевірка ГД, +рульового пристрою, засобів навігації та зв’язку, якірного при- +строю — проводка судна (лоцманська) — зв’язок судна з портом та +інформація — визначення/прогноз гідрометеообставин — обмежен- +ня з плавання в районі порту, сезонні таблиці та карти, настанови — +баластування судна — контроль міцності, стійкості та водонепро- +никності — перевірка та підготовка швартовного пристрою судна. +Документування суднових операцій здійснюється та оформляється у +вигляді процедур та інструкцій. Процедура — це комплекс об’єднаний +спільністю мети, дій (функцій), викладених у формі документа, що +визначає призначення та завдання цього комплексу, склад, зміст та +порядок виконання дій (функцій), що входять до нього, та їх кінце- +вий результат. +Основу процедур складають суднові операції. Процедура може ві- +дображати суднову операцію повністю або її складові. Інструкція — +це розвиток та деталізація процедури. Вона є документом, що визна- +чає технологію виконання передбачених процедурою дій (функцій). +Основний склад процедур наводиться у положенні щодо процедур +документації СУБ компанії. Вимоги міжнародних та національних +нормативних документів виконуються в компаніях та на суднах без +дублювання їх у документах нижчого рівня. У документації СУБ пра- +вомірно лише посилювати чи деталізувати вимоги документів най- +вищого рівня, прив’язуючи їх до конкретних особливостей роботи +своїх суден. У процесі роботи документація СУБ має коригуватися +та доповнюватися на основі розслідувань (аналізів) аварій, невідпо- +відностей, нещасних випадків тощо. Найбільший відсоток важких +аварій світового флоту падає на людський фактор, пов’язаний з на- +вігаційною вахтою на містку та машині. Для полегшення дій судно- + +269 +водія та механіка значного поширення набули суднові перевірочні +листи (чек-листи). Ці чек-листи наводяться у документації СУБ +кожної компанії та рекомендуються для використання при повсяк- +денній виробничій діяльності судна. За рекомендацією ІМО (резо- +люція А.864(20) від 27 листопада 1997 року), при проведенні робіт, +пов’язаних з підвищеним ризиком (на висоті та за бортом, у закри- +тих та погано вентильованих приміщеннях, вогневі роботи тощо), +судна повинні використовувати відповідні чек-листи. При викорис- +танні чек-листів під час вахти судноводій/механік повинен врахову- +вати наступне: +– заповнений чек-листів суднової операції не звільняє осіб, які +несуть ходову навігаційну вахту, від відповідальності за невірні дії; +– чек-лист є юридичним документом і поряд із записами в судно- +вому/машинному журналі може бути доказом правильних дій судно- +водія/механіка в екстремальних ситуаціях; +– про заповнення чек-листа необхідно зробити запис у судново- +му/машинному журналі; +– чек-листи заповнюються тільки ручкою синім або чорним чор- +нилом, забороняється використовувати олівець; +– на всі пункти чек-листа має бути відповідь ТАК; +– якщо якийсь із пунктів чек-листа не виконаний, суднова опера- +ція не повинна проводитися, а про ситуацію необхідно негайно допо- +вісти капітану/старшому механіку за належністю; +– часто заповнювані чек-листи (зміна вахт, постановка трала +тощо) кожен судноводій/механік заповнює один раз за рейс, а потім +тільки робить відмітку в судновому/машинному журналі про його ви- +користання; +– чек-листи при плаванні у складних умовах необхідно заповню- +вати одразу; +– на кожному заповненому чек-листі повинні стояти дата, підпис +та прізвище особи, яка заповнила його; +– всі заповнені чек-листи повинні зберігатися на судні щонай- +менше два роки. У разі невідповідності чек-листа судновим умовам +необхідно направити призначеній особі компанії доповідь про не- +відповідність з обґрунтуванням коректури відповідного чек-листа. +Список усіх чек-листів, використовуваних під час роботи судна, має +бути вивішений на видному місці містка/машинного відділення (над +штурманським столом, над пультом управління головним двигуном) +[4–10]. + +270 +На підставі огляду нормативних документів випливає, що, поки +безпілотні судна не дотримуються правил Міжнародної морської +організації, вони будуть розглядатися як не судоходні, як такі, що +не підлягають страхуванню. Але час не стоїть на місці і вже є для без- +екіпажних суден ескізи регулювання правових відносин. Для пов- +них автономних суден, якщо ступінь автоматизації судна дозволяє +виконувати плавання без екіпажу на борту при постійному спосте- +реженні за судном та управляти його рухом персоналом за межами +судна, або без постійного моніторингу та керування персоналом +поза судном. +Суднові документи. Оскільки багато суднових документів мають +відношення до екіпажу судна та його функцій, необхідно замінити +айсклоуз, що наявність або підтримка частини суднових документів +для автономних суден у прийнятому тлумаченні повинні бути заміне- +ні. Для автономного судна необхідно консолідувати право не мати на +борту суднових документів, а їх інспекційний контроль органи влади +зможуть здійснити через судновласника в електронній та альтерна- +тивній формі. +Капітан судна, екіпаж судна. Існуючі стандарти передбачають, що +основною функцією капітана судна є управління суднами у сенсі на- +вігації. У випадку автономного судна функція управління навігацією +судна автоматизована та забезпечується або повністю судновою тех- +нічною системою, або під керівництвом судновласного прибережно- +го персоналу. Функції управління суднами, включаючи відправлен- +ня, щодо напівавтономного судна можуть бути виконані судовими +автоматичними пристроями або фахівцями судновласників, розта- +шованими за межами автономного судна. +Мінімальний судновий екіпаж. Для повністю автономних суден +ця вимога не застосовується взагалі. Сертифікат мінімального складу +напівавтономного судна повинен враховувати ступінь автоматизації +(автономії) судна. Оскільки повністю автономне судно не має на бор- +ту екіпажу, документ, що встановлює кількість екіпажу є безглуздям. +Вимоги до кваліфікації персоналу. Управління автономним суд- +ном, а також у присутності екіпажу і при його відсутності слід підтри- +мувати або здійснюватися за допомогою фахівців поза автономним +судном. А до членів екіпажу автономного судна та фахівців з управ- +ління автономними судами повинні розробляти та встановлювати +кваліфікаційні вимоги. Найбільш відповідним правовим інструмен- +том для встановлення кваліфікаційних вимог до зазначених членів + +271 +екіпажу та фахівців є положення про дипломи членів екіпажу мор- +ських суден. +Управління судном. Відповідальність за безпечне управління ав- +тономним судном може бути покладена на судновласника, який +повинен мати спеціалістів, компетентних у сфері управління авто- +номними суднами. Такі фахівці виходять за межі автономного судна, +контрольованого ними (на березі або на іншому судні або кораблі), +але повинні мати всі необхідні інструменти технічного та організа- +ційного характеру для управління суднами. Судновласник також має +обов’язок призначити особу, відповідальну за управління автономним +судном щодо кожного автономного судна (прибережного капітана). +Ця відповідальна людина може одночасно керувати кількома судна- +ми. Оскільки управління автономними суднами є дуже конкретним +завданням, яке вимагає концентрації спеціальних компетенцій, про- +понується надати право судновласнику укласти угоду про управління +автономним судном зі спеціалізованою організацією, компетентною +в управлінні автономним суднам. У той самий час, відповідальність +за безпечну роботу автономного судна, як і раніше, лежить на суд- +новласнику. +Такі коригувальні коментарі для запровадження нових технологій +вже введені в морське законодавство. У 2018 році DNV GL розробив +документ «Autonomus and remotely operated ships», у 2020 р. РМРС ви- +дав «Положення щодо класифікації морських автономних та дистан- +ційно керованих суден (МАНС)». Вимогами до систем автономних та +дистанційно керованих суден є надійність, безпека та ступінь авто- +матизації, що є не гіршими, ніж у суднах з екіпажем. Автономні судна +повинні мати мінімальну кількість споруд, а також корисний простір +судна та рекреаційних відділів. +На автономних суднах ставка робиться на локальну мережу суд- +на та системи зв’язку. Локальна мережа повинна бути реалізована з +можливістю функціонування в будь-якому агрегаті, тоді як несправ- +не обладнання повинно бути виключено з мережі під час усунення +невдачі. +Однією з опцій інтегрованої системи є обчислювальна система, +яка відповідає за управління суднами, повинна бути спроектована за +мажоритарним принципом, з обчислювачем, який видає некоректні +значення, що повинні бути відключені від загальної системи під час +перезавантаження та перевірки, після чого він повинен бути реінте- +грованим. + +272 +Неможливо відхилити такий аспект, як реалізація автономних +суден з можливістю участі у рятувальних операціях, для яких необ- +хідно обладнати судно штучним інтелектом у формі робототехніч- +них засобів. +У разі відмови працювати з автономним та дистанційно керова- +ним судном воно повинно бути доставлене до найближчого порту або +ремонтні роботи проводити на борту. У той самий час повинні бути +вирішені такі завдання: +перевезення до найближчого порту; +організація доступу до судна; +оцінка доцільності ремонту. +Рішення цієї проблеми полягає у створенні товариства порятунку +автономних та віддалено керованих суден, під егідою Міжнародної +морської організації. +Наявність людини на борту віддалено керованого судна вимагає +роботи професійного психолога з медичною освітою, вирішення пси- +хологічних проблем, таких як галюцинації, розвиток депресії, а також +інші порушення людського організму. +Також не можна забувати про такий аспект морської діяльності, +як піратство, який у різних формах існує з моменту зародження суд- +ноплавства. +У випадку фізичного захоплення центру дистанційного управлін- +ня повинна бути реалізована система передачі повноважень управ- +ління на резервно-керовані структури, розташовані в інших центрах. +Перехоплення суднового управління може здійснюватися на спеці- +ально відібраних цілях — суднах. Крім того, такі атаки можуть бути +замасковані як «піратська атака». Передача помилкових даних може +бути безпосередньо спрямована на захоплення управління судном, +але може побічно дозволити роботу судна на основі алгоритмів та не- +правильних рішень у центрі пульта дистанційного управління. +Особливості дизайну та експлуатації автономних та віддалено ке- +рованих суден вимагають: +– Впровадження суворих вимог до правових аспектів відносин +транспортних операцій. +– Використання сертифікованого обладнання та програмного за- +безпечення. +– Впровадження модульного принципу обладнання. +– Можливості «гарячої заміни» обладнання. +– Уніфікація органів управління [11]. + +273 +Але виробничі технології не стоять на місці, і багато іноземних +компаній не очікують створення та затвердження нормативної бази +для безпілотних суден та швидко розвиваються та створюють повну +модель автономних суден та самого автономного судна. Такими ком- +паніями є: +– Англійська Rolls-Royce Convice, яка разом з Finferries у грудні +2018 року, поблизу Турку, спеціально перетворені під автономний ре- +жим 53. 8-метрового типу порому «Falco». Проект називався SVAN +(Safer Vessel with Autonomous Navigation). Тести були успішними, по- +ром контролювався з командного пункту, розташованого за 50 км від +експерименту. +– Норвезька компанія Yara та Kongsberg Gruppen у жовтні 2017 р. +завершили розробку повністю електричної автономної вантажівки, +що називається Yara Birkeland. Як пише газета The Wall Street Journal +перший у світі автономний вантажний корабель Yara Birkeland було +введено в експлуатацію наприкінці 2018 року. Після спуску на воду +розробники тестували системи автопілотів приблизно півтора року. +Цей процес відбудеться в три етапи. На першому етапі судном управ- +ляє команда на борту. На другому етапі оператор дистанційно кон- +тролює тести, які здійснюються на маршруті довжиною 32.5 милі. +Наступний етап — електроход керується власним комп’ютером, ви- +користовуючи GPS та численні датчики, щоб визначити положення +інших морських об’єктів, а також для безпечного причалювання. Все +вищезгадане про безпілотні судна та їх випробування доводить, що +прогрес у розвитку безпілотних технологій не стоїть на місці, але з +розвитком будь-якої технології, особливо в галузі морського тран- +спорту, потрібно ретельно розробити нормативну базу. Але, на жаль, +про досконале опрацювання ще рано говорити. +Основною проблемою, яка вирішується для суден без екіпажів, +є дотримання вимог безпеки навігації та запобігання забруднен- +ню навколишнього середовища, а також відповідальність судно- +власників як частина використання безпілотних суден. В даний час +безпілотні морські дослідження MAS проходять в «комфортних» +умовах: +– тестування судноплавства дронів відбувається на достатній від- +стані від берега з впевненим, безперервним, безперебійним сегмен- +том зв’язку з безпілотним судном; +– за відсутності близькості до інших суден; +– якщо є хороша зона супутникового покриття; + +274 +– з повною відсутністю тіньових секторів для суднових РЛС; +– забезпечено безперебійну роботу АІС, GPS, гірокомпаса, лага, +ехолота, за винятком помилок у переданій інформації; +– за наявності достатніх орієнтирів, глибин, СНО можливо дуб- +лювати позиціонування суден у просторі; +– при низькій швидкості маневрування; +– з повною відсутністю складних гідрометеорологічних чинників +(штормовий вітер, хвилювання моря з високою бальністю, сильна те- +чія, наявність значного льоду, айсбергів, інородних вільно плаваючих +предметів з низьким коефіцієнтом відбиваючого сигналу). +Варто звернути увагу на ряд проблем, які в майбутньому виник- +нуть з суднами без екіпажу: +1) як боротьба за життєздатність судна без екіпажу у разі аварії +будь-якого виду (защемлення, зіткнення, пожежа, контроль води та +інше); +2) у випадку повного блок-ауто відмова всього джерела живлення, +включаючи резервні джерела живлення; хто може відремонтувати і за +який час; +3) дії безпілотника в піратських водах; +4) екстрена віддача якоря, хто буде бігти на бак, щоб віддати якір; +5) плавання в льодових умовах (в льоду не йдуть прямо). Потрібні +постійні маневри та часті реверси мають підтримувати безпечну від- +стань попереду рухомого судна, льодоколу, несподівано до відкритих +перешкод. +6) виникнення ситуації невизначеності при дотриманні правил +МППСС-72. Невизначеність є вираженою рисою морського тран- +спорту. З усією ретельністю вивчення питань навігації фактор не- +визначеності присутній і буде присутній навіть при вищому ступені +автоматизації. Таким чином, основні напрямки у сфері безпілотних +технологій на морському транспорті повинні розглядатися як про- +блема вирішення невизначеності сприйняття інформації під час роз- +бігу суден, котрі рухаються в складних умовах, у причалі, перегляду +правил для запобігання зіткнення та законодавчої бази у разі аварій- +ної ситуації. +На підставі вище викладеного розробка технології безекіпажного +судоводіння та його застосування ведеться багатьма країнами, орга- +нізаціями та компаніями, які здійснюють дослідження, технологічні +та транспортні проекти. Інтенсивні розробки ведуть як установи, так і +університети — Массачусетський інститут технології, Колумбійський + +275 +університет, Плімутський університет, Учоанський університет тех- +нологій та транснаціональні корпорації та класифікаційні суспіль- +ства. Взаємне використання технологічних проектів може дозволити +впровадженню у майбутньому повністю перейти до будівництва без- +екіпажних суден, а також значно розширює можливості для розвитку +суднобудівної промисловості. Детальне вивчення проектів у сфері +безекіпажного судноплавства дозволить створити техніко-економіч- +не обґрунтування будівництва таких суден та визначити необхідний +та остаточний набір технологій для їх реалізації. Телекомунікації тех- +нології, електронні датчики та системи, технологія електронної на- +вігації вже вводяться у секторі морської промисловості. Економічні +судна є найбільш складним технічним транспортом, в якому осо- +блива роль призначена для автоматичної системи управління. Най- +ближчим часом неможливо уявити цивільний флот без автономних +безекіпажних суден. +В роботі розглянуто, насамперед, регуляторні та правові аспек- +ти, але не можуть бути відкинуті технічні, пов’язані з описом та +аналізом існуючих проектів безекіпажних суден. Безекіпажні суд- +на відрізняються за ступенем обладнання засобами вимірювальної +техніки та устаткування. На безекіпажних суднах не існує ходового +містка, надбудови, житлових приміщень та системи життєдіяльнос- +ті екіпажу. +У травні 2018 року в рамках секретаріату Міжнародної морської +організації була створена міжгалузева цільова група на морських ав- +тономних поверхнях суден. На 99-й сесії Комітет морської безпеки +розпочав обговорення постійного регулювання сегмента автоном- +ного перевезення, включаючи людський фактор, систему безпеки, +взаємодію з портами, пілотною проводкою, ліквідацією наслідків +аварій та захисту морського середовища для кораблів різних рівнів +автономності. +Слід також зазначити, що в рамках єдиного морського європей- +ського проекту до 2025 року планується створити єдину «екосистему» +логістики автономної доставки. У той самий час проект реалізується +на принципах державно-приватного партнерства за участю провід- +них гравців морської промисловості: Wartsila, Rolls Royce, Abb, Meyer +Turku, Finnferries, Ericsson, Cargotec та ін. [12] +Дефіцит часу на прийняття рішення щодо забезпечення безпеки +судна призводить до необхідності виділення тільки тієї інформації, +яка потрібна для виконання основного завдання управління і при- + +276 +йняття рішень. Виникає проблема попереднього відбору та аналізу +інформації, необхідної для реалізації механізму логічного висновку +і вироблення практичних рекомендацій [13]. З такою проблемою +справляються інтелектуальні системи, розраховані на експлуатацію в +контексті певних невизначеностей протягом тривалого періоду часу. +Відзначається, що для того, щоб система відповідала інтелектуальній +автономії, вона повинна володіти однією або декількома наступними +можливостями: навчання; ситуаційна обізнаність; міркування; пла- +нування; людино-машинні інтерфейси; прийняття рішень; приве- +дення в дію. Під «автономним судном» розуміється — «морське судно +з датчиками, автоматизованою навігацією, руховими і допоміжними +системами, з логікою прийняття рішень для проходження по планам +місії, налаштуванням виконання місії і роботи без втручання лю- +дини», — представлено у звіті американського бюро судноплавства +(ABS) про автономні судна (Autonomous Vessels: ABS ’Classification +Perspective) за 2016 рік [14]. +Відповідно до звіту ABS про автономні судна (Autonomous Vessels: +ABS’ Classification Perspective) за 2016 рік існують такі рівні авто- +матизації систем [14]: людський контроль (human control), деякі +функції автоматизації (some functions automated), звичайні операції +автоматизації, людина готова взяти на себе відповідальність (normal +operations automated; human ready totake over), критичні функції без- +пеки автоматизації, людська присутність (safety-critical functions +automated; human present), повна автономія критичних функцій без- +пеки і моніторингу навколишнього середовища на час рейсу (full +autonomy of safety-critical functions and environmental monitoring for +duration of trip), повна автономія без доступних для людини інтер- +фейсів управління (full autonomy with no human-available control +interfaces). +В даний час безпілотні засоби — це концепт-проект, в якому увагу +зосереджено на інтегрованій сенсорній технології і попередженні зі- +ткнень. Основні елементи інтелектуальної системи, що використо- +вується, забезпечують управління безекіпажним судном: автономна +навігаційна система, система попередження зіткнень, система мо- +ніторингу та управління двигуном, автоматизовані системи шварту- +вання. +Швартовні операції суден (рисунок 1) входять до складу небез- +печних процесів судноплавства. Прогрес в безпеці швартування +суден досягається в результаті використання інноваційних техно- + +277 +логій. На багатьох причалах існує досвід роботи таких технологій. +Але статистика свідчить, що такі системи швартування ще не ді- +йшли до такої досконалості, щоб повністю виключити небезпечні +ситуації. + +Рис. 1. Застосування інноваційних технологій швартування суден +Міжнародна морська організація схвалила вимоги до безпеки +швартування суден та дизайну обладнання [10]. +Нові вимоги включатимуть оцінку повної лінії причалів, включаю- +чи новий режим технічного обслуговування та швартове обладнання. +На 102-му засіданні Комітету з питань безпеки моря Міжнародної +морської організації було прийнято пакет обов’язкових вимог, у тому +числі щодо безпеки еквівалентних операцій, повідомляє прес-реліз +Міжнародної морської організації. +На засіданні Міжнародної морської організації одна із прийнят- +них вимог пов’язана з причалами, що повинні і забезпечити захист +праці та безпечне пришвидшення суден, а також зменшити кількість +наслідків аварій, які відбуваються під час роботи. Можливо, що ре- +зультати цієї зустрічі матимуть значний вплив на проектування судна, +зокрема на пристрої швартовних лебідок та відповідного обладнання +на палубі. +В даний час інструкції SOLAS (II-2 / 3–8) вважаються правила- +ми для палубного обладнання, що використовується для причальних + +278 +операцій, шляхом визначення максимально допустимого наванта- +ження для кожної одиниці обладнання та оснащення. +Інструкції спрямовані на запобігання обмеженню доступу до ро- +бочої області та мінімізацію обмеження видимості пропорційної +зони, щоб уникнути впливу динамічних навантажень швартування +персоналу, що бере участь у причалюванні. +Це правило II-2 / 3–8 додає нові предмети до вимог дизайну. Спе- +ціальна інформація повинна бути включена в так званий план бук- +сирування та причалювання, описаний у нових інструкціях для про- +ектування Міжнародної морської організації 1/1620 «Рекомендації +щодо проектування причальних пристроїв та вибору відповідного +швартового обладнання та оснащення для безпечного причалюван- +ня». У той самий час затвердження плану не вимагається адміністра- +цією порту прапора. +Що стосується інспекції та технічного обслуговування, Комітет +прийняв нові положення для всіх суден, незалежно від розміру та +дати будівництва судна, вимагаючи перевірки обладнання причалу, +включаючи кабелі та мотузки. Перевірка Shridge зараз включає кіль- +кість, силу, розмір, довжину, характеристики та обмеження. Подаль- +ші стандарти містяться в новому посібнику MSC.1 / CHERC.1621 +«Рекомендації щодо інспекції та обслуговування вологого обладнан- +ня, включаючи швартування». +Вимоги до швартовних пристроїв є особливо актуальними для +конструкторів суден та суднобудівників, і їх слід обговорювати з клі- +єнтом-судновласником. Вимоги до перевірки технічного обслугову- +вання та заміни зіпсованого обладнання в основному важливі для +судновласників та операторів. +Поправки набирають чинності з 1 січня 2024 року. +Процес швартування можливо розділити на кроки: +1) підхід судна на бажану відстань до причалу з поворотом у пра- +вильному напрямку; +2) підхід судна за допомогою буксирів до певної позиції по відно- +шенню до причалу та утримування у цьому положенні під час подан- +ня швартування; +3) затягування судна до причалу за допомогою спеціального об- +ладнання [15]. Кожен з цих етапів причального процесу індивіду- +альний. +Захід судна в порт призначення, з точки зору складності навігації, +забезпечення радіоелектронного контролю та контролю інформацій- + +279 +ного навантаження, може бути диференційованим на ряд етапів, які +можна назвати фазами судна. Такий поділ дозволяє більш чітко ви- +сунути вимоги до точності визначення місця розташування судна у +порту, а також дозволить оцінити безпеку суднобудівництва та заходи +щодо зменшення впливу на можливі надзвичайні ситуації на кожно- +му етапі судноплавства. Таке розділення забезпечується в 1983 році +постановою Міжнародної морської організації A.529 (13), але це сто- +сується вузького аспекту судноплавства: точність розташування [15]. +У той же час безпека суднозаходу залежить від великої кількості фак- +торів. Виходячи з вищезазначеної практики суднових вод, можливо +окремо розібрати чотири етапи суднозаходу. +Перший етап суднозаходу. +Відповідно до Резолюції A.529 (13) «Компенсаційні стандарти» +рейс судна можна розділити на вхід до гавані та підходи до неї, а та- +кож воду, яка має обмеження маневру та інші води. Для цього поді- +лу майже всю відстань першого етапу суднозаходу відносить до етапу +«інших вод». Для цього місця шлях руху точність навігації не повинна +бути гіршою, ніж 4 % від відстані небезпеки, але не більше 4 морських +миль [15]. На цьому етапі рейсу говоримо про відстані до небезпеки, +що розраховуються десятками миль. Тоді порядок необхідної точнос- +ті є долі та одиниці миль. +Саме цей етап суднозаходу, як показують статистичні дані, харак- +теризується відносно низькою ймовірністю інцидентів та катастроф, +що пояснює вказаний знижений рівень запиту до точності визначен- +ня координат судна. +Слід зазначити, що перераховані параметри систем спостеріга- +ються в ідеальних умовах. Але на практиці існують особливості, які +обмежують можливості перелічених систем, такі як обмеження здат- +ності діапазону узбережних РЛС (± 75 м), наявності зон та «радіоті- +ні», а також екранування великим судном навколо розташованого +невеликого судна. +Аналіз зазначеної інформації, а також параметрів суднових наві- +гаційних інструментів дає можливість зробити висновок: у першій ін- +формаційній фазі суднозаходу перераховані засоби навігації, залежно +від їх ідеальної роботи, задовільно забезпечують необхідну точність +визначення розташування судна, що заходить у порт. +Другий етап суднозаходу. +Другий інформаційний етап суднозаходу відноситься до стадії +рейсу, визначеного в «стандартах оцінки» [15], як «вхід до гавані та + +280 +підходів до неї, а також воду, в якому свобода маневру обмежена». +Відповідно до [15], «вартість допустимої похибки місця залежить від +місцевих умов, а його визначення є функцією відповідних адміні- +страцій». +Зрозуміло, що в умовах обмеженого маневру підходу до воріт фар- +ватера потрібна більша точність місцезнаходження, ніж це було на +першому етапі. Ця заява є актуальною, оскільки періодично спосте- +рігаються навали суден на воротах фарватера. +Таким чином, з точки зору інформаційного модуля для визначен- +ня точності навігації на третьому етапі суднозаходу, як у другому, іс- +нуючі системи задовільно виконують свої функції, але в критичних +ситуаціях їх ненормального функціонування на судні необхідно мати +резерв для автономного визначення простору з точністю щонаймен- +ше 10–15 л. +Четверта фаза суднозаходу. +Ця фаза характеризує причальний процес швартування судна. +Особливість цієї фази носія судна полягає в тому, що підхід судна до +причалу здійснюється, як правило, коли двигун швартовного судна +вимкнено, що призводить до повної практично неконтрольованої +поведінки. Тому завдання безаварійного швартування багато в чому +визначається оператором, який контролює технологію швартування +[16; 17]. +Більшість надзвичайних ситуацій у причалі пояснюються від- +сутністю технічних засобів об’єктивного контролю підходу судна до +пристані. Аналізуючи навали суден на причали та їх об’єктах, можна +стверджувати, що існує точне знання не тільки розташування суд- +на щодо причалу, а й облік впливу найбільш складного компонента +будь-якого технологічного процесу. +Зростаючі вимоги до безпеки навігації на кожному з етапів судно- +заходу висуваються не тільки для покращення технічного обладнання +суден, а передусім зміцнення технічного контролю за діями опера- +тора [18; 19]. Тому Міжнародна морська організація та адміністрація +морських портів світу в останні роки здійснюють активну роботу зі +створення [20]: +– розділення шляхів суднопроходів в місцях з інтенсивним ру- +хом; +– зон з обов’язковими або добровільними радіоповідомленнями +між суднами, коли вони наближаються один до одного або прохо- +дять; + +281 +– удосконалення системи управління рухом суден (СУРС) у пор- +тах та підходів до них з поступовим збільшенням автоматизації конт- +ролю за якістю судноплавства, доставки в морських районах; +– забезпечення засобами високоточного розташування суден у +прибережних водах, використовуючи контрольні та коригувальні ди- +ференціальні станції глобальних навігаційних супутникових систем +(ДГНСС) ГЛОНАСС та GPS-типу; +– суцільного радіочастотного покриття (виключити тіньові зони) +прибережні смуги морських територій — глобальної морської кому- +нікаційної системи та забезпечення безпеки (ГМСЗБ) з цілодобовим +надійним УКВ-зв’язком; +– супутникової морської системи зв’язку ІНМАРСАТ, що забез- +печує глобальне та ефективне спілкування з суднами, розташовани- +ми в будь-якій частині світу. +Як частина роботи, проведеної в Міжнародній морській організа- +ції, щоб переглянути главу 5 «Навігаційна безпека» Конвенції про за- +хист людського життя на морі (SOLAS), передбачається найближчим +часом вставити принципово нову автоматичну інформацію (іденти- +фікацію) системи (AIS) на морському флоті. Перша версія AIS, вве- +дена у всьому світі, виконує три основні функції: +– автообмін навігаційними даними між суднами, коли необхідна +розбіжність у морі; +– передача даних про судно та його вантаж до прибережних по- +слуг, коли воно плаває в контрольованих областях, з обов’язковими +повідомленнями; +– перенесення навігаційних даних з судна до прибережних СУДС, +забезпечуючи більш точну та надійну проводку в зоні дії системи. +Таким чином, автоматична інформаційна система — це морська +навігаційна система, в якій взаємний автоматизований інформацій- +ний радіообмін використовується як між суднами, так і між суднами +та прибережними службами, під час яких вони передають інформа- +цію про позивний та назву кожного судна (для їх ідентифікації), їх +координати, параметри (розміри, навантаження, осадка тощо), цілі +рейсу, параметри руху (курс, швидкість тощо) для вирішення про- +блем попередження зіткнень суден, моніторингу дотримання режиму +плавання та загального моніторингу статусу безпеки в контрольова- +ному морському районі. +Серед найважливіших компонентів розвитку мережі АІС слід +розглядати введення служби диференціальної підсистеми глобаль- + +282 +них навігаційних супутникових систем (ДГНСС) типу американ- +ського GPS, додавання яких діфпідсістемами вирішує пробле- +му високоточного визначення місця судна з підводною точністю +(d5 M). +Таким чином, незважаючи на широке впровадження високоточ- +них навігаційних систем (ГНСС ГЛОНАСС, GPS), а також засобів +автоматичної ідентифікації суден (АІС), проблема забезпечення без- +пеки швартування залишається на останньому етапі суднозаходу [16]. +Четвертий етап швартування є найскладнішим та відповідальним, що +вимагає безперервного радіоелектронного контролю процесу набли- +ження судна до причалу, а вимірювання до причалу потрібно визна- +чити з точністю долі метра. +Аналіз літератури показує, що основний резерв вдосконален- +ня потребує вдосконалення інтелектуально-інформаційних систем +швартування різних типів. Потрібно враховувати, що кожна шварто- +ва робота має свої особливості відповідно до погодних, кліматичних, +структурних особливостей суден [21], незалежно від того, яка ситуа- +ція, надзвичайна ситуація або вантажна робота: +– швартування до судна, що лежить у дрейфі; +– швартування до судна, що рухається; +– швартування до судна, що стоїть на якорі; +– швартування кормою до причалу в портах. +Автоматизовані системи швартування раціоналізують експлу- +атацію причалу і забезпечують максимальну віддачу роботи порту. +Швартування в автоматичному режимі гарантує надійне кріплення +судна і надає переваги з точки зору технічної та екологічної безпе- +ки. Функції сигналізації таких систем використовуються в режимі +реального часу. +Для проникнення в сутність автоматизованих процесів шварту- +вання і стикування виділяють основні автоматизовані пристрої швар- +тування і стикування: магнітний; лазерний і вакуумний. +Якщо аналізувати швартувальні операції, побачимо, що прийняті +заходи, хоча зменшують рівень аварійності, але проблема безпеки за- +лишається актуальною завдяки багатьом факторам, включаючи слаб- +ке інформування судноводія про поточні параметри швартування. +Для покращення управління та прийняття належного рішення судно- +водію потрібні спеціальні технічні засоби швартування, що оперують +даними вимірювань реальних параметрів розташування, швартуваль- +ного судна за допомогою системи, яка отримує та обробляє поточну + +283 +інформацію про зміну цих параметрів, що видає оператор судноводію +в зоровій формі небезпечної ситуації та що сигналізує звуковим сиг- +налом, кольоровим сигналом. Технічним варіантом такого рішення +може бути система аналізу швартування та контролю над підходом +судна до причалу з попередженням поточного середовища — інди- +катор безпеки, наприклад, який є технічним інструментом, який +виконує прийом, обробку та зберігання інформації, необхідної для +швартування. Відповідно до використання розробленої прогностич- +ної математичної моделі та програмного забезпечення цей пристрій +повинен відображати результати обробки даних на екрані індикато- +ра, як у формі ймовірнісної картини підходу судна до причалу, так і +рекомендації судноводію у формі резервного часу та прогнозованої +відстані. Ці вимоги на вищому технічному рівні застосовуються до +безекіпажного судноплавства. +Розглянемо характеристики систем швартування, які прийняті +для безекіпажного судноплавства: +Магнітна система автоматичного швартування (рисунок 2) конт- +ролює процес за комплексом динамічних впливів. Система склада- +ється зі здвоєних мертвих якорів, носових і кормових, оснащених +магнітними подушками для надійного і міцного кріплення до будь- +якого корпусу, плоского або вигнутого, пофарбованого або покрито- +го корозією. +Подушки можуть пересуватися за корпусом з урахуванням змін по +висоті. Магнітна система має жорсткі обмеження: дорожнеча експлу- +атації (енергоспоживання, професійне обслуговування), додаткове +навантаження на корпус (вітри можуть деформувати борт) — подуш- +ки потрібно ставити в районі шпангоутів, що означає пристосовува- +тися під конкретний корпус. У надійності є сумніви, оскільки трос, +що лопнув, замінюється, а подушка, що вийшла з ладу, — не має замі- +ни. Дана система знайшла своє застосування на швидкому прийнятті +рішення судном — пороми. Є заборона використання системи авто- +матичного навантаження на танкерах. Така заборона випливає з того, +що система при поздовжньому «протягуванні» корпусу вздовж при- +чалу, під дією хвилі або проходить поруч судна, змінює навантаження +в шпринг і поздовжніх з системою контролю натягу кінців. Така дія +призводить до деформації корпусу. +Застосування технології вакууму в швартових операціях і її роз- +робки ведуть багато компаній, які здійснюють науково-дослідні, тех- +нологічні системи швартування. + +284 + +Рис. 2. Конструкція системи швартування «The intelligent Dock Locking» +Вакуумні системи автоматичного швартування (рисунок 3) для +утримання судна біля причалу замість канатів використовують ва- +куумні подушки. У кожної подушки є своє контрольоване робоче +навантаження, яке може забезпечити надійне фізичне з’єднання +судна з причалом. Вакуумні подушки випробовуються і класифіку- +ються під наглядом міжнародного класифікаційного товариства Det +Norske Veritas (DNV), результати якого суміщені з сучасними триви- +мірними апаратними засобами, показують діапазон ходів і пружну +еластичність автоматичних систем на рівні швартування за допомо- +гою канатів. Інформація про навантажені утримання надходить від +вимірювання рівнів вакууму і поперечних сил в носовій і кормовій +тумбах. Оскільки вакуумна система може тримати судно ближче до +причальної стіни, ніж перехрещений канат, ця система має причаль- +ну продуктивність. Маючи інформацію про всі умови швартування +в режимі реального часу, оператор повністю контролює швартуваль- +ний стан судна. + +ManipulatorArmHydraulics +HydraulicsPowerUnit +MagnetPadsincluding +HydraulicCyiinder +PadEyeConnoction +Framo285 + +Рис. 3. Вакуумна система швартування «Auto Moor» +Такі системи високоефективні. Тисячоліття для швартування су- +ден використовують канати, але протягом багатьох років процедура +не стає менш небезпечною. +Автоматичні вакуумні швартові системи вирішують проблему на- +тиском однієї кнопки. І менше ніж за 1/4 хвилини дозволяє спрацю- +вати. Такі системи тримають судна всіх розмірів у одному місці в пор- +тах, де присутні брижі та довгі хвилі. +Лазерна система швартування (рисунок 4) яка відноситься до кла- +су інструментальних систем, безперервно веде розрахунок дальності +до судна кожним далекоміром. На основі отриманих даних система +обрисовує візуальне положення судна з розрахунковим кутом щодо +пірсу. Крім дальності і кута, система розраховує швидкість зближення +або віддалення з пірсом як носа, так і корми. У разі наближення суд- +на на близьку відстань з перевищенням зазначених в налаштуваннях +швидкостей, відразу сигналізує про це через індикацію в інтерфейсі, +а також через сирену на пірсі. +Оцінюючи характеристики систем швартування, розробники без- +екіпажних судів схильні до використання лазерних систем. Осно- +вною особливістю другого етапу швартування є зближення судна з +причалом. При швартуванні часто неминучий контакт судна з при- + +TRELLEBORG +01286 +чалом з ненулевою швидкістю, який називається навалом. Класифі- +кують навали як навмисні, так і випадкові, що виникають при кон- +такті судна з причалом, іншим стаціонарним об’єктом або з іншим +судном, розташованим на відстані або паркуванні [15]. Оскільки роз- +міри судна фіксуються, єдиним способом уникнути навалу судна на +причалі є ретельне вимірювання швидкості підходу судна та відстані +до причалу. Розміщення судна до причалу, як правило, здійснюєть- +ся за допомогою буксирів [15; 16]. З початку етапу зближення вони +розгортають судно правою стороною паралельно причалу. Завдання +буксирів включає підводку судна близько до причалу і тримання його +в цій позиції, доки не будуть заведені та обтягнуті швартові. Поста- +новка судна до причалу є небезпечною технологічною операцією, яка +вимагає кваліфікованих та своєчасних дій судноводія, який управляє +технічними засобами судноводіння, доставки та буксирів при збли- +женні судна з причалом [15; 16]. + +Рис. 4. Концепція лазерної системи швартування +Відмітна характеристика лазерної системи — сканування лазерно- +го променя у вертикальній площині і отримання профілю відстаней +з подальшою обробкою і визначенням відстані до причалу чи іншого +об’єкта. Якщо аналізувати особливості лазерної дальнометрії, вона +покаже, що експлуатація дальнометрії на причалах виявила свою на- + +LEO screen +Wind speed, wind direction +Monitor screen +Temperature +Distance (m) +Distance (m +26.8 +26.9 +sis +Speed +19 +19 +Acouisitoncontrolcabinet +Laser +senso +DCd +computer +Sea level, flow rate +Quick release hook287 +дійність, легкість експлуатації, мінімум технічного обслуговування. +Однак ця система не може вирішити всі проблеми порушення пра- +вил, які найчастіше встановлюються адміністрацією порту під час +швартування. Тому необхідно більш глибоко розглянути можливість +інформаційної підтримки причального процесу. Аналіз показує, що +для забезпечення безпеки швартування використовується не весь ін- +формаційний потенціал цих систем. Виявилося, що лазерна система +швартування, що формується програмним забезпеченням для лазер- +ної системи, дозволяє розширити інформаційну підтримку процесу +швартування. Така система працює на підставі відстані з двох датчи- +ків, розраховує швидкість і прискорення щодо цього об’єкта, а також +можливо і визначення центру обертання судна. За рахунок застосу- +вання в пристрої датчика кута нахилу при розрахунках будуть ком- +пенсуватися качка корабля і різні розмірені параметри суден і при- +чалів. У цих системах виробляються точні вимірювання в реальному +часі, дані про відстані і швидкості судна. Інформаційні потоки даних +за параметрами зближення судна з причалом, виміряні лазерною +швартовою системою великотоннажних суден (ЛСШКС), переда- +ється до телеметричного пристрою за допомогою інтерфейсу модуля, +призначеного для поєднання цих технічних засобів. Через переда- +вальну антену поточна інформація надходить у радіопристрій, розта- +шований на судні. Перетворена для подальшої обробки інформація +через інтерфейс надходить у блок обчислення, де параметри розра- +ховуються протягом всього швартування судна. Індикатор забезпечує +такі режими візуалізації: +1. Відображає розраховану ймовірність перевищення швидкості +судна під час контакту з причалом. +2. Хронологія зближення судна з причалом. +3. Комбінований режим відображення фактичної швидкості суд- +на та ймовірність перевищення швидкості на момент контакту з +причалом. +4. Автоматичний режим включення аналізу поточної ситуації +з прогнозними оцінками підходу судна до причалу. Найбільш інфор- +мативним є автоматичний режим включення аналізу поточної ситуа- +ції з передбачуваними оцінками підходу судна до причалу, що дозво- +ляє попередити судноводія про те, яка ситуація може виникнути під +час першого дотику судна до причалу. +«Trelleborg», «Strainstall», «A. & Marine (Thai) Co., Ltd.» і +«MARIMATECH» є ключовими розробниками автоматизованих + +288 +систем швартування в світі. Система «Smart Dock», розроблена +«Trelleborg», складається з двох лазерних датчиків, контролера і +центрального персонального комп’ютера. Дані про процес стиков- +ки, а також аварійні сигнали при досягненні ризику критичних меж +подаються декількома способами, в тому числі за допомогою вели- +кого екрану на причалі. Персональний комп’ютер в центрі управ- +ління реєструє дані і забезпечує графічне представлення всього +процесу [22]. +Система швартування «MARIMATECH» використовує два лазе- +ри, які встановлені на пристані і міряють відстань до сторони набли- +ження суден, далі обчислює швидкість і кут нахилу судна. Концепція +системи «MARIMATECH» заснована на дистанційній передачі да- +них. Дані відображаються на встановленому на причалі цифровому +великому екрані, бездротових пристроях, таких як портативні пей- +джери або кишенькові персональні комп’ютери, на комп’ютерних +моніторах диспетчерської. +Лазерна система швартування «Dock Aler» від «Strainstall» ви- +користовує блоки безпечного для очей лазера, встановлені по оби- +дві сторони від головки причалу, для вимірювання відстані від носа +до корми щодо причалу, а також забезпечує швидкість і кут нахилу +судна до причалу. Дані від цих лазерів надходять в центральну сис- +тему управління, де вони можуть відображатися в диспетчерській, і +передаватися переносним пейджерам, кишеньковим персональним +комп’ютером і / або дисплеєм [23]. +Висновки: Світові концерни, дослідницькі компанії роблять спро- +би для втілення концепції безекіпажного судноводіння в реальність. +Для цього необхідно поєднати безаварійну експлуатацію судна та за- +конів держави прапора, рішення портових органів загальної міжна- +родної юрисдикції. Застосовувані інновації, що використовуються в +безекіпажному судноводінні, дали привід для дискусій в журналах, +на конференціях і семінарах з розвитку судноплавства. У судноплав- +стві одна з фундаментальних змін — це реалізація концепт-проектів +безекіпажного судноводіння. Цей напрямок включає одну з пере- +ваг — підвищення безпеки судноводіння за рахунок використання +інновацій. +У роботі представлено огляд рівнів управління автономними сис- +темами в судноплавстві. Наголос зроблено на системи швартування. +Наведено характеристики вакуумних, лазерних, магнітних систем. +Безекіпажне судноводіння схиляється до використання систем ла- + +289 +зерного швартування за рахунок розширення можливостей інформа- +ційного забезпечення швартування із застосуванням системи, яка ви- +дає рекомендації у вигляді резервного часу і прогнозованої дистанції, +що знижує ймовірність помилок. Як підсумок — безпека швартуван- +ня підвищується. + +Рис. 5. Стикувальна система «Dock Aler» [23] +СПИСОК ВИКОРИСТАНОЇ ЛІТЕРАТУРИ +1. Pipitsoulis C. The EU eMaritime initiative — Single Window, with a view to the +near future. In Logious Conference. Rotterdam, 2010. +2. Пунченко Н. О. Праксеологія безекіпажних засобів водного транспор- +ту, ризики автономни систем. Інформаційні технології та комп’ютерне +моделювання ІТКМ-2021: міжнародна науково-практична конферен- +ція. 5–10 липня 2021 року, Івано-Франківськ. Івано-Франківськ, 2020. +С. 35–36. +3. Strelbitskyi V., Punchenko N., Tsyra O. Shaping the future of the marine in- +dustry as a condition for adaptation in an innovative society. Інтелектуальні +системи та інформаційні технології ISIT-2021. 13–19 вересня 2021 року +Одеса. Одеса, 2021. С. 116 –120. ISBN 978–617–7711–43–7. +4. Медународная конвенция по охране человеческой жизни на море, SOLAS +74/88. СПБ ЗАО ЦНИИМФ, 1996. 720 с. +5. 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Статистическое исследование распределения вре- +менной базы циклов регулирования скорости швартовки вероятностной +модели отказа системы «человек — машина». Сборник научных трудов. +Новороссийск: МГА имени адмирала Ф. Ф. Ушакова, 2007. Вып. 12. +С. 94–97. +20. Росторгуева Н. Ю., Юсупов Л. Н., Демьянов В. В. Компьютерное моде- +лирование аварийной ситуации при швартовке судна в условиях дестаби- +лизирующих возмущений. Сборник научных трудов. Новороссийск: МГА +имени адмирала Ф. Ф. Ушакова, 2007. Вып. 12. С. 92–94. +21. Бурханов М. В., Ермолаев Г. Г. и др. Справочник капитана дальнего пла- +вания. М.: Транспорт, 1988. 248 с. +22. SmartDock® Laser Docking Aid System [Електронний ресурс]. URL: http:// +www.trelleborg.com/en/marinesystems/products--solutions--and--services/ +docking--and--mooring/docking--aid--system/smart--dock--laser. +(дата +обращения: 19.07.2021). +23. Jetty monitoring and management systems [Електронний ресурс]. URL:http:// +www.strainstall.com/files/9214/9693/6079/43917_James_Fisher_Jetty_Moni- +toring_V1_WEB. pdf (дата обращения: 25.07.2021). +АВТОМАТИЧНИЙ СИНТЕЗ МЕРЕЖ ПЕТРІ ПРИ РОЗРОБЦІ +АЛГОРИТМІВ ЛОГІЧНОГО УПРАВЛІННЯ +Гурський О. О. +У роботі розглядається актуальна задача, пов’язана з розробкою мето- +дів автоматичного синтезу мереж Петрі. Важливість розробки цих методів +обумовлена розвитком інтелектуальних систем, що забезпечують автома- +тизацію трудомістких процесів. +Запропоновано принцип автоматичного синтезу мереж Петрі та певних +алгоритмів логічного управління на основі функціонування штучної нейрон- +ної мережі. Представлений математичний опис методу зміни коефіцієнтів +міжнейронних зв’язків мережі при синтезі мереж Петрі. +У програмному середовищі Matlab/Simulink 2012a були проведені експе- +рименти, пов’язані зі спільним функціонуванням штучної нейронної мережі +і мереж Петрі. Функціонування мереж Петрі в середовищі Matlab/Simulink +було представлено за допомогою Statflow діаграм. У результаті експери- +ментів були отримані часові характеристики функціонування штучної не- +йронної мережі, яка забезпечує композицію мереж Петрі. На основі часових + +292 +характеристик була встановлена принципова придатність застосування +штучної нейронної мережі для забезпечення автоматичної композиції мереж +Петрі. +В результаті було вирішено задачу, яка пов’язана з розробкою системи +спільного функціонування нейронної мережі і мереж Петрі для формування +алгоритмів та послідовних обчислень. Тим самим одержали подальший роз- +виток методика автоматичного синтезу мереж Петрі та методика роз- +робки певних алгоритмів на основі функціонування нейронної мережі. +The important task was solved during the scientific research related to the de- +velopment of the methods for automatic synthesis of Petri nets. The importance of +development of these methods is due to the evolution of intelligent systems. These +systems provide the automation of labor intensive processes. +The principle of automatic synthesis of Petri nets and the implementation of cer- +tain algorithms for tuning complex control systems based on the functioning of an +artificial neural network are proposed. The mathematical description of the method +for changing the coefficients in neural connections of network in the synthesis of Petri +nets is presented. +The experiments were conducted in the Matlab\Simulink 2012a environment. +These experiments were bound to the joint functioning of an artificial neural network +and Petri nets. The functioning of Petri nets was presented in the Matlab \ Simulink +environment using Statflow diagrams. +As a result of the experiments we have obtained the temporal characteristics of +the functioning of artificial neural network providing the composition of Petri nets. +The fundamental suitability of using artificial neural network to provide the auto- +matic composition of Petri nets was determined on the basis of analysis of temporal +characteristics. +The problem linked to the development of system for the joint functioning of neu- +ral network and Petri nets for the formation of algorithms and sequential calcula- +tions was solved in this work. Thus the method of automatic synthesis of Petri nets +and the method of developing of the certain algorithms based on the functioning of a +neural network were further developed. +Мережі Петрі як прикладний математичний апарат досить відомі +в області моделювання і аналізу дискретних динамічних або логіко- +динамічних систем. Також мережі Петрі відомі як форми представ- +лення паралельних алгоритмів і обчислень [1]. +Актуальність розробки принципів автоматичного синтезу мереж +Петрі лежить в області автоматизації процесу розробки алгоритмів +логічного управління. Як приклад варто відзначити так звану задачу +про «розумну мурашку», яка представлена в роботах [2; 3]. Мураха за +допомогою проб та помилок, мутації будує автомат своєї поведінки. +Але безсумнівно, що процес синтезу алгоритму носить інтелектуаль- + +293 +ний характер, в даному випадку можливо задіяти відповідну інтелек- +туальну технологію, пов’язану зі штучними нейронними мережами і +їх алгоритмами навчання [4]. +Таким чином, нами вирішується задача, пов’язана з розробкою +принципів синтезу алгоритмів і відповідних композицій мереж Петрі +на основі певної інтелектуальної технології. +У роботі представлено етап розвитку певної інтелектуальної сис- +теми до застосування штучної нейронної мережі та алгоритми на- +строювання штучних нейронних мереж, пов’язаних з автоматичним +синтезом мереж Петрі. +Відомо, що можливість автоматичного синтезу та існування ме- +тодів автоматичної побудови мереж Петри відзначалися ще в роботі +Джеймса Пітерсона [5]. З того часу з’явився ряд наукових публіка- +цій, пов’язаних з автоматичною генерацією і композицією мереж +Петрі, у яких відображаються особливості побудови мереж Петрі, +засновані на певних методах [6–9]. Аналогічно з’явилася робо- +та [10], у якій автоматичний синтез мереж Петрі здійснюється на +основі методу перевірки досяжності дискретно-безперервних мереж +[11; 12]. Якщо метод перевірки досяжності деякого стану в просторі +змінних пов’язаний з перетворенням дискретно-безперервної мере- +жі (ДБ-мережі) до одного переходу (елемента мережі Петрі), то при +автоматичному синтезі мережі Петрі процес зворотний, з одного +переходу перетворюється мережа Петрі, яка представляє досяжність +деякого стану гібридної системи (з керованою структурою — СКС) +[13; 14]. +Досяжність стану СКС можна забезпечити при наявності відпо- +відного алгоритму логічного управління. Такий алгоритм дозволить +реалізувати k-процес функціонування СКС ∑I+1. У даному випадку +повинна існувати послідовність запусків переходів ДБ-мережі, що +представляє модель системи. Таким чином, засоби ДБ-мереж дозво- +ляють досліджувати досяжність системи на основі правил редукції +мережі, а правила редукції мережі і методи перевірки досяжності віді- +грають важливу роль у розробці формуючого автомата, синтезуючого +мережу Петрі. +Далі розглянемо формування алгоритмів на базі методу перевірки +досяжності ДБ-мереж. +Формування алгоритмів на базі методів перевірки досяжності дис- +кретно-безперервних мереж. Перевірка досяжності системи шля- +хом редукції безперервної і дискретної частин ДБ-мережі полягає + +294 +в «згортці» мережі за певними правилами до макропереходу. Таким +чином, при формуванні алгоритму дискретну мережу Петрі також +можна розгорнути — сформувати аналогічно, як згорнути до макро- +переходу. +Для формування мережі Петрі, що представляє алгоритм логічно- +го управління, були виділені такі правила формування матриці інци- +дентності W: +–  рядок повинен починатися з 0 або +1 і значення в рядках повин- +ні чергуватися — 0, +1, 0, -1, 0 і т. д.; +–  поява хоча б однієї +1 у стовпці повинна супроводжуватися по- +явою хоча б однієї -1 у тому ж стовпці; +–  у рядку не може йти підряд дві та більше +1 або -1 навіть через +нулі; +–  для виключення формування занадто складних алгоритмів в +одному рядку не може бути більше двох пар +1, -1. +Фрагмент алгоритму формування матриці інцидентності згідно з +вищенаведеними правилами представлений у вигляді Stateflow діа- +грами на рисунку 1. З рисунка 1 видно, що автомат представлений +паралельними станами StateC4, StateC5, StateC6 … StateCN, де N — +кількість рядків формованої матриці інцидентності. Перехід з підста- +ну State19 або State24 у підстани State20 або State25, тобто поява –1, +супроводжується переходом з підстану State22 або State26 у підстани +State23 або State27 (появою +1 у тому ж стовпці). +Слід зазначити, що перехід зі State19 або State24 в State20 або +State25 може супроводжуватися залежно від умови data01> -10 з ви- +тримкою за часом або без умови. У цьому випадку формується мере- +жа Петрі, у якій мають місце переходи з наступними умовами спра- +цьовування: +0 +( ): ( +) +1& +& +i +j +i +j +k +p +I t +p +J +g +t +t +∀ +∈ +µ += +< +< +, +( ): ( +) +1& +i +j +i +k +p +I t +p +t +t +∀ +∈ +µ += +< +, +де μ(pi) — маркування вхідних позицій переходу tj; g — граничне зна- +чення J0j деякого критерію якості роботи системи; tk — час витримки +по спрацьовуванню переходу. +Переходи з різними умовами спрацьовування вибираються за- +лежно від значення сигналу формування алгоритму data14 або data15 +і т. д. Сигнали формування алгоритму V1 …. Vn відіграють важливу +роль у визначенні динаміки станів автомата формування матри- + +295 +ці інцидентності мережі Петрі. Поява тієї або іншої одиниці +1 +реалізується залежно від значення сигналів V1 …. Vn. Наприклад, +перехід зі стану State22 в State23 може здійснюватися за умовою +[data24>0.5&data15>2.5], де data24 — локальна змінна Stateflow-діа- +грами, а data15 — значення сигналу V1. + +Рис. 1. Stateflow-діаграма, що представляє автомат формування матриці ін- +цидентності (зв’язків між елементами мережі Петрі) +Таким чином, дана Stateflow-діаграма здатна представляти вели- +ку кількість усіляких алгоритмів, навіть можливо непередбачуваних +експертом. Створення алгоритму визначається залежно від сигналів +V1 …. Vn, а ці сигнали можливо коректувати, якщо алгоритм є неза- +довільним. +Як показано на рисунку 2, залежно від установлених сигналів +V1 …. Vn і за значеннями показників — J01, J02, J03 автомат формування + +StateC4 +after(2000.tick +[data28>0.5&data14≤0.9] +[data02>-10] +[data14<0.9] +State 18 +State19 +State 20 +State 21 +State 17 +after(50,tick) +data4=0; +data4= -1; +after(50,tick) +data4=0; +data4=0; +data4=1; +exitdata24=1; +exit:data24=0; +[data14>0.9] +[data22>0.5&data14≤0.9] +after(2000.tick) +StateC5 +after(2000,tick) +[data26>0.5&data15<2.2] +[data02>-10] +[data15>0.5] +State 23 +State: 24 +State 25 +State 31 +State 22 +after(50,tick) +data5=0; +data4= -1, +after(50,tick) +data5=1; +data5=0; +data5=0; +exit:data25=1; +exit:data25=0; +[data15<0.5] +[data22>0.5&data15<2.2] +after(2000,tick) +[data240.5&data15<2.5] +StateC6 +after(2000,tick) +[data25>0.5&data16<2.2] +[data02>-10] +[data16>1.2] +State 27 +State:28 +State 29 +State 30 +State 26 +[data15<0.5] +after(50.tick) +data6= -1, +after(50,tick) +data6=1; +data6=0; +data6=0; +data6=0; +exitdata26=1; +exitdata26=0; +[data16<1.2] +[data25>0.5&data16<1.2] +after(2000,tick)296 +матриці інцидентності виробляє послідовність значень, з яких скла- +дається матриця інцидентності мережі Петрі. + +Рис. 2. Структурна схема, що відображає модель формування мережі Петрі +Однак виключення експерта в побудові мережі Петрі та у визна- +ченні деякого алгоритму управління веде до того, що представляється +відсутність прикладного характеру синтезованої мережі Петрі. У та- +кому випадку в роботі [15] була запропонована автоматична компо- +зиція мережі Петрі на базі функціонування нейронної мережі, яка +представляє інтелектуальну технологію у визначенні деякого алго- +ритму логічного управління. +Надалі модуль визначення сигналів V1 …. Vn буде представляти- +ся нейронною мережею, а Stateflow-діаграми показані на рисунку 1, +можуть бути представлені відповідними синхронно функціонуючими +мережами Петрі. +Формування алгоритмів на базі функціонування штучної нейронної +мережі. Таким чином, синтез мережі Петрі на основі функціонуван- +ня штучної нейронної мережі становить область формування й авто- +матичного синтезу мереж Петрі [5; 8]. Як показано на рисунку 3, у +цьому випадку нейронна мережа взаємодіє на принципах зворотного +зв’язку із синхронно функціонуючими мережами Петрі. Із цих син- +хронно функціонуючих мереж можливо сформувати композицію, +яка буде відображати певний алгоритм дій, реалізованих штучною +нейронною мережею. Матриця коефіцієнтів міжнейронних з’єднань +вихідного шару нейронної мережі має певну аналогію з матрицею ін- +цидентності мережі Петрі. Таким чином, нейронна мережа генерує + +ABToMaTopMyBaHHMaTpML +MoAynbMepekeTpi +iHUMAeHTHOCTi +Step8 ++fata1i +tp1 +Step7 +d=t=12 +l=t=1 +Outz +tp2 +u(o) +Step8 +Hd=t=13 +d=ts2 +tp3 +n.3 +Out3 +u(og) +Step5 +d=t=14 +dst=3 +In.4 +Out4 +data15 +tp4 +μ(P4/ +Step4 +l=t=4 +Out5 +Step3 +data16 +tp5 +μ(Ds) +Step2 +d=t=17 +d=t=5 +Qut? +μ(Pg) +tp6 +Step1 +d=t=18 +d=t= +1- 7 +Out7 +MoAynb BM3HayeHHAcWrHaniB +tp7 +u(p) +Step +d=t=01 +d=t=7 +n8 +Quts +tp8 +u(pg) +cbopMyBaHHanropMTMy +d=t=02 +datasl +ns +Qut? +tata03 +Chart3 +n10 +Out10 b +Subsysteme +01, +202 +J03297 +вихідні сигнали, аналогічні матриці інцидентності синтезованої ме- +режі Петри. + +Рис. 3. Схема синтезу штучної нейронної мережі і мереж Петрі при форму- +ванні відповідних алгоритмів логічного управління в системі, w11,… wnj — ко- +ефіцієнти міжнейронних з’єднань; t7,…t12 — дискретно-безперервні переходи, +що забезпечують зв’язок між штучною нейронною мережею і мережами Петрі +Функціонування мережі Петри можна описати рівнянням: +1 +1 +| +| +k +k +k +M +M +A U +− +− += ++ +⋅ +, +де +0 +| ( +),.... ( +) |T +k +n +M +p +p += µ +µ + — вектор маркування мережі Петрі на k-му +кроці; +1 +k +M − — вектор маркування мережі Петрі на k–1 кроці; | +| +A — +матриця інцидентності, яка визначає взаємозв’язок позицій і пере- +ходів у мережі; +1 +k +U +− — управляючий вектор. +При цьому для даного випадку, якщо ( +) +1 +ip +µ += , де i=1…n, то зміню- +ється значення відповідного параметра, наприклад, при настроюван- +ні системи. Згідно зі схемою, представленою на рисунку 3, нейронна +мережа представляє частину виразу +1 +| +| +k +A U +− +⋅ + та генерує матрицю ін- +цидентності | +| +A синтезованої мережі Петрі. +Якщо певний алгоритм дій при функціонувані деякої системи не- +задовільний, то треба указати, на якому переході мережі Петрі була +виявлена помилка в системі. Це необхідно для перенастроювання +ней ронної мережі. +Такий принцип автоматичного синтезу мереж Петрі неодноразово +розглядався у наукових роботах [15–17], у яких показані різні експе- + +W11 +10 +S +W12 +M +13 +Wnj +n +10 +WTyyHa HeИpoHa MepeKa +/.Artificial neural networks +Mepexi eTpi /Petri Nets/298 +рименти для підтвердження принципової придатності такого методу +формування певних алгоритмів. +Синтез мереж Петрі може бути заснований на композиції і деком- +позиції мереж Петрі, тому що будь-яка мережа Петрі може складатися +з однотипних функціональних підмереж [18]. Як показано на рисунку +4, при декомпозиції мережі Петрі N1 можна виділити функціональ- +ні підмережі, які виконують різні логічні операції (АБО, І, операцію +умовного переходу). + +Рис. 4. Декомпозиція мережі Петрі N на функціональні підмережі N1, N2, N3 +При реалізації зв’язків між функціональними підмережами фор- +мується мережа Петрі яка представляє певний алгоритм логічного +управління. У відомих роботах синтез мереж Петрі реалізуєтся на +основі композицій і декомпозицій певних функціональних підмереж +[18; 19]. +Однак такі функціональні підмережі можуть функціонувати ра- +зом зі штучною нейронною мережею. У цілому штучна нейронна +мережа, що взаємодії з функціональними підмережами, може пред- +ставляти роботу різних мереж Петрі як композицію роботи окремих +підмереж. +Таким чином, згідно зі схемою, представленою на рисунку 3, ДБ- +мережа містить дискретні підмережі, пов’язані дискретно-безперерв- +ними переходами ti +3, ti +4, де i=1…N [13]. Кожна така підмережа є мере- +жею Петрі, яку можна розглядати незалежно від усієї ДБ-мережі. + +p +N? +p +10 +N +P11 +Onepauia +yMoBHoro nepexoAy +Onepain AbO299 + +Рис. 5. Формування мережі Петрі при взаємозв’язку функціональних підмереж +Нейронна мережа формує сигнали Vs=|V1 …. V5|Т, згідно з якими +здійснюється рух маркерів у мережах Петрі. При цьому рух маркерів +носить погоджений характер. Наприклад, вихід маркера з позиції Р2 +супроводжується появою маркера в позиції Р3. +Погоджений характер зміни маркування в мережах Петрі дає мож- +ливість виконати композицію цих мереж в одну загальну мережу Пе- +трі. Як показано на рисунку 6 а, для композиції мережі Петрі необ- +хідно об’єднати переходи, які одночасно спрацьовують у конкретний +момент часу. На рисунку 6 а переходи t1, t3, t7, t8, t9 поєднуються пунк- +тирними кривими. Наприклад, переходи t3, t7 поєднуються в один пе- +рехід t3,7, який спрацьовує в окремому випадку в момент часу t2. За +допомогою такого об’єднання можна перетворити різні мережі в одну +загальну мережу Петрі. +Згідно з рухом маркерів у мережах Петрі забезпечується фор- +мування значень матриці інцидентності мережі Петрі, так само, як +послідовна активізація підстанів Stateflow-діаграми, фрагмент якої +представлено на рисунку 1. Як показано на рисунку 6 б, з кожним +кроком формується мережа Петрі згідно із процесом формуван- +ня матриці інцидентності. Слід зазначити, що в окремому випад- +ку поява переходу t1 була помилковою, тому що, наприклад, зміна +маркування спричинила небажану зміну критерію якості роботи +системи. У цьому випадку деякий блок автонастроювання повинен + +L +Pm +10300 + +Рис. 6. Візуалізація автоматичного формування мережі Петрі + +Step No 1 +Step No 2 +StepNo4 +t10 +D +p +a) +Composition of Petri net +b) Generation of Petri net301 +випадковим образом змінити відповідні коефіцієнти міжнейронних +з’єднань, зміна яких надалі дозволила би сформувати необхідну ди- +наміку маркування, відповідну до мережі Петрі, організованої напри- +клад на 4-му кроці. +Формування алгоритму при роботі нейронної мережі із синхронно +функціонуючими підмережами Петрі здійснюється при зміні коефі- +цієнтів міжнейронних з’єднань. Зміна коефіцієнтів міжнейронних +з’єднань тягне за собою коректування відповідного алгоритму. +У цьому випадку деякий алгоритм має місце як при наявності пев- +ної локальної штучної нейронної мережі. +Слід врахувати, що може бути деяка кількість вихідних алгоритмів +при синтезі системи логічного управління і відповідно можна виділи- +ти деяку кількість локальних штучних нейронних мереж, як показано +на рисунку 7. +У процесі класифікації алгоритмів запускається відповідна ло- +кальна нейронна мережа, яка вже безпосередньо буде брати участь у +формуванні певного алгоритму. +У такому випадку автоматичний синтез мереж Петрі можна пред- +ставити у два етапи. На першому етапі вибір певного алгоритму і +відповідної мережі Петрі з можливих варіантів. На другому етапі ко- +ректування обраного алгоритму і мережі Петрі. Послідовність фор- +мування такого алгоритму можна представити у вигляді рисунку 8, де +відображені відповідні етапи синтезу мережі Петрі, що представляє +формований алгоритм. +Ці два етапи, які представлено на рисунку 8, можна реалізувати +за допомогою штучної нейронної мережі та її тренування. У цьому +випадку необхідно представити інтелектуальну систему, що формує +алгоритми логічного управління при автоматичному синтезі і компо- +зиції мереж Петрі. Надалі необхідно представити структурну схему та- +кої інтелектуальної системи і при цьому визначити метод тренування +штучної нейронної мережі при автоматичному синтезі мереж Петрі. +Алгоритми настроювання штучних нейронних мереж при автоматич- +ному синтезі мереж Петрі. +Штучна нейронна мережа, як обчислювальна схема, що включає +безліч обчислювальних одиниць — нейронів, може представити пев- +ну інтелектуальну систему при наявності певного методу зміни ко- +ефіцієнтів міжнейронних зв’язків. Саме подібна зміна коефіцієнтів +міжнейронних зв’язків, яка має місце в процесі навчання нейрон- +ної мережі, може відігравати важливу роль у прояві інтелектуальних + +302 + +Рис. 7. Фрагмент схеми, що представляє візуалізацію автоматичного формування мережі Петрі +на основі функціонування + +Xp1 +Xp2 +CMrHaMAA@OpMyBaHHA +Xo +Ta6WLi iHLMAeHTHOCTi +C +Xp3 +W11 +W12 +W +11 +13 +KoMno3Muig, +°23 +nepexoAyMepexki +12 +M +nj +WTyyHaHeMpoHaMepeKa +/-Artificialneuralnetworks +Xo +p +10 +W11 +10 +Xpn +W12 +W +03 +11 +13 +MepekieTpi/PetriNets303 + +Рис. 8. Схема формування алгоритму логічного управління і відповідного +синтезу мережі Петрі +особливостей нейронної мережі при розв’язані певних задач. В окре- +мому випадку такі задачі можуть бути пов’язані з автоматичним син- +тезом мереж Петрі, а також з синтезом алгоритмів логічного управ- +ління деяких об’єктів [3; 6]. +Автоматичний синтез і композиція мереж Петрі припускає +використання відповідних певних методів. Однак для того щоб +сформована мережа Петрі була застосовна для розв’язку певно- +го завдання, необхідне застосування інтелектуальних технологій, +здатних замінити експерта в області формування певних алгорит- +мів. Наприклад, заміна експерта в області формування алгоритмів +настроювання різних багаторівневих систем автоматичного управ- +ління [20]. +Особливості функціонування нейронної мережі при автоматичній +генерації мережі Петрі. Спочатку було встановлено, що автоматична +генерація мережі Петрі повинна виконуватися при функціонуванні +ней ронної мережі, що визначає інтелектуальну технологію форму- +вання алгоритму управління деяким об’єктом. +Така нейтронна мережа є багатошаровою і прямонаправленою. +Кожний шар нейронної мережі несе певне функціональне наван- +таження. Перший шар нейронної мережі забезпечує класифікацію + +ETan 1 +AnropuTmnoriyHoro +Bu6ip +AnropuTm oriyHoro +ynpaBiHH N1 +ynpaBniHHANk +neBHoro +anropuTMy +AnropuTM oriHoro +ynpaBniHHN2 +OuiHKa +AnropuTm oriyHoro +npWAaTHOcTi +yNpaBniHHANen +ETan 2 +KopMryBaHH +KiHeb +o6paHoro +epeBipkayMoB +anropuTMy +3aBepWeHHA304 + +Рис. 9. Спрощена структурна схема системи, що формує алгоритми логічного +управління при автоматичній композиції мережі Петрі на базі функціонуван- +ня штучної нейронної мережі + +Mepexki leTpi /Petri nets/ +IPn +06'EKT +yNpaBniHHA +V +bnoK +ud2 +X(t) +popMyBaHH9 +yMOB i 3HayeHb +V2 +KpMTepiiB KOcTi +pO6OTW CWCTeMM +Controller +MoAyJb CMHTe3y i +bNOK aBTOHaCTpOIOBaHHA +aHai3y Mepexki ieTpi +D/C +/ Synthesis and analysis +/ Tuning unit / +of Petri nets / +3aBAaHHA +W61(1) +(i(s) +W21(7) +(BИxiAHi +AaHi)X +W +W12(2) +Y1 +W66(31) +(s)s +W13(3) +y2 +fy +W14(4) +Kacwbikatop +(s) +W15(5) +Y: +((s) +0 +AropTM 1 +「eHepaTop +iMnybciB +f.(s +AnropuTM 2 +IHTeeKTyabHa +HeipoHHa Mepexa +/ Neural network / +CWCTeMa305 +можливих алгоритмів. Внутрішній шар визначає алгоритми управлін- +ня. Вихідний шар забезпечує формування певної матриці інцидент- +ності мережі Петрі, що представляє алгоритм логічного управління +об’єктом. Як показано на рисунку 9, нейронну мережу можна розді- +лити на сектори, кожний сектор представляє певний алгоритм управ- +ління і відповідну матрицю інцидентності мережі Петрі. У зв’язку з +тим, що формування алгоритму представляється як покроковий — +поетапний процес, кожний крок при формуванні алгоритму супро- +воджується активізацією певного нейрона, названого початковим. +Найперший початковий нейрон можна назвати командним, тому що +після його активізації локальна нейронна мережа починає функціо- +нувати. Вибір командного нейрона для його активізації здійснюється +на етапі класифікації алгоритмів. Такий процес класифікації також +можна реалізувати за допомогою штучної нейронної мережі. Слід за- +значити, що відправні нейрони W є в кожному секторі відповідної ло- +кальної нейронної мережі. Перенастроювання вагових коефіцієнтів +міжнейронних з’єднань, пов’язаних з початковими нейроном, спри- +чиняє коректування відповідного алгоритму, якщо він не задоволь- +няє певним вимогам. +Нейронна мережа як обчислювальна схема визначає матрицю +інцидентності мережі Петрі набором коефіцієнтів міжнейроних +з’єднань +( ) +ij k +w +, пов’язаних з початковими нейронами. Матриця інци- +дентності розглянутої мережі, представленої на рисунку 9, має такий +вигляд: +1 +2 +3 +4 +5 +6 +0 +11(1) +12(2) +13(#) +14(4) +15(5) +16(6) +1 +21(7) +22(8) +23(9) +24(10) +25(11) +26(12) +2 +31(13) +32(14) +33(15) +34(16) +35(17) +36(18) +3 +41(19) +42(20) +43(21) +44(22) +45(23) +46(24) +4 +51(25) +52(26) +53 +t +t +t +t +t +t +p +w +w +w +w +w +w +p +w +w +w +w +w +w +p +w +w +w +w +w +w +p +w +w +w +w +w +w +W +p +w +w +w += +(27) +54(28) +55(29) +56(30) +5 +61(31) +62(32) +63(33) +64(34) +65(35) +66(36) +6 +71(37) +72(38) +73(39) +74(40) +75(41) +76(42) +7 +81(43) +82(44) +83(45) +84(46) +85(47) +86(48) +w +w +w +p +w +w +w +w +w +w +p +w +w +w +w +w +w +p +w +w +w +w +w +w +. +Кількість стовпців матриці інцидентності W визначається кіль- +кістю початкових нейронів, а кількість рядків визначається кількістю +вихідних нейронів n-го (вихідного) шару нейронної мережі. + +306 +Певні умови спрацьовування відповідних переходів мережі Петрі +визначаються ваговими коефіцієнтами вхідних з’єднань початкових +нейронів. Набір вагових коефіцієнтів вхідних з’єднань початкових +нейронів також можна представити у вигляді матриці: +1 +2 +3 +4 +5 +6 +1 +11(6) +12(12) +13(18) +14(24) +15(30) +16(36) +2 +21(2) +22(8) +23(14) +24(20) +25(26) +26(32) +3 +31(3) +32(9) +33(15) +34(21) +35(27) +36(33) +4 +41(4) +42(10) +43(16) +44(22) +45(28) +46(34) +5 +51(5) +52(11) +t +t +t +t +t +t +N +w +w +w +w +w +w +N +w +w +w +w +w +w +N +w +w +w +w +w +w +N +N +w +w +w +w +w +w +N +w +w +w += +53(17) +54(23) +55(29) +56(35) +6 +61(1) +62(7) +63(13) +64(19) +65(25) +66(31) +w +w +w +N +w +w +w +w +w +w +. +У цій матриці N кількість рядків N1 …. N6 відповідає різним умо- +вам спрацьовування переходів, а кількість стовпців відповідає кіль- +кості кроків формування алгоритму. +Згідно з рисунком 3 процес формування елементів матриці інци- +дентності мережі Петрі здійснюється на базі вихідних сигналів y1…y8 +нейронної мережі, що забезпечують паралельне — синхронне функ- +ціонування відповідних мереж Петрі. Це дає можливість представити +деяку композицію з відповідних мереж Петрі, яка відображає алго- +ритм логічного управління певним об’єктом [15]. +Якщо алгоритм логічного управління об’єктом не відповідає за- +даним вимогам, при яких здійснюється відповідна зміна значень +критеріїв якості роботи системи, то блок автонастройки (Tuning unit) +повинен змінити певні коефіцієнти міжнейронних з’єднань згідно з +інцидентною матрицею синтезованої мережі Петрі. +Особливості архітектури нейронної мережі, що здійснює синтез ме- +реж Петрі і формування алгоритмів логічного управління. Виходячи з +вищерозглянутої схеми, представленої на рисунку 9, можна виділити +деяку певну архітектуру нейронної мережі, яка може застосовуватися +при формуванні алгоритму управління, відображеного відповідною +мережею Петрі. Така архітектура нейронної мережі, зображена на ри- +сунку 10, представляється двошаровою зі зворотними зв’язками і з +елементами затримки сигналів. +Особливість функціонування такої нейронної мережі полягає в +тому, що в будь-який момент часу може бути активним тільки один +нейрон з n можливих нейронів у вхідному шарі. При цьому активіза- + +307 +ція лише одного нейрона у вхідному шарі може викликати активіза- +цію N нейронів у вихідному шарі. + +Рис. 10. Архітектура нейронної мережі, що використовується при формуван- +ні інцидентної матриці мережі Петрі +Розрахунки синаптичних коефіцієнтів вихідних нейронів обчис- +люються на основі синаптичних коефіцієнтів вхідних з’єднань почат- +кових нейронів мережі за формулою: +( ) +( ) +1 +1 +m +nk u +nk +k u +nk +nk +n +w +w +b +w +w += + + += +⋅ +− ++ +− + + + + +∑ +, +де +( ) +nk u +w + — синоптичний коефіцієнт n-го входу вхідного k-го нейрона; +nk +w — синоптичний коефіцієнт k-го входу вихідного n-го нейрона; +( ) +k u +b + — величина зсуву вхідного k-го нейрона. +Ця формула розрахунків коефіцієнтів міжнейроних зв’язків ви- +значена з умови активізації лише одного вхідного нейрона з n мож- +ливих нейронів, у будь-який момент часу. Кількість відправних ней- +ронів мережі повинна бути такою, щоб не повторювалися комбінації +значень сигналів виходів Y1 … Yn. +Для перевірки принципової придатності розглянутої архітекту- +ри нейронної мережі в програмному середовищі MATLAB/Simulink +була реалізована відповідна схема, що представлена на рисунку 11. + +2 +Xo +以 +M +(s +11 +W21 +W. +11() +X1 +Y2 +Ow, +5 +M +22 +W. +M +21(u) +n+12 +Wn+1le +W2k +Wik (u) +X.k +Yn +Wk +M +n+1k- +f(s) +k +LWnk(u) +n+1308 + +Рис. 11. Структурна схема нейронної мережі з початковими нейронами + +Y1 +Y4 +X1 +0 +1 +W11 +HeipoH4 +Constanto +事 +Add +Gain9 +Gain10 +本术本 +Scope3 +0 +2 +t, sec. +Unit Delay4 +HoyaTKoBMM +Gain11 +netsum3 +hardlim3 +HeMpOH1 +Gain1 +netsum +hardlim +Scope2 +W13 +Y2 +Gain15 +Y5 +Gain2 +-T +Constant2 +0 +Constant3 +X2 +W +HeipoOH 5 +0 +t, sec. +H +Scope4 +Y2 +Gain14 +W21(u) +22 +netsum4 +hardlim4 +netsum1 +hardlimt +Scope1 +Gain4 +Ws1(u) +m +T- +1 +HoyaTKoBWM +.4 +-1 +Y6 +Gain5 +0 +Constant7 +HeMpOH 2 +Gain16 +Constant +Constant4 +X3 +W +W31 +0 +2 +HeMpOH 6 +t, sec. +2/u) +Scope5 +Y3 +Gain19 +H +0 +hardlim5 +netsum2 +hardlim2 +Scope +netsum5 +Gain7 +2 +4 +t, sec. +W. +Y5 +-1 +b3 +HoyaTKoBWM +-4 +Gain8 +0 +HeMpOH 3 +Constant1 +Constant5 +Gain20 +2 +t, sec. +Y6 +TI N +Unit Delay1 +2 +Unit Delay2 +t, sec. +Unit Delay3309 +Як вид но з рисунку 11, представлена схема нейронної мережі, що +складається з 3 відправних і 3 вихідних нейронів, має зворотні зв’язки +з елементами затримки сигналу. +Згідно з вищенаведеною формулою представимо наступні розра- +хунки деяких коефіцієнтів міжнейронних з’єднань відповідної ней- +ронної мережі: +3 +32( ) +32 +2( ) +2 +32 +1 +1 +1 (| 4 | (1 1 1)) 1 1 +1 +u +u +n +n +w +w +b +w +w += + + += +⋅ +− ++ +− = ⋅ +− +− ++ + ++ − = + + + + +∑ +; +3 +31( ) +31 +1( ) +1 +31 +1 +1 +1 (| 4 | (1 +0 +0)) 1 1 +3 +u +u +n +n +w +w +b +w +w += + + += +⋅ +− ++ +− = ⋅ − +− ++ ++ ++ − = + + + + +∑ +. +З відповідних часових діаграм активізацій нейронів, представ- +лених на рисунку 11, видно, що в будь-який момент часу активний +тільки один нейрон з 3 початкових, при цьому кількість активних +вихідних нейронів різна. Тому що в кожний момент часу активний +лише один нейрон у вхідному шарі, то розрахунки коефіцієнтів між- +нейронних з’єднань були виконані вірно. +Алгоритм настроювання нейронної мережі за дозволеними комбіна- +ціями. Розглянутий алгоритм настроювання нейронної мережі відпо- +відає алгоритму навчання з послідовним підкріпленням знань, при +якому мережі не надаються бажані значення вихідних сигналів, а за- +мість цього мережі ставиться оцінка, гарний вихідний сигнал або по- +ганий [21]. +Передбачається, що в нейронній мережі в певний момент часу +може бути активний лише один нейрон, названий початковим, з +n можливих нейронів у шарі. Виходячи із цього, сутність настро- +ювання нейронної мережі можна відобразити в такий спосіб: якщо +активність початкового нейрона привела до небажаної ситуації, то +зв’язки із цим нейроном W повинні притерпіти зміни (рисунок 12). +При цьому зміна зв’язків з початковим нейроном повинна відбува- +тися таким чином, щоб не порушити правила формування мережі +Петрі. +При обліку правил формування мережі Петрі коефіцієнти міжней- +ронних з’єднань, пов’язаних з вихідним нейроном, повинні зміни- +тися певним чином залежно від сформованої матриці інцидентності. +Отже, якщо при активізації певних нейронів була отримана небажана +реакція деякої системи, то вагові коефіцієнти зв’язків цих нейронів +wij слід змінити у такий спосіб: + +310 +(0) +1 +1 +1 +n +n +ij +ij +im +ij +ik +i +j +j +w +w +S +w +f +F += += + + + + += η⋅ +⋅ ++ +− +⋅ +⋅ + + + + + + + + + + +∑ +∑ +, +( +) ( +) +( +) ( +) +1 + +1 +0 +0 + +1 +0 +T +T +ij +im +ij +ik +i +T +T +ij +im +ij +ik +npu +w +S +w +f +F +npu +w +S +w +f + +⋅ +⋅ +− +⋅ +> + +=  +⋅ +⋅ +− +⋅ += + +∑ +∑ +∑ +∑ +, +( ) +ij i +ih +w +n += η⋅ +, +де +1 +2 +0 +11 +12 +1 +1 +22 +2 +2 +1 +1 +2 +j +j +ij +j +j +i +i +i +ij +ij +t +t +t +w +p +w +w +w +w +p +w +w +W +w +p +w +w +w +w +− += +⇒ +∑ +∑ +∑ +∑ + + + + + + + + + + + + — матриця інцидентнос- +ті формованої мережі Петрі і сформований вектор +1 + +T +j +ij +w +w +w += +∑ +∑ +∑ + +1 + +T +j +ij +w +w +w += +∑ +∑ +∑ + +; +ij +w +∑ + сума всіх значень i-го рядка матриці W ; +, +im +ik +S +f — вектори дозволених комбінацій ваг міжнейронних з’єд- +нань, що не порушують правила формування мережі Петрі; +1 +2 +3 +4 +5 +6 +7 +8 +1 +2 +3 +1 +1 +2 +2 +3 +3 +1 +1 +4 +4 +5 +5 +6 +6 +7 +7 +8 +8 +1 +2 +3 +1 +2 +2 +1 +0 +0 +0 +0 +0 +0 +0 +1 +0 +1 +0 +1 +0 +0 +0 +0 +0 +0 +1 +1 +0 +0 +0 +1 +0 +0 +0 +0 +0 +1 +1 +0 +, +; +0 +0 +0 +1 +0 +0 +0 +0 +1 +0 +1 +0 +0 +0 +0 +1 +0 +0 +0 +1 +0 +1 +0 +0 +0 +0 +0 +1 +0 +0 +1 +1 +0 +0 +0 +0 +0 +0 +0 +1 +0 +1 +1 +0 +0 +0 +0 +0 +0 +0 +0 +1 +1 +0 +1 +1 +0 +1 +1 +1 +i +i +i +i +i +i +i +i +i +i +i +k +m +k +m +k +m +k +m +k +m +k +m +k +m +k +m +i +i +i +m +m +f +f +f +f +f +f +f +f +S +S +S +f +s +f +s +f +s +S +f +f +s +f +s +f +s +f +s +f +s +S +S +S +s +s +S += += += +9 +10 +11 +12 +13 +14 +15 +16 +1 +2 +3 +3 +2 +4 +4 +5 +5 +6 +6 +7 +7 +8 +8 +0 +0 +0 +0 +0 +0 +0 +0 +1 +0 +0 +1 +0 +0 +0 +0 +0 +0 +1 +1 +0 +0 +0 +0 +0 +1 +1 +0 +, +; +0 +1 +0 +1 +0 +1 +0 +1 +1 +0 +1 +1 +0 +1 +0 +1 +0 +1 +0 +1 +0 +1 +0 +0 +0 +0 +1 +1 +0 +0 +1 +1 +0 +0 +0 +0 +0 +0 +0 +1 +1 +1 +1 +0 +0 +0 +0 +0 +0 +0 +0 +0 +1 +0 +1 +i +i +i +i +i +i +i +i +k +k +k +m +k +m +k +m +k +m +k +m +k +m +f +f +f +f +f +f +f +f +f +f +f +s +f +f +s +f +s +f +s +f +s +f +s += + + +311 +1 +2 +3 +4 +5 +6 +7 +8 +1 +2 +3 +1 +1 +2 +2 +3 +3 +1 +1 +4 +4 +5 +5 +6 +6 +7 +7 +8 +8 +1 +2 +3 +1 +2 +2 +1 +0 +0 +0 +0 +0 +0 +0 +1 +0 +1 +0 +1 +0 +0 +0 +0 +0 +0 +1 +1 +0 +0 +0 +1 +0 +0 +0 +0 +0 +1 +1 +0 +, +; +0 +0 +0 +1 +0 +0 +0 +0 +1 +0 +1 +0 +0 +0 +0 +1 +0 +0 +0 +1 +0 +1 +0 +0 +0 +0 +0 +1 +0 +0 +1 +1 +0 +0 +0 +0 +0 +0 +0 +1 +0 +1 +1 +0 +0 +0 +0 +0 +0 +0 +0 +1 +1 +0 +1 +1 +0 +1 +1 +1 +i +i +i +i +i +i +i +i +i +i +i +k +m +k +m +k +m +k +m +k +m +k +m +k +m +k +m +i +i +i +m +m +f +f +f +f +f +f +f +f +S +S +S +f +s +f +s +f +s +S +f +f +s +f +s +f +s +f +s +f +s +S +S +S +s +s +S += += += +9 +10 +11 +12 +13 +14 +15 +16 +1 +2 +3 +3 +2 +4 +4 +5 +5 +6 +6 +7 +7 +8 +8 +0 +0 +0 +0 +0 +0 +0 +0 +1 +0 +0 +1 +0 +0 +0 +0 +0 +0 +1 +1 +0 +0 +0 +0 +0 +1 +1 +0 +, +; +0 +1 +0 +1 +0 +1 +0 +1 +1 +0 +1 +1 +0 +1 +0 +1 +0 +1 +0 +1 +0 +1 +0 +0 +0 +0 +1 +1 +0 +0 +1 +1 +0 +0 +0 +0 +0 +0 +0 +1 +1 +1 +1 +0 +0 +0 +0 +0 +0 +0 +0 +0 +1 +0 +1 +i +i +i +i +i +i +i +i +k +k +k +m +k +m +k +m +k +m +k +m +k +m +f +f +f +f +f +f +f +f +f +f +f +s +f +f +s +f +s +f +s +f +s +f +s += + +ih +n — вектор комбінацій вагових коефіцієнтів вхідних зв’язків ви- +хідного нейрона; +1 +2 +3 +4 +1 +1 +2 +3 +4 +1 +0 +0 +0 +0 +1 +0 +0 +0 +0 +1 +0 +0 +0 +0 +1 +i +i +i +i +h +h +h +h +n +n +n +n +n +N +n +n +n += +. + +Рис. 12. Схема, що відображає зв’язки початкового нейрона +з позначеними вагами міжнейроних з’єднань + +W +22(i8) +w +32(i9) +W +82(o44) +Wi(i) +W21(u) +W: +ij(o) +W +ij(u)312 +Представлені вище вектори можливих комбінацій синоптичних +коефіцієнтів зв’язків нейронів дозволяють нейронній мережі в про- +цесі функціонування виконати композицію лише певних мереж Пе- +трі, тому що не всі можливі комбінації коефіцієнтів міжнейронних +зв’язків представлені. Очевидно, що ці мережі Петрі можуть відоб- +ражати суто певні алгоритми управління об’єктами або, в окремому +випадку, алгоритми настроювання певних систем управління. Однак +слід зазначити, що розглянута архітектура нейронної мережі, що ви- +користовується при автоматичному синтезі мереж Петрі, має певну +особливість, необхідну при формуванні різних алгоритмів управління. +Представлений нами алгоритм настроювання певної ней ронної +мережі з вихідними нейронами дає можливість виконати певний +крок у розробці інтелектуальної системи, що формує алгоритми ло- +гічного управління об’єктами при автоматичному синтезі і компо- +зиції мереж Петрі. Автоматично синтезована мережа Петрі дозволяє +представити результат формування алгоритму управління об’єктом і +тим самим дозволяє фахівцеві виробити, при необхідності, потрібне +коректування алгоритму. +Слід зазначити, що в даній інтелектуальній системі, яка пов’язана +з автоматичним синтезом мереж Петрі, була представлена спроба +використання принципу навчання з підкріпленням, яка відображає +область штучного інтелекту, нейромережевого моделювання і управ- +ління, що активно розвивається. Тим самим інтелектуальна система, +що розробляється, пов’язана із синтезом мереж Петрі і з формуван- +ням, наприклад, алгоритмів настроювання особливого класу систем +управління, достатньою мірою вписується в рамки сучасного розви- +тку інтелектуальних технологій, особливо актуальних в наш час. +Далі розглянемо ще один алгоритм настроювання нейронної ме- +режі, що виключає наявність дозволених комбінацій коефіцієнтів +міжнейронних зв’язків нейронної мережі. +Алгоритм настроювання нейронної мережі по перебору можливих ва- +ріантів. Принцип настроювання нейронної мережі з перебору мож- +ливих варіантів аналогічний вищенаведеному алгоритму за винятком +його формалізації. У цьому випадку, якщо певний алгоритм дій не- +задовільний, то необхідно вказати, на якому з переходів мережі Пе- +трі була виявлена помилка в системі. Це необхідно для перенастро- +ювання штучної нейронної мережі. Так, якщо значення показників +якості роботи деякої системи збільшується, то необхідно відповідно +зв’язок між переходом ti і позицією pi ліквідувати. Але при цьому не- + +313 +обхідно додати новий зв’язок між переходом ti і сусідньою позицією +pi+1. Таким чином, наприклад, мережа Петрі, що представлена на ри- +сунку 13 a, змінюється в мережу Петрі, представлену на рисунку 13 b. +Відповідно повинні змінитися коефіцієнти міжнейронних зв’язків +штучної нейронної мережі. +Математично це можна формалізувати в такому виді: + +, +1 +, +, +, +1 +1 +1, +1, +1, +1 +1 +( +) +( ) (1 | +( ) +( ) | +) +( ) +| +( ) +( ) | +i j +k +i j +k +i j +k +i j +k +i +j +k +i +j +k +i +j +k +w +t +w +t +w +t +w +t +w +t +w +t +w +t ++ ++ ++ ++ ++ ++ += +⋅ +− +⋅ +⋅δ ++ +× +× +⋅ +⋅δ + +(1) +при i=2,4,6… + +, +1 +1 +, +1 +, +, +1 +1 +1, +1 +1, +1, +1 +1 +( +) +( ) (1 | +( ) +( ) | +) +( ) +| +( ) +( ) | +i j +k +i j +k +i j +k +i j +k +i +j +k +i +j +k +i +j +k +w +t +w +t +w +t +w +t +w +t +w +t +w +t ++ ++ ++ ++ ++ ++ ++ ++ ++ += +⋅ +− +⋅ +⋅δ ++ +× +× +⋅ +⋅δ + +(2) +при i=2,4,6… + +, +1 +, +, +, +1 +1 +1, +1, +1, +1 +1 +( +) +( ) (1 | +( ) +( ) | +) +( ) +| +( ) +( ) | +i j +k +i j +k +i j +k +i j +k +i +j +k +i +j +k +i +j +k +w +t +w +t +w +t +w +t +w +t +w +t +w +t ++ ++ +− +− +− ++ += +⋅ +− +⋅ +⋅δ ++ +× +× +⋅ +⋅δ + +(3) +при i=1,3,5… + +, +1 +1 +, +1 +, +, +1 +1 +1, +1 +1, +1, +1 +1 +( +) +( ) (1 | +( ) +( ) | +) +( ) +| +( ) +( ) | +i j +k +i j +k +i j +k +i j +k +i +j +k +i +j +k +i +j +k +w +t +w +t +w +t +w +t +w +t +w +t +w +t ++ ++ ++ ++ +− ++ +− +− ++ += +⋅ +− +⋅ +⋅δ ++ +× +× +⋅ +⋅δ + +(4) +при i=1,3,5… +де +, ( ) +i j +k +w +t + — коефіцієнт міжнейронного з’єднання, який визначає від- +повідний зв’язок у мережі Петрі, що формується на кроці tk; +, +1 +( +) +i j +k +w +t + +, +відповідний коефіцієнт міжнейронного з’єднання на кроці tk+1. +Матриця коефіцієнтів міжнейронних зв’язків N має певну анало- +гію з інцидентною матрицею мережі Петрі. Наприклад, з інцидент- +ною матрицею W1 мережі Петрі, представленої на рисунку 13 a. При +помилці на переході t1 інцидентна матриця W1 змінюється відповідно +в матрицю W2 у такий спосіб: + +314 + +Рис. 13. Алгоритми логічного управління, що представлені мережами Петрі, +які відображають процеси поетапного настроювання багаторівневої системи + +3HayeHHA +V0 +3HayeHH9 +0 +3HaYeHH +0 +pyxaeTbco Hy +pyxaeTbc o Hy +pyxaeTbc o Hy +3 +p +p +p +5 +Y +3HayeHH napaMeTpa +3HayeHH napaMeTpa +3HayeHHA +3pocTae +个k,3pocTae +napaMeTpa +个k. +3pocTae +p +p +p +4 +6 +3HayeHH napaMeTpa +3HayeHH9 napaMeTpa +3HayeHH9 napaMeTpa +3MeHWyeTbcq +1k, 3MeHWyeTbcq +k. +(KoopWHyroyw piBeHb +(CTaini3yroywM piBeHb +(KoopHyrOywi piBeHb +ynpaBiHH) +ypaBJiHHg) +ynpaBiHH) +0 +p +CTON +lyck +omwka +a +Ha nepexoni +3HayeHH +3HayeHHA, +3Ha4eHH9 J +903 +902 +01 +pyxaeTbc o max +pyxaeTbc o max +pyxaeTbc o max +0 +p +3HayeHH napaMeTpa : +3HayeHH9 napaMeTpa +3HayeHH9 +3pocTae +个k,3pocTae +napaMeTpa +k. +个k, +3pocTae +p6 +p +p 4 +2 +3HayeHH apaMeTpa +3HayeHH9 napaMeTpa +3HayeHH9 napaMeTpa +k. +3MeHWyeTbc9 +↓ k, 3MeHWyeTbcq +(KoopAWHyrouwi piBeHb +CTabini3yro4wM piBeHb +(KoopAWHyroywi piBeHb +ypaBniHH) +ynpaBiHH) +ynpaBniHH) +p8 +p +6) +CTOn ( +lyck (315 +1 +2 +3 +4 +1 +2 +3 +4 +1 +1 +2 +2 +3 +3 +4 +4 +1 +2 +5 +5 +6 +6 +7 +7 +8 +8 +9 +9 +1 +1 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +1 +1 +0 +0 +0 +0 +1 +1 +0 +0 +1 +1 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +0 +1 +1 +0 +0 +1 +1 +0 +1 +0 +0 +0 +1 +0 +0 +0 +0 +0 +0 +1 +0 +0 +0 +1 +0 +0 +0 +0 +0 +0 +0 +0 +t +t +t +t +t +t +t +t +p +p +p +p +p +p +p +p +W +W +p +p +p +p +p +p +p +p +p +p ++ +− ++ +− ++ +− ++ +− += +⇒ += ++ +− ++ +− +− +− ++ ++ +. +Рядки р1 і р2 матриці W1 були змінені згідно з виразом (3). Відповід- +но, якщо на переході ti виявлена помилка, то +1 +1 +δ = +. У цьому випадку, +якщо є зв’язок між переходом ti і позицією pi то +, +, +1 +( ) +( ) +1 +i j +k +i j +k +w +t +w +t ++ +⋅ += . +Отже, згідно з виразом ( +) +, +, +1 +1 +1 +( ) +( ) +0 +i j +k +i j +k +w +t +w +t ++ +− +⋅ +×δ += + і коефіцієнт між- +нейронного зв’язку, на кроці +1 +kt + стане також рівним нулю +, +1 +( +) +0 +i j +k +w +t + += +. +Таким чином, відповідний зв’язок у мережі Петрі, що формується, +зникне. +В іншому випадку, якщо відсутній зв’язок між переходом ti +і позицією pi, то +, +, +1 +( ) +( ) +0 +i j +k +i j +k +w +t +w +t ++ +⋅ += +, ( +) +, +, +1 +1 +1 +( ) +( ) +1 +i j +k +i j +k +w +t +w +t ++ +− +⋅ +×δ += +. +При цьому, якщо був присутній сусідній зв’язок між переходом ti і +позицією pi+1, то +1, +1, +1 +1 +( ) +( ) +1 +i +j +k +i +j +k +w +t +w +t ++ ++ ++ +⋅ +⋅δ = і, отже, коефіцієнт між- +нейронного зв’язку збільшиться на одиницю +, +1 +, +( +) +( ) 1 +i j +k +i j +k +w +t +w +t ++ += ++ . +Таким чином, з’явиться відповідний зв’язок у мережі Петрі, що +формується. +Якщо +на +переході +ti помилка +не +виявлена, +то +1 +0 +δ = +, +( +) +, +, +1 +1 +1 +( ) +( ) +1 +i j +k +i j +k +w +t +w +t ++ +− +⋅ +×δ += і, отже, +, +1 +, +( +) +( ) +i j +k +i j +k +w +t +w +t ++ += +. +Експерименти. У програмному середовищі MATLAB/Simulink +2012 були проведені експерименти, пов’язані зі спільною роботою +нейронної мережі з мережами Петрі. Функціонування мереж Петрі +у програмному середовищі MATLAB/Simulink було реалізовано за +допомогою Statflow-діаграм. Фрагмент Stateflow-діаграм, що пред- +ставляють роботу мереж Петрі, представлено на рисунку 14. State1, +State2, State3 і State4 є станами однієї мережі Петрі. Нейронна мережа +пов’язана з роботою відразу трьох таких мереж Петрі. Це показано на +рисунку 15. + +316 + +Рис. 14. Stateflow-діаграми, що представляють роботу мереж Петрі + +StateA +StateC1 +[data01>0.9] +[data01-0.9] +after(9,tick) +State1 +State2 +State3 +State4 +data1=0 +data1=0: +data1=1: +data1=1: +data2=1 +data2=1 +data2=0 +data2=0 +after(9,tick) +StateC2 +[data02>0.9] +[data02<-0.9] +after(9,tick) +State5 +State6 +State7 +State8 +data3=0: +data3=0 +data3=1: +data3=1: +data4=1 +data4=1 +data4=0 +data4=0317 + +Рис. 15. Структурна схема нейронної мережі, що синтезує мережу Петрі + +Xt1 +Xp1 +0 ++1 +0 +2 +uo ++t2 +Xp2 +Constant47 +P +0 +Constant4g +Scope9 :18 +Add1 +dotprod21 +2 +Unit Delayg +t3 +Xp3 +2 +0 +0 +2 +Scope9 :2r +++1 +0 +2 +-2: +1 +C onstant44 +t, sec. +2 +t, sec. +dotprod29 +.4 +0 +Constant3g +Xp1 +u(p +Constant45 +p ++ +hardlim2 +dotprod20 +netsum12 +dotprod30 +4 +data1 +0 +Constant48 +tansig7 +Scope9 :19 +P +Scope9 :27 +Constant48 +-1 +0 +dotprod32 +netsume ++data01 +dotprod31 +Constant34 +Constant50 +JΛ +！！！ +Xt2 +dotprod33 +0.5 +Constant27 +Constant55 +ScoDe9 :28 +dotprod40 +Constant56 +Xp2 +μ(p: +0 +Scope9 a3 +Constant5 +Constant37 +P +dotprod34 +dotprod23 +-4 +0.5 +Constant52 ++ +hardlim1 +tansig9 +Scope9 :25 +Scope9 :29 +Constant38 +netsum8 +P +dotprod35 +netsumg +dotprod24 ++? +0 +-1 +Constant29 +0 +Constant40 +p +Constant35 +dotprod36 +Constant28 +dotprod25 +Scope9 ±30 +0.5 +u(p +t3 +口 +0 +0 +Constant53 +ZF +Constant32 +sdx +Scope9 :23 +Constant54 +0 +dotprod39 +口 +0 +Constant41 +Scope9 331 +Constant33 +tansig10 +Scope9 26 +dotpro d26 +事 +P +0.5 +Lw +dotprod38 +netsum10 +hardlim +Constant42 +netsum11 +H! +Constant31 +data6 +P +0 +dotprod27 +0 +dotprod22 +Scope9 :17 +Constant30 +C onstant43 +Constant36 +Chart2 +dotpro d28 +Unit Delay10 +Unit Delays +Unit Delay7318 +На рисунку 15 також представлена засобами середовища MATLAB/ +Simulink двошарова штучна нейронна мережа, що складається з шес- +ти нейронів із вихідними сигналами Xp1, Xp2, Xp3, пов’язаними з ме- +режами Петрі. +Структурна схема цієї нейронної мережі і мереж Петрі аналогічна +спрощеній схемі, яка представлена на рисунку 3. На рисунках 14 і 15 +наведені всі необхідні параметри системи, яка представляє спільне +функціонування нейронної мережі і мереж Петрі для автоматичного +формування мереж Петрі і певних алгоритмів. +Система, структурна схема якої наведена на рисунку 4, здатна +представити функціонування різних мереж Петрі. +Рівняння (2) описує таке спільне функціонування мереж Петрі і +штучної нейронної мережі. +Якщо матриця інцидентності A мережі Петрі має певну анало- +гію з матрицею коефіцієнтів міжнейронних з’єднань вихідного шару +ней ронної мережі, то штучна нейронна мережа генерує вихідні сиг- +нали +1 +k +V +A U +− += +⋅ +, відповідні значенням матриці інцидентності мере- +жі Петрі, що формується. +На рисунках 15 і 16 представлені часові діаграми функціонуван- +ня мережі Петрі, що складається із трьох позицій і трьох переходів. +Функціонування такої мережі Петрі представляє система спільної ро- +боти штучної нейронної мережі і Stateflow-діаграм. Вихідні сигнали +штучної нейронної мережі Xp1, Xp2, Xp3 відповідають матриці інци- +дентності мережі Петрі, що формується. А вихідні сигнали μ(р1) μ(р2) +μ(р3) представляють зміну маркування мережі Петрі в часі. В окремо- +му випадку представляється робота мережі Петрі, показаної на ри- +сунку 16. +Як видно з часових діаграм, якщо присутній сигнал на вході J1 +(J01 >0), то спрацьовує перехід t2. Якщо з’являється сигнал на вхо- +ді J2 (J01 >0), то спрацьовує перехід t3. Одночасне спрацьовування +переходів t2 і t3 відповідає конфліктній ситуації в роботі мережі +Петрі. +Аналізуючи часові характеристики, наведені на рисунках 15 і 16, +можна зробити висновок про принципову придатність розглянутої +системи представляти роботу різних мереж Петрі. Важлива складова +такої системи — це наявність штучної нейронної мережі, тренування +якої пов’язане з автоматичним синтезом мережі Петрі. Таким чином, +зміна коефіцієнтів міжнейронних зв’язків при тренуванні мережі +пов’язана зі зміною синтезованої мережі Петрі. + +319 + +Рис. 16. Процес функціонування синтезованої мережі Петрі + +Xp1 +2 +Xt2 +Xp2 +0 +2 +2 +Xp3 +,sec. +sec320 +Математичний опис зміни коефіцієнтів міжнейронних з’єднань +при тренуванні мережі було представлено як одну зі спроб реалізації +перебору можливих варіантів з’єднань у мережі Петрі. У цьому ви- +падку сформована мережа Петрі є візуальним відображенням набору +коефіцієнтів міжнейронних з’єднань штучної нейронної мережі. +Висновки. Нами було вирішено задачу, пов’язану з розробкою +системи спільного функціонування нейронної мережі і мереж Пе- +трі для формування алгоритмів і послідовних обчислень. Тим самим +одержали подальший розвиток методики автоматичного синтезу +мереж Петрі і розробки певних алгоритмів на основі функціонуван- +ня нейронної мережі. Був представлений математичний опис змі- +ни коефіцієнтів міжнейронних зв’язків мережі при синтезі мережі + Петрі. +Розроблені методики синтезу мереж Петрі дозволяють підійти до +вирішення практичної задачі, пов’язаної з автоматизованим настро- +юванням складного класу багаторівневих автоматичних систем коор- +динуючого управління. У цьому випадку синтезована мережа Петрі +дозволяє представити процес і алгоритм настроювання відповідної +системи управління. +Автоматизоване настроювання автоматичної системи координуваль- +ного управління при синтезі мереж Петрі. Практичне застосування +розглянутих методів автоматичного синтезу мереж Петрі може бути +в області автоматизації процесів настроювання певного класу багато- +рівневих автоматичных систем координувального управління [22; 23]. +На основі відомих наукових праць можна зробити висновок, +що спочатку при синтезі координувальну систему автоматичного +управління треба розглядати як однорівневу, тобто необхідно вико- +нувати синтез системи, починаючи з нижнього рівня, а потім пе- +реходити до синтезу верхніх рівнів [22–25]. Але в деяких випадках +можливі й інші варіанти. Наприклад, синтез координувальної сис- +теми автоматичного управління (КСАУ) приводами робота-мані- +пулятора доцільно було починати з контуру регулювання верхнього +рівня, потім необхідно було налаштувати нижній рівень, а потім па- +раметри настроювання верхнього рівня необхідно було коректува- +ти. Було встановлено, що можливі різні варіанти алгоритмів синтезу +координувальних системи, а кожний з алгоритмів може приводити +до різних результатів. Таким чином, виникає задача формування, +отже, пошуку алгоритму, який дозволить досягти бажань значень +показників якості роботи координувальної системи. У цьому випад- + +321 +ку виникає задача, подібна до задачі досяжності системи в гібрид- +ному (дискретно-безперервному) просторі станів, яка розглядалася +в роботах [14; 26]. +В даному випадку розробляється система параметричного синтезу +КСАУ на базі математичного апарата дискретно-безперервних мереж +(ДБ-мереж), яка дозволяє досліджувати властивість досяжності сис- +теми шляхом редукції безперервної і дискретної частин мережі [12]. +Перша спроба розробки такої системи була запропонована в роботі +[27], у якій мережею Петрі представлявся алгоритм самонастроюван- +ня певних параметрів нейро-нечіткої системи управління. У цьому +випадку запропоновано в системі, що розробляється, реалізувати +формування алгоритму параметричного синтезу на основі методів +перевірки досяжності ДБ-мережі. Виконана розробка автомата в се- +редовищі MATLAB/Simulink формує матрицю інцидентності мережі +Петрі дискретно-подійної частини ДБ-мережі, отже, формує мережу +Петрі, що представляє алгоритм параметричного синтезу координу- +вальної системи автоматичного управління. +Мета роботи є зниження необхідних обчислювальних і часових +ресурсів на розробку складних багаторівневих систем автоматичного +управління. +Для досягнення поставленої мети потрібно було розробити сис- +тему, яка здатна сформувати необхідний алгоритм параметричного +синтезу і виконати необхідний порядок дій згідно зі сформованим +алгоритмом. +Координувальна система автоматичного управління приводами +робота-маніпулятора представляється як дворівнева система [28; 29]. +Структурна схема моделі такої системи, що реалізована засобами се- +редовища MATLAB/Simulink, представлена на рисунку 17. Верхній +рівень управління системи пов’язаний з відпрацьовуванням помилок +регулювання за положенням зхвату Lm і за кутом повороту маніпуля- +тора αm, а нижній рівень пов’язаний з відпрацьовуванням неув’язок +співвідношень змінних, що представляють траєкторію руху зхвату +в циліндричній системі координат. Дворівневий закон цієї системи +управління можна представити так: +[ +] +1 +2 + +T +q +p +Lm +m +u +u +u +u +u α += ++ += +; +де +1 +2 +21 +2 +3 +31 +(1 +) +( ) +(1 +) +q +q +q +u +k +k +p +u +t +u +k +k +p +⋅ ++ +⋅ + + + + += += +⋅ψ + + + + +⋅ ++ +⋅ + + + + + — закон управління нижнього рівня; + +322 +1 +1 +11 +2 +4 +41 +( +( ) +( )) +(1 +) +( +( ) +( )) +(1 +) +p +mz +m +p +p +mz +m +u +L +t +L +t +k +k +p +u +u +t +t +k +k +p +− +⋅ +⋅ ++ +⋅ + + + + += += + + + + +α +− α +⋅ +⋅ ++ +⋅ + + + + + — закон управління +верхнього рівня; +( ) +( +) +( ) +( ) +m +m +m +t +f L +L +t +k +t +b +ψ += +⋅ ++ +⋅α +− + — відхилення (неув’язка) від спів- +відношення параметрів у момент часу t; +( ) +m +L +t , +( ) +m t +α + — регульовані зміни; +f(Lm) — нелінійна залежність, що відображена в системі у вигляді +ланки NU (рисунок 17), що описує траєкторію руху зхвата в коорди- +натах Lm – αm; +k1, k11, k2, k21 k3, k31, k4, k41 — параметри налаштування системи які +необхідно визначити з урахуванням прояву ефекту поділу руху; +αm.Z(t), Lm.Z(t) — задаючі впливи за кутом повороту і положенням +маніпулятора в площині F; +p — оператор диференціювання. +У даній роботі об’єкти системи координувального управління +описуються такими передатними функціями: +1 +1 +1 +( ) +( ) +( ) +( ) +L +L +X +p +k +W +p +u p +p Q +p += += +⋅ +, +2 +2 +2 +( ) +( ) +( ) +( ) +k +X +p +W +p +u +p +p Q +p +α +α += += +⋅ +, +у яких kL, kα — коефіцієнти передачі, QL(p), Qα(p) — деякі поліноми, +такі, що QL(0)=1, Qα(0)=1. +Рівняння кінематики робота встановлює зв’язок між різними ко- +ординатами. Рівняння Xi=F(q1, q2), де q1, q2 — координати Lm, αm від- +творюючих систем, визначають математичну модель механічної час- +тини робота. +Для параметричного настроювання даної координувальної сис- +теми автоматичного управління були реалізовані блоки формування +значень наступних інтегральних показників якості роботи системи: +1 +1 +0 +0 +2 +1 +1 +2 +( +( +( ) +( ) ) +( )) +( +( )) +m +t +t +mz +m +L +m +t +t +J +L +t +L +t +u +t dt +fL +t dt += +β ⋅ +− ++ += +∫ +∫ +; +1 +3 +4 +3 +0 +2 +1 +2 +01 +( ) +( ) +( ) +( ) +m +m +m +m +t +t +t +t +L +L +L +L +t +t +t +t +J +f +t dt +f +t dt +f +t dt +f +t dt + + + + += +− +− +− + + + + + + + + + + + + +∫ +∫ +∫ +∫ +; +1 +1 +0 +0 +2 +2 +2 +. +2 +( +( +( ) +( ) ) +( )) +( +( )) +m +t +t +m z +m +m +t +t +J +t +t +u +t dt +f +t dt +α += +β ⋅ α +− α ++ += +α +∫ +∫ +; + +323 + +Рис. 17. Структурна схема моделі автоматичної системи координувального +управління з контуром параметричного налаштування + +Block of adjusting settings +Position controlsystem +Lmz(t) +(0) "1 +PID(s) +u, +Outi +0.72 +口 +te: +0.3s+1 +PID Controller5 +Saturation3 +室 In3 +Out2 +Denspor +Transfer Fcn3 +Scope +Subsystem2 +1 +1/s +Coordination control system +Constant7 +Integratore [ +PID(s) +Qutt +PID Controller +In2 +I K, +±1/s +回 +Out2 +Table3PNU +ubsystem4 +Integrator1 +Graph7 +Scope11 +PID(s) +_ In1 +1/s +Constants +K3 +事_ In2 +Constant3 +中opMyBaHHA +PID Controller3 +Out2 +Subsystem +e2 +PID(s +Out ++() +1.47 ++1n2 +K4 +0.4g+1 +αm(t) +PID Controller8 +Out2 +Gain3 +Saturationg +Transfer Fcng +Scope1 +Subsystem1 +Control of angle KoHTyp perynroBaHH KyTa noBopoTy +尚 +Display +Jo1 +αmz(t) +Constant13 +Integrator1 +尚 +Graph5 k4 +Constants +_In1 +Graph3 J01 +Xin2 out2 +1 +1/s +Subsystem3 +Constante +Integrator4 +Setpoint speed +Display +Ji +3aBAaHHAiHTeHCMWBHOCTi +In +→ 1/s +Jo2 +Out2 +Constant14 Integrator12 +Subsystem7 +Generato +回 +aph4 +Constant4 +Block forming integral +indicator +± 1/s +Constant1 +XY Graphs +1-D T(u) +(n)1 0- ++n +± 1is +回 +onstant16 +ntegrator16 +事 In2 +Qut +Graph +Subsystem +Setpoint trajectory +Circuit of parametric optimization +KoHTyp napaMeTpMyHoi HacTpoikM +Step8 +fata1t +tp1 +nT +no +μ(pg) +data12 +datat +tp2 +n2 +Out2 +μu(p2) ++in3 +out +tp3 +室 In4 +Out +μ(P4) +Step +a15 +tp4 +data4 +童In5 +Out +step3 +tp5 +μ(p5) +data5 ++ Ine +Outd +tp6 +μ(g) +Step1 +童In +Out +tp7 +μ(p7) +Signals determination unit +Step +Vs +data7 +tp8 +事 In8 +Oute +rBa)r +ing +Outs ++gata03 +Chart3 +Jln10 +Ouol +X。 +Machine forming +Subsystemt +incidence matrix (AΦl) +Petri net +αm +[ypckui A.A. +Gurskiy A.A. 2016324 +1 +3 +4 +3 +0 +2 +1 +2 +02 +( ) +( ) +( ) +( ) +m +m +m +m +t +t +t +t +t +t +t +t +J +f +t dt +f +t dt +f +t dt +f +t dt +α +α +α +α + + + + += +− +− +− + + + + + + + + + + + + +∫ +∫ +∫ +∫ +; +1 +0 +2 +3 +( ) +t +t +J +t dt += ψ +∫ +; +1 +3 +4 +3 +0 +2 +1 +2 +2 +2 +2 +2 +03 +( ) +( ) +( ) +( ) +t +t +t +t +t +t +t +t +J +t dt +t dt +t dt +t dt + + + + += +ψ +− ψ +− +ψ +− ψ + + + + + + + + + + + + +∫ +∫ +∫ +∫ +, +де (t1 – t0)=(t3 – t2)=(t4 – t1)=(t5 – t3), t0 + Variable Preview +DesignVars(1,1) +- +.5 +2 +6 +8 +10 +12 +14 +16 +18 +20 +Name: +'K1 +Time (seconds)distillation cermo/Check Custom Bouncs1 +18 +16 +14 +12 +10 +6 +6 +8 +10 +12 +14 +16 +18 +20 +Time (seconds)334 + + +Рис. 28. Результати параметричної оптимізації за допомогою модуля Response +Optimization середовища MATLAB/Simulink при початкових значеннях +k1=0,3; k2=0; k3=0; k4=0,2 +Подальший розвиток дослідження, пов’язаного з формуванням +алгоритмів, дозволить створити на основі накопичених знань екс- +пертів інтелектуальну систему настроювання складних багаторівне- +вих систем на базі завдань управління й особливостей технологічно- +го об’єкта. + + MATLAB Workspace +clistillation_dermo/Check Custorn Bounds +Name +Value +K1 +2.1623 +田 +K2 +-0.4157 +6 +日 +K3 +-0.0675 +K4 +0.8618 + Model Workspace (distillation_demo) +Name +Value +@distillation_optim + +-10 + Variable Preview +DesignVars1(1,1) = +-20 +0 +2 +4 +10 +12 +14 +16 +18 +20 +Name: +"K1 - +Time (seconds)cistillation cermo,Check Custorm Bouncs' +25 +20 +15 +10 +5 +10 +2 +6 +8 +10 +12 +14 +16 +18 +20 +Time (seconds)337 + +Рис. 31. Спрощена структурна схема координувальної системи управління +приводами робота з системою автоматичного настроювання + +Hn4 +BepxHin piBeHb KCAy +X12(t) +Position control system +PID(s) +Controller +Xi(t) +HuKHui ypoBeHb KCAy +(0)x +X2(t) +ui +PID(s) +Controller +Saturation4 +ypaBiHHA +bnok +y, (t) +06'eKT +Scope2 +ΦopMyBaHHA +X2(t) +Wi +PID(s) +u2 +KoopAMHyBalbHui piBeHb +Controller +Saturation4 +Soope3 +ynpaBiHHA +Control of angle +X2 z(t) +PID(s) +GAOK BM3HayeHHA +Controller +3HayeHb KpWTepiiB +AKOCTi po6oTM +PerynaTop KyTa +noBopoTy +CWCTeMM +3aBAaHHA +Coordinationcontrolsystem +3a TpaeKTopier0 +() +pyxy +D/C +NepeTBoproBay +C/D +Machine forming +KoHTypnapaMeTpW4Hoi HacTpoMkM +incidence matrix (AΦl) +Stepe +事-/fata1 +tp1 +tp2 +JoriyHa yacTMHa +tp3 +P +tp4 +Step4 +=t=4 +tp5 +Po +P +iata5 +tp6 +Signals +Step1 +: +tp? +Vs +(1) +P6 +determination unit +=t: +tp8 +ats +MoAynb BM3HayeHHA cWrHaniB +Chart3 +opMyBaHHAanropuTMiB +Jdi(tk), +Jd2(tk), Jd3(tk) +iHUWAeHTHOCTi +(AΦl) +StateC4 +after(2000,tick) +[data28>0.5&data14<0.9] +, [data02>-10] +[data14<0.9] +State18 +State19 +State20 +State21 +State 17 +after(50,tick) +data4= -1 +after(50,ick) +data4=0; +data4=0 +data4=1; +data4=0 +exitdata24=1: +exit:data24=0; +[data14>0.9] +[data22>0.5&data14<0.9] +after(2000,tick) +StateC5 +after(2000,tick) +[data26>0.5&data15<2.2] +:7 +[data02>-10] +data15>0.5] +State23 +State 24 +State25 +State 31 +State22 +after(50,tick) +data5= +data4= -1 +after(50,tick) +data5=0; +data5=0; +data5=1; +exit:data25=1 +exit:data25=0 +[data15<0.5] +[data22>0.5&data15<2.2] +after(2000,tick) +[data24>0.5&data15<2.5] +ΦparMeHT Stateflow AiarpaMW opMyBaHHA MaTpui iHLMAeHTHocTi Mepeki eTpi338 +регуляторів, спрощена структурна схема якої представлена на рисун- +ку 31 [14]. Як видно з рисунку, система складається із двох частин — +неперервно-подійної частини і дискретно-подійної частини. +НПЧ представляє координувальну систему управління приводами +робота, а ДПЧ представляє алгоритм упорядкування дій при синтезі +КСУ і, у тому числі систему автоматичного настроювання. +Координувальна система автоматичного управління є дворів- +невою. Регулятори верхнього рівня відпрацьовують сигнали не- +узгодженості e1(t)=X1Z(t)–X1(t) і e2(t)=X2Z(t)–X2(t), де X1Z(t), X2Z(t), X1(t), +X2(t) — задані і фактичні значення регульованих змінних. Регулятори +нижнього рівня відпрацьовують відхилення від співвідношень змін- +них ψ=f(X1)⋅X1+k⋅X2–b, де X1, X2 — регульовані змінні; f(X1) — неліній- +на залежність, що відображена в системі у вигляді нелінійної ланки, +що описує траєкторію руху робота як керованого об’єкта в координа- +тах X1 — X2; k, b — коефіцієнт і вільний член. +Закон управління можна представити у такому вигляді: +[ +] +2 +21 +1 +11 +1 +1 +2 +4 +41 +3 +31 +2 +(1 +) +( ) +(1 +) +( ) +(1 +) +( ) +(1 +) +( ) +T +q +p +k +k +p +p +k +k +p +e p +u +u +u +u +u +k +k +p +p +k +k +p +e +p +⋅ ++ +⋅ +⋅ψ ++ +⋅ ++ +⋅ +⋅ + + += += ++ += + + +⋅ ++ +⋅ +⋅ψ ++ +⋅ ++ +⋅ +⋅ + + +, +де k2, k21, k4, k41 — параметри настроювання нижнього рівня КСАУ; +k1, k11, k3, k31 — параметри настроювання верхнього рівня КСАУ; +p=d/dt — оператор диференціювання; +, +q +p +u +u — вектори управління +нижнього і верхнього рівнів; u1 і u2– управляючі впливи. +Параметри настроювання k1, k2, k3, k4 КСАУ повинні бути визна- +чені системою автоматичного настроювання з урахуванням часової +співпідпорядкованості процесів регулювання. +Як видно з рисунку 31, процес формування елементів матриці +інцидентності мережі Петрі на базі сигналів визначення алгорит- +му Vs описується за допомогою Stateflow-діаграми середовища +MATLAB/Simulink [14]. Однак з урахуванням аналізу опису про- +цесу формування матриці інцидентності Stateflow-діаграми надалі +в минулому замінені на дискретно-безперервні мережі середовища +DС-net. +Слід зазначити, що Stateflow-діаграма менш інформативна для +розробки логічних модулів, наприклад, відсутня візуалізація зв’язків +між паралельними станами State31 — State35, що викликає труднощі +в розробці певних алгоритмів. ДБ-мережа в цьому випадку має деякі +переваги у візуалізації алгоритму і процесу функціонування логічного +модуля (I), що формує елементи матриці інцидентності, і також ДБ- + +339 +мережа має переваги в аналізі алгоритму за допомогою використання +методів аналізу мереж Петрі. +Отже, доцільно для моделювання і синтезу розглянутої системи +управління використовувати програмне середовище DС-net, яке має +у своєму розпорядженні засоби ДБ-мереж. +Програмне середовище DС-net спеціалізоване в напрямку ана- +лізу і синтезу складних технологічних систем з логіко-динамічним +характером функціонування. У нашому випадку, як і в попередньо- +му, розглянута система управління і синтезу, спрощена структурна +схема якої представлена на рисунку 31, за принципом функціону- +вання аналогічна логіко-динамічній. У системі присутні як дискрет- +ні +( ) +d +k +J +t +, +( ) +d +k +u t +, так і неперервні сигнали X1(t), X2(t), спостерігається +багаторежимний характер функціонування. Таким чином, надалі не- +обхідно визначити принципи формування алгоритмів на базі засобів +DС-net. +Принципи формування алгоритму за допомогою генерації мережі Пе- +трі, на базі засобів ДБ-мереж. Згідно з рисунком 31, послідовність опе- +рацій у системі при параметричному синтезі залежить від сигналів Vs +завдання алгоритму. Ці сигнали Vs можуть бути вироблені нейронною +мережею, адаптованою для виконання автоматичного настроювання +певної системи, в окремому випадку — системи координувального +управління. +В остаточному підсумку, спрощена структурна схема такої системи, +побудованої на базі нейронної мережі з можливостями самонастрою- +вання, буде мати вигляд, представлений на рисунку 32. У цій системі +алгоритм параметричного настроювання рівнів управління визнача- +ється нейронною мережею, у якій коефіцієнти міжнейроних з’єднань +змінюються в процесі функціонування блоком автонастройки. +Блок автонастройки вибірково змінює коефіцієнти міжнейро- +них з’єд нань випадковим чином. При цьому вибір коефіцієнтів між- +нейронних з’єднань для зміни здійснюється на базі значень критеріїв +якості роботи системи, а також на базі аналізу згенерованої мережі Пе- +трі, що представляє алгоритм параметричного настроювання системи. +У попередній системі, спрощена структурна схема якої представ- +лено на рисунку 31, матриця інцидентності мережі Петрі формуєть- +ся за допомогою модуля, функціонування якого було представлено +Stateflow-діаграмою. У розглянутій системі, реалізованій на базі не- +йронної мережі, замість Stateflow-діаграм використовуються мережі +Петрі. + +340 + +Рис. 32. Спрощена структурна схема системи, у якій здійснюється параме- +тричне настроювання регуляторів координувального рівня управління +Нейронна мережа реалізує процес композиції мереж Петрі (рису- +нок 33). У результаті процесу представляється матриця інцидентності +мережі Петрі, яка відображає алгоритм упорядкування дій при пара- +метричній настройці координувальної системи. +У програмному середовищі DС-net була реалізована така систе- +ма, у якій координувальний рівень управління синтезується на базі +функціонування мереж Петрі і нейронної мережі. На рисунку 33 +представлена схема даної системи засобами середовища DС-net. +Як видно з рисунка 33, нейронна мережа двошарова. Коефіцієнти +міжнейронних з’єднань 2-го шару безпосередньо визначають інци- +дентну матрицю генерованої мережі Петрі. А вагові коефіцієнти 1-го +шару визначають послідовність необхідних додаткових умов спра- +цьовування певних переходів мережі Петрі, пов’язаних з показника- +ми якості функціонування системи ψ , J, де +1 +3 +0 +2 +( ) +( ) +t +t +t +t +J +t dt +t dt += +ψ +− +ψ +∫ +∫ +, +(t1 – t0)=(t3 – t2), t0J +min +02 ++1 +611 +t11 +115 +p13 +: +t20 +/t12/ +p10 +HeipoHHa Mepexa +03 +/Neural network/ +AnropuTM +Mepexki eTpi/Petri Nets +△J. +p +min +01 +p +Pi +P3 +个k +AJ.=>J +00 +P3 +k2 +min +p4 +0 +ka +Ps +/ Automatic +P6 +0 +0 +0 +J=>J +Composition of Petri Net / +03 +min353 + +Рис. 42. Часові характеристики процесу настроювання координувальної системи автоматичного управління проце- +сом охолодження продуктів у тунельній камері + +XY Graph +uele +1 +回 +XY Graph1 + uel +0 +0 +回 +X +AJ. +1500 +50 +YAxis +Y Axis +1000 +500 +c +0 +100 +200 +300 +400 +500 +600 +700 +800 +900 +1000 +100 +200 +300 +400 +500 +: 600 +700 +800 +900 +1000 +B +A +B +3 +50 +k3 +50 +A +YAxis +YAxis +100 +200 +300 +400 +: 500 +600 +700 +800 +900 +1000 +100 +200 +300 +400 +500 +: 600 +700 +800 +900 +1000 +×10, t, cek. +x10, t, cek. +uele +2 +uele +4 +AJ. +200 +AJ +01 +03300 +YAxis +YAxis +200 +100 +100 +'B +D +o +1000 +100 +200 +300 +100 +200 +300 +400 +: 500 +600 +700 +800 +900 +400 +500 +600 +700 +800 +900 +100 +k2 +- +50 +0 +ki +c +YAxis +B +Y Axis +5 +-10 +A : +-15 . +100 +200 +300 +400 +500 +600 +700 +800 +900 +1000 +0 +100 +200 +300 +400 +500 +600 +700 +800 +900 +1000 +X Axis +×10, t, cek. +X Axis +x10, t, cek.354 +управляючий вплив u2 за швидкістю руху транспортера в тунельній +камері — температура повітря на виході з тунельної камери X2, °С; +01 +10 +X += − + °С; +02 +4 +X += − °С; W31(p) = 0, W32(p) = W3(p) = 1, X2 = X3, +X03 = X04 = 0. +Закон управління розглянутої системи: +[ +] +1 +2 +T +u +u +u += +; +де +1 +1 +0,05 +1 +u +k +p + + += +⋅ ++ +⋅ϕ + + + + +; +1 +2 +3 +0,05 +0,05 +1 +1 +u +k +k +e +p +p + + + + += +⋅ ++ +⋅ϕ + +⋅ ++ +⋅ + + + + + + + + +; +( ) +[ 1 +3] +t +X +b +ϕ += − +⋅ ++ + — відхилення від заданого співвідношення зна- +чень регульованих змінних; +0 +b = +; +1 +2 +[ +( ) +( )]T +X +X t +X +t += + — вектор регу- +льованих змінних; e(t) = Х2Z – Х2(t); Х2Z — задане значення температу- +ри на виході з холодильної тунельної камери, °С. +З рисунку 42 видно, що на кожному етапі настроювання приріст +ΔJ0i, i=0…3 відповідного критерію якості роботи системи (2) зводить- +ся до мінімального значення при зміні певного параметра настрою- +вання kj, j=1…3. На часовому інтервалі від 0 до точки А настроюєть- +ся регулятор № 3 верхнього рівня управління, на ділянці від А до В +настроюється регулятор № 1 координувального рівня управління. +Потім на ділянці В–С коректується параметр настроювання k3 регу- +лятора № 3 і в остаточному підсумку на 4 -му етапі настроюється ре- +гулятор № 2 координувального рівня. +Таким чином, система одержує кінцеві значення параметрів на- +строювання k1, k2, k3 КСАУ, які забезпечують відповідну якість регу- +лювання з урахуванням забезпечення режиму поділу руху [19]. +Кожний етап процесу настроювання, представлений на рисун- +ку 42, реалізується згідно зі згенерованою мережею Петрі, яка відо- +бражає процес настроювання КСАУ. +Штучна нейронна мережа реалізує формування і функціонування +мережі Петрі покроково. На кожному кроці представляється мережа +Петрі відповідно під номерами 1, 2 і т. д., як показано на рисунку 43. +Наприклад, згідно з рисунком 43, якщо перехід t1 веде до небажаної +ситуації — значення інтегральних показників якості системи за межа- +ми припустимого, то відзначається помилка на переході t1 і змінюють- +ся коефіцієнти міжнейронних з’єднань таким чином, що синтезується +мережа Петрі, представлена під номером 3. Отже, якщо були помилки +на переходах t1 і t2, то сформується мережа Петрі під номером 4 і так +далі, згідно з операціями, представленими на рисунку 43. + +355 + +Рис. 43. Візуалізація процесів синтезу різних мереж Петрі, які відображають +етапи настроювання координувальної системи автоматичного управління +Як видно з часових характеристик, представлених на рисунку 42, +процес настроювання системи здійснюється за умови стійкої її ро- +боти. Усі значення збільшень установлених критеріїв якості роботи +системи рухаються до нуля, що вказує не тільки на стійку роботу +синтезованої системи управління, але і на позитивний результат на- +строювання. Сформована мережа Петрі, що представлена на рисунку +41, відображає відповідний алгоритм настроювання системи, однак +коректування цієї мережі Петрі користувачем або експертом спричи- +нить впровадження в процес перенастроювання штучної нейронної +мережі. Отже, процес узгодження таких дій, які тягнуть зміну мережі +Петрі згідно з рисунком 43, важливо розглянути як окремий спосіб +тренування штучної нейронної мережі з учителем. + +t2 +Ne2 +No1 +01 +min +Ps个k3 +P +P3 +P +Po +C +Po +P2 +P4 +1k2 +P2 +P4 ++k2 +P6 +Ik3 +个 ++k, +Iks +HoMMJIka Ha Hepexoni +IoMIka Ha Iepexoi t +No3 +No5 +01 +min +二 +01 +Ps个ks +Pi +Ps个k3 +P3 +P1 个k, +po +Po +P4 lk. +P6/k3 +.3 +P2 +P4 ↓k2 +P6 +02 +↓ks +oMMJIKHHa +IoMIKH Ha +epexolax += +epexolax +12 +1 +03 +min += +min +2 +N6 +N4 +Jmin +01 +min +01 +Ps个k3 +P5个k3 +PI个k, +P +P3 +P3 +个k2 +O +O +O +Po +Po +. +P6/k +t3 +P2 +P6/ks +P2 +P4 +1k2 +O += +min +02 +min += +03 +min356 +Висновки. Нами було вирішено поставлену задачу, пов’язану з +розробкою системи автоматизованого настроювання багаторівневих +координувальних систем автоматичного управління. 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Дубна С. М. и др. Разработка алгоритмов управления процессами охлаж- +дения продуктов в туннельных камерах. Холодильна техніка та технологія. +Одесса, 2018. № 5. С. 67–71. ISSN 0453–8307. +СИСТЕМА АВТОМАТИЗОВАНОГО КОНТРОЛЮ ТЕХНІЧНОГО +СТАНУ ТА ДІАГНОСТУВАННЯ ПОТУЖНИХ ОБЕРТОВИХ +ЕЛЕКТРИЧНИХ МАШИН +Граняк В. Ф. +У роботі запропоновано перспективну апаратно-програмну реалізацію +системи автоматизованого контролю та діагностування потужних обер- +тових електричних машин. Реалізацію зазначеної автоматизованої системи +пропонується здійснювати на основі нестандартної штучної нейроподібної +мережі, що виступає в якості ключового елемента формування логічного +висновку, як типового представника системи виключної складності. Пока- +зано, що запропоноване рішення може розглядатись як окремо взятий уні- +кальний випадок, що має значну практичну цінність, оскільки може бути +адаптованим для вирішення задач широкого класу. +Було показано, що одним з найбільш перспективних вхідних сигналів, +що може використовуватися при побудові таких систем є вібросигнал. +Зокрема, зазначений параметр володіє достатньо високою інформатив- +ністю та може бути виміряний безпосередньо в режимі реального часу +роботи електричної машини без необхідності суттєвого втручання у її +конструкцію. + +359 +З метою підвищення ефективності роботи системи автоматизованого +контролю та діагностування було визначено та теоретично обґрунтовано +тривалість часових реалізацій вібросигналу, що доцільно використовувати +при отриманні коефіцієнтів взаємокореляції вібросигналів у досліджуваних +вузлах. А також запропоновано інтегральні високоінформативні числові +критерій оцінки впливу неврівноваженості ротора, семетричного зростан- +ня напруженості основного електро-магнітного поля, асиметрії струмів у +статорному колі та дефектів підшипників на коефіцієнти вейвлет-перетво- +рення у вигляді середньоквадратичного значення вейвлет коефіцієнтів інфор- +мативних смуг частот при дослідженні часового інтервалу, що значно пере- +вищує період обертання ротора електричної машини. Показано, що зазначені +критерії мають понижену чутливість до впливу неінформативних одиничних +збурень, які можуть виникати в процесі роботи електричної машини. +The paper proposes a promising hardware and software implementation of an +automated monitoring system and diagnostics of powerful rotating electric machines. +The implementation of this automated system is proposed to be carried out on the +basis of a non-standard artificial neural network, which acts as a key element in +forming a logical conclusion, as a typical representative of a system of exception- +al complexity. It is shown that the proposed solution can be considered as a single +unique case that has significant practical value, as it can be adapted to solve prob- +lems of a wide class. +It was shown that one of the most promising input signals that can be used in the +construction of such systems is a vibrating signal. In particular, this parameter is +quite informative and can be measured directly in real time of the electric machine +without the need for significant intervention in its design. +In order to increase the efficiency of the automated control and diagnostic sys- +tem, the duration of time realizations of the vibration signal was determined and +theoretically substantiated, which should be used in obtaining the correlation co- +efficients of vibration signals in the studied nodes. Also, was proposed integrated +highly informative numerical criteria for estimating the influence of rotor unbalance, +symmetric increase of main electromagnetic field strength, asymmetry of currents in +the stator circuit and bearing defects on wavelet transform coefficients in the form +of root mean square value. exceeds the period of rotation of the rotor of the electric +machine. It is shown that these criteria have a reduced sensitivity to the influence of +uninformative single perturbations that may occur during the operation of the elec- +tric machine. +Сьогодні склалася стійка тенденція до розвитку систем авто- +матизованого контролю та діагностування обертових електричних +машин, що обумовлюється як збільшенням кількості відповідного +обладнання, яке відпрацювало свій гарантійний строк, так і роз- +витком сучасної обчислювальної техніки та методів обробки вимі- +рювальної інформації [1]. Проте на сьогодні не існує узагальненої + +360 +теорії побудови таких систем, що суттєво ускладнює їх практичну +реалізацію. +В процесі аналізу імовірності появи дефектів при роботі оберто- +вих електричних машин було показано, що для будь-якої електрич- +ної машини під час оцінювання надійності її роботи доцільне засто- +сування методу слабких ланок, що дозволяє виокремити найбільш +типові дефекти, які з прийнятною імовірністю варто очікувати при +експлуатації такого обладнання [2]. Статистичний аналіз найбільш +імовірних дефектів, що характерні для електричних машин, показав, +що такими дефектами є: незбалансованість ротора, пошкодження +підшипників, пошкодження ізоляції (пробій) обмоток ротора, по- +шкодження ізоляції (пробій) обмоток статора, пошкодження крі- +плень стержнів чи деформація статора та порушення механічної +жорсткості кріплень [3]. +Тож, на основі сказаного, можна дійти висновку, що розробка +системи автоматизованого контролю та діагностування потужних +обертових електричних машин, що базувалася б на розвиненій теоре- +тичній концепції побудови такого обладнання, є актуальною науко- +во-прикладною задачею. +Розробка узагальненої апаратної структури системи автоматизо- +ваного контролю технічного стану та діагностування гідроагрегатів. +Реалізація системи автоматизованого контролю та діагностування +потужних обертових електричних машин має характеризуватися +гнучкістю та можливістю модернізації у широких межах, залежно +від умов та особливостей експлуатації, а також необхідної ефектив- +ності [4; 5]. Тож, до загальних принципів побудови таких систем +варто віднести модульний підхід до нарощування кількості вимірю- +вальних каналів з можливістю відносно легкої модернізації шляхом +підключення додаткових пристроїв та зміни програмного алгоритму +роботи систем. +Крім цього є очевидною необхіднісь застосування дворівневої +апаратної системи обробки вхідної інформації (результатів вимірю- +вання). Зокрема перший рівень доцільно реалізувати у вигляді дис- +кретних числових перетворювачів (мікроконтролерів), що здійснюва- +тимуть формування пакетів вимірювальної інформації у придатному +для подальшої обробки вигляді. Залежно від кількості вимірювальних +каналів, складності вимірювальних алгоритмів та доступної апарат- +ної продуктивності на першому рівні можуть застосовуватися на один +агрегат один або декілька числових перетворювачів [4; 5]. + +361 +Другий апаратний рівень, що доцільно реалізувати на основі штуч- +ної нейроподібної мережі, може бути представлений у вигляді висо- +копродуктивного сервера, що здійснюватиме попередню обробку па- +кетів вхідних даних та розрахунок на їх основі високоінформативних +критеріїв, що характеризують технічний стан електричної машини. +З метою збільшення швидкості роботи алгоритму та враховуючи зна- +чну кількість інформації, що має передаватися від блоку попередньої +обробки до штучної нейроподібної мережі (ШНМ), зазначені алго- +ритмічні операції доцільно виконувати у межах одного апаратного +рівня [6]. +У найпростішому випадку, при побудові системи автоматизовано- +го контрнолю технічного стану та діагностування обертової електрич- +ної машини структура такої системи може бути подібною до [7; 8]. +Структурну схему однієї з найпростіших систем автоматизованого +контролю та діагностування електричної машини наведено на рис. 1. +Пристрій працює таким чином: n віброперетворювачів 11–1n +здійснюють перетворення рівня віброприскорення, у n ключових +вузлах електричної машини, в рівень постійної напруги, значення +якої підсилюється до значення, придатного для роботи системи у n +масштабюучих підсилювачах 61–6n; n смугових фільтрів 81–8n від- +фільтровують вищі гармоніки вхідного сигналу, що не досліджуються +в процесі віброконтролю, пропускаючи на вихід лише ті гармонічні +складові, за якими проводиться контроль вібраційного стану. Сигнал +з виходів n смугових фільтрів 81–8n надходить на входи n елементів +аналогової пам’яті 91–9n відповідно, де запам’ятовують у момент +надходження з виходу формувача 7 одиничного сигналу, що відпові- +дає повороту ротора електричної машини на визначений кут α. Цей +же сигнал логічної одиниці з виходу формувача 7 поступає на перший +вхід першого порту мікроконтролера 13 та служить сигналом почат- +ку операції вимірювального перетворення віброприскорення. Після +цього на другому виході першого порту мікроконтролера 13 форму- +ється адресний сигнал, що відповідає першому інформаційному вхо- +ду аналогового мультиплексора 11, що призводить до встановлення +сигналу з його першого входу на його виході. Тоді на першому ви- +ході першого порту мікроконтролера 13 формується сигнал запуску +аналого-цифрового перетворення, що поступає на другий вхід циф- +ро-аналогового перетворювача 12, на перший вхід якого поступає +сигнал з виходу аналогового мультиплексора 11, результат цифро- +аналогового перетворення зчитується з виходу цифро-аналогового + +362 +СКП +Ф +Ω +Ф +Ω +Ф +Ω +MX +X1 +X2 +Xn +PC +Memory +... +Мікроконтролер +... +11 +1n +5 +61 +62 +6n +81 +82 +8n +91 +92 +9n +11 +12 +15 +14 +13 +АЦП +^ +# +PORT 1 +Таймер +SPI +PORT 2 +PORT 3 +F +7 +... +A1 +A2 +Am +... +10 +f +f / k +2 +6n+1 +a +U +12 +a +U +a +U +Xn+1 +Ω +9n+1 +T +U +3 +6n+2 +Xn+2 +Ω +9n+2 +X +U +4 +6n+3 +Xn+3 +Ω +9n+3 +d +U +16 +17 + +Рис. 1. Структурна схема однієї з найпростіших систем автоматизованого контролю +та діагностування обертової електричної машини + +363 +перетворювача 12 через перший вхід другого порту мікроконтроле- +ра 13 при приході на вхід другого порту мікроконтролера 13 сигналу +закінчення вимірювального перетворення. Після цього на другому +виході першого порту мікроконтролера 13 формується адреса наступ- +ного інформаційного входу аналогового мультиплексора 11. Решта +операцій повторюється циклічно, доки не буде отримано цифрове +значення сигналу на усіх входах аналогового мультиплексора 11, що +відповідають рівням віброприскорення у всіх ключових точках агре- +гату, значенню температури поточної полюсної обмотки, поточному +значенню осьового зміщення ротора та величини повітряного зазору +між ротором та статором. Після завершення цих операцій вимірю- +вальна система переходить у режим очікування наступного одинич- +ного імпульсу з виходу формувача 7, а після його отримання операції +повторюються циклічно. +На виході сенсора кутового положення 5 формується сигнал при +повороті ротора електричної машини на заданий кут α, який посту- +пає на вхід формувача 7. У формувачі 7 цей сигнал перетворюється у +сигнал логічної одиниці та поступає, окрім других входів елементів +аналогової пам’яті 81–8n+3 та першого входу першого порту мікро- +контролера 13, на вхід подільника частоти 10, на виході якого, при +надходженні на його вхід k-го імпульсу, що відповідає коефіцієнту ді- +лення частоти, формується сигнал логічної одиниці, який поступає +на вхід таймера мікроконтролера 13, де служить сигналом запису по- +точного числа, відрахованого таймером мікроконтролера 13. При по- +вороті ротора електричної машини на кут 360 градусів (повний оберт) +на виході сенсора кутового положення 5 формується сигнал подовже- +ної тривалості що у формувачі перетворюється на подовжений сиг- +нал логічної одиниці, який слугує для мікроконтролера 13 маркером +початку нового обороту ротора, що використовується для перевірки +правильності роботи подільника частоти 10. +На виході безконтактного датчика температури 2 формується сиг- +нал постійної напруги, що пропорційний температурі поточної по- +люсної обмотки ротора. Цей сигнал з виходу безконтактного датчика +температури 2 надходить на вхід n+1-го масштабюучого підсилюва- +ча 6, де підсилюється до рівня, придатного для подальшої цифрової +обробки. З виходу n+1-го масштабюучого підсилювача 6 підсилений +сигнал надходить на перший вхід n+1-го елемента аналогової пам’яті +9, де запам’ятовується при надходженні на його другий вхід керуючо- +го сигналу з виходу формувача 7. + +364 +На виході безконтактного датчика осьового зміщення ротора 3 +формується сигнал постійної напруги, що пропорційний поточно- +му осьовому зміщенню ротора. Цей сигнал з виходу безконтактний +датчик осьового зміщення ротора 3 надходить на вхід n+2-го мас- +штабуючого підсилювача 6, де підсилюється до рівня, придатного для +подальшої цифрової обробки. З виходу n+2-го масштабюучого під- +силювача 6 підсилений сигнал надходить на перший вхід n+2-го еле- +мента аналогової пам’яті 9, де запам’ятовується при надходженні на +його другий вхід керуючого сигналу з виходу формувача 7. +На виході безконтактного датчика повітряного зазору між ротором +та статором 4 формується сигнал постійної напруги, що пропорцій- +ний поточному осьовому зміщенню ротора. Цей сигнал з виходу дат- +чика повітряного зазору між ротором та статором 4 надходить на вхід +n+3-го масштабуючого підсилювача 6, де підсилюється до рівня, при- +датного для подальшої цифрової обробки. З виходу n+3-го масшта- +буючого підсилювача 6 підсилений сигнал надходить на перший вхід +n+3-го елемента аналогової пам’яті 9, де запам’ятовується при над- +ходженні на його другий вхід керуючого сигналу з виходу формувача 7. +Виміряні значення віброприскорення у всіх ключових точках +електричної машини, температури поточної полюсної обмотки ро- +тора, поточного осьового зміщення ротора, повітряного зазору між +ротором та статором, а також числовий код, відрахований таймером +за час повороту ротора електричної машини на кут kα, передається +через перший 14 та другий 16 пристрої перетворення інтерфейсу та +лінію зв’язку на сервер 17. Додатково на сервер 17 поступає вимірю- +вальна інформація від штатних сенсорів струму та напору. На сервері +17 здійснюється попередня обробка первинної вимірювальної інфор- +мації, прийняття рішення про наявність/відсутність дефектів, а та- +кож індикація результатів операцій контролю та діагностування. +Зовнішня пам’ять 15 застосовується для проміжного зберігання +отриманих числових значень, пропорційних виміряним величинам, +та, при потребі, програмного коду роботи мікроконтролера 13. +Розробка та теоретичне обґрунтування концепції побудови нейроподіб- +ної мережі, як ключового елементу прийняття рішень системи автоматизо- +ваного контролю та діагностування. Однією з головних тенденцій розви- +тку сучасної науки є збільшення питомої ваги систем, що можуть бути +віднесені до класу систем з виключною складністю [9; 10]. Головною +особливістю систем цього класу є наявність великої кількості зв’язків та +(або) факторів впливу, класичний математичний опис яких є неможли- + +365 +вим або недоцільним внаслідок суттєвого зростання складності моделі, +що робить її непридатною для практичного використання [10; 11]. +Враховуючи масштаби суспільного запиту на наукові підходи, що +можуть бути використані для розв’язання задач зазначеного класу, +цілком логічний активний розвиток концепцій, які виходять за межі +класичного математичного моделювання. І хоча на сьогоднішній +день найбільш поширеним методом вирішення таких задач ще зали- +шається метод експертного висновку [12], проте очевидно, що сучас- +ний рівень розвитку науки та техніки потребує інших, більш швидких +автоматизованих, а отже і менш трудомістких підходів, які можуть +бути використані для побудови технічних систем оперативного реагу- +вання. До таких підходів можна віднести відносно нові напрямки не- +чіткої логіки та нейроподібного моделювання [13]. Проте суттєвим їх +недоліком є відсутність чіткого алгоритму побудови термів чи вибору +вхідних параметрів та типу структури нейроподібної мережі. Відтак, +побудова кожної окремо взятої системи є унікальним технічним рі- +шенням, що має значну науково-практичну цінність. +Однією із задач, що має значний практичний інтерес та пов’язана +з необхідністю аналізу та формування логічного висновку у системі, +що відноситься до систем виключної складності, є задача діагносту- +вання обертових електричних машин [14]. +Одним з найперспективніших видів моніторингу технічного стану +та діагностування електричних машин є вібродіагностування [14; 15], +оскільки практично миттєва реакція вібросигналу на зміну технічно- +го стану є незамінною якістю останнього в аварійних ситуаціях, коли +визначальним чинником є швидкість постановки діагнозу і прийнят- +тя рішення. Крім того, віброакустичний сигнал має високу інформа- +тивність та при достатній кількості контрольованих точок дозволяє +з високою вірогідністю не лише встановлювати факт наявності того +чи іншого дефекту, а й потенційно виявляти місце його локалізації та +прогнозувати час його розвитку [16]. +Виключна складність при формуванні віброакустичних параме- +трів електричної машини пов’язана з динамічністю збурюючих впли- +вів, обумовлених доволі складною конструкцією механічної частини +електричної машини, що включаює у себе значну кількість просто- +рово розподілених елементів з пружними та в’язкими зв’язками [17]. +Крім цього, як було показано, аналіз одного лише вібросигналу не +дозволяє забезпечити достатньо високу вірогідність контролю, а отже +і досягти прийнятної ефективності системи діагностування. Тому су- + +366 +часні концепції побудови таких систем передбачають аналіз не лише +віброакустичного сигналу, а й інших додаткових параметрів, що неми- +нуче призводить до підвищення складності об’єкта дослідження [6]. +Оскільки побудова чіткої математичної моделі механічних за’язків +обертової електричної машини є практично неможливою, останню +доцільно розглядати як «чорну скриньку». Тобто моделювати не її +структуру, а зовнішнє функціонування [14]. Тому вирішення постав- +леної задачі доцільно здійснювати з застосуванням штучної нейропо- +дібної мережі (ШНМ). +Оскільки діагностування неминуче передбачає необхідність при- +йняття логічних висновків, є очевидним, що зазначений об’єкт є +класичним прикладом задачі формування логічного висновку в сис- +темах виключної складності за допомогою нейроподібної мережі. +Тож, алгоритм вирішення цієї задачі та структура запропонованої +нейроподібної мережі може розглядатися як окремо узятий унікаль- +ний випадок, що має значну практичну цінність, оскільки може бути +адаптованим для вирішення задач подібного типу. +Для побудови ШНМ необхідно спочатку визначити, яка інформа- +ція може надходити на її входи і що необхідно отримати в результаті +функціонування ШНМ. +Враховуючи аналіз, проведений раніше, побудову зазначеної сис- +теми діагностування пропонується здійснювати на базі вимірюваль- +них каналів віброакустичного сигналу та вимірювального каналу тем- +ператури, що здійснює послідовне вимірювання температури лобової +частини кожної із полюсних обмоток ротора. +У системі передбачені також додаткові канали, що здійснюють +вимірювання в режимі реального часу роботи машини таких параме- +трів, як потужність навантаження, частота обертання ротора та інших +необхідних технічних характеристик. +Ці дані надходять до підсистеми поточного моніторингу, звідки, +після попередньої обробки, передаються у підсистему діагностуван- +ня. Попередня обробка сигналів включає в себе дискретне вейвлет- +перетворення (ДВП) кожного із отриманих віброакустичних сигналів +з використанням різних материнських вейвлетів, з подальшим роз- +рахунком на основі отриманих коефіцієнтів ДВП високоінформатив- +них критеріїв, максимально чутливих до інформативних чинників +вібрації. На основі часової реалізації віброприскорення чи вібро- +швидкості, що типово вимірюються при роботі електричних машин +[18], здійснюється також аналітичний розрахунок віброзміщення, + +367 +методика якого детально описана у роботі [19]. Крім цього, у підсис- +темі поточного моніторингу проводиться розрахунок кутового при- +скорення ротора на основі миттєвих значень його швидкості обер- +тання та інші додаткові параметри електричної машини, що можуть +бути використані в якості вхідних величин ШНМ. +Отже, на вхід ШНМ мають надходити такі дані: +• всі значення віброзміщення, що перевищують допустиму норму +по кожному із вібросенсорів за певний інтервал часу із часовою фік- +сацією цих значень на проміжок часу Δτ; +• значення високоінформативних критеріїв, розрахованих на +основі віброакустичного сигналу; +• температура кожної з полюсних обмоток із фіксацією на один +оберт для роторних обмоток; +• струми у фазах статора; +• кутове прискорення ротора; +• значення механічної напруженості у ключових вузлах опорних +конструкцій; +• інші додаткові параметри технічного стану машини, що можуть +використовуватися для підвищення ефективності роботи системи +діагностування. +Враховуючи результати проведеного аналізу, запропоновано +структуру ШНМ для реалізації задачі діагностування, яку можна +представити у вигляді, наведеному на рис. 2. +Як видно з рис. 2, передбачається побудова чотиришарової не- +однорідної нестандартної ШНМ. +Кількість вхідних нейронів нульового шару (на рис. 2 вони зобра- +жені колами) відповідає кількості додаткових параметрів, що пода- +ються на входи ШНМ. Вхідні нейрони виконують функцію прийнят- +тя числових даних та їх сортування. +Перший шар ШНМ (нейрони якого позначені квадратиками із +цифрою 1) містить N∙М+K нейронів. Кожен із перших N∙М нейронів +отримує значення високоінформативного критерію, максимально чут- +ливого до інформативних чинників вібрації. Особливу групу ней ронів +зазначеного шару формують K останніх нейронів, на входи яких над- +ходить температура відповідної полюсної обмотки. Додатково на кожен +із нейронів першого шару надходить інтегральна інформація (інеграль- +ний критерій), сформована нульовим шаром нейронів на базі внутріш- +нього аналізу вимірювальної інформації від додаткових вимірювальних +каналів (кутового прискорення, потужності навантаження тощо). + +368 +Високоінформативний +критерій 1 +……………………….. +Високоінформативний +критерій m +Вібросенсор 1 +1 +1 +…….. +Неприпустимі значення +віброзміщення +Неприпустимі значення +віброзміщення +……………………….. +1 +1 +…… +………………………… +Неприпустимі значення +віброзміщення +……………………….. +1 +1 +…… +Рівень води +Зміна зазору між +ротором та статором +2 +2 +2 +3 +3 +3 +3 +3 +Незбалансованість ротора +Порушення жорсткості +Дефект турбінного +підшипника +Дефект опорного +підшипника +Пошкодження (пробій) +обмоток ротора +Осьове зміщення +ротора +Температура 1-ї +полюсної обмотки +……………………….. +Температура K-ї +полюсної обмотки +Блок температури полюсних +обмоток +1 +1 +2 +…… +Неприпустимі значення +температури полюсних +обмоток +Вібросенсор 2 +Високоінформативний +критерій 1 +Високоінформативний +критерій m +Вібросенсор N +Високоінформативний +критерій 1 +Високоінформативний +критерій M +Кутове прискорення +ротора +3 +Пошкодження (пробій) +обмоток статора +3 +Пошкодження кріплення +стержнів чи деформація +статора +3 +Порушення гідродинаміки +потоку +3 +Асиметрія силової +електричної мережі +Струм фази А +Струм фази B +Струм фази C +Механічна напруженість +опорної конструкції + +Рис. 2. Структура штучної нейроподібної мережі + +369 +Функції перетворення кожного із нейронів запропонованої штуч- +ної нейроподібної меежі формуються у результаті передексплуатацій- +ного навчання на основі статистичної інформації про особливості ро- +боти електричних машин дросліджуваного класу. Нейрони першого +шару призначені для коректування високоінформативних критеріїв +та показників температури полюсних обмоток із урахуванням інфор- +мації від додаткових вимірювальних каналів. Такий підхід є виправда- +ним, виходячи з того, що електрична машина є системою зі складни- +ми механічними зв’язками. Тож, при виникненні локальних збурень, +обумовлених неінформативними факторами, результуюча дія яких +має характеристики, подібні до впливів, обумовлених певними ви- +дами інформативних параметрів, в переважній більшості випадків +суттєвого спотворення зазнаватиме вимірювальна інформація на ви- +ході лише окремо взятого сенсора чи групи сенсорів, локалізованих у +певній області машини. +Другий шар нейронів ШНМ (позначений цифрою 2) містить N+1 +нейрон, N з яких отримує узагальнену критеріальну інформацію від +кожного із сенсорів віброприскорення та здійснює їх інтегральну об- +робку. На цьому етапі реалізується попередня задача імовірнісного +аналізу наявності інформативних параметрів та усувається надлиш- +ковість вимірювання, враховуючи неминучу залежність числових +критеріїв, що подаються на вхід ШНМ, від понад одного інформа- +тивного параметру. Останній нейрон другого шару призначений для +інтегральної обробки градієнта температур полюсних обмоток елек- +тричної машини. На нейрони цього шару, функції перетворення яких +були сформовані на етапі передексплуатаційного навчання, додатко- +во поступає інформація про перевищення рівня віброзміщення або +недопустимого перегріву полюсних обмоток. +Спрацювання ШНМ відбувається лише у випадку, коли хоча б в +одному із вібросигналів міститься надмірне віброзміщення або має +місце надмірний перегрів обмоток. В цьому випадку функція актива- +ції N нейронів другого шару може бути представленою як: + +0 +1 +( ) +( +, +) +( +), +M +i +i +j +j +a +sign a +a +p += +φ += +− +Δτ ⋅ +ψ +∑ + +(1) +де Δτ — часова затримка на вимикання; ai — поточне значення ві- +брозміщення, що поступає на відповідний нейрон; a0 — порогове +значення віброзміщення; pi — скоректований j-й інформативний +критерій; ψ(pi) — функція впливу скоректованого j-го інформатив- + +370 +ного критерію; sing(ai – a0, Δτ) — релейна функція з затримкою на +вимикання. +Функція перетворення N+1-го нейрону формується аналогічно, +з тією відмінністю, що спрацювання його релейної функції відбува- +ється при перевищенні температури хоба б однієї полюсної обмотки +деякого усталеного значення. +Третій шар ШНМ (позначений цифрою 3) містить 9 нейронів, ко- +жен з яких відповідає одному з чинників, які є досліджуваними при- +чинами виникнення вібрацій чи перегріву обмоток. У цьому шарі від- +бувається усереднення проміжних висновків, зроблених нейронами +другого шару, на основі їх інтегрального аналізу. +Слід зазначити, що логічний висновок такої системи, сформо- +ваний нейронами третього шару, носитиме ймовірнісний характер. +Перевищення певного встановленого значення ймовірності для +причин надмірного віброзміщення або надмірного перегріву обмо- +ток, що відносяться до дефектів, формує логічний висновок про їх +наявність. +Розробка високоінформативних діагностичних ознак наявності най- +більш поширених дефектів обертових електричних машин. Серед існу- +ючих достатньо описаних та вивчених підходів, придатних для ана- +лізу часової реалізації вібросигналу, що може бути отриманий під час +роботи реальної електричної машини, можна виділити перетворення +Фур’є та дискретне вейвлет-перетворення (ДВП). Проте варто від- +значити, що перетворення Фур’є математично є більш складним за +ДВП, а отже при забезпеченні однакової швидкодії потребуватиме +більших апаратних затрат, а також не передбачає можливості дослі- +дження локалізованих збурень взагалі [20]. Зазначені особливості ро- +блять його малоефективним для використання у сучасних системах +аналізу вібраційних сигналів електричних машин. Тоді як ДВП, буду- +чи у першу чергу адаптованим до виявлення саме локалізованих піко- +вих збурень, не передбачає наявності готових інструментів, призна- +чених для сепарації періодичної та аперіодичної складових. Виходячи +зі сказаного, можна дійти висновку про необхідність розробки нових +підходів до виявлення періодичних складових вібросигналу саме на +основі ДВП, які можуть викликатися типовими дефектами обертових +електричних машин. +За результатами статистичного дослідження причин виходу з ладу +асинхронних електродвигунів (які є найбільш поширеним типом +обертових електричних машин) встановлено, що у 79 % випадків при + +371 +відмові останніх мав місце один із трьох типів аномального відхилен- +ня технологічних параметрів, а саме: механічний дебаланс ротора, +пошкодження підшипників чи асиметрія струму у статорному колі +[3]. При цьому результуючий вібросигнал на ранніх етапах розвитку +дефектів, як правило, характеризується накладанням значної кіль- +кості рівноцінних збурюючих чинників, частина з яких має аперіо- +дичний характер [14; 21]. +Особливістю вібросигналів, обумовлених зазначеними типами +дефектів, є їх квазіперіодичний характер [14; 21]. Це призводить до +того, що при проведенні стандартного вейвлетаналізу наявність на- +ведених дефектів на ранніх етапах їх розвитку не призводить до появи +локального зростання амплітуди окремих коефіцієнтів ДВП, а отже +буде малопомітною при аналізі результатів перетворення. +Одна з головних ідей вейвлетного представлення сигналів на різ- +них рівнях декомпозиції (розкладання) сигналу полягає в розділенні +функцій наближення до сигналу на дві групи: що апроксимує — гру- +бу, з достатньо повільною часовою динамікою змін, і що деталізує — +з локальною і швидкою динамікою змін на тлі плавної динаміки, з +подальшим їх дробленням і деталізацією на інших рівнях декомпози- +ції сигналів. Це можливо як в часовій, так і в частотній областях пред- +ставлення сигналів вейвлетами. В цьому випадку базисна вейвлет- +функція дозволяє сконцентрувати увагу на тих або інших локальних +особливостях аналізованих процесів. Причому за своєю суттю дета- +лізація неперервного вейвлет-перетворення (НВП) є нічим іншим, +як визначенням функції взаємокореляції між материнською вейвлет- +функцією та досліджуваним сигналом, що випливає з математичної +моделі такого перетворення [20; 22]: + +* +, +( , ) +( ) +( ) +a +W a +f t +t dt ++∞ +τ +−∞ +τ = +⋅ψ +∫ +, +(2) +де W(a,τ) — функція деталізації (результат вейвлет-перетворення); +a — параметр масштабу; τ — параметр зсуву; f(t) — функція, що аналі- +зується; +* +, ( ) +a +t +τ +ψ + — комплексно спряжена вейвлет-функція. +Враховуючи те, що обчислення при вейвлетперетворенні здійсню- +ються шляхом зміни масштабу «вікна» аналізу, зсуву його в часі, мно- +ження на сигнал та інтегрування по всій осі часу [22; 23], то геометрич- +ний зміст такого перетворення можна представити як пошук ділянок +аналізованої функції у часовій та частотній областях, що за своєю фор- +мою будуть корельованими з материнською вейвлет-функцією. + +372 +Аналогічний фізичний зміст зберігається й у ДВП, при здійсненні +якого коефіцієнти деталізації можуть бути розраховані таким чином +[20; 23]: + +1 +2 +, +j +j +k +n +k +n +n Z +d +g +c + +− +∈ += +⋅ +∑ + +(3) +де +j +k +d — k-й коефіцієнт деталізації j-ї частотної смуги; g — коефіцієнт +материнської вейвлет-функції; cj+1 — апроксимуючий коефіцієнт по- +передньої частотної смуги, розраховуються так: + +1 +2 +, +j +j +k +n +k +n +n Z +c +h +c + +− +∈ += +⋅ +∑ + +(4) +де h — коефіцієнт масштабуючої функції. +Для старшої частотної смуги в якості апроксимуючих коефіцієнтів +використовується часова реалізації досліджуваного сигналу. +В такому випадку задача реєстрації зазначених дефектів може бути +розбита на дві підзадачі: підбір материнського вейвлету, який був би +максимально наближений до обумовленої дефектом складової вібро- +сигналу, та розробка критерію, який би давав змогу кількісно оцінити +вплив обумовленого наявністю дефекту коливання на коефіцієнти +вейвлет-перетворення окремих частотних смуг та характеризувався б +високою селективністю по відношенню до нього. +Аналіз наведених у літературі описів вібраційних сигналів, обу- +мовлених неврівноваженістю ротора, показує, що зазначений дефект +призводить до появи коливань, які містять гармонічну складову, ло- +калізовану на роторній частоті обертання, а також її другій та третій +гармоніці. Причому амплітуда коливань з переходом на другу та тре- +тю гармонічні складові різко зменшується [14; 21]. Зазначений факт +обумовлює доцільність аналізу при його пошуку частотного діапазо- +ну, що включає у себе частоту обертання ротора та, меншою мірою, +частотні діапазони, які відповідають подвоєній та потроєній роторній +частоті. А підбір материнського вейвлету доцільно здійснювати ви- +ходячи з ознак, властивих одиничному гармонічному коливанню. Як +показує дослідження літературних джерел, найбільш спорідненим з +одиничним гармонічним коливанням серед типових материнських +вейвлет-функцій можна вважати вейвлет Хаара та вейвлет Добеши +4-го порядку. Проте варто відзначити, що кожен із них має свої суттє- +ві структурі відмінності [23]. +Також, враховуючи періодичність вібраційного сигналу, обумовле- +ного наявністю дебалансу ротора, і ту обставину, що при дослідженні +кожне із гармонічних коливань представляється як окремий сплеск, + +373 +варто очікувати періодичну зміну значень вейвлет-коефіцієнтів у ча- +совій області в межах смуг частот, що включають у себе роторну час- +тоту, а також її другу та третю гармоніки. Причому амплітуди таких +періодичних змін будуть напряму пов’язані зі ступенем розвитку де- +фекту. Тож виконується нерівність [24]: + +, +сп +р +t +T +>> + +(5) +де tсп — тривалість часової реалізації досліджуваного сигналу; Tр — пе- +ріод обертання ротора електричної машини. +Доцільним є застосування інтегрального підходу до аналізу коефі- +цієнтів вейвлет-перетворення. Відтак, у якості шуканого числового +критерію наявності зазначеного дефекту може бути використано усе- +реднене квадратичне значення вейвлет-коефіцієнтів досліджуваних +частотних смуг у межах часового інтервалу, тривалість якого значно +більша за період обертання ротора. Такий підхід дозволить врахувати +наявність як додатних, так і від’ємних максимумів вейвлет-коефіці- +єнтів у межах досліджуваного часового інтервалу, а також характери- +зуватиметься пониженою чутливістю до неінформативних збурень, +обумовлених аперіодичними збурюючими силами, що можуть вини- +кати в процесі експлуатації електричної машини. Виходячи зі сказа- +ного, математично числовий критерій оцінки впливу дебалансу рото- +ра на коефіцієнти вейвлет-перетворення зазначених частотних смуг +може бути представлений таким чином [24]: + +2 +1 +1 +, +n +äåá +i +ñï +ð +i +k +d ïðè óìîâ³ t +T +n +� +� +�� +� + +(6) +де n — кількість коефіцієнтів вейвлет-перетворення досліджуваної +частотної смуги; di — і-й коефіцієнт вейвлет-перетворення досліджу- +ваної частотної смуги. +З метою підтвердження неведених вище теоретичних міркувань +було проведено експериментальне дослідження з використанням +електричної машини в режимі холостого ходу з моментом інерції ро- +тора — 0,002 кг∙м2, частотою обертання в режимі холостого ходу — +720 об/хв (12 Гц) та додатково внесеним дебалансом 0,002 кг∙м. +П’єзоакселерометр було закріплено на корпусі електричної машини +таким чином, що вимірювальна вісь була напрямлена строго перпен- +дикулярно ротору електричної машини. Частота дискретизації сиг- +налу становила 232 Гц, довжина часової реалізації досліджуваного +сигналу — 214 значень. + +374 +При перетворенні отриманого сигналу віброприскорення за +допомогою вейвлета Хаара та подальшого розрахунку запропоно- +ваного числового критерію для кожної із частотних смуг з та без +використання дебалансу було отримано результати, наведені на +рис. 3 та 4. +0 +0,05 +0,1 +0,15 +0,2 +0,25 +0,3 +0,35 +0,4 +0,45 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +0 +5 +10 +15 +20 +25 +30 +35 +40 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +Рис. 3. Залежність усередненого квадратичного вейвлет-коефіцієнтів Хаара +для кожної із частотних смуг вібросигналу без використання дебалансу +0 +0,05 +0,1 +0,15 +0,2 +0,25 +0,3 +0,35 +0,4 +0,45 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +0 +5 +10 +15 +20 +25 +30 +35 +40 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +Рис. 4. Залежність усередненого квадратичного вейвлет-коефіцієнтів Хаара +для кожної із частотних смуг вібросигналу при наявності дебалансу + +375 +Також було виконано аналогічне перетворення за допомогою вейвле- +та Добеши 4-го порядку. Результати розрахунку наведені на рис. 5 та 6. +Рис. 5. Залежність усередненого квадратичного вейвлет-коефіцієнтів Добе- +ши 4-го порядку для кожної із частотних смуг вібросигналу без використання +дебалансу +Рис. 6. Залежність усередненого квадратичного вейвлет-коефіцієнтів Добе- +ши 4-го порядку для кожної із частотних смуг вібросигналу при наявності +дебалансу + +0,45 +0,4 +0,35 +0,3 +0,25 +0,2 +0,15 +0,1 +0,05 +0 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +1440 +35 +30 +25 +20 +15 +10 +5 +0 +1 +2 +3 +4 +5 +6 +7 +8 +6 +10 +11 +12 +13 +140,45 +0,4 +0,35 +0,3 +0,25 +0,2 +0,15 +0,1 +0,05 +0 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +1440 +35 +30 +25 +20 +15 +10 +5 +0 +1 +2 +3 +4 +5 +6 +7 +8 +6 +10 +11 +12 +13 +14376 +Як випливає з аналізу залежностей, наведених на рис. 3–6, най- +більш інформативними для виявлення дебалансу ротора, як і очі- +кувалося, є смуги частот, що відповідають частоті обертання ротора +електричної машини та її другої та третьої гармоніки (відповідно 11, +12 та 13 частотні смуги). Порівняння ж результатів, отриманих при +розкладанні сигналу на основі вейвлету Хаара та вейвлету Добеши +4-го порядку, показали, що обидва вейвлета характеризуються при- +близно однаковою достатньо високою чутливістю до наявності до- +сліджуваного дефекту. Тож, враховуючи той факт, що перетворення +на основі материнської вейвлет-функції Хаара є математично більш +простим (потребує меншої кількості математичних операцій) [20; 22; +23], можна зробити висновок, що використання саме останнього є +більш ефективним для виявлення зазначеного дефекту. +Аналізуючи наведені у літературі описи вібраційних сигналів, обу- +мовлених пошкодженнями підшипників обертової електричної ма- +шини, ми встановили, що зазначена група дефектів викликає доволі +складний за формою квазіперіодичний вібраційний відгук, частота +якого відповідає роторній частоті електричної машини [14; 21]. Врахо- +вуючи ту обставину, що вібраційний відгук, обумовлений пошкоджен- +ням підшипників, в межах одного періоду характеризуватиметься де- +кількома піками, очевидно, що для виявлення такого пошкодження +доцільним буде застосування материнських вейвлет-функцій старших +порядків. Це пояснюється тим, що при зростанні порядку материн- +ської вейвлетфункції типово зростає число її осциляцій. Тож, для вей- +влет-функції N-го порядку буде справедливим вираз [20; 22; 23]: + +( ) +0, +0,1,..., +1. +kt +t dt +k +N ++∞ +−∞ +ψ += += +− +∫ + +(7) +Оскільки розрахунок коефіцієнтів переважної більшість дискрет- +них вейвлет-функцій є доволі трудомістким [20; 22; 23], а форма ві- +браційного відгуку при пошкодженнях підшипників характеризу- +ється доволі складною структурою, яка однозначно не асоціюється +з жодним із відомих вейвлетів, у якості базових вейвлет-функцій +пропонується використання вейвлетів Добеши. Головною перевагою +зазначеного сімейства вейвлет-функцій є можливість відносно про- +стого аналітичного розрахунку їх коефіцієнтів для функції довільно- +го порядку [25]. В такому випадку математичний числовий критерій +оцінки впливу наявності дефектів підшипників на коефіцієнти вей- +влетперетворення частотних смуг буде аналогічним критерію наяв- + +377 +ності дебалансу ротора (6) за умови використання зазначених мате- +ринських вейвлет-функцій. +З метою підтвердження неведених вище теоретичних міркувань +було проведено експериментальне дослідження з використанням +асинхронної електричної машини АИМ90La6У2.5, номінальною по- +тужністю 0,75 кВт та синхронною швидкістю обертання 1000 об/хв +(16,67 Гц) при її експлуатації в режимі холостого ходу. Дефект підшип- +ника було імітовано шляхом застосування підшипників при відсутнос- +ті масляної плівки. Інші параметри експерименту були повністю ана- +логічними дослідженню впливу дебалансу ротора, описаному вище. +При перетворенні отриманого сигналу віброприскорення за допо- +могою вейвлета Добеши 4-го порядку та подальшого розрахунку се- +редньоквадратичного вейвлет-коефіцієнтів для кожної із частотних +смуг при роботі електричної машини у режимі холостого ходу було +отримано результати, наведені на рис. 7 та 8. +Аналогічне перетворення отриманого вібросигналу було викона- +но за допомогою вейвлета Добеши 6-го порядку. Результати розра- +хунку наведені на рис. 9 та 10. +Як випливає з аналізу залежностей, наведених на рис. 7–10, най- +більш інформативними для виявлення дефекту підшипників, як +0 +0,05 +0,1 +0,15 +0,2 +0,25 +0,3 +0,35 +0,4 +0,45 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +0 +0,05 +0,1 +0,15 +0,2 +0,25 +0,3 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +Рис. 7. Залежність усередненого квадратичного вейвлет-коефіцієнтів Добе- +ши 4-го порядку для кожної із частотних смуг вібросигналу при наявності +мастила у підшипнику + +378 +0 +0,05 +0,1 +0,15 +0,2 +0,25 +0,3 +0,35 +0,4 +0,45 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +0 +0,05 +0,1 +0,15 +0,2 +0,25 +0,3 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +Рис. 8. Залежність усередненого квадратичного вейвлет-коефіцієнтів Добе- +ши 4-го порядку для кожної із частотних смуг вібросигналу при відсутності +мастила у підшипнику +0 +0,02 +0,04 +0,06 +0,08 +0,1 +0,12 +0,14 +0,16 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +0 +0,1 +0,2 +0,3 +0,4 +0,5 +0,6 +0,7 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +Рис. 9. Залежність усередненого квадратичного вейвлет-коефіцієнтів Добе- +ши 6-го порядку для кожної із частотних смуг вібросигналу при наявності +мастила у підшипнику + +379 +0 +0,02 +0,04 +0,06 +0,08 +0,1 +0,12 +0,14 +0,16 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +0 +0,1 +0,2 +0,3 +0,4 +0,5 +0,6 +0,7 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +Рис. 10. Залежність усередненого квадратичного вейвлет-коефіцієнтів Добе- +ши 6-го порядку для кожної із частотних смуг вібросигналу при відсутності +мастила у підшипнику +і очікувалося, є частотна смуга, що відповідає частоті обертання ротора +(12 частотна смуга), та її друга (13 смуга частот) і третя (14 смуга частот) +гармоніки. Порівняння ж результатів, отриманих при розкладанні сиг- +налу на основі вейвлету Добеши 4-го, 6-го порядку, показали справед- +ливість зроблених раніше припущень про доцільність використання +для виявлення зазначеного дефекту вейвлетів старших порядків. +У свою чергу для вібросигналів, обумовлених асиметрією струму у +статорному колі, є характерною наявність гармонічної складової вібро- +сигналу, локалізованої на частоті напруги живлення електричної мережі +[14; 21]. Зазначений факт обґрунтовує доцільність аналізу частотного діа- +пазону, що включає у себе частоту напруги живлення, та використання +вейвлетів Хаара та Добеши 4-го порядку виходячи з міркувань, наведе- +них вище. В такому випадку числовий критерій оцінки впливу електро- +магнітної асиметрії статорного кола на коефіцієнти вейвлетперетворен- +ня зазначених частотних смуг може бути представлений так [26]: + +2 +1 +1 +, +n +äåá +i +ñï +æ +i +k +d ïðè óìîâ³ t +T +n +� +� +�� +� + +(8) +де Tж — період напруги живлення статорного кола. +З метою підтвердження неведених вище теоретичних міркувань +було проведено експериментальне дослідження з використанням + +380 +асинхронної електричної машини, описаної у попередньому досліді. +Інші параметри експерименту були повністю аналогічними дослі- +дженню впливу дебалансу ротора, описаному вище. +При перетворенні отриманого сигналу віброприскорення за допо- +могою вейвлета Хаара та подальшого розрахунку усередненого ква- +дратичного вейвлет-коефіцієнтів для кожної із частотних смуг при +роботі електричної машини у штатному режимі та обриві фази А було +отримано результати, наведені на рис. 11 та 12. +Також було виконано аналогічне перетворення отриманого вібро- +сигналу за допомогою вейвлета Добеши 4-го порядку. Результати роз- +рахунку наведені на рис. 13 та 14. +Як випливає з аналізу залежностей, наведених на рис. 11–14, най- +більш інформативною для виявлення асиметрії живлення, як і очі- +кувалося, є частотна смуга, що відповідає частоті напруги живлення +електромережі 50 Гц (13 частотна смуга). Порівняння ж результатів, +отриманих при розкладанні сигналу на основі вейвлету Хаара та вей- +влету Добеши 4-го порядку показало, що обидва вейвлета характе- +ризуються приблизно однаковою достатньо високою чутливістю до +наявності досліджуваного дефекту. Тож, виходячи з наведених вище +міркувань, можна зробити висновок про доцільність використання +саме вейвлета Хаара для вирішення поставленої задачі. +0 +0,05 +0,1 +0,15 +0,2 +0,25 +0,3 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +0 +0,05 +0,1 +0,15 +0,2 +0,25 +0,3 +0,35 +0,4 +0,45 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +0 +0,02 +0,04 +0,06 +0,08 +0,1 +0,12 +0,14 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +Рис. 11. Залежність усередненого квадратичного вейвлет-коефіцієнтів Хаара +для кожної із частотних смуг вібросигналу при роботі електродвигуна у штат- +ному режимі + +381 +0 +0,05 +0,1 +0,15 +0,2 +0,25 +0,3 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +0 +0,05 +0,1 +0,15 +0,2 +0,25 +0,3 +0,35 +0,4 +0,45 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +0 +0,02 +0,04 +0,06 +0,08 +0,1 +0,12 +0,14 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +Рис. 12. Залежність усередненого квадратичного вейвлет-коефіцієнтів Хаара +для кожної із частотних смуг вібросигналу при обриві фази А +0 +0,05 +0,1 +0,15 +0,2 +0,25 +0,3 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +0 +0,05 +0,1 +0,15 +0,2 +0,25 +0,3 +0,35 +0,4 +0,45 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +0 +0,02 +0,04 +0,06 +0,08 +0,1 +0,12 +0,14 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +Рис. 13. Залежність усередненого квадратичного вейвлет-коефіцієнтів Добе- +ши 4-го порядку для кожної із частотних смуг вібросигналу при роботі елек- +тродвигуна у штатному режимі + +382 +0 +0,05 +0,1 +0,15 +0,2 +0,25 +0,3 +0,35 +0,4 +0,45 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +Рис. 14. Залежність усередненого квадратичного вейвлет-коефіцієнтів Добе- +ши 4-го порядку для кожної із частотних смуг вібросигналу при обриві фази А +Висновки. 1. Запропоновано використання та розроблено структу- +ру ШНМ в якості ключового елемента формування логічного висно- +вку в системі діагностування гідроагрегатів, як типового представ- +ника системи виключної складності. Показано, що запропоноване +рішення може розглядатись як окремо взятий унікальний випадок, +що має значну практичну цінність, оскільки може бути адаптованим +для вирішення задач широкого класу. +2. Набув подальшого розвитку алгоритм аналізу систем типу «чор- +на скринька» з розподіленими параметрами шляхом незалежної інте- +гральної обробки інформації на локалізованих ділянках, з подальшим +її загальним аналізом у нейронному шарі верхнього рівня. Показано, +що зазначений підхід дає змогу вилучити вплив неінформативних +чинників, які за структурою своєї дії є подібними до інформативного +впливу, проте носять локальний характер. +3. Визначено та теоретично обґрунтовано тривалість часових ре- +алізацій вібросигналу, що доцільно використовувати при отриманні +коефіцієнтів взаємокореляції вібросигналів у досліджуваних вузлах. +Встановлено, що тривалість таких реалізацій повинна бути кратною +частоті періоду обертання ротора електричної машини. +4. Запропоновано інтегральні високоінформативні числові кри- +терій оцінки впливу неврівноваженості ротора, семетричного зрос- +тання напруженості основного електромагнітного поля, асиметрії + +383 +струмів у статорному колі та дефектів підшипників на коефіцієнти +вейвлет-перетворення у вигляді середньоквадратичного значення +вейвлет-коефіцієнтів інформативних смуг частот при дослідженні +часового інтервалу, що значно перевищує період обертання ротора +електричної машини. Показано, що зазначені критерії мають пони- +жену чутливість до впливу неінформативних одиничних збурень, які +можуть виникати в процесі роботи електричної машини. +СПИСОК ВИКОРИСТАНОЇ ЛІТЕРАТУРИ +1. Левицький А. С., Федоренко Г. М., Грубой О. П. Контроль стану потуж- +них гідро- та турбогенераторів за допомогою ємнісних вимірювачів пара- +метрів механічних дефектів: монографія. Київ: Інститут електродинаміки +НАН України, 2011. 242 с. +2. Бигус Г. А., Даниев Ю. Ф., Быстрова Н. А., Галкин Д. И. 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Особливості +побудови системи моніторингу технічного стану та діагностування гідро- +агрегатів: монографія. Вінниця: ВНТУ, 2019. 91 с. +18. Колесников А. Е. Акустические измерения. Ленинград: Судостроение, +1983. 256 с. +19. Vedmitskyi Y. G., Kukharchuk V. V., Hraniak V. F., Wojcik W. et al. New +non-system physical quantities for vibration monitoring of transient processes at +hydropower facilities, integral vibratory accelerations. Przegląd electrotechnicz- +ny. 2017. № 3. P. 69–72. DOI:10.15199/48.2017.03.17 +20. Воробъёв В. И., Грибунин В. Г. Теория и практика вейвлет-преобразова- +ния. Санкт-Петербург: ВСУ, 1999. 204 с. +21. Ширман А. Р., Соловьев А. Б. Практическая вибродиагностика и мони- +торинг состояния механического оборудования. Москва: Машиностро- +ение. 1996. 276 с. +22. Broughton S. A., Bryan K. Discrete fourier analysis and wavelets: applications to +signal and image processing. New Jersey: John Wiley & Sons, Inc., 2008. — 355 p. +23. Polikar R. The Wavelet tutorial. Roma: Rowan University, College of Engineer- +ing Web Servers, 2001. 79 p. +24. Граняк В. Ф., Кацив С. Ш., Кухарчук В. В. Використання дискретного +вейвлетаналізу віброакустичного сигналу для виявлення дебалансу рото- +ра обертових електричних машин. Наукові праці ДонНТУ. Серія: Інфор- +матика, кібернетика та обчислювальна техніка. 2021. № 1 (32). C. 32–40. +25. Добеши И. Десять лекций по вейвлетам. Ижевск: НИЦ «Регулярная и ха- +отическая динамика», 2001. 464 с. +26. Граняк В. Ф., Гайдамак О. Л. Використання дискретного вейвлет-аналізу +вібро-акустичного сигналу для виявлення асиметрії живлення обертових +електричних машин змінного струму. Вібрації в техніці та технологіях. +2021. № 2 (101). C. 62–70 + +385 +Розділ ІІІ +НОВІ ІНФОРМАЦІЙНІ ТЕХНОЛОГІЇ В ОСВІТІ +АВТОМАТИЗОВАНА ІНФОРМАЦІЙНА СИСТЕМА ОБЛІКУ +ПІДВИЩЕННЯ КВАЛІФІКАЦІЇ ВИКЛАДАЧІВ +Іванова Л. В., Котлик Д. О. +У статті розкриваються сучасний стан інформатизації закладів осві- +ти, інформаційне забезпечення управлінської діяльності керівника закладу +освіти. Наводиться порівняльний аналіз комерційних комплексних автома- +тизованих систем управління навчальним процесом із автоматизованими +системами управління власних розробок закладів вищої освіти, а також їхні +функціональні можливості в управлінні навчальним процесом та їхні особли- +вості. +Представлені матеріали, що стосуються проектування автомати- +зованої інформаційної системи обліку підвищення кваліфікації викладачів +закладу освіти. Встановлено, що реалізація цієї системи — це об’єктивна +необхідність, яка обумовлена реформуванням діяльності освітніх закладів +та доцільністю автоматизації оцінювання якості підвищення кваліфікації +викладачів навчальних закладів для швидкого прийняття управлінських рі- +шень щодо їх атестації та педагогічної діяльності. +У статті представлена автоматизована інформаційна система обліку +підвищення кваліфікації викладачів закладу освіти, яка дозволяє зберіга- +ти, обробляти та контролювати результати підвищення кваліфікації та +атестації викладачів. Визначено, що застосування комплексного підходу до +зберігання результатів підвищення кваліфікації та атестації викладачів за- +безпечує: оперативний моніторинг інформації про підвищення кваліфікації +викладачів для проходження чергової атестації; зручне заповнення та збере- +ження інформації; можливість контролю підвищення кваліфікації виклада- +чів з боку працівників методичного кабінету. +Визначено схему інформаційних потоків, спосіб зберігання і виведення +даних, розглянуто сучасні технології, які дають можливість аналізувати і +створювати візуальне представлення даних для здійснення процесів обліку, +моніторингу та контролю. Спроектовані база даних та інтерфейс корис- +тувача інформаційної системи обліку підвищення кваліфікації та атестації +викладачів закладу освіти. +Створена автоматизована інформаційна система обліку підвищення +кваліфікації викладачів закладу освіти проходить апробацію в робочому про- + +386 +цесі методичного кабінету коледжу для обліку результатів підвищення ква- +ліфікації та проходження атестації викладачів Відокремленого структур- +ного підрозділу «Одеський технічний фаховий коледж Одеської національної +академії харчових технологій»». +The article reveals the current state of informatization of educational institu- +tions, information support of management activities of the head of the educational +institution. The comparative analysis of commercial complex electronic systems of +management of educational process with electronic systems of management of own +developments of higher educational institutions, and also their functional possibili- +ties in management of educational process and their characteristic is resulted. +Materials related to the design of an automated information system for account- +ing for professional development of teachers of educational institutions are present- +ed. It is established that the implementation of this system is an objective necessity, +which is due to the reform of educational institutions and the feasibility of auto- +mating the quality assessment of teachers by teachers to quickly make management +decisions on their certification and teaching. +The article presents an automated information system for accounting for in-ser- +vice training of teachers of educational institutions, which allows you to store, pro- +cess and control the results of in-service training and certification of teachers. It is +determined that the application of a comprehensive approach to the storage of results +of in-service training and certification of teachers provides — operational monitor- +ing of information about in-service training of teachers to pass the next certification; +convenient filling and saving of information; possibility of control of advanced train- +ing of teachers by employees of a methodical office. +The scheme of information flows, the method of data storage and output are de- +termined, modern technologies are analyzed, which give the opportunity to analyze +and create a visual representation of data for the implementation of accounting, +monitoring and control processes. The database and the user interface of the infor- +mation system of the account of advanced training and certification of teachers of +educational institution are designed. +The created automated information system of the account of advanced training +of teachers of educational institution passes approbation in working process of a me- +thodical office of college for the account of results of advanced training and passing +of certification of teachers of Separated structural subdivision «Odessa Technical +Applied College Odessa National Academy of Food Technologies». +Освіта має винятково важливе значення для соціально-економіч- +ного розвитку та культурного збагачення суспільства, наділяючи лю- +дей відповідними знаннями та вміннями для покращення навичок, +здатності до продуктивної праці в умовах подальшого глобального +розвитку, домінантою якої є інтелектуальна економіка. Для України +актуальним є завдання ефективного забезпечення та організації на- + +387 +вчання учнів/здобувачів освіти у системі освіти, що трансформуєть- +ся, утворюючи нову інформаційну ментальність всіх зацікавлених +сторін. Розв’язання цього завдання вимагає постійного моніторингу +та оцінювання стану системи освіти, в основі яких лежать збір, опра- +цювання інформації, аналіз освітніх даних, необхідних для забезпе- +чення ухвалення обґрунтованих управлінських рішень [1]. +Одним із провідних напрямів розвитку сучасної освіти є її інфор- +матизація. Реалізація цього напряму дає можливість зробити освіту +більш ефективною, гнучкою, сучасною, такою, що відповідає міжна- +родним стандартам. +У концепції Національної програми інформатизації зазначено, +що сутність інформатизації полягає в сукупності взаємопов’язаних +організаційних, правових, політичних, соціально-економічних, на- +уково-технічних, виробничих процесів, що спрямовані на створення +умов для задоволення інформаційних потреб, реалізації прав грома- +дян і суспільства на основі створення, розвитку, використання ін- +формаційних систем, мереж, ресурсів та інформаційних технологій, +створених на основі застосування сучасної обчислювальної та кому- +нікаційної техніки [2; 3]. +Однією з характерних особливостей модернізації українського +суспільства є його глобальна інформатизація, яка зумовила масштаб- +не запровадження інформаційно-комунікаційних технологій (ІКТ) в +освітній процес, що дає змогу педагогу вирішувати методичні завдан- +ня на якісно вищому рівні. Вихідні концептуальні положення означе- +ної проблеми викладені у Законі України «Про національну програму +інформатизації», Концепції Національної програми інформатизації, +Указі Президента України від 20.10.2005 р. № 1497 «Про першочер- +гові завдання щодо впровадження новітніх інформаційних техноло- +гій», Державній програмі «Інформаційні та комунікаційні технологій +в освіті і науці на 2006–2010 роки» та інших нормативних документах. +Інформатизація освіти залежить від об’єктивних умов та сучасних +тенденцій розвитку інформаційного суспільства, до яких варто відне- +сти такі: +– забезпечення мобільності інформаційно-комунікаційної діяль- +ності користувачів в інформаційному просторі (Mobility), подальший +розвиток мобільно орієнтованих засобів та ІКТ доступу до електрон- +них даних; +– розвиток технології хмарних обчислень та віртуалізації, корпо- +ративних, загальнодоступних і гібридних ІКТ-інфраструктур, а також + +388 +запровадження технології хмарних обчислень (Cloud Computing and +Virtualization, Private, Public and Hybrid Clouds, ICT-infrastructures, +Fog Сomputing); +– накопичення та опрацювання значних обсягів цифрових даних, +формування та використання електронних інформаційних баз і сис- +тем (Big Data, Data Mining, Data Bases), зокрема електронних бібліо- +тек (Electronic Libraries, Repositories) та наукометричних баз даних +(Scientometric Data Bases); +– розвиток користувальних характеристик Інтернету людей +(Internet of People — ІоР), розгортання топології широкосмугових +високошвидкісних каналів електронних комунікацій (Broadband +Communication Channels), систем формування ІКТ-просторів без- +дротового доступу користувачів до електронних даних (Cordless Ac- +cess to Digital Data, WiFi, Bluetooth, Cellular Networks); +– формування Інтернету речей (Internet of Things — ІоТ), розви- +ток його програмно-апаратних засобів, зокрема мікропроцесорних, +та інтеграційних платформ, для забезпечення налаштування, управ- +ління та моніторингу електронних пристроїв за допомогою сучасних +телекомунікаційних технологій; +– розвиток робототехніки (Robotics), робототехнічних систем, зо- +крема 3D-принтерів і 3D-сканерів; +– розвиток систем захисту даних в інформаційних системах та проти- +дія кіберзлочинності (Data Security and Counteraction of Cybercriminality); +– розвиток індустрії виробництва програмних засобів (Software +Development Industry), зокрема видання електронних освітніх ресурсів; +– забезпечення сумісності ІКТ-засобів та ІКТ-додатків, побудо- +ваних на різних програмно-апаратних платформах (Compatibility); +– розвиток мереж постачальників ІКТ-послуг (ринку ІКТ-аут сор- +серів), передусім хмарних сервісів (Cloud Services), та мережі Центрів +опрацювання даних (Computing Center Network) [24]. +Невідкладного вирішення потребують проблеми розвитку та +впровадження інформаційно-комунікаційних технологій у вітчиз- +няній освіті, ключові з яких виокремлені в Національній доповіді +2016 р. «Про стан і перспективи розвитку освіти в Україні» [23]. +Першою є проблема формування і широкого впровадження єди- +ного освітнього інформаційного простору України та забезпечення +належного наукового супроводу цих процесів. +Другою є проблема розгортання та удосконалення необхідних +елементів інфраструктури регіональних інформаційних і телекомуні- + +389 +каційних мереж, взаємопов’язаних як між собою, так і з глобальною +мережею Інтернет, що дозволить подолати «цифрову нерівність» у +різних регіонах України, зокрема в сільській місцевості. +Третьою проблемою є низький рівень інформаційно-комуніка- +ційно-технологічних компетентностей (ІКТ-компетентностей) та +інформаційних компетентностей населення, застосування застарілих +підходів у навчанні та низька мотивація суб’єктів навчального про- +цесу щодо використання прогресивних ІКТ. Варто зазначити, що +мас штабний характер застосування засобів ІКТ в глобальній системі +освіти зумовив появу нових методів і форм навчання (електронне на- +вчання, мобільне навчання, застосування в освіті хмарних техноло- +гій, масових відкритих освітніх курсів тощо), що повільно запрова- +джуються в сучасній національній системі освіти України. +Четверта проблема — фактична несформованість цілісної націо- +нальної політики застосування інформаційно-комунікаційних тех- +нологій в освіті, недосконала нормативно-правова база, що не забез- +печує побудову інформаційного суспільства та, як наслідок, гальмує +інформатизацію освіти в Україні. Завдання інформатизації освіти +не знайшли належного системного відображення в чинних законах +України з питань освіти та сучасних проектах. Суттєвим недоліком +нинішньої освітньої політики є недооцінка важливості стимулюван- +ня ініціатив із запровадження інформаційно-комунікаційних техно- +логій, що ініційовані закладами освіти, науковими установами, осві- +тянами, громадськими організаціями та приватним бізнесом. +Останніми роками інформація стає одним з найважливіших ви- +робничих факторів і одним з головних важелів управління будь-якої +організації, в тому числі й освітнього закладу. +Інформатизація освіти — це процес зміни її змісту, методів і орга- +нізаційних форм, спрямований на досягнення нової якості освіти на +основі застосування інформаційних технологій. Вона повинна допо- +могти розв’язанню двох основних завдань школи: освіта — для всіх, +і нова якість освіти — кожному. +Інформатизація управління освітньою установою пов’язана з при- +йняттям більш обґрунтованих управлінських рішень на основі авто- +матизованої обробки соціально-економічної, психолого-педагогіч- +ної та іншої інформації. Сьогодні інформатизація управління освітою +розглядається на декількох рівнях, а саме: +– окремому — інформатизація охоплює управління окремими на- +вчальними закладами; + +390 +– загальному — загалом охоплює кілька навчальних закладів од- +ного району чи регіону, передбачається частковий інформаційний +обмін між навчальними закладами та органами управління освітою; +– системному — поетапно охоплює всі освітні установи даної те- +риторії з організацією повного інформаційного обміну на підставі +єдиних інформаційних стандартів, що веде до формування єдиного +інформаційного простору освіти. +Ефективність інформатизації закладу освіти значною мірою зале- +жить від наукового обґрунтування цього процесу. Якщо узагальнити +різні погляди науковців на інформатизацію закладу освіти, то мож- +на зазначити, що більшість з них приділяють увагу такій функції, як +підтримка управлінських рішень. Результати аналізу наукових праць +та власного досвіду підтверджують, що інформаційні технології да- +ють можливість підвищити ефективність усіх складових процесу роз- +робки та реалізації управлінського рішення: отримання необхідної +інформації, розробка управлінського рішення, доведення управлін- +ського рішення до виконавців, контроль за виконанням управлін- +ського рішення. +Однією з особливостей сучасної соціально-освітньої ситуації є са- +мостійність освітніх установ. З одного боку, це активізує творчі сили +педагогічних колективів, сприяє розвитку інноваційних процесів в +освітніх установах. З іншого боку, процес управління освітніми уста- +новами значно ускладнився і вимагає його якісного перетворення. +Якісне перетворення процесу управління освітнім закладом у свою +чергу вимагає якісного зростання професійних фахівців, які здійсню- +ють цей процес. +Численні можливості використання інформаційних технологій +розглядали О. Андріянова, З. Пожидаєва, Н. Сомилкіна, Л. Заброд- +ська, Л. Жиліна, Е. Палат, М. Бухаркіна, М. Моїсеєва, А. Петров +[4]. Л. Даниленко вважає, що застосування комп’ютерів в управ- +лінській діяльності дає можливість забезпечити своєчасне надання +оперативної інформації працівнику, який приймає рішення, з ураху- +ванням її характеру; своєчасне надання аналітичної інформації; на- +дання оптимального обсягу інформації; надання рекомендацій з ви- +бору рішень та скорочення тривалості процесу вироблення рішення +[5]. Погоджуючись з напрацюваннями науковців, зазначимо, що в +швидкоплинних умовах актуальним стає прискорення використан- +ня інформаційних потоків у навчальному закладі. У наукових працях +це питання висвітлюється фрагментарно, а питання комплексного + +391 +застосування інформаційних потоків в навчальному закладі не ви- +світлено взагалі. +Результати аналізу наукових праць та власного досвіду підтвер- +джують, що інформаційні технології дають можливість підвищити +ефективність усіх складових процесу розробки та реалізації управлін- +ського рішення: отримання необхідної інформації, розробка управ- +лінського рішення, доведення управлінського рішення до виконав- +ців, контроль за виконанням управлінського рішення. +За результатами презентації першого етапу проекту «Дебюрокра- +тизація управління освітою», реалізованого Міністерство освіти і на- +уки України за підтримки ГО DOCCU і Швейцарсько-Українського +проекту DECIDE у співпраці експертів Офісу ефективного регулю- +вання BRDO, в якому проводилося дослідження системи управління +загальною середньою освітою в Україні, розроблено проекти змін до +11 чинних НПА та створення двох нових НПА, які забезпечать циф- +ровізацію шкільного діловодства, що потребує суттєвої модернізації. +Головною задачею проекту було надати експертну підтримку для +розуміння того, що потрібно зробити, щоб спростити процедури зві- +тування та діловодства, а також налагодити процеси обміну даними в +галузі загально-середньої освіти. +В ході проекту було сформовано фокус-групи, учасниками яких +стали освітяни, а також проаналізовано документи, які фігурують в +діяльності шкіл. Це дозволило виявити основні проблеми та численні +бюрократичні перепони, що стоять на заваді ефективного функціо- +нування вітчизняної освітньої галузі. +Ось лише кілька цифр, які показово характеризують надмірну за- +бюрократизованість процесів і процедур у цій галузі: 48 видів папе- +рових документів школи зобов’язані вести та зберігати; 70 000 пачок +паперу щомісяця витрачають українські школи на ведення цієї доку- +ментації; 62 400 000 грн щороку коштує державі такий обсяг паперу. +Узагальнюючи такий поточний стан, ми можемо зробити такі ви- +сновки. +Звітність переважно дублюється у цифровому та паперовому ва- +ріантах для різних реципієнтів. Обмін інформацією між ними не на- +лагоджений та потребує врегулювання. +Звітна інформація вноситься у ручному режимі. Це унеможлив- +лює впровадження сучасних освітніх сервісів та не дозволяє повною +мірою інтегрувати необхідні інформаційні освітні ресурси та забезпе- +чити обмін даними з ключовими державними реєстрами. + +392 +Також було змодельовано нові процеси електронного обліку, всту- +пу, відрахування, переводу учнів та дітей засобами модернізованої +інформаційно-телекомунікаційної системи «Автоматизований ін- +формаційний комплекс освітнього менеджменту» (АІКОМ). Нове +технічне рішення дозволить впровадити нові цифрові підходи, що +сприятимуть дебюрократизації та дерегуляції управління освітою. +Очевидно, що інформатизація системи освіти в Україні потребує +суттєвої модернізації не тільки у сфері загально-освітньої підготовки, +а і на інших рівнях освіти. +Актуальність проблеми інформатизації управління навчальним за- +кладом полягає у створенні, впровадженні та розвитку комп’ютерно +орієнтованого освітнього середовища на основі інформаційних сис- +тем, мереж, ресурсів і технологій. Головною метою є підготовка фа- +хівця, в тому числі керівника закладу освіти до діяльності в умовах +інформаційного суспільства, комплексна перебудова педагогічного +процесу, підвищення його якості та ефективності. Вирішенню цього +питання сприяє інформатизація навчального закладу. +Засоби інформаційно-комутаційних технологій, які застосовують- +ся в управлінні освітнім закладом, повинні у сукупності представляти +собою систему, засновану на використанні сучасних методів керівни- +цтва об’єктом системи освіти, застосуванні математичних моделей і +методів у процесі прийняття рішень та створенні необхідної інформа- +ційної бази на основі засобів комп’ютерної техніки і зв’язку, що за- +безпечує досягнення нової якості у підвищенні ефективності системи +фахової передвищої та вищої освіти. Керівнику навчального закладу в +умовах інформаційного суспільства важливо звернути особливу увагу +на сучасні підходи у роботі з інформаційними матеріалами (збір, об- +робка, накопичення, зберігання, пошук і розповсюдження інформа- +ції), підготувати педагогічний колектив до реалізації засад «безпапе- +рової інформатики» у побудові документообігу навчального закладу. +З вищесказаного можна зробити певні висновки: управління за- +кладом освіти включає у себе велике коло питань: педагогічних, гос- +подарських, соціально-педагогічних, економічних, правових, фінан- +сових. Інформатизація суспільства загалом і інформатизація освіти +зокрема, привела ці системи у відповідність з потребами і можливос- +тями сучасного інформаційного суспільства. Важливим фактором +удосконалення управління є інформаційні технології, які надають +масу нових можливостей, а саме: дозволяють накопичувати і понов- +лювати великі обсяги інформації, є інструментом оптимізації часу і + +393 +коштів, що витрачаються на вирішення окремих задач управління, +сприяють підвищенню якості прийнятих управлінських рішень за +рахунок надання оперативної і достовірної інформації про стан ке- +рованого об’єкта. +Актуальність теми обумовлена низкою факторів, а саме: +— обсяг інформації про хід і результати освітнього процесу стає +вищим, ніж рівень достатнього розуміння цієї інформації; +– механічна обробка без певного стандартного алгоритму не дає +оперативних даних, що дозволяють приймати оптимальні управлін- +ські рішення за результатами діяльності; +– робота закладу освіти в інноваційному режимі потребує багато- +гранного аналізу освітньої діяльності, оперативного простеження ди- +наміки змін і своєчасного коригування; +– складні інформаційні моделі (автоматизовані системи управлін- +ня закладом освіти), як правило, не виправдовують себе з фінансової +точки зору, тому необхідно і доцільно комп’ютерні технології вводити +там, де алгоритм управління досить простий і технічно здійсненний +з відносно невеликими витратами. +Наша мета — представити автоматизовану комплексну систему +обліку підвищення кваліфікації педагогічних та науково-педагогіч- +них працівників закладу освіти, яка дозволяє зберігати, обробляти та +контролювати результати підвищення кваліфікації та атестації педа- +гогічних та науково-педагогічних працівників закладу освіти. +Аналіз існуючих систем автоматизації моніторингу освітньої діяль- +ності та управління закладом освіти. Освітня управлінська інформа- +ційна система — це не тільки набір формалізованих та інтегрованих +операційних процесів, процедур та організаційно-правових заходів, +але й повноцінна інституційна культура, яка забезпечує суспільство +актуальними та достовірними даними про стан розвитку освіти. +Відомі системи управління освітнім процесом орієнтовані на під- +тримку основних функцій навчання (особливо в дистанційній фор- +мі) і не завжди охоплюють такі комунікаційні процеси планування, +виконання, навчання, аналізу, звітування та контролю. Крім того, +серед відомих систем управління навчанням як правило виокремлю- +ють системи дистанційного навчання та моніторингу якості. На нашу +думку, тільки комплексні електронні системи можуть стати ефектив- +ною інформаційною підтримкою для всіх категорій користувачів сис- +теми — від здобувача освіти до керівника навчального закладу. Саме +це обумовило вибір та актуальність тематики досліджень. + +394 +Однак базовою для всіх інших функцій інформатизації навчаль- +ного закладу є функція отримання, фіксації, зберігання та перетво- +рення інформації. Ця функція є широкою у зв’язку з тим, що інфор- +мація потрібна не тільки для прийняття управлінських рішень. Саме +ця функція створює умови для реалізації ще однієї важливої функції +інформатизації навчального закладу — задоволення інформаційних +потреб учнів, студентів, працівників, потенційних споживачів освіт- +ніх послуг, працівників інших освітніх установ та структур управління +освітою. +Серед важливих компонентів інформатизації освіти є розроблення +програмного забезпечення. Програми, які використовують у закладах +освіти, поділяють на такі програмні засоби: навчальні (скеровують на- +вчання з огляду на наявні знання та індивідуальні здібності студентів, +а також сприяють засвоєнню нової інформації); діагностичні (тесто- +ві — призначені для діагностування, перевірки, оцінювання знань, +умінь, здібностей студентів); тренувальні (розраховані на повторення +та закріплення пройденого навчального матеріалу); бази даних (схо- +вища інформації з різних галузей знань, у яких за допомогою запитів +на пошук у різних галузях знань знаходять необхідні відомості); імі- +таційні (представляють певний аспект реальності за допомогою па- +раметрів для вивчення її основних структурних чи функціональних +характеристик); моделюючі (відображають основні елементи і типи +функцій, моделюють певну реальність); інструментальні (забезпечу- +ють виконання конкретних операцій, тобто оброблення тексту, скла- +дання таблиць, редагування графічної інформації) [6]. +Наразі Міністерство освіти і науки України активно приєднуєть- +ся до проектів цифрової трансформації у ключових сферах. Систе- +ма управління проектами від Мінцифри налічує вже 94 об’єкти циф- +ровізації в Україні за різними напрямами. Цифровізація вже відіграла +важливу роль у сфері освіти і науки України. Її мета — щоб всі освітні +послуги стали більш доступними та контрольованими. Реалізація цих +проектів передбачає впровадження цифрових сервісів в освіту і науку, +автоматизацію освітніх та управлінських процесів +Серед презентованих програм, зокрема: +Цифровізація дошкільної, загальної середньої та позашкільної +освіти (е-Школа). У межах проєкту е-Школа вже функціонує сучас- +ний онлайн-ресурс «Всеукраїнська школа онлайн» для змішаного та +дистанційного навчання учнів 5–11 класів із матеріалами, що відпо- +відають державній програмі. А в найближчих планах — створення + +395 +кабінету вчителя, де можна буде відстежувати навчальний прогрес, +створювати та модифікувати уроки. +Цифровізація вищої, фахової передвищої та професійної освіти +(е-Університет). У межах проєкту е-Університет заплановано: +– автоматизація вступної кампанії; +– автоматизація процесів набору та навчання (стажування) іно- +земців та осіб без громадянства; +– запровадження електронного ліцензування; +– модернізація Єдиної державної електронної бази з питань освіти; +– створення та модернізація єдиної електронної системи моніто- +рингу працевлаштування випускників. +Модернізація систем подання документів та проведення держав- +ної атестації наукових установ і закладів вищої освіти в частині прове- +дення ними наукової діяльності, розвиток репозитарію академічних +текстів та підключення до нього локальних репозитаріїв і створення +електронної системи доступу до нинішніх цифрових сервісів науко- +вого призначення — серед цілей проєкту е-Наука. +Цифровізація фінансування та послуг у сфері науки (е-Наука). +Слід зазначити, що на сьогоднішній день існують діючі ІС моні- +торингу діяльності навчальних закладів. Серед відомих систем управ- +ління навчальним процесом у закладі вищої освіти на ринку України +можна відзначити такі: +– автоматизована система управління навчальним процесом для +вищих навчальних закладів усіх рівнів акредитації АСК «Вищий на- +вчальний заклад», розроблена у Науково-дослідницькому інституті +(НДІ) прикладних інформаційних технологій, яка є частиною інфор- +маційно-виробничої системи «Освіта» [7]; +– система управління навчальним процесом для вищих навчаль- +них закладів «Директива», розроблена у ТОВ «Комп’ютерні інформа- +ційні технології» [8]; +– пакет програм «Деканат», розроблений приватним підприєм- +ством «Політек-СОФТ», до складу якого входить модуль «ПС Сту- +дент» [9]. +Поряд з цим у багатьох великих закладах вищої освіти функціону- +ють і власні розробки подібних систем. До них можна віднести: +– електронну систему управління закладом вищої освіти «Сократ» +Вінницького національного аграрного університету [10]; +– інформаційно-аналітичну систему управління закладом вищої +освіти «Університет» Херсонського державного університету; + +396 +– засоби автоматизації управління навчальним закладом, що ді- +ють в НУ «Львівська політехніка» та Львівському національному уні- +верситеті імені Івана Франка; +– автоматизовану інформаційну систему «Електронний універ- +ситет» [11], створену у Хмельницькому національному універси- +теті. +Проведемо аналіз двох інформаційних систем автоматизації +управління навчальним процесом у внз, а саме: автоматизована +система управляння (АСУ) «ВНЗ», яку розробив Науково-дослід- +ницький інститут прикладних інформаційних технологій в комер- +ційних цілях та АСУ «Сократ», що самостійно розроблена та за- +проваджена у Вінницькому національному аграрному університеті. +Насамперед потрібно сказати про загальні принципи роботи цих +двох систем. +Інформаційна система АСУ «ВНЗ» побудована у вигляді WEB- +додатка програми, тобто її робота вимагає підключення до всесвіт- +ньої мережі Internet. Всі дані зберігаються й обробляються на сервері, +який фізично знаходиться в м. Києві, а не там, де ведеться експлуа- +тація системи (у підрозділах університету в містах Львові, Харкові та +Черкасах). Для роботи з системою не потрібно встановлювати спеці- +альне програмне забезпечення. +Структура системи АСУ «ВНЗ» реалізована на модульній основі, +де кожен модуль може використовуватися самостійно (рис. 1). АСУ +«ВНЗ» вирішує велику кількість автоматизованих функцій управлін- +ня, у тому числі [7]: +– електронну реєстрацію, обробку даних та документообіг в єди- +ній інформаційній системі для кожного структурного підрозділу +окремо і установи в цілому; +– планування, контроль та аналіз навчальної діяльності; +– оперативний доступ до інформації, що супроводжує навчальний +процес; +– єдину систему звітів, як внутрішніх, так і за вимогами Міністер- +ства освіти і науки (МОН) України; +– системи безпеки даних з урахуванням вимог законодавства; +– можливості безпосереднього обміну даними з інформаційно- +виробничими системами «Освіта» та «Education». +Також система включає АС «Конструктор звітів», що дозволяє +формувати інформацію і надавати її користувачам у найбільш зруч- +ному вигляді. + +397 + +Рис. 1. Модулі АСУ «ВНЗ» +Автоматизована система управляння «Сократ» — система управ- +ління якістю освітньої діяльності університету працює як відкрита +інформаційна система, адаптована під потреби викладачів, студентів +та адміністрації університету [10]. +Натомість система АСУ «Сократ» власної розробки ВНАУ по- +вністю автономна, сервер системи знаходиться на території навчаль- +ного закладу та за необхідності може працювати у всесвітній мережі +Internet. Для роботи з системою також не потрібно встановлювати +спеціальне програмне забезпечення, вистачить будь-якого зручного +користувачам браузера (Microsoft Internet Explorer, Mozilla Firefox, +Google Chrome, Safari, Opera). Система надає доступ практично до +всієї інформації з мережі Internet в будь-який час та можливість дис- +танційного навчання. Система потребує адміністрування у зв’язку з +постійними нововведеннями та розширенням її структури та універ- +ситету в цілому. +Розглянемо детальніше складові АСУ «Сократ». +Персональний кабінет викладача — це складова роботи виклада- +ча, за допомогою якої можливо проводити дистанційне навчання, ве- +дення електронних журналів та змогу обміну інформацією з іншим +користувачам системи. +Персональний кабінет студента — це навчальна складова студен- +та, за допомогою якої можливо проводити дистанційне навчання. +Автоматизована система управління АСУ «Деканат» дає змогу: +формувати та зберігати персональні дані студентів; формувати дані +про успішність, модулі, заліки, іспити; ведення моніторингу якості +знань; ведення контролю навчального процесу. +Бухгалтерія — це кліент-серверна багатокористувацька програ- +ма, альтернатива до програми «1С:Бухгалтерія» яка зроблена за Web- +технологіями. + +ACY"BH3" +AC"ekaHar" +AC "IlpuiMaIbHa KoMicin" +AC"CTyuMicTeyKo"398 +Бібліотечна система «Софія» дозволяє зберігати і використовува- +ти різного типу та змісту електронні документи та зручним способом +для кінцевого користувача представляти їх. +Методичний кабінет проводить управління процесами створення +та впровадження методичних розробок викладача. +Центр здоров’я дозволяє вести медичні дані про захворювання +студентів в електронному вигляді, виписки медичних довідок та на- +дання в автоматичному режимі інформації деканату. +Відділ кадрів викладачів займається веденням особових справ ви- +кладачів. +Відділ кадрів студентів займається веденням особових справ сту- +дентів. +Відділ діловодства займається всією документацією, листами та +розсилкою їх структурам, до яких вони відносяться. +Дистанційне навчання дає змогу проходження тестів та перегляду +інформації з Інтернету. + +Рис. 2. Електронна автоматизована система управління (АСУ) «Сократ» +та її складові +Головна відмінність АСУ «Сократ» — використання персональних +кабінетів студента, викладача, співробітника, навколо яких форму- +ється інформаційне поле (рис. 3). +Персональний кабінет викладача передбачає: +– ведення електронного журналу (який можуть переглядати сту- +денти); +– перегляд розкладу занять і навчальних планів з навчальної час- +тини on-line; +– розклад занять на мобільному телефоні; +– створення тестів для студентів; + +BiuiiioBoucTBa +Binii KaapiB cTyeHTiB +BiuaiIkaapiBBHk.lalayiB +IepcoHa.IbHHiKaoiHeTcTyaeHTa +lepcoHa.IbHHHKaoiHeTBHKIaIaa +ACy"Cokpar" +ACyIekaHaT +MeTOTHHHHKaoiHeT +LHcTaHIiHHeHaBaHHy +Bio.rioTeHacHcTeMa"Cobia' +Byxra.Itepis399 + +Рис. 3. Складова електронної системи «Сократ», персональний кабінет +викладача +– доступ до автоматизованої бібліотечної системи «Софія»; +– можливість публікації власних методичних матеріалів для вико- +ристання їх в навчальних картках дисциплін; +– можливість самопублікації власних наукових матеріалів у елек- +тронному репозиторії; +– доступ до WEB-чату, блогів, форумів всередині системи. +Персональний кабінет студента передбачає (рис. 4): +– перегляд своєї навчальної картки; +– пошук та перегляд інформаційних ресурсів в бібліотеці; +– проходження тестування; +– доступ до WEB-чатів, мікроблогів, студентських форумів. +Електронна система «Сократ» має зв’язки з мобільними тех- +нологіями та соціальними мережами. Так, викладачі мають мож- +ливість одержувати свій розклад на мобільний телефон. В системі +«Сократ» можливо здійснити формування дистанційних курсів на +основі матеріалів навчальної картки дисципліни, відеолекцій та ве- +бінарів. + +PoboM cTin BMknaAaya KoBanbyyk OnekcaHApAHApinoBy +Ha ronoBHy +CninbHOTa +bopyM +BuXiA +MoiHaBy.MatepianM +EPo3KnaA +MaTep.3BMKopWcT.nKB +BMknaaaya2012-2013 +HanaHHAAocTynyKoneraM +p03KnaA3aHATb3yy0.yacTMHM +KOHBepTopypdf(ckayaTW) +apkywie:0 +MOA.BinOMOCTei:0 +HaBaHTaKeHHAMMPO3Knan +ycxoBWuio +San.BigoMocTei.:0 +BineOSHATTA +BMKOpCTOEyETbCR:0 +ek3.BnoMOcTei:0 +naHyBanibHWK3aBAaHb +MeTOAHyHIBKasIBKM +BinoMocTeisKP:0 +BinOMOCTensnpaKT.:0 +MoiKapTKMAWCLMnniH +"TecT-MawcTep" +Bi6nioTeka +Pi3He +BCIKaDTKMAMCUMnNIH +TeCTiB:1 +katanor +MOAAOKYMeHTaLi +nirTaH:0 +PeWTWHr:0 +Deno3MTopin +MOATPYAOBaKHHXKayBK +KapTOk +BHKOpMCTOByETbCA.0 +Minbion.opMynap +MOI3aABHBI +AMCUMNNIH:O +peifTIHr(bes TecTiB):0 +WEB-oyxrantepiq +CaMoapxiByEaHHA:0 +YCBITI +MoiapxiBw +"Kopwew" +CaKapeApn +BeDiHaw +TOBiAOMNeHHA +eneKTPOHHIXKHIr:0 +DyonikauiA HOBMH +BCboroCTopiHOK:0 +MOnaHKeTa +MinGoogle +icTopigKabepm +NOBiAOMIeHHA +BWKOpICTOByETbCR:0 +HagicnaHo:0400 + +Рис. 4. Складова електронної системи «Сократ», персональний кабінет +здобувача освіти +Безперечна перевага системи АСУ «ВНЗ» — наявність блоку +«Приймальна комісія» та його зв’язок з міністерською програмою +«Вступ». Блок «Студмістечко» підтримує звітність гуртожитків. Вза- +галі АСУ «ВНЗ» орієнтована на формування звітності та виконання +функцій АСУ «Деканат», «Приймальна комісія», «Студмістечко» та +не передбачає інформаційної підтримки дистанційної форми на- +вчання, формування банку методичних матеріалів, зв’язку з бібліо- +течними ресурсами. +Перевага електронної системи «Сократ» в орієнтації на студента, +викладача, методиста, адміністрації закладу, їх запитів з питань ме- +тодичної інформаційної підтримки та контролю. Недоліком є необ- +хідність створення нових модулів та інтеграції з загальнодержавними +програмними продуктами. +До популярних систем автоматизації та моніторингу в освітній ді- +яльності можна віднести: +1. Інформаційно-виробнича система «Освіта», розроблена у На- +уково-дослідницькому інституті (НДІ) прикладних інформаційних +технологій [12]; +2. Інформаційна система «Вступ.ОСВІТА.UA» [13]; + +Boopna +ga1 +Tec +MosKaranss capica +Mitianioreeuni oopMinAp +KaranarGitnioteaBaHAy +Poanansaon +Webbyramepa +Cninuota BHAy401 +3. Програмно-апаратний комплекс «Автоматизований інформа- +ційний комплекс освітнього менеджменту», розроблений ДНУ «Ін- +ститут освітньої аналітики» [14]; +3.1. E-Journal; +4.Програмний комплекс «КУРС: Освіта», розроблений ТОВ «Нові +знання» [15]; +4.1. «Курс:Школа»; +4.2. «Україна. ІСУО»; +4.3. Портал «NZ.UA»; +4.4. «Курс:Дошкілля»; +5. Автоматизована система підвищення кваліфікації педагогіч- +них працівників закладів загальної середньої освіти, розроблена ТОВ +«Актівмедіа» [16]. +Проведемо аналіз систем автоматизації та моніторингу в освітній +діяльності. +Загальнодержавна інформаційно-виробнича система «Освіта» за- +безпечує єдине цілісне інформаційне середовище України в галузі +освіти та являє собою сукупність адміністративних, правових, про- +грамних та апаратних засобів. +Автоматизована система ідентифікації особистості в суспільстві та +державі стає неодмінним атрибутом адміністративного функціону- +вання цивілізованих країн. Базовою інформацією про людину в будь- +якій системі ідентифікації є персональна інформація: прізвище, ім’я, +по батькові, дата і місце народження, фотографія. +На етапі становлення єдиного інформаційного простору України +стає необхідним впровадження єдиної загальної системи докумен- +тального супроводу громадян, заснованої на невід’ємному поєднанні +інформаційної системи обліку даних та системи виробництва доку- +ментів. Відповідно до закону «Про освіту» отримання базової освіти +є обов’язковим для всіх громадян, тому система, що передбачає вве- +дення в базу даних персональних даних громадянина з цифровою фо- +тографією, повинна стати основою для присвоєння індивідуального +ідентифікаційного податкового номера за погодженням з Державною +податковою адміністрацією. +Така багатофункціональна інформаційно-виробнича система збо- +ру та обліку даних про фізичних осіб та їх документального супроводу +розроблена Інститутом кібернетики і ЗАТ «НДІ прикладних інфор- +маційних технологій» Кібернетичного центру НАН України спільно з +Міністерством освіти і науки України. + +402 +Рис. 5. Головна сторінка інформаційно-виробничої системи «Освіта» + +G『OOBHA +?ABTOPW3ALIA +yKP +ENGIPyC +poIBC《OcBiTa》 +oKyMeHTW +nporpaMu +KOHTaKTM +8 +OnMC CMCTeMM +V +3pa3KM,nocTaHOBM,Haka3M, +@opyM, HOBMHM, nWTaHHA Ta +3BOPOTHIM3B'3OK +aKTyanbHaIHbopMauIA +BIANOBIAI,ONMCOHOBeHb +BMrOTOBeHHA AOKyMeHTiB npO BWLy OcBiTy +BWrOTOBAeHHA AOKyMeHTiB +Po3'CHeHHAnpouecy 3aMOBeHHA Ta +OTpWMaHHA AOKyMeHTiB npo BWuy OCBiTy. +npoBWuyocBiTy +AIA +山IkinbHWi yyHiBCbKMi KBWTOK +IA +epcoHiikoBaHMi3axwujeHMiBinniApo6ok +AokyMeHT,WoniATBepAKyeocooyyyH +AkIcHanpoAyKuIABIAnpoBIAHoro +BMpo6HMKa36araToplYHMMAocBIAoM +ABTOMaTM3OBaHaCMcTeMaYnpaBniHH《BH3 +CucTeMa ynpaBniHHA HaByanbHMM npoOuecOM +KPAIHN +AABWLWXHaBYaNbHWX3aKNaAiByciXpiBHiB +JHIJOM +MASTER'S +akpeAwTauii +MAFICTPA +DIPLOMA +Mo OcBiTa +EAMHMiiHbopMauiMHO-OcBiTHiMnpOCTip +bnaHKM +AOATKN +IHTepaKTMBHOiB3aeMOAII BCIX yyaCHMKIB +AeTanbHiwe +ocBiTHboro npouecy +HOBWHW O +OHOBIEHHA? +3AKOHOIABCTBO? +BWrOTOBeHHA +AOKyMeHTiB npo OcBiTy +14KoB2021 +3 Jlvc 2021 +Haka3 MiHicTepcTBa ocBiTwi HaykKu YkpaiHu No 97 +pWBiTaHHA3HeM3aXWCHИKiBi3aXMCHWLb +Buiwna HoBa Bepcia nporpaMw Education +epeitw> +HaKa3 MiHicTepcTBa ocBiTИ i HayKM YkpaiHM No811 +YKpaiHM +2.2.10.11 +24 Cep 2021 +14 Jun 2021 +HaKa3 MiHicTepcTBa ocBiTW i HayKM YkpaiHM N716 +BiTaHHA Ao H He3aneXHOcTi YKpaiHW! +Buiwna HoBa Bepcig nporpamu Education +epeBipkaAOkyMeHTa +locTaHOBa Ka6iHeTy MiHicTpiB YkpaiHM No1260 +2.2.10.9 +npoocBiTy +25 Tpa 2021 +ocTaHOBa Ka6iHeTy MiHicTpiB YkpaiHM N752 +pOLec3aMOBJeHHATaBMrOTOBeHHAAOAaTKiB +14 4ep 2021 +Haka3 MiHicTepcTBa ocBiTwi HayKMYkpaiH No1474 +NepeiTW> +AoAMnnoMaBponeMcbkoro3pa3KaBiAnoBiAHo +Buiuna HoBa Bepcin nporpaMw Education +oHaka3yMOHNo102Bin25.01.2021poky +2.2.10.8403 +На сьогоднішній день вже створена й успішно функціонує інфра- +структура, яка забезпечує збір первинних даних і охоплює всю тери- +торію України до районного рівня. +Основні цілі створення ІВС «ОСВІТА»: +– аналіз кадрового потенціалу держави та прогнозування тенден- +цій відносно змін у структурі професійного складу; +– аналіз кількісних показників національних трудових ресур- +сів; +– створення типових інформаційних та програмних засобів для +ефективного керування навчальним закладом; +– моніторинг діяльності навчальних закладів; +– аутентифікація документів про освіту державного зразка; +– впорядкування надання пільг учням та студентам. +Відповідно +до +призначення +головними +завданнями +ІВС +« ОСВІТА» є: +– створення ефективного автоматизованого комплексу для вироб- +лення управлінських рішень у галузі освіти в Україні; +– створення ефективного автоматизованого комплексу для управ- +ління вищим навчальним закладом у складі типової АС «Вищий на- +вчальний заклад»; +– створення та супровід єдиної бази даних навчальних закладів +України; +– створення та супровід єдиної бази даних учнів та студентів +в Україні; +– впровадження реєстру вищих, професійно-технічних та загаль- +них середніх навчальних закладів; +– отримання та аналіз інформації щодо діяльності освітніх закла- +дів України; +– підтримка ведення інформаційної бази Міністерства освіти і на- +уки України щодо документів у галузі освіти, їх власників та методич- +ної бази аналізу фахового складу населення; +– упорядкування процедур надання відповідно до чинного зако- +нодавства пільг учням та студентам; +– автоматизація збору та збереження інформації, що стосується +документів у галузі освіти; +– автентифікація інформації на різних етапах збору і обробки да- +них в ІВС «ОСВІТА»; +– підвищення рівня захисту від підробок документів у галузі +освіти; + +404 +– централізація та вдосконалення процесу виготовлення доку- +ментів у галузі освіти, а також дублікатів їх пластикових карток у ви- +падках втрати або пошкодження; +– забезпечення цілісності, достовірності та актуалізації інформа- +ції щодо виготовлених документів у галузі освіти; +– ідентифікація виготовлених ІВС «ОСВІТА» документів у галузі +освіти; +– отримання статистичних даних, надання необхідної статистич- +ної інформації державним органам та підприємствам; +– забезпечення захисту інформації від несанкціонованого доступу +відповідно до вимог чинного законодавства. +Інформаційно-виробнича система ІВС «ОСВІТА» включає систе- +му збору даних про фізичних осіб (включаючи цифрове фото) з ви- +користанням мережі Інтернет, центрального банку даних, виробни- +чого комплексу з виготовлення та обліку документів. Інформаційна +безпека системи реалізована з використанням сучасних програмних і +криптографічних засобів, що дозволяє повністю виключити можли- +вість несанкціонованого доступу до інформації. +ІВС «ОСВІТА» впроваджена в Міністерстві освіти і науки Украї- +ни для інформаційного та документального супроводу навчального +процесу. Вона охоплює всі етапи навчання — від середньої школи до +закладів вищої освіти, забезпечує збір даних про особу та централізо- +ване виготовлення електронних шкільних квитків, електронних сту- +дентських квитків та документів про освіту. У 2000 році результатом +функціонування системи стало виготовлення та постановка на облік +понад 1,8 мільйона документів про освіту в Україні. На сьогоднішній +день центральний банк містить інформацію про понад 39 мільйонів +документів та їх власників. +Оскільки персональні дані людини, що містяться ІВС «ОСВІТА», +використовуються в подальшій життєдіяльності людини в державі, +система повинна бути тісно пов’язана з діяльністю не тільки в галузі +освіти, а й у сферах відповідальності інших відомств і адміністратив- +них органів України: Міністерства внутрішніх справ, Державної по- +даткової адміністрації України, Міністерства оборони, Міністерства +охорони здоров’я, Міністерства транспорту, обласних та міських дер- +жавних адміністраціях. В даний час узгоджені принципи взаємодії і +виробляються спільні роботи з Міністерством транспорту і Держав- +ною податковою адміністрацією України. Результатом цієї взаємодії +є система обліку та надання пільг. + +405 + +Рис. 6. Головна сторінка «Вступ.ОСВІТА.UA» + +BcTyn.OCBITA.UA +OCBITA.UA +Bce po Bcry +Bcenpo3HQ +3HO-OHAMH +PeMTMHrW BH3 +BCTy.OCBITA.UA +3aKAaAKM +FAQ +Hpo caMt +popym +AaHi0TpMMaHi3EAE5O18.11.202104:00 +HaCTynHeOHOB^eHH9Ao09:0022.11.2021) +Ai3HaMCyCKiAbKM6aAiBOTpiOHOIo6MBcTynMTMHa6IOAKeT. +- OTpMMaMiHcbopMauionpo cneuiaAbHocTiyKoKHomyBMi. +- 3po6 BiAnoBiAaAbHMM BM6ip HaByaAbHoro 3aKAaAy +- AMBMCbpeiTMHrOBicnMCKMOHAaMHyAMnHi-cepnHi2O21pOKy. +oLyKHaBYaAbHOrO 3aKAaAy +oWyK CneLiaAbHocTi +O6epiTbperioH +O6epiTbOCBiTHiMCTyniHb406 +Інформаційна система «Вступ.ОСВІТА.UA». Інформація, що роз- +міщена на сайті інформаційної системи «Вступ.ОСВІТА.UA», отри- +мана з Єдиної державної бази з питань освіти (ЄДЕБО) на підставі +укладених договорів із Державним підприємством «Інфоресурс», що +є розпорядником ЄДЕБО. +Інформаційна система «Вступ.ОСВІТА.UA» здійснює інформу- +вання широкої громадськості про перебіг подання заяв щодо всту- +пу, рекомендації до зарахування та зарахування до закладів вищої +освіти під час проведення вступної кампанії з метою забезпечення +відкритості та прозорості при проведенні прийому до закладів ви- +щої освіти. +Також сайт створений з метою інформування абітурієнтів, їх бать- +ків, освітніх експертів та інших зацікавлених осіб про умови вступу +до закладів вищої освіти України та надання статистичної інформації +про результати вступу до закладів вищої освіти у минулих роках. +На сайті розміщується інформація про всі діючі заклади вищої +освіти в Україні, які здійснюють прийом абітурієнтів на навчання для +здобуття ступеня молодшого спеціаліста, бакалавра або магістра. +По кожному закладу вищої освіти надається контактна інформа- +ція, інформація про спеціальності та освітні програми, за якими здій- +снюється підготовка молодших спеціалістів, бакалаврів та магістрів. +Інформація включає дані про конкурсні предмети, ліцензійні обсяги, +обсяги державного замовлення та інше. +Програмно-апаратний комплекс «Автоматизований інформаційний +комплекс освітнього менеджменту» (ПАК «АІКОМ») — електронна +система управління освітою, яка є модернізованою Державною ін- +формаційною системою освіти (ДІСО), призначена для обробки дер- +жавних електронних інформаційних ресурсів та персональних даних +у сфері освіти в рамках єдиного інтегрованого середовища. +Основна мета — забезпечення переходу до електронного докумен- +тообігу (звітність, комунікація, сповіщення, опитування, голосуван- +ня, оперативне збирання даних) та оптимізація даних бізнес-процесів +у сфері дошкільної, загальної середньої, позашкільної та професійної +(професійно-технічної) освіти та управлінь освітою місцевого та об- +ласного рівнів (створення відповідних модулів в ПАК «АІКОМ»), +що дасть змогу суттєво підвищити достовірність освітньої статис- +тичної та адміністративної інформації та покращити на цій основі +якість управлінських рішень, зокрема щодо розподілу коштів освіт- +ньої субвенції та інших бюджетних коштів для фінансування освіти, + +407 + +Рис. 7. Головна сторінка ПАК «АІКОМ» + +AIKOM +3aKaNM OHNaMH +Bxin Ao o6nikoBoro 3anvcy +O6epiTb o6nacTb +KinbkicTb 33CO: +Yurivk +Sumy +1174 +Rivne +Belgorod +Kyiv +HUOU +Zhytomyr +Kharkiv +Bila Tserkva +aponb +Ternopil +Ukraine +Vinn +3abynu naponb? +Kramatorsk +3abynM noriH? +Kropyvnytskyi +Chernivts +Kryyi Rih +Zaporizhzhia +Donets +Balti +Nikopol +Moldova +Ro +Mykolaiv +Melitopol +Baca408 +забезпечить передумови для відмови від паперових документів в рам- +ках загальної дебюрократизації. +Очікувана модернізація передбачає створення електронних ка- +бінетів здобувача освіти та педагогічного працівника дошкільної, +загальної середньої, позашкільної та професійної (професійно-тех- +нічної) освіти, що уможливить отримання ними доступу до усіх дер- +жавних інформаційних освітніх сервісів та полегшить отримання +зведених деперсоналізованих даних для формування в автоматич- +ному режимі звітності, необхідної для Державної служби статистики +України. +Серед інших цілей модернізації є також розвиток безкоштовного +державного електронного щоденника та журналу, розгортання єди- +ної системи авторизації для державних освітніх сервісів, підключен- +ня альтернативних програмних рішень ринку освітніх інформацій- +них послуг до центральної бази даних з використанням АРІ ПАК +« АІКОМ» тощо. +Одним з популярних цифрових інструментів, який забезпечує +базову цифровізацію системи загальної середньої освіти, є система +електронних журналів. Такі цифрові інструменти створюють нові +можливості для забезпечення безперервної взаємодії та ефективної +співпраці між чотирма групами учасників процесу — адміністрація +школи, вчителі, учні та батьки. +Починаючи з грудня 2020 року доступний для впровадження та +використання в ЗЗСО безкоштовний державний сервіс електронних +журналів на базі програмно-апаратного комплексу «Автоматизова- +ний інформаційний комплекс освітнього менеджменту» (EJournal), +створений командою Міністерства освіти і науки України та Держав- +ної наукової установи «Інститут освітньої аналітики», який введено в +дослідну експлуатацію наказом МОН від 22.12.2020 № 1545. Рішення +про його використання приймає ЗЗСО на добровільній основі. +Переваги запровадження електронного журналу для різних груп +учасників освітнього процесу: +Для адміністрації школи: +– можливість оперативно готувати освітню звітність, діаграми +успішності по класах і предметах; +– аналіз результативності роботи педагогів; +– облік відвідування; +– можливість відслідковувати динаміку успішності учнів, класів, +школи; + +409 + +Рис. 8. Можливості системи E-Journal + +epKaBHi6e3KOWTOBHieneKTpOHHi +WOAeHHMKMTaKyPHan +Any3aknaAiB3aranbHoicepeHboiocBiTM +JKniAKnIOANTMC +ponpoekT +MOXKJMBOCTiCWCTeMM +EneKTpOHHi xyPHaJIM +EneKTpOHHi wOAeHHMKH +Po3KnaA +31 +SaXMCTCMCTeMI +CMHXpOHisauis410 +– підвищення рейтингу закладу освіти. +Для вчителів: +– звільнення від надлишкової паперової роботи; +– простий доступ до актуального розкладу у смартфоні або +комп’ютері; +– можливість завантажувати навчальні матеріали для ознайом- +лення та допомоги у підготовці домашніх завдань; +– економія часу для підготовки до уроків; +– зручний поділ класів на групи без паперових журналів; +– просте автоматичне формування складних звітів за підсумками +семестру або навчального року; +– ефективна комунікація з учнями та батьками. +Для учнів: +– зручний доступ до навчальних матеріалів і домашніх завдань; +– участь в онлайн вебінарах і конференціях, організованих школою; +– можливість перегляду матеріалів уроків у зручний час (у т. ч. у +період відсутності в школі); +– можливість віддаленої взаємодії з учителями; +– можливість самостійного контролю успішності навчання. +Для батьків: +– можливість оперативно отримувати інформацію про успішність +та відвідування дітей; +– ефективний контроль засвоєння знань та виконання домашніх +завдань; +– пряма комунікація з учителями; +– можливість брати участь в оцінці якості освітніх послуг. +«КУРС:Освіта» — це програмний комплекс, до складу якого вхо- +дять наступні ключові складові: +Комп’ютерна програма «КУРС:ШКОЛА» для загальноосвітніх +навчальних закладів та її складові — «КУРС:ШКОЛА +» для місце- +вих органів управління освітою (відділи, управління, департаменти +освіти районних та міських органів влади) і «КУРС:САЙТ» для авто- +матизації передачі даних на WEB-портали верхнього рівня. +Дозволяє автоматизувати і якісно керувати навчальними процеса- +ми. Генерує обов’язкові форми звітності ЗНЗ-1 і 83-РВК, затверджені +наказом № 766 МОНМС України від 02.07.2012 року, форму статис- +тичної звітності 77-РВК, затверджену наказом Держкомстату № 317 +від 06.08.2010 року і пересилає їх електронні версії згідно з підпоряд- +кованістю. Допомагає встановити навантаження вчителям. Складає + +411 + +Рис. 9. Інтерфейс програми «КУРС:ШКОЛА» +розклад занять як в ручному, так і в автоматичному режимі. Має модуль +електронних класних журналів. Програма «КУРС:ШКОЛА» може пра- +цювати в двох режимах: з доступом і без доступу до мережі Інтернет. +Портал ІСУО — інформаційна система управління освітою. При- +ймає і консолідує дані із закладів загальної середньої освіти, генерує +обов’язкові форми звітності ЗНЗ-1, 76-РВК, 77-РВК, 83-РВК, Д-4, +Д-5, Д-6, Д-7, Д-8, затверджені діючим законодавством, і пересилає +їх електронні версії згідно з підпорядкованістю. Дозволяє здійснюва- +ти пошук інформації. Полегшує вибірку необхідних даних і складан- +ня користувацьких звітів. Має надійні алгоритми захисту інформа- +ції від несанкціонованого використання. Кожен регіон України має +власне доменне ім’я і, відповідно власну Систему управління освітою +регіону. Склад і функціонал може доповнюватися і нарощуватися в +залежності від завдань і потреб. +Портал «NZ.UA» — це публічний сайт для всіх учасників освітньо- +го процесу: учнів, батьків, вчителів та інших працівників освіти. +Дозволяє вчителям виставляти оцінки і вести облік відвідуваності +в класних журналах та учнівських щоденниках. Зручно спілкувати- +ся та обмінюватися інформацією всім учасникам освітнього процесу. + +KYPC +X回 +Onepaui +CnMCKM +3BiTW +CepBic +AoBinka +8 +20 +Aa +JoaM +Knacw +Posknaa +KypHan +HaBaHTae. +HaB4. N.aH +NpeaMeTW +NpMMiweHH: +3BITW +βopMM +Bci +Buknanaui +Y4Hi +PeWTa ++ +> +I: +2 +☆ +CTBOPVTИ +MIMHIW +BwaanMTM +EkcnopT +Apyk +Ko.nOHKM +KoHTaKTW +EaTbKM +Cneuian. +epeTTHiTb CroAM 3aronoBOK KonOHKM A rpynyBaHH +[Bu6ye AopiBHIoe: 0] +HanaWTyBaTW... +itini +O CHOBHi +CneuiabHi - y4Hi +# +NI6 (noBHicTro] +Nocana +Knac +CTapocTa +CTaTb +I/H +Bik +3Mano3a6e3nEeskoToBHE +口 +0.00 +BaHeHko Muko.na CeprioBuy +YyeHb +11 +13.01.2002 +17.04 01.09.2008 +BaceTHKo BacMni BacMnboBWy +YyeHb +11 +团 +12.08.2001 +17,09 01.09.2008 +BnaceHKo Mapi CepriBHa +YyeHb +11 +21.09.2001 +17.08 01.09.2015 +「op6aHb AHTOH MuKOaoBW4 +YyeHb +11 +13.08.2002 +16.09 01.09.2008 +F +JeH4yk XpecTH IBaHOBW4 +YyeHb +10 +22.12.2004 +14.0517.09.2009 +Jinek BonouMMup IBaHoBu +YyeHb +10 +21.06.2004 +14.1101.09.2009 +Mopen NaB.no CeprioBuy +YyeHb +11 +13.06.2002 +16.1101.09.2008 +O neHyek Hatanka CepriBHa +YyeHb +10 +24.04.2004 +15,00 01.09.2013 +O neceHko Mapig MukonaiBHa +YyeHb +10 +21.11.2004 +14,06 01.09.2009 +10 +CuM4eHKO AHHa 0neKciBHa +YyeHb +10 +01.06.2003 +15.1101.09.2011 +11 +CoBeHKo JonMMa MuKo.aiBHa +YyeHb +11 +A +27.06.2002 +16.1001.09.2008 +15 +15 +国国 +[1111] +4t, 23 Tpa 2019 r. +1[01-09-2018 1131-05-2019] +N B CWCTeMi: 23 +Bepcig 179 R3 (1.79.3)412 + +Рис. 10. Головна сторінка «Україна.ІСУО» + +MoBa: ykpaiHCbka +YkpaiHa. ICyO +B3AEMOAIE3 +HUOU +ITC +AICO +3aoynunaponb? +YBiNTW +HbopMauiMHacWcTeMaynpaBniHHqocBiToo +『onoBHa +MOKnWBOCTi +okyMeHTW +Nowykwkonu 3a No Q +iaTpuMka +apTHepw: +AAMiHicTpaTWBHWMycTpiM +MIHICTEPCTBO +MiHicTepCTBO OCBiTw i HayKM +OCBITMIHAYKW +AL BiHHMLbKOi QAA +YKPAIHM +YOH BonMHCbKoi QAA +JyubK +YepHIriB +CyMM +AOHAHinponeTpoBCbkoi QAA +PiBHe +IHCTWTYT +KMTOMMP +KMiB +OHoHebkoiQA +OCBITHbOTAHAITVIKM +YOH KWTOMupCbkOi QAA +IbBiE +NontaBa +XapkiB +KaBHa HayKOBaycTaHOBa +AOHMC 3akapnaTcbkoi QAA +IHCTMTYT +XHebHMubKMN +Yepkach +JyraHCbk +AOH3anopi3bkoiQA +MOEPHI3ALII +BiHHMLA +3MICTYOCBITW +OHIBaHO-ΦpaHkiBCbkoiQA +yokropoA +AHinpo +lepxaBHa HaykOBa ycTaHOBa +OHBOKuiBCbkoiMicbkpaAM +AoHeubk +(KMAA) +ABTOMATM3OBAHMM +OHKwiBCbKoiQAA +HOOPMALIMHM +AIKOMMEHEAXKMEHTY +KOMNNEKCOCBITHbOrO +AOH KipoBorpaACbkoi QAA +3anopiiokg +Oaeca +MMKonaiB +AOH yraHCbkoi QA +XepcoH +AICO +OHbBiBCbkoQAA +OHMkonaiBCbkoiQAA +ciMpepononb +OHQAeCbkoiQA +AOHonTaBCbkoiQAA +CeBacT +ABTOPM3OBAHMM +EJEKTPOHHMM413 + +Рис. 11. Головна сторінка порталу «NZ.UA» +Публікувати домашні завдання як для всього класу, так і персонально +для кожного учня. Батьки завжди будуть в курсі того, що відбувається +в школі, навіть якщо вони дуже зайняті або живуть і працюють да- +леко від своїх чад. Існує можливість архівувати дані, аналізувати від- +відуваність і успішність як вчителям, так і батькам. Дозволяє робити +висновки та різні статистичні вибірки. Портал «NZ.UA» автоматично +синхронізується з програмою «КУРС:ШКОЛА», що значно полегшує +роботу користувачам. +Комп’ютерна програма «КУРС:ДОШКІЛЛЯ». Ця програма при- +значена для ведення єдиної бази даних дитячої дошкільної установи, +управління процесами, обліку дітей дошкільного віку і автоматичного +(натисненням однієї кнопки) складання обов’язкового статистичного +звіту за формою 85-к. Програма «КУРС:ДОШКІЛЛЯ» враховує відо- +мості про педагогічний склад, вихованців, їх батьків або опікунів, до- +помагає вести контроль і відображення відвідуваності протягом тиж- +ня, місяця, року для окремих груп так і для усього закладу в цілому, +покращує ефективність роботи дитячої дошкільної установи, створює +комфортніші умови для плідної роботи персоналу. Програма підтри- +мує дві мови (українську і російську), розмежовує права і рівні доступу +до даних. Надає можливість роботи в розрахованому на одного корис- +тувача і мережевому режимі з підтримкою персоналізації інтерфейсу. +Використовує новітні інтелектуальні методи представлення даних. + +NZ +MoBa: YkpaiHcbka +EneKTpOHHi KnacHi KypHanN Ta WOAeHHMKM3MOKMBocTAMMAMCTaHuiMHOrO HaByaHH +Bxin Ha caiT +AK +JoriH +EneKTpoHHi +HaByanbHi +npauroBaTn +Im'kopucTyBayaabo e-mail +BNZ.UA +LOAEHHMK +ypHann +Naponb +Naponb +3aynwnaponb +a6o noriH? +TTT +OnikAiTen +WkinbHa +Po3knaA +Npocai +Aonomora +WkinbHoro +品 +TexHiYHa niATpMMKa +6a3aAaHMX +DOOOO +3aHATb +Biky +PeecTpaLigWkonM +KoHKypCHWi +ATecTaig +CTaTWCTWYHi +BW6ip +neAaroriyHvx +3BiTW +H +npauiBHWkiB +niApyHWkiB414 + +Рис. 12. Інтерфейс програми «КУРС:ДОШКІЛЛЯ» +Автоматизована система підвищення кваліфікації педагогічних пра- +цівників закладів загальної середньої освіти (АПК) призначена для під- +тримки процесу проходження навчання за програмами підвищення +кваліфікації педагогічних працівників закладів загальної середньої +освіти. +На новій платформі можна переглянути курси і програми під- +вищення кваліфікації, оформити замовлення на проходження на- +вчання, створити власний кабінет для зберігання інформації про хід +і результати навчання, здійснити оплату, отримати сертифікати вста- +новленої форми про підвищення кваліфікації тощо. +Надання послуг здійснюється відповідно до вимог Постанов +Кабінету Міністрів України № 800/1133 від 21 серпня і 27 грудня +2019 року щодо порядку підвищення кваліфікації педагогічних і +науково-педагогічних працівників. Послуги надаються на підставі +угоди, яка стає доступною зареєстрованому користувачу в процесі +формування замовлення на обраний курс. Оплата за послуги здій- +снюється користувачем на підставі рахунку-фактури одним із до- +ступних способів: на банківську картку, онлайн, банківським пе- +реказом. Після завантаження всіх передбачених для конкретного +курсу документів і здійснення оплати користувач отримує в свій +кабінет сертифікат встановленого зразка, а також акт про надання +послуг. + +回 +X +Onepauii +Tapwpikauig +CnMCKW +3BITW +CepBic +AoBiaka +N B CHCTeMi: 40000 +国区 +AiTw +Wa6noH BiaBiayBaHocTi +Ta6enb 06niky po6o4oro4acy +NepcoHan +AHTponOMeTpia +BiaBiAyBaHicTb +TapwbikauiiHwicnucoK +@opma +n baTbKM +MnopT +XapyyBaHHA +85-K +OcHOBHi cnWCKM +3AopoB'g +Tapwbwkauig +3BiTW +CepBic +AoBiaka +8 ++ +8 +国 +CTBOpWTW +3MiHTM +BuaanT EkcnopT +CTBOPITW +EkcnopT +KO.OHKM +3aranbHMi cnMcoK +Fpyna +lepeTATHiTb CIOAM 3aronOBOK KOOHKM AN rpynyBaHHA +KnauHiTb TyT A,AR CTBOpeHHR pinbTpy +# +Bubye +NIE(nOBMicTIo) +[pyna +Craryc rpynM +8 +KnauHiTb TyT A/I CTBopeHHR βinbTpy +0 +onoBko M. B. [1111] +NH, 3 Tpy 2018 p. +1 [01-09-2015 11 31-08-2016] +Bepcig 15 R5 (1.15.5)415 + +Рис. 13. Автоматизована система підвищення кваліфікації педагогічних працівників закладів загальної середньої +освіти + +NIABMLEHHAKBAIPIKALIi: +AHMIHICTPATOPNOCNYI416 +Документами, на підставі яких видається сертифікат про підви- +щення кваліфікації, є: +для дистанційної форми навчання: електронний документ про +проходження відповідного онлайн-курсу; +для дуальної форми навчання: +1) електронний документ про проходження відповідного онлайн- +курсу; +2) довідка про проходження практики за місцем роботи за підпи- +сом керівництва закладу освіти. +Провівши аналіз інформаційних систем управління навчаль- +ним процесом та систем автоматизації та моніторингу в освітній +діяльності, можна зробити висновок, що перевагами універсаль- +них систем є простіше початкове налаштування, яке потребує +лише наявності підключення до мережі Internet, відсутність по- +треби адміністрування бази даних з боку користувача. Техноло- +гічні процеси у таких системах вибудувані згідно з вимогами і +нормативними документами Міністерства освіти і науки. Однак у +жертву широкомасштабності та універсальності була віддана про- +думаність окремих специфічних функцій та зручність користува- +ча. Натомість спеціалізовані електрон ні системи управління по- +требують спеціального адміністрування, але це дозволяє їм бути +більш гнучкими до будь-яких потреб закладу освіти. Значною пе- +ревагою цієї системи є те, що всі модулі використовують єдину +базу даних як викладачів, так і здобувачів освіти. Також система +спонукає персонал до підвищення виконавчої дисципліни, тому +що не дозволяє довільно змінювати вихідну інформацію, створює +необхідність використання сучасних інструментів навчання та ко- +мунікацій (корпоративної пошти, чату, науково-освітньої спіль- +ноти тощо). +Результати дослідження дозволяють сформувати такі рекомен- +дації: +1. Створення електронної системи управління навчальним про- +цесом повинно враховувати цілі та завдання аудиторії користувачів +(студентів, викладачів, співробітників, адміністрації закладу); +2. Впровадження комплексної електронної системи управління +навчальним закладом буде дійсно ефективним при умові технічної, +програмної та організаційної підтримки. +Автоматизована інформаційна система обліку підвищення кваліфі- +кації викладачів. Нова реформа освіти в Україні та системи після- + +417 +дипломної педагогічної освіти (ППО) вимагає моніторингу процесу +підвищення кваліфікації працівників навчальних закладів. Це забез- +печить спостереження та аналіз впровадження відповідного процесу +професійного розвитку в навчальних закладах з метою виявлення +проміжних та кінцевих результатів. Загалом це сприятиме прийнят- +тю відповідних управлінських рішень для регулювання та коригу- +вання навчального процесу для забезпечення його якості. Водночас +ефективність моніторингу та своєчасність необхідних змін залежать +від автоматизації обробки наявних даних про діяльність навчального +закладу. Це визначає можливість використання відповідного про- +грамного забезпечення, зокрема спеціалізованих інформаційних +систем (ІС). +Судячи з розглянутих вище застосунків, можна зробити висновок, +що існує багато варіацій систем автоматизації освітнього процесу. +У кожного з них є свої переваги та недоліки, також варто відмітити, +що більшість розглянутих рішень працюють в онлaйн-форматі. Піс- +ля їхнього аналізу можна виділити основну функціональність, яка +повин на бути у розробленій системі, а саме: +зрозумілий інтерфейс; +швидкість роботи; +простота налаштування та запуску; +наявність різних типів доступу; +створення окремих груп користувачів; +інтеграція на різні середовища; +можливість реалізації додаткових модулів; +високий ступінь безпеки; +широка функціональність. +Усі інформаційні системи незалежно від архітектури і сфери ви- +користання складаються з двох частин: функціональної, до якої +належать елементи системи, що визначають її функціональні мож- +ливості, призначення, функції управління, та забезпечувальної +(рис. 14). +Функціональна частина складається з підсистем, комплексів за- +дач, автоматизованих робочих місць. Функціональна підсистема — +це самостійна частина системи, що виконує конкретні функції та +завдання управління і характеризується відповідним цільовим при- +значенням, певною методикою проведення розрахунків економічних +показників, підпорядкованістю та технологічними особливостями +експлуатації. Перелік функцій конкретної інформаційної системи + +418 +залежить від сфери її застосування, об’єкта управління. Відповідно +до виділених функціональних підсистем і до фаз управління визнача- +ється комплекс задач, що здійснюється з урахуванням основних фаз +управління: планування, обліку, контролю, аналізу, регулювання. Ви- +бір і обґрунтування комплексу функціональних задач — один із най- +важливіших елементів створення інформаційних систем [22]. + +Рис. 14. Структурна схема інформаційної системи +Забезпечувальна частина інформаційної системи складається з під- +систем, які є інструментами для реалізації функціональної частини. +До їх складу входять організаційне, правове, інформаційне, лінгвіс- +тичне, математичне, програмне, технічне, ергономічне забезпечення. +Підсистема організаційно-методичного забезпечення є сукуп- +ністю правил, документів, інструкцій та положень, що забезпечують +створення системи та взаємодію її складових частин у процесі функ- +ціонування. Організаційне забезпечення реалізує такі функції: +– аналіз існуючої системи керування організацією, де буде вико- +ристовуватися інформаційна система, і виявлення завдань, що під- +лягають автоматизації; + +IHbopMaiiHa cncTeMa +DvHKioHaJIbHa YacTHHa +3aoe3neyyBaJIbHa yacTHHa +yHKioHaJIbHa IincHcTeMa +OpraHi3aiiHe 3a6e3eyeHHA +KoMJekc 3alay +IpaBoBe3a6e3leyeHHy +InbopMaiiHe 3a6e31leyeHHA +JIiHTBicTyHe3a6e31IeHeHH +MaTeMaTMyHe 3a6e3eyeHH4 +IporpaMHe 3a6e31leyeHHy +TexHiyHe3a6e31eyeHHy +EproHoMiyHe3a6e31leyeHH419 +– підготовка завдань до вирішення на комп’ютері, включаючи +технічне завдання на проектування інформаційної системи і техніко- +економічне обґрунтування її ефективності; +– розроблення управлінських рішень, методології вирішення за- +вдань, спрямованих на підвищення ефективності системи керування. +Документи визначають технологію функціонування інформацій- +ної системи, методи вибору і застосування користувачами техноло- +гічних прийомів для одержання конкретних результатів при функціо- +нуванні інформаційної системи. +Підсистема правового забезпечення — сукупність законодавчих +актів, правових норм і нормативів, що пов’язані з функціонуванням +інформаційної системи. Нормативними документами визначаєть- +ся порядок одержання, перетворення й використання інформації. +Правове забезпечення базується на юридичному підході до організа- +ційних і функціональних аспектів розроблення системи. Конструк- +тивно функції управління в правовій сфері реалізуються у вигляді +нормативно-правових актів, планів, методик, обов’язкових для всіх +державних стандартів. Нормативно-правові акти поділяються на за- +конодавчі, нормативні акти міністерств і відомств, акти місцевих ор- +ганів управління, локальні нормативні акти. +Інформаційне забезпечення — це сукупність методів і засо- +бів розміщення й організації інформації, що включає єдину сис- +тему класифікації і кодування повідомлень, схем інформаційних +потоків, а також методологію побудови баз даних. Інформаційне +забезпечення включає сукупність показників, довідкових даних, +класифікаторів та кодифікаторів інформації, масиви інформації +на відповідних носіях і є однією з основних ланок функціонування +інформаційної системи, що містить ресурси, заради використання +яких і ведеться розробка системи. Засобами інформаційного за- +безпечення досягається інформаційна сумісність даних різних ін- +формаційних систем. Для організації їх взаємодії дані повинні бути +описані однотипово. +Для формування і ведення баз даних використовується спеціаль- +ний комплекс програм — система керування базами даних (СКБД). +Цей комплекс забезпечує створення логічної структури бази даних, +введення та редагування бази даних, пошук і збереження даних, до- +ступ до окремих записів, полів тощо. +Формування інформаційного забезпечення є однією із найвід- +повідальніших ланок створення інформаційної системи. Викону- + +420 +ються роботи з впорядкування інформаційної бази, розроблення +єдиної системи класифікації і кодування інформації, визначення +методів вводу, збереження, накопичення і відновлення інфор- +мації. +Математичне забезпечення — сукупність математичних методів, +моделей, алгоритмів обробки інформації. Воно містить засоби забез- +печення, методи вибору розв’язування, оптимізації, математичного +програмування, математичної статистики, технічну документацію. +Технічна документація з цього виду забезпечення передбачає опис за- +дач, завдання з алгоритмізації, економіко-математичні моделі задач і +програм для реалізації функціонування інформаційних систем, опи- +си пакетів прикладних програм. Спеціалісти математичного забезпе- +чення займаються постановкою задач та використання математичних +аналітичних і числових методів. +Програмне забезпечення включає узгоджений комплекс про- +грам, що уможливлює локальне і спільне функціонування всіх +компонентів інтегрованого середовища, а також сукупність про- +грам для стабільної роботи комплексів технічних засобів. До складу +програмного забезпечення входять системні і прикладні програмні +засоби, а також інструктивно-методичні матеріали. До системних +належать програми, які забезпечують діяльність комп’ютерних +операційних систем. Вони призначені для організації обчислю- +вального процесу і вирішення стандартних завдань обробки ін- +формації. Зокрема це операційні системи, антивірусне програмне +забезпечення, командно-файлові процесори та ін. Прикладні про- +грамні засоби — це сукупність програм, що розробляються при +створенні системи конкретного функціонального призначення. +Вони включають пакети прикладних програм для збору даних і їх +обробки при вирішенні функціональних завдань. До таких засобів +належать системи: +– підготовки документів (текстових, табличних, графічних); +– оброблення фінансово-економічної інформації; +– керування базами даних; +– підтримки прийняття рішень і експертні системи тощо. +Технічне забезпечення — це технічні засоби, які призначені для +роботи інформаційної системи, а також відповідна документація на +ці засоби і технологічні процеси. Створення інтегрованого інформа- +ційного середовища пов’язано з розбудовою інформаційної інфра- +структури, до складу якої входить: + +421 +– апаратне забезпечення (базис усього комплексу технічних за- +собів, призначений для оброблення і перетворення різних видів ін- +формації); +– програмне забезпечення; +– засоби зберігання даних; +– комунікаційні засоби для забезпечення передачі інформації +в межах системи й обмін даними із зовнішнім середовищем; +– комп’ютерна мережа. +Ергономічне забезпечення охоплює сукупність методів і засобів, +що використовуються на різних етапах розроблення та функціону- +вання системи, і призначені для створення оптимальних і безпечних +умов високоефективної безпомилкової роботи персоналу і клієнтів. +Впровадження інформаційних систем застосовується з метою +підвищення ефективності обробки інформації за рахунок не тільки +опрацювання і збереження рутинної інформації, автоматизації звітів, +але і за рахунок принципово нових методів управління, заснованих +на моделюванні дій при прийнятті рішень. +Інформаційне сприяння створенню кадрових умов визначає не- +обхідність отримання, фіксації та використання такої інформації: +штатного розкладу та посадових обов’язків працівників; анкетних да- +них на кожного працівника; графіка підвищення кваліфікації праців- +ників, графіка атестації працівників; бібліографічних та анотованих +списків літератури; картотеки педагогічного досвіду; індивідуальних +планів роботи викладачів, планів самоосвіти. +Варто відмітити, що наразі не існує спеціалізованих інформацій- +них систем для обліку, моніторингу процесу підвищення кваліфікації +на рівні навчального закладу. З метою зменшення кількості докумен- +тів в ході підвищення кваліфікації та атестації викладачів, які необхід- +но відстежувати та обробляти, пропонується створити автоматизовану +інформаційну систему обліку підвищення кваліфікації та атестації на- +уково-педагогічних та педагогічних працівників закладу освіти. +Мета створення інформаційної системи полягає у такому: +– забезпечення ефективності процесу підвищення кваліфікації та +атестації педагогічних та науково-педагогічних працівників закладу +освіти за допомогою інформаційної підтримки задач прогнозування і +планування організації цього процесу; +– зручний автоматизований контроль за процесом підвищення +кваліфікації педагогічних та науково-педагогічних працівників за- +кладу освіти; + +422 +– контроль за виконанням нормативів по кількості годин підви- +щення кваліфікації педагогічних та науково-педагогічних працівни- +ків закладу освіти за розрахунковий період; +– представлення розрахункових показників (кількість годин +підвищення по кожному викладачу, менше 150 годин підвищення, +тощо); +– формування звітів щодо результатів підвищення кваліфікації та +атестації педагогічних та науково-педагогічних працівників закладу +освіти; +– аналітика результатів за напрямами щодо підвищення кваліфі- +кації та атестації педагогічних та науково-педагогічних працівників +закладу освіти. +Визначення діапазону дії і меж застосувань бази даних: +– навчально-методичні кабінети закладів освіти. +Визначення складу користувачів і областей застосування: +– працівники навчально-методичних відділів закладів освіти. +Визначення представлень користувачів, що підтримуються +БД: +– зберігання і обробка інформації стосовно планування та резуль- +татів підвищення кваліфікації викладачів коледжу. +Вимоги користувачів: +– автоматизація обліку і контролю процесу підвищення кваліфі- +кації та атестації педагогічних та науково-педагогічних працівників +закладу освіти; +– автоматизація планування, фіксування і контролю підвищення +кваліфікації педагогічних та науково-педагогічних працівників за- +кладу освіти; +– автоматизація формування показників підвищення кваліфікації +та атестації педагогічних та науково-педагогічних працівників закла- +ду освіти. +Вимоги до інформаційної системи: +Система повинна забезпечувати можливість виконання таких +функцій: +– ініціалізацію системи (введення інформації про педагогічних +та науково-педагогічних працівників закладу освіти, перелік баз для +підвищення кваліфікації і т. п.); +– введення і корекцію інформації про педагогічних та науково- +педагогічних працівників закладу освіти та результати їх підвищення +кваліфікації; + +423 +– одержання відомостей про підвищення кваліфікації та атестації +педагогічних та науково-педагогічних працівників закладу освіти. +Система повинна забезпечувати можливість виконання таких за- +питів: +Запит, що виконує вибірку даних та повертає список педагогічних +та науково-педагогічних працівників закладу освіти певної категорії +(вибір здійснюється через форму «Пошук за категорією»). +Запит, що виконує вибірку даних та повертає список педагогічних +та науково-педагогічних працівників закладу освіти певної циклової +комісії/кафедри. +Запит, що повертає список педагогічних та науково-педагогічних +працівників закладу освіти із педагогічним званням «викладач-мето- +дист». +Запит, що повертає список педагогічних та науково-педагогічних +працівників закладу освіти в із науковим ступенем/вченим званням +«доктор наук». +Запит, що виконує підрахунок загальної кількості годин з підви- +щення кваліфікації педагогічних та науково-педагогічних працівни- +ків закладу освіти. +Запит, що повертає список педагогічних та науково-педагогічних +працівників закладу освіти із вченим званням «кандидат наук». +Запит, що виконує вибірку даних та повертає інформацію за дата- +ми підвищення. +Запит, що виконує вибірку даних та повертає інформацію резуль- +татів підвищення кваліфікації педагогічних та науково-педагогічних +працівників закладу освіти по конкретному педагогічному та науко- +во-педагогічному працівнику закладу освіти. +Запит, що виконує вибірку даних за роком атестації. +Запит, що виконує вибірку даних викладачів, які по підвищенню +мають менше 150 годин за 5 років. +Вихідними даними є: +– інформаційні картки педагогічних та науково-педагогічних пра- +цівників закладу освіти з їх особистою інформацією; +– атестаційні картки педагогічних та науково-педагогічних пра- +цівників закладу освіти; +– плани підвищення кваліфікації педагогічних та науково-педаго- +гічних працівників закладу освіти; +– поточні відомості про підвищення кваліфікації педагогічних та +науково-педагогічних працівників закладу освіти; + +424 +– підсумки підвищення; +– різноманітні звіти та плани. +Вимоги до надійності, вимоги до забезпечення надійного функці- +онування програми: +– передбачити контроль введення інформації; +– передбачити блокування некоректних дій користувача при ро- +боті із системою; +– забезпечити цілісність збереженої інформації. +Процес проектування ІС являє собою послідовність переходів від +неформального мовного опису інформаційної структури предметної +області до формалізованого опису об’єктів предметної області в тер- +мінах деякої моделі. Проектування ІС складається з таких етапів: +– системний аналіз предметної області; +– концептуальне проектування; +– логічне проектування; +– фізичне проектування. +Системний аналіз передбачає мовний опис реальних об’єктів +предметної області, визначення зв’язків між об’єктами, дослідження +характеристик об’єктів і зв’язків. Результати дослідження використо- +вуються при концептуальному проектуванні БД. +Для визначення складу і структури предметної області застосову- +ються або функціональний, або предметний підходи. Функціональ- +ний підхід застосовує рух «від задач» і використовується у тих ви- +падках, коли заздалегідь відомі функції майбутніх користувачів БД, а +також відомі всі задачі, для інформаційних потреб яких створюються +БД. В цьому випадку на основі виробничих документів, опитувань +замовників можна чітко визначити мінімальний набір об’єктів пред- +метної області та їх взаємозв’язок. +Предметний підхід застосовується у тому випадку, коли інфор- +маційні потреби майбутніх користувачів чітко не визначені. В цьо- +му випадку не можна чітко визначити мінімальний набір об’єктів +предметної області. В опис предметної області включаються об’єкти +та зв’язки, які є найбільш характерними та найбільш суттєвими +для неї. БД називається предметною і може використовуватися для +розв’язання задач, які заздалегідь не визначені. +У практичній діяльності використовується комплексний підхід, +який, з одного боку, дозволяє розв’язувати конкретні інформаційні +та функціональні задачі, а з іншого боку — враховує можливість до- +давання нових застосувань. + +425 +У загальному випадку існують два підходи до проектування БД: +низхідне проектування і висхідне проектування. +Низхідне проектування починається з визначення наборів даних, +потім визначаються елементи даних для кожного з таких наборів. +Цей процес включає в себе ідентифікацію різних типів сутностей і +визначення атрибутів кожної сутності. Низхідне проектування вклю- +чає операції декомпозиції, що передбачає заміну вихідної множини +відношень, що входять в схему БД, іншою множиною відношень, які +є проекціями вихідних відношень. +Цей підхід рекомендується застосовувати у тих випадках, коли +кількість, різноманітність та складність сутностей, зв’язків і транз- +акцій значна за розмірами. Найбільш поширеними моделями для +цього проектування є моделі «сутність — зв’язок» (ER-моделі, Entity- +Relationship model). +Висхідне проектування починається з виявлення елементів да- +них, які потім групуються в набори даних. Спочатку визначаються +атрибути, які потім об’єднуються в сутності. Висхідне проектування +включає операції синтезу, що передбачає виконання компоновки із +заданої множини функціональних залежностей між об’єктами пред- +метної області вихідних відношень схеми БД. +Цей підхід рекомендується застосовувати у тому випадку, якщо +розробляється невелика БД з незначною кількістю об’єктів, атрибу- +тів і транзакцій. +Концептуальне проектування полягає у створенні концептуальної +моделі, яку відображає концептуальна схема БД. На цьому етапі ви- +значаються об’єкти, зв’язки між об’єктами, атрибути, ключові атри- +бути. +Логічне проектування полягає у створенні логічної моделі на +основі вибраної моделі даних. На цьому етапі необхідно вже знати, +яка СУБД буде застосовуватися в системі (ієрархічна, мережна, реля- +ційна, об’єктно орієнтована). Для перевірки вірності логічної моделі +застосовується нормалізація. Крім того, логічна модель перевіряєть- +ся на умову забезпечення всіх транзакцій користувачів. +Фізичне проектування полягає в описі засобів фізичної реалізації +логічного проекту БД. Фізичні моделі визначають засоби розміщення +даних в середовищі зберігання і засоби доступу до цих даних, які під- +тримуються на фізичному рівні. +Аналіз предметної області. Відповідно до законодавства педаго- +гічні та науково-педагогічні працівники зобов’язані постійно під- + +426 +вищувати свій професійний і загальнокультурний рівень та педа- +гогічну майстерність. Але такий обов’язок урівноважується правом +педагогічних працівників на вільний вибір освітніх програм, форм +навчання, закладів освіти, установ і організацій, інших суб’єктів +освітньої діяльності, що здійснюють підвищення кваліфікації. По- +шук інформації про підвищення кваліфікації педагогічний пра- +цівник може здійснювати у будь-який спосіб — безпосередньо на +сайтах суб’єктів підвищення кваліфікації, на різноманітних інфор- +маційних чи спеціальних ресурсах, у тематичних групах, через запит +необхідної інформації безпосередньо у суб’єкта підвищення квалі- +фікації тощо. +Заклади освіти, в яких працюють педагогічні та науково-педаго- +гічні працівники, сприяють їхньому професійному розвитку та під- +вищенню кваліфікації. Виходячи з цього, Міністерство освіти і на- +уки України покладає на керівництво усіх закладів освіти обов’язок +здійснювати контроль та максимально активно сприяти професійно- +му розвитку та підвищенню кваліфікації педагогічних та науково-пе- +дагогічних працівників на засадах, визначених законодавством, та за +процедурами, визначеними Порядком підвищення кваліфікації педа- +гогічних та науково-педагогічних працівників, затвердженим поста- +новою Кабінету Міністрів України від 21 серпня 2019 р. № 800 «Деякі +питання підвищення кваліфікації педагогічних та науково-педагогіч- +них працівників». Активна підтримка педагогічних працівників адмі- +ністрацією закладу — роз’яснення нової процедури підвищення ква- +ліфікації, допомога (у разі потреби) у визначенні компетентностей, +удосконалення яких педагогічні працівники потребують найбільше, +тощо — є запорукою формування педагогіки партнерства в закладі +освіти, його сталого розвитку, збереження здорового мікроклімату в +колективі, покращення діяльності закладу освіти та якості освіти за- +галом. +Для закладів вищої та фахової передвищої освіти підвищення +кваліфікації є обов’язковою складовою системи забезпечення якос- +ті освіти. Як правило, підвищення кваліфікації здійснюється за про- +грамою підвищення кваліфікації, у тому числі шляхом участі у се- +мінарах, практикумах, тренінгах, вебінарах, майстер-класах тощо. +Окремі види діяльності науково-педагогічних працівників (участь у +програмах академічної мобільності, наукове стажування, само освіта, +здобуття наукового ступеня, вищої освіти) можуть бути визнані під- +вищенням кваліфікації. Процедура зарахування окремих видів ді- + +427 +яльності, їх результатів та обсяг підвищення кваліфікації науково- +педагогічних працівників визначаються вченими (педагогічними) +радами відповідних закладів освіти. Науково-педагогічні працівники +самостійно обирають форми, види, напрями та суб’єктів підвищення +кваліфікації. +Законодавство встановлює різні вимоги до періодичності та об- +сягів підвищення кваліфікації науково-педагогічних працівників, які +здійснюють свою професійну діяльність на різних рівнях освіти. Так, +науково-педагогічні працівники закладів фахової передвищої освіти +зобов’язані підвищувати свою кваліфікацію щорічно, а загальна кіль- +кість академічних годин для підвищення кваліфікації упродовж п’яти +років не може бути меншою за 120 годин, з яких певна кількість го- +дин обов’язково має бути спрямована на вдосконалення знань, вмінь +і практичних навичок у роботі зі студентами з особливими освітніми +потребами та дорослими студентами. Крім цього, обсяг щорічного +підвищення кваліфікації науково-педагогічних працівників закладів +фахової передвищої освіти встановлюється засновником (або упо- +вноваженим ним органом). +Обсяг (тривалість) підвищення кваліфікації науково-педагогіч- +них працівників установлюється в кредитах Європейської кредитної +трансферно-накопичувальної системи (один кредит ЄКТС становить +30 годин) за накопичувальною системою і для науково-педагогіч- +них працівників закладів вищої та післядипломної освіти протягом +п’яти років не може бути меншим ніж шість кредитів ЄКТС. Нако- +пичувальна система передбачає можливість враховувати обсяги під- +вищення кваліфікації чи інших видів професійного удосконалення, +які визнаються підвищенням кваліфікації і які здійснювалися науко- +во-педагогічним працівником будь-коли впродовж міжатестаційного +періоду. Науково-педагогічних працівникам закладів освіти вперше, +призначеним на посади: керівника, заступника керівника закладу +вищої, післядипломної освіти, керівника, заступника керівника фа- +культету, інституту чи іншого структурного підрозділу, керівника ка- +федри, завідувача аспірантури, докторантури закладу вищої освіти — +підвищення кваліфікації відповідно до займаної посади протягом +двох перших років роботи є обов’язковим. Обсяги такого підвищення +кваліфікації визначаються вченою (педагогічною) радою відповідно- +го закладу освіти. +Результати підвищення кваліфікації враховуються під час: прове- +дення атестації педагогічних працівників закладів вищої та післяди- + +428 +пломної освіти, обрання на посаду за конкурсом чи укладення трудо- +вого договору з науково-педагогічними працівниками. +Атестація педагогічних працівників — це система заходів, спрямо- +вана на всебічне комплексне оцінювання їх педагогічної діяльності, +за якою визначаються відповідність педагогічного працівника займа- +ній посаді, рівень його кваліфікації, присвоюється кваліфікаційна +категорія, педагогічне звання. Атестація може бути черговою або по- +зачерговою. Чергова атестація здійснюється один раз на п’ять років. +Умовою чергової атестації педагогічних працівників є обов’язкове +проходження не рідше одного разу на п’ять років підвищення ква- +ліфікації на засадах вільного вибору форм навчання, програм і на- +вчальних закладів. Для організації та проведення атестації педагогіч- +них працівників у навчальних та інших закладах, органах управління +освітою щороку до 20 вересня створюються атестаційні комісії І, ІІ і +ІІІ рівнів [18]. +У процесі вивчення професійної діяльності керівних кадрів на- +вчальних та інших закладів атестаційна комісія з’ясовує: +– виконання програми розвитку навчального закладу та результа- +ти інноваційної діяльності; +– стан організації навчальної та виховної роботи, додержання ви- +мог державних освітніх стандартів; +– результати державної атестації навчального закладу; +– результати перевірок, проведених Державною інспекцією на- +вчальних закладів, місцевими органами управління освітою та інши- +ми органами державного нагляду (контролю); +– додержання вимог до забезпечення безпечних та нешкідливих +умов навчання учнів; +– підсумки моніторингу роботи з педагогічним колективом та інши- +ми працівниками навчального закладу; +– ефективність взаємодії з громадськими організаціями та органа- +ми шкільного самоврядування; +– додержання педагогічної етики, моралі; +– звіти керівника про свою роботу на загальних зборах (конфе- +ренціях) колективу навчального закладу; +– аналіз розгляду звернень громадян. +Визначення схеми інформаційних потоків автоматизованої ін- +формаційної системи обліку підвищення кваліфікації викладачів. +Потік інформації базується на потоці паперових або електронних +документів. Залежно від цього його можна виміряти або кількістю + +429 +оброблених та переданих одиниць паперових документів, або загаль- +ною кількістю рядків у цих документах. +Автоматизована інформаційна система обліку підвищення квалі- +фікації викладачів отримує дані від джерела інформації. Ці дані над- +силаються для зберігання або обробки в системі, а потім надсилають- +ся споживачу (рис. 14). +Споживачем може бути людина, пристрій чи інша інформаційна +система. Зворотний зв’язок може бути встановлений між споживачем +та самою інформаційною системою (від споживача до одержувача ін- +формації). +В нашому випадку джерелом інформації є педагогічні та науково- +педагогічні працівники закладу освіти, а споживач інформації — ке- +рівні структури. +Автоматизована інформаційна система обліку підвищення ква- +ліфікації викладачів включає вхідну інформацію (дані викладача, +сертифікати, дипломи) та вихідну інформацію (звіти, плани, розра- +хунки) і функціонує в інформаційному середовищі. За допомогою +засобів обробки інформації вхідна інформація перетворюється на ви- +хідну, з якою потім може працювати завідувач методичного кабінету +(рис. 15). +Джерело інформації +(плани, звіти педагогічних та науково-педагогічних працівників закладу осві- +ти, сертифікати, свідоцтва про проходження підвищення кваліфікації педа- +гогічних та науково-педагогічних працівників закладу освіти, результати ро- +боти, накази атестаційних комісій) +↓ +Отримання інформації +(циклові комісії, кафедри) +↓ +Збереження й обробка інформації +(навчально-методичні відділи, методичні кабінети) +↓ +Виведення інформації +(навчально-методичні відділи, методичні кабінети) +↓ +Споживач інформації +(керівники структурних підрозділів, атестаційні комісії вищого рівня) +Рис. 15. Ланцюг надходження інформації + +430 + +Рис. 16. Структурна схема інформаційної системи +Працівник методичного кабінету, взаємодіючи з інтерфейсом ІС, +взаємодіє з базою даних і може редагувати будь-які дані, створювати +звіти чи надавати інформацію для подальшого розгляду, опрацюван- +ня та корегування керівнику навчально-методичного кабінету. +Концептуальне моделювання. Для створення концептуальної та +логічної моделі бази даних ІС була обрана реляційна модель, введе- +на Е. Ф. Коддом в 1970 році як спосіб зробити системи управління +базами даних більш незалежними від якогось конкретного додатка. +Це математична модель визначена в термінах логіки предикатів і те- +орії множин, а використовувані нею системи застосовуються в сис- +темах мейнфреймів, персональних комп’ютерів і мікрокомп’ютерів. +Продукти, які зазвичай називаються реляційними базами даних, +фактично реалізують модель, яка є лише наближенням до математич- +ної моделі, визначеної Коддом. Три ключових терміна широко вико- +ристовуються в моделях реляційних баз даних: стосунки, атрибути і +домени. Стосунок — це таблиця зі стовпцями і рядками. Іменовані +стовпці стосунка називаються атрибутами, а домен — це набір зна- +чень, які можуть приймати атрибути. +Основною структурою даних реляційної моделі є таблиця, в якій +інформація про конкретний об’єкт (скажімо, працівника) представ- +лена в рядках (також званих кортежами) і шпальтах. Таким чином, +«ставлення» в «реляційній базі даних» відноситься до різних таблиць +в базі даних. Стосунок являє собою набір кортежів. У стовпчиках +перераховані різні атрибути об’єкта (наприклад, ім’я співробітни- + +BxiAHi +06po6ka +BAxiAHi +·AaHi; +IHpopMauiMHi +• 3BiTW; +IHbopMauia +CWCTeMW; +nnaHw; +4 +npauiBHK; +rpabikw; +yCTaTKyBaHHA +inbopmauia +YnpaBniHHA +.oco6a,o +3BOPOTHM3B'A30K +npwimae +piweHHA; +aBTOMaTWYHe +ynpaBAiHHA431 +ка, адреса або номер телефону), а рядок є фактичним екземпляром +об’єкта (конкретного співробітника), який представлений відношен- +ням. В результаті кожен кортеж таблиці Employee представляє різні +атрибути одного співробітника. Всі стосунки (і, отже, таблиці) в ре- +ляційній базі даних повинні дотримуватися деяких основних правил, +які можна кваліфікувати як стосунки. По-перше, впорядкування +стовпців в таблиці несуттєво. По-друге, в таблиці не може бути од- +накових кортежів або рядків. І, по-третє, кожен кортеж буде містити +одне значення для кожного з його атрибутів. +Реляційна база даних містить кілька таблиць, кожна з яких схожа +на таку в «плоскій» моделі бази даних. Одна із сильних сторін реля- +ційної моделі полягає в тому, що в принципі будь-яке значення, що +має місце в двох різних записах (що належать до однієї таблиці або до +різних таблицях), має на увазі взаємозв’язок між цими двома запи- +сами. Проте для забезпечення явних обмежень цілісності відносин +між записами в таблицях також можуть бути визначені явно, шля- +хом ідентифікації відносин батько — дитина, що характеризуються +привласненням потужності (1: 1, (0) 1: M, M: M). Таблиці також мо- +жуть мати призначений єдиний атрибут або набір атрибутів, які мо- +жуть діяти як «ключ», і можуть використовуватися для однозначної +ідентифікації кожного кортежу в таблиці. Ключ, який може вико- +ристовуватися для однозначної ідентифікації рядка в таблиці, нази- +вається первинним ключем. Ключі зазвичай використовуються для +об’єднання даних з двох або більше таблиць. Наприклад, таблиця +Employee може містити стовпець з ім’ям Location, який містить зна- +чення, відповідне ключу таблиці Location. Ключі також важливі при +створенні індексів, які полегшують швидкий пошук даних з великих +таблиць. Будь-який стовпець може бути ключем, або декілька стовп- +ців можуть бути згруповані разом в складений ключ. Немає необхід- +ності заздалегідь визначати всі ключі. Стовпець можна використо- +вувати в якості ключа, навіть якщо він спочатку не був призначений +для цієї мети. Ключ, який має зовнішній, реальний сенс (наприклад, +ім’я людини, ISBN книги або серійний номер автомобіля), іноді на- +зивають «природним» ключем. Якщо жодний природний ключ не +підходить (подумайте про багатьох людей на ім’я Іван), може бути +призначений довільний або сурогатний ключ (наприклад, вказуючи +ідентифікаційні номери співробітників). На практиці більшість баз +даних мають як згенеровані, так і природні ключі, оскільки згене- +ровані ключі можуть використовуватися всередині, щоб створювати + +432 +зв’язки між рядками, які не можуть зламатися, в той час як природні +ключі можна використовувати менш надійно, для пошуку і для інте- +грації з іншими базами даних (наприклад, записи в двох незалежно +розроблених базах даних можуть бути співставлені номером соціаль- +ного страхування, за винятком випадків, коли номери соціального +страхування невірні, відсутні або змінені). +З концептуального проектування починається створення концеп- +туальної схеми бази даних, в основі якої лежить концептуальна модель +даних. Концептуальна модель представляє загальний погляд на дані. +Розрізняють два головних підходи до моделювання даних при концеп- +туальному проектуванні: семантичні моделі; об’єктні моделі. +Семантичні моделі головну увагу приділяють структурі даних. +Найбільш поширеною семантичною моделлю є модель «сутність — +зв’язок» (Entity Relationship model, ER-модель). ER-модель скла- +дається із сутностей, зв’язків, атрибутів, доменів атрибутів, ключів. +Моделювання даних відображає логічну структуру даних, так само, +як блок-схеми алгоритмів відображають логічну структуру програми. +Об’єктні моделі головну увагу приділяють поведінці об’єктів да- +них і засобам маніпуляції даними. Головне поняття таких моделей — +об’єкт, тобто сутність, яка має стан і поведінку. Стан об’єкта визна- +чається сукупністю його атрибутів, а поведінка об’єкта визначається +сукупністю операцій, специфікованих для нього. +Зближення цих моделей реалізується в розширеному ER-моделю- +ванні (Extended Entity Relationship model, EER-модель). +ER-моделювання являє собою низхідний підхід до проектуван- +ня бази даних, який починається з визначення найбільш важливих +даних, які називаються сутностями (entities), і зв’язків (relationships) +між даними, які повинні бути представлені в моделі. Потім в модель +заноситься інформація про властивості сутностей і зв’язків, яка на- +зивається атрибутами (attributes), а також всі обмеження, які від- +носяться до сутностей, зв’язків і атрибутів. ER-модель дає графічне +представлення логічних об’єктів і їх відношень в структурі БД. Сут- +ність дозволяє моделювати клас однотипних об’єктів. Сутність має +унікальне ім’я у межах системи, що моделюється. Оскільки сутність +відповідає деякому класу однотипних об’єктів, то передбачається, що +в системі існує багато екземплярів даної сутності. Об’єкт, якому від- +повідає сутність, має набір атрибутів, які характеризують його влас- +тивості. При цьому набір атрибутів повинен бути таким, щоб можна +було розрізняти конкретні екземпляри сутності. + +433 +Для автоматизованої інформаційної системи обліку підвищення +кваліфікації викладачів відповідно до предметної області визначено +сутності: «Викладач», «Підвищення кваліфікації», «Атестація», «На- +прям підвищення», «Бази підвищення кваліфікації», «Результати під- +вищення». +Сутність «Викладач» (атрибути: табельній номер, фото, ПІБ, ци- +клова комісія/кафедра, номер телефону, E-mail, кваліфікаційна кате- +горія, педагогічне звання, науковий ступінь/вчене звання, спеціаль- +ність за дипломом). +Сутність «Атестація» (атрибути: № п/п, ПІБ, кваліфікаційна ка- +тегорія, рік попередньої атестації, запланована атестація, категорія, +статус категорії, педагогічне звання, статус педагогічного звання). +Сутність «Заплановане підвищення» (атрибути: номер підвищен- +ня, табельний номер, ПІБ, код курсу, місце проходження, форма під- +вищення, вид підвищення, дата останнього підвищення, дата почат- +ку, дата закінчення, відмітка про виконання). +Сутність «Інформаційна база підвищення кваліфікації» (атрибути: +код курсу, емблема, назва, адреса, телефон, E-mail, сайт). +Сутність «Напрями та форми підвищення кваліфікації» (атрибути: +код напряму, назва напряму підвищення кваліфікації). +Сутність «Результати підвищення» (атрибути: код документу, тип +документу, виданий кому, виданий ким, напрям, тема підвищення, +дата видачі, кількість годин, кількість кредитів, додаткове (незапла- +новане). +Розроблений концептуальний проект було перевірено на надлиш- +ковість та на відповідність транзакціям користувачів. +Перевірка на надлишковість передбачає перевірку ER-моделі з +метою виявлення надлишкових даних і вилучення їх, в тому випад- +ку, якщо вони визначені. Надлишкові зв’язки виявляються в тому, що +між двома сутностями є декілька шляхів і вони дублюють один іншо- +го (це не відноситься до зв’язків, які представляють різні асоціації). +Перевірка моделі на відповідність транзакціям користувачів вико- +нується на основі таких підходів: +– перевірка того, чи представляє модель всю інформацію (сутнос- +ті, атрибути, зв’язки), яка необхідна для кожної транзакції; +– перевірка по ER-діаграмі маршруту кожної транзакції. +Перевірка моделі на надлишковість та на відповідність транзак- +ціям користувачів дозволяє зробити висновок, що концептуальний +проект відповідає всім необхідним вимогам. + +434 + +Рис. 17. Концептуальна модель (ER-модель) + +PesynbTaTW niABWeHHA +HanpAMW Ta opMW niABWeHHA KBaipikaii +KoAAOKyMeHTy +KoA HanpaMy +Twn AOKyMeHTy +ATecTaLig +Ha3Ba HanpAMy niABWeHHA KBaniikaLii +BugaHwi (KoMy) +u/UaN & +BAAaHMM (KMM) +00 +nI6 +BuA niABMeHHA +HanpaM +Pik nonepeAHoi aTecTaii +TeMa niABWWeHHA +3an/aHoBaHa aTecTayig +AaTa BwAayi +KaTeropig +KbKICTb『OAMH +CTaTyc KaTeropii +KinbkicTb KpeAWTiB +NeAarori4He 3BaHHA +AoAaTKOBe (He 3an/aHOBaHe) niABWWeHHA +HpopMaiMHa 6a3a niAiMeHHA KBaipiKai + KoA kypciB +EM6neMa +BuknaAay +Ha3Ba + Ta6e/bHiHOMep +Aapeca +3anaHOBaHeniABMJeHH +ΦOTO +TeepoH +nI6 +E-mail + HoMep niABMWeHHA +nocaaa +CaWT +Ta6e/lbHwi HOMep +LMkoBa KoMicig +nI6 +HoMep TenepoHy +Micue npoxo^xeHHA +E-mail +TeMa nigBWWeHHA KBanipikaii +KBanipikaivHa KaTeropig +eAarori4He 3BaHHA +BMA NiABMWeHHA +HayKoBa cTyniHb/ B4eHe 3BaHf +AaTa noyaTky +CneLia/bHicTb 3a AWn/oMoM +AaTa 3akiH4eHHA +NpwMiTKa +KinbkicTb roAMH/KpeAWTis ECTS +BiAMiTKa npo BMKOHaHHA435 +Слід звернути увагу на те, що розроблений концептуальний про- +ект не є єдиним проектом, який відповідає поставленій задачі. Мож- +ливі варіанти розробки системи із застосуванням інших зв’язків між +сутностями або із застосуванням розширеної ER-моделі. +Застосування ER-діаграм дозволяє забезпечити просте і наочне +уявлення про головні логічні об’єкти БД і про зв’язки, які між цими +об’єктами існують. Також до переваг ER-діаграми слід віднести те, +що вони добре інтегрують з реляційною моделлю. +Між сутностями встановлюються зв’язки, які вказують, яким чи- +ном сутності співвідносяться або взаємодіють між собою. Розрізня- +ють такі зв’язки: +– між двома сутностями (бінарний зв’язок); +– між трьома сутностями (тернарний зв’язок); +– між N сутностями (N-арний зв’язок); +– між однією сутністю (рекурсивний зв’язок). +Найбільш поширеними є бінарні зв’язки. Зв’язок показує, яким +чином екземпляри сутностей пов’язані між собою. Бінарні зв’язки +бувають: +– 1:1 (один до одного); +– 1:M (один до багатьох); +– N:M (багато до багатьох). +Сутності «Інформаційна база підвищення кваліфікації» та «Запла- +новане підвищення» пов’язані зовнішнім ключем по полю «Код кур- +су» зв’язком «один до багатьох», бо одна база підвищення може бути +декілька раз запланована у різних викладачів. +Сутності «Викладач» та «Заплановане підвищення» пов’зані зо- +внішнім ключем по полю «Табельний номер» та «ПІБ» (тобто таблиця +«Викладач» є головною, а таблиця «Заплановане підвищення» — під- +порядкованою) зв’язком «один до багатьох», бо для одного викладача +може бути заплановано декілька підвищень. В таблиці «Заплановане +підвищення» є штучний ключ «Номер підвищення». +Сутності «Викладач» та «Результати підвищення» зв’зані зовніш- +нім ключем по полю «Табельний номер» та «Виданий (кому)» (тобто +таблиця «Викладач» є головною, а таблиця «Результати підвищен- +ня» — підпорядкованою) зв’язком «один до багатьох», бо один викла- +дач може мати багато документів (результатів) підвищень. В таблиці +«Результати підвищення» є штучний ключ «Код документа». +Сутності «Напрям та форми підвищення кваліфікації» та «Резуль- +тати підвищення» пов’зані зовнішнім ключем по полю «Код напря- + +436 +му» та «Напрям» (таблиця «Напрям та форми підвищення» — голо- +вна, а таблиця «Результати підвищення» — підпорядкована) зв’язком +«один до багатьох», бо один напрям буде багато раз обиратись викла- +дачами. +Сутності «Напрям та форми підвищення кваліфікації» та «Резуль- +тати підвищення» пов’зані зовнішнім ключем по полю «Код напряму» +та «Напрям» (таблиця «Напрям та форми підвищення» — головна, а +таблиця «Результати підвищення» — підпорядкована) зв’язком «один +до багатьох», бо один напрям буде багато раз обиратись викладачами. +Сутності «Викладач» та «Атестація» пов’зані зовнішнім ключем по +полю «Табельний номер» та «ПІБ» (таблиця «Викладач» — головна, а +таблиця «Атестація» — підпорядкована) зв’язком «один до багатьох», +бо один викладач буде неодноразово атестуватися (через кожні 5 ро- +ків). У таблиці «Атестація» доцільно додати поле-лічильник «№ п/п», +яке буде штучним ключем. +Логічне проектування. Логічне проектування виконується для пев- +ної моделі даних. Для реляційної моделі даних логічне проектування +полягає у створенні реляційної схеми, визначенні числа і структури +таблиць (табл. 1–6), формуванні запитів до бази даних (рис. 17), ви- +значенні типів звітних документів (рис. 18), розробці алгоритмів об- +робки інформації (рис. 20), створенні форм для вводу і редагування +даних в базі даних (рис. 19) і рішенні ряду інших задач. Концептуальні +моделі за певними правилами перетворюються в логічні моделі даних. +Коректність логічних моделей перевіряється за допомогою правил +нормалізації, які дозволяють переконатися в структурній узгодженос- +ті, логічній цілісності і мінімальній надлишковості прийнятої моделі +даних. Модель також перевіряється з метою виявлення можливостей +виконання транзакцій, які будуть задаватися користувачами. +Створений на попередніх етапах набір відношень логічної моделі +БД повинен бути перевірений на коректність об’єднання атрибутів +у кожному відношенні. Перевірка виконується шляхом застосування +до кожного відношення процедури послідовної нормалізації. Норма- +лізація гарантує, що отримана модель не буде мати протиріч і буде +мати мінімальну надлишковість. Атрибути в результаті нормалізації +будуть згруповані відповідно до існуючих між ними логічних зв’язків. +Для забезпечення коретності логічної моделі, у разі виявлення від- +ношень, які не відповідають вимогам нормалізації, необхідно повер- +нутися на попередні етапи проектування і перебудувати помилково +створені елементи моделі. + +437 +Таблиця 1 +Таблиця містить особисту інформацію про викладача і має наступні поля +Назва поля бази даних +Тип даних +Розмірність +Призначення +Табельний номер +Числовий +Довге ціле +Ключове поле таблиці +Фото +Поле об’єкта OLE +– +Фото викладача +ПІБ +Короткий текст +60 +Призвіще, ім’я, по баткові викладача +Посада +Короткий текст +20 +Для відображення посади викладача +Циклова комісія +Короткий текст +255 +Циклова комісія, на якій працює викладач +Номер телефону +Короткий текст +20 +Номер телефону +E-mail +Короткий текст +60 +Електронна адреса викладача +Кваліфікаційна категорія +Короткий текст +20 +Кваліфікаційна категорія, яку має викладач +Педагогічне звання +Короткий текст +20 +Педагогічне звання викладача +Науковий ступінь / вчене звання +Короткий текст +20 +Науковий ступінь / вчене звання викладача +Спеціальність за дипломом +Короткий текст +255 +Спеціальність викладача за дипломом +Примітка +Короткий текст +255 +Для додатковї інформації + +438 +Таблиця 2 +Атестація містить дані про атестацію викладача і має наступні поля +Назва поля бази даних +Тип даних +Розмірність +Призначення +№ п/п +Лічильник +Довге ціле +Ключове поле таблиці +ПІБ +Текст (числовий) 60 +ПІБ викладача (дані беруться з таблиці +«Викладач») +Кваліфікаційна категорія +Короткий текст +30 +Дані про кваліфікаційну категорію, яку +на даний момент має викладач +Рік попередньої атестації +Дата та час +Короткий формат дати Дата проходження попередньої атестації +Запланована атестація +Дата та час +Короткий формат дати Дата проходження запланованої атестації +Категорія +Короткий текст +60 +Обрана категорія +Статус категорії +Короткий текст +60 +Отримання, підтвердження або підви- +щення категорії +Педагогічне звання +Короткий текст +60 +Обране педагогічне звання +Статус педагогічного звання Короткий текст +60 +Отримання або підтвердження + +439 +Таблиця 3 +Заплановане підвищення містить інформацію про плани підвищення кваліфікації викладачів і має наступні поля +Назва поля бази даних +Тип даних +Розмірність +Призначення +Номер підвищення +Лічильник +Довге ціле +Ключове поле таблиці +Табельний номер +Числовий (дані беруться +з другої таблиці) +Довге ціле +Id викладача, з яким пов’заний +запис +ПІБ +Числовий (дані беруться +з другої таблиці) +Довге ціле +ПІБ викладача +Місце проходження +Числовий (дані беруться +з другої таблиці) +Довге ціле +Інформація про місце проходження +Форма підвищення +Короткий текст +20 +Форми підвищення +Вид підвищення +Короткий текст +255 +Види підвищення +Дата початку +Дата та час +Короткий формат +дати +Запланована дата початку підви- +щення +Дата закінчення +Дата та час +Короткий формат +дати +Запланована дата закінчення під- +вищення +Кількість годин/кредитів +ЄКТС +Короткий текст +15 +Запланованя кількість годин +Відмітка про виконання +Логічний +Так / ні +Пройдене підвищення чи ні + +440 +Таблиця 4 +Інформаційна база підвищення кваліфікації містить інформацію про бази +для підвищення кваліфікації і має наступні поля +Назва поля +бази даних +Тип даних +Розмірність +Призначення +Код курсу +Числовий +Довге ціле +Ключове поле таблиці +Емблема +Поле об’єкта OLE +- +Емблема бази +Назва +Короткий текст +255 +Назва бази підвищення +Адреса +Короткий текст +80 +Місце розташування бази +Телефон +Короткий текст +50 +Телефонні дані +E-mail +Короткий текст +150 +Електронна адреса +Сайт +Гіперпосилання +- +Посилання на сайт +Таблиця 5 +Напрями та форми підвищення мають наступні поля +Назва поля бази даних +Тип даних +Розмірність +Призначення +Код напряму +Числовий +Довге ціле +Ключове поле таблиці +Назва напряму підви- +щення кваліфікації +Короткий +текст +Довге ціле +Назва напряму +Обмеження цілісності запобігають появі в БД суперечливих даних. +Вирішення цієї проблеми на стадії проектування полягає у такому: +– наявність обов’язкових і необов’язкових значень даних для +атрибутів (NULL, NOT NULL); +– наявність обмежень для доменів атрибутів (визначення області +значень або діапазону значень); +– цілісність сутностей (обов’язкова наявність Primary Key в кож- +ному відношенні); +– цілісність посилання (зв’язування таблиць за допомогою Foreign +Key); +– обмеження предметної області (бізнес-правила), які реалізу- +ються як засобами БД, так і на рівні застосувань. +Після створення логічної моделі даних реляційна схема аналізуєть- +ся на коректність об’єднання атрибутів в одному відношенні. Пере- +вірка коректності виконується шляхом застосування послідовної нор- +малізації до кожного з відношень. Метою цієї перевірки є отримання +гарантій того, що схема бази даних знаходиться щонайменше в 3-й +нормальній формі або в нормальній формі Бойса — Кодда. Якщо ця +умова не виконується, то необхідно повернутися на попередні етапи + +441 +Таблиця 6 +Результати підвищення мають наступні поля +Назва поля бази даних +Тип даних +Розмірність +Призначення +Код документу +Короткий текст +Довге ціле +Ключове поле таблиці +Тип документу +Короткий текст +Довге ціле +Назва типу документу +Виданий (кому) +Числовий +Довге ціле +Назва бази підвищення +Виданий (ким) +Числовий +Довге ціле +ПІБ викладача +Напрям +Числовий +Довге ціле +Назва напряму підвищення +Тема підвищення +Короткий текст +255 +Тема підвищення +Дата видачі +Дата та час +Короткий формат дати +Дата видачі документу +Кількість годин +Числовий +10 +Отримана кількість годин за підви- +щення +Кількість кредитів +Числовий +10 +Отримана кількість кредитів за під- +вищення +Додаткове (не заплановане) +Короткий текст +255 +Інформація про додаткове підви- +щення + +442 + +Рис. 18. Запити до бази даних + +Рис. 19. Звітна документація + +BvKnaAayi neBHoi kaTeropii +Buknaaayi no LK +BMKnaAayi-MeToAMCTM +AoKTop HayK +3ara/bHa kinbkicTb roAMH no nigBMweHHIO +KaHAMAaTM HayK +MeHWe 150 roAMH +No AaTiniABMeHHA +Pe3yAbTaT niABMWeHH o IE +Pik aTeCTauil9 +BuKaqayi +9 +BuKknaAayi no LIK +BMKaAayi-MeTOAMCTW +AoKTop HayK +9 +3ara/IbHMi 3BiT no pe3ynbTaTaM niABWWeHH9 3a neBHV +9 +3BiT no KaTeropiqM +3BiT no kinbKocTi roAMH niABWWeHHA KBaiikaLii +3BiT pe3ynbTaTiB niABWWeHHA no I6 +9 +HpopMaiMHa 6a3a niaBMWeHHA KBani@iKaui +9 +IHpopMauig no aTeCTaLil(3a pOKoM) +IHOpMaLiA NO AaTi niABMWeHHA +KaHAMAaTM HayK +9 +KoHTaKTHi AaHi BMK/aAayiB KO/eA) +9 +MeHWe 150 roAMH niABWWeHH9443 + +Рис. 20. Форми для введення та редагування даних + +Рис. 21. Алгоритм роботи інформаційної системи + +围 +ATecTaLig +国 +Bkaaay +BknaKa aTecTaLig +BklaAka BwKlaAayi +BklaAka nigEMeHH9 KBanipikaLii +『onoBHa +围 +3an/aHoBaHe nigBMWeHHg +IHpopMaLiMHa 6a3a niaiwueHHA KBanipikaii +国 +NOAyMHeHHag opMa PesynbTaTW niABMeHHA +nlowyk MeHWe 15OroAMH no Aiana3oHy AaT +Nowyk niaBMueHH no AaTi +Nowyk no kaTeropii +PesyAbTaTW niAEWWeHHA +Pe3ynbTaTM NiaBMWeHHA OA4MHeHHa pOpMaoHaTOK +3aBaHTakeHH +OqikyBaHH in +KOpHcTyBaHa +Hi +Buoip +Tak +BKJIa/IKH +3aBaHTaKeHH +opaHoIBKJIa,IKH +BHoip +Hi +HOTpi6HOrO +JIYHKT +Tak +epersi, +BBeJIeHHTa +IpyKJaHHX +Hi +Pobora +3aBepllleHa +Tak +KiHellb444 +проектування і перебудувати помилково створені фрагменти мо- +делі. Перевірка логічної моделі бази даних показує, що реляційна +схема знаходиться в 4-й нормальній формі й корегування моделі не +потрібно. +Після перевірки логічної моделі за допомогою правил нормаліза- +ції система аналізується на предмет виконання транзакцій користу- +вачів, які задаються на початкових етапах проектування. У разі не- +можливості виконання певних транзакцій необхідне корегування +моделі бази даних. +Розробка застосувань. Застосування — програма або програмна +система, яка призначена для рішення деякої сукупності задач в даній +предметній області, або яка являє собою типовий інструментарій, що +застосовується в різних областях. +На цьому етапі вирішуються такі задачі: +– проектування транзакцій; +– проектування інтерфейсів користувачів. +Транзакція може складатися з декількох операцій по роботі з БД, +які переводять БД з одного цілісного стану в інший. Розрізняють +транзакції по отриманню певної інформації з БД і транзакції по зміні +даних в БД (оновлення, вилучення, додавання). Транзакції також мо- +жуть бути змішані. +Інтерфейс користувача — сукупність функціональних компонен- +тів, які забезпечують взаємодію користувача з системою. +Для зручного використання автоматизованої інформаційної сис- +теми обліку підвищення кваліфікації викладачів закладу освіти було +розроблено максимально зручний та інтуїтивно зрозумілий інтер- +фейс. +У вкладці «Викладачі» користувач може переглянути, додати або +ввести зміни в інформаційну картку викладача, переглянути, роздру- +кувати та зберегти звіти щодо наукового ступеня/вченого звання ви- +кладачів та різної звітної інформації. +На цій вкладці знаходяться три розділи: +– головна інформація; +– інформація щодо наукового ступеня та вченого звання викладачів; +– звітна інформація. +В розділі «Головна інформація» знаходиться інформаційна картка +викладача та контактні дані викладачів. Інформаційна картка при- +значена для створення, редагування зберігання, пошуку головної ін- +формації про викладача. + +445 + +Рис. 22. Вкладки інформаційної системи + +Рис. 23. Вкладка «Викладачі» + +Buxaadaut +Seinxa isfopaapie +Inpopmayiina cucmeMa obxixy nideugeunxxsauipxggifma amecmauifeuxaadauis +BCTOJTTCKOHAXI +tTidouuennaKeaibikauii +LAP +TOAOBNe MEHIO +Bauadevi +JideugruxxKpaificegii +Imtcmigieeataadevis +Bapd +AmecmayiaBukaadauis +NNNA +Kowmpas +Beinna isfopmagisBuKaadayi +Ingpopmayia odo Haykoboi cmyneni ma +Torobha ingpopmayia +Beimhainpopmauia +Bueho2o3BahhaBuknadaie +IHpopMaiiHa KapTKa BHaaya +BHKIaHayi-MeToJHHCTH +KoHTaKTHi aHi BHKIaayiB +KaHIHaTH HayK +BHkianayi no LIK +HoKTopaHayK +Horyk BHkaayin o Kateropii +3araJbH 3Bir o KBaipikaiHM +KaTeropiM +Ha3an446 +В розділі «Інформація щодо наукового ступеня та вченого звання +викладачів» знаходяться три кнопки: «Викладачі-методисти», «Кан- +дидати наук» та «Доктори наук», які призначені для вибору певної +інформації. +В розділі «Звітна інформація» знаходяться звіти стосовно викла- +дачів коледжу «Викладачі по ЦК», «Пошук викладачів по категорії», +«Інформація про викладачів коледжу» або «Загальний звіт за кваліфі- +каційними категоріями». +У вкладці «Підвищення кваліфікації», користувач може запланувати +підвищення, ввести результати підвищення, проконтролювати підви- +щення певних викладачів, а також переглянути, роздрукувати та збе- +регти звіти різної звітної інформації стосовно підвищення кваліфікації. +На цій вкладці знаходяться такі розділи: +– планування та результати; +– контроль; +– звітна інформація. +Розділ «Планування та результати» містить в собі три форми, які +призначені для введення інформації. +Перша кнопка відкриває форму «Запланувати підвищення» — для +планування підвищення кваліфікації викладачів. +Друга кнопка відкриває форму «Внести результати підвищення», +яка призначена для внесення та зберігання даних про результати під- +вищення кваліфікації викладача. +Третя кнопка відкриває форму «Додати нову базу підвищення» — +призначена для створення запису про можливі бази підвищення ква- +ліфікації, де зберігаються контактні дані. +Розділ «Контроль» містить три запити для пошуку інформації. +Натиснувши на кнопку «Пошук запланованого підвищення по +даті», відкриваємо нову форму для введення діапазону дат, після чого +формується звіт. +Друга кнопка відкриває форму «Менше 150 годин підвищення» — +ця форма служить для відбору інформації про викладачів, у яких за +останні 5 років менше 150 годин підвищення кваліфікації. +Натиснувши на третю кнопку «Результати підвищення по ПІБ», +відкриваємо вікно запиту, в яке потрібно ввести ПІБ викладача, ін- +формація про якого нас цікавить, та натискаємо кнопку «ОК» для +отримання результату. +Розділ «Підвищення кваліфікації» — це «Звітна інформація». +В цьому розділі знаходяться три звіти. + +447 + +Рис. 24. Вкладка «Підвищення кваліфікації» + +Рис. 25. Вкладка «Атестація викладачів» + +ideuueHHa K6anigbiKauii +ranyeanha ma pe3yabmamu +Konmpoab +Beimhaingopmauia +3aaHyBainBMmeHH +3araJibHa KibkicTb roHH IIO +oIyk mineHeH Ho JaTi +inBHeHHro KBaibikari +MeHe 150 ro inEHeH +3arabHwit3Bitope3yIbTataM +BHecTH pesyJIbTaTH minEHIeHH +BMeHHaeBHMMPK +PesybTaTH iEHeH o IIE +iaH inBHeHH Keaiikani +Ha3aAmecmauia 6ukadaui +Lranyeanna +Konmpoab +Beimha inpopmayia +Arecrarima KapTka +IHpopMain 3a pokoM aTecTai +aTecTyrOHOro +Ha3an448 +В першому звіті «Загальна кількість годин з підвищення кваліфі- +кації» ми бачимо ПІБ викладача, дату підвищення, кількість отрима- +них годин, кредитів та їх суму. +Другий звіт «Загальний звіт за результатами підвищення за певний +рік» побудований за допомогою запиту на вибірку. +Третя кнопка «План підвищення кваліфікації» відкриває сформо- +ваний план підвищення кваліфікації, дані для якого беруться з форми +«Заплановане підвищення» та відбираються за вказаним роком — ор- +ганізовано за допомогою запиту на вибірку. +У вкладці «Атестація викладачів» користувач може створити або +змінити атестаційну картку викладача, контролювати інформацію +про атестацію за роком, переглянути, роздрукувати та зберегти звіти +різної звітної інформації стосовно підвищення кваліфікації. +На цій вкладці знаходить три розділи: +– планування; +– контроль; +– звітна інформація. +У розділі «Планування» знаходиться одна кнопка «Атестаційна +картка», призначена для планування атестації викладача. +У розділі «Контроль» знаходиться кнопка «Інформація за роком +атестації», натиснувши на неї, бачимо вікнонце запиту для введення +року атестації. +У розділі «Звітна інформація» знаходиться одна кнопка «Перелік +видів підвищення атестованого», яка відкриває сформований доку- +мент про перелік окремих видів підвищення. +Висновки та перспективи запровадження автоматизованої інфор- +маційної системи обліку підвищення кваліфікації викладачів закладу +освіти. +Наразі автоматизована інформаційна система обліку підвищення +кваліфікації викладачів пройшла тестування та апробацію в навчаль- +но-методичному кабінеті ВСП «ОТФК ОНАХТ» щодо відповідності +реалізованих функцій системи поставленим задачам, а саме: забез- +печенню ефективності процесу підвищення кваліфікації та атестації +педагогічних та науково-педагогічних працівників закладу освіти за +допомогою інформаційної підтримки задач прогнозування і плану- +вання організації цього процесу; зручному автоматизованому кон- +тролю за процесом підвищення кваліфікації педагогічних та науково- +педагогічних працівників закладу освіти; контролю за виконанням +нормативів по кількості годин підвищення кваліфікації педагогічних + +449 +та науково-педагогічних працівників закладу освіти за розрахунковий +період; представленню розрахункових показників (кількість годин +підвищення по кожному викладачу, менше 150 годин підвищення, +тощо); формуванню звітів про результати підвищення кваліфікації та +атестації педагогічних та науково-педагогічних працівників закладу +освіти; аналітиці результатів за напрямами щодо підвищення квалі- +фікації та атестації педагогічних та науково-педагогічних працівників +закладу освіти. Зручний інтерфейс автоматизованої інформаційної +системи обліку підвищення кваліфікації викладачів закладу освіти +забезпечує швидкий пошук необхідної інформації, дозволяє одразу +включитися в підготовку професійних документів, підвищує ефек- +тивність, якість роботи і скорочує терміни її виконання. +На основі запропонованої моделі автоматизованої інформаційної +системи обліку підвищення кваліфікації викладачів можливе здій- +снення моніторингу процесу підвищення кваліфікації за допомогою +реалізації таких запитів і звітів, як: +– визначення загальної кількості слухачів, які здійснили підви- +щення кваліфікації у закладі та за визначений навчальний рік зокрема; +– розподіл слухачів за джерелами оплати освітньої послуги з під- +вищення кваліфікації; +– визначення кількості та типу освітніх закладів, працівники яких +підвищують кваліфікацію; +– розподіл слухачів за спеціалізаціями, рівнем освіти, стажем ро- +боти, кваліфікаційною категорією в цілому та за певний навчальний +рік зокрема; +– визначення обсягу годин підвищення кваліфікації певного слу- +хача за відповідний проміжок часу: навчальний рік, декілька років, +п’ятирічний термін тощо; +– порівняння результатів навчальної діяльності слухача у розрізі +кваліфікаційної категорії: спеціаліст, друга, перша, вища категорії; +– порівняння результатів навчальної діяльності залежно від фор- +ми навчання: очна, заочна, очно-дистанційна; +– порівняння результатів навчальної діяльності у розрізі навчаль- +них програм підвищення кваліфікації; +– визначення можливого комбінування різних навчальних про- +грам для забезпечення ефективного здійснення підвищення кваліфі- +кації викладачем з гармонійним розвитком його професійних компе- +тентностей і дотримання вимог постанови № 800 Кабінету Міністрів +України [17]; + +450 +– визначення актуальної форми навчання (очної, очно-дистан- +ційної, заочної), календарних періодів внаслідок здійснення аналі- +зу розподілу слухачів відповідно до зазначених критеріїв за декілька +років; +– відслідковування спеціалізації, спектра вчених ступенів та вче- +них звань, посад викладацького складу закладу, що опосередковано +визначатиме якість результатів підвищення кваліфікації; +– моніторинг планування для викладача та виконання ним запла- +нованого підвищення кваліфікації; +– відслідковування змін у тематиці та напрямів підвищення квалі- +фікації певного викладача за необхідний проміжок часу; +– виключення можливості запису викладача на один і той же на- +прям підвищення кваліфікації за певний атестаційний період; +– ефективне планування процесу підвищення кваліфікації педа- +гогів у майбутньому. +В цілому зазначена модель автоматизованої інформаційної систе- +ми обліку підвищення кваліфікації викладачів має забезпечити: +– покращення якості цього процесу завдяки автоматизації плану- +вання курсів підвищення кваліфікації педагогів відповідно до існую- +чих потреб та аналізу результатів навчальної діяльності слухачів; +– зменшення часових затрат працівників закладу освіти на підго- +товку документів внутрішньої звітності (навчальної програми, жур- +налу обліку курсів підвищення кваліфікації; календарних графіків +тощо) за рахунок одноразового введення відповідних даних та їх бага- +торазового використання; +– зменшення часових затрат адміністрації закладу на моніторинг +документації внутрішньої звітності; +– підвищення якості планування спільної діяльності закладу із за- +кладами ППО, районними методичними кабінетами та відповідни- +ми представниками об’єднаних територіальних громад регіону щодо +професійного розвитку педагогів у період завдяки проведенню різно- +стороннього аналізу результатів навчальної діяльності науково-педа- +гогічних та педагогічних працівників за допомогою методів матема- +тичної статистики тощо. +У перспективі інформаційна система буде зберігатися на віддале- +ному сервері для підвищення захищеності бази та можливості дистан- +ційної роботи. Автоматизована інформаційна система обліку підви- +щення кваліфікації викладачів може бути рекомендована для роботи +структурних підрозділів навчально-методичного напряму у закладах + +451 +вищої та фахової передвищої освіти для моніторингу та обліку підви- +щення кваліфікації та атестації педагогічних та науково-педагогічних +працівників. +СПИСОК ВИКОРИСТАНОЇ ЛІТЕРАТУРИ +1. Розвиток інформаційних систем управління освітою як інструмент реа- +лізації державної освітньої політики : монографія / за ред. С. Л. Лондара ; +ДНУ «Інститут освітньої аналітики». — Київ, 2020. — 258 с. +2. Гуменюк В. В. Інформаційне забезпечення управління загальноосвітнім +навчальним закладом : дис. ... канд. пед. наук: 13.00.01 / Центральний +ін-т післядипломної педагогічної освіти АПН України. — К., 2001. — +220 с. +3. Про Концепцію національної програми інформатизації: Закон України за +станом на 9 лютого 2006 р. // Відомості Верховної Ради. — Офіц. вид. — +К., 2006. — № 22. +4. Забродська Л. М. 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Автоматизована система підвищення кваліфікації педагогічних праців- +ників закладів загальної середньої освіти [Електронний ресурс]. — Режим +доступу: +http://activemedia.ua/news/pochala-pratsiuvaty-avtomatyzovana- +systema-pidvyshchennia-kvalifikatsii-pedahohichnykh-pratsivnykiv-zakladiv- +zahalnoi-serednoi-osvity/. — Назва з екрану. +17. Деякі питання підвищення кваліфікації педагогічних та науково-педаго- +гічних працівників: постанова Кабінету Міністрів України від 21 серпня +2019 р. № 800 [Електронний ресурс]. — Режим доступу: https://zakon.rada. +gov.ua/laws/show/800–2019- %D0 %BF#Text +18. Типове положення про атестацію педагогічних працівників: наказ Мі- +ністерства освіти і науки України від 06.10.2010 № 930 [Електронний +ресурс]. — Режим доступу: https://zakon.rada.gov.ua/laws/show/z1255– +10#Text +19. Львов М. С., Співаковський О. В., Щедролосьєв Д. Є. Інформаційна +система управління вищим навчальним закладом як платформа реаліза- +ції управління академічним процесом // Комп’ютер у школі та сім’ї. — +2007. — № 2. — С. 3–6. +20. Грабовський П. П. Проектування інформаційної системи моніторингу +процесу підвищення кваліфікації педагогів // Інформаційні технології та +засоби навчання. — 2019. — Т. 73, № 5. — С. 206–218. +21. Грабовський, П. П. Інфологічна модель бази даних інформаційної сис- +теми моніторингу процесу підвищення кваліфікації педагогів // Технічна +інженерія. — 2020. — 1 (85). — С. 115–120. +22. Страхарчук В. П. Інформаційні системи і технології в банках : навч. +посіб. [Електронний ресурс]. — Режим доступу: https://pidruchniki. +com/1584072022211/bankivska_sprava/informatsiyni_sistemi_i_ +tehnologiyi_v_bankah. +23. Національна доповідь про стан і перспективи розвитку освіти в Україні / +НАПН України. —К. : Педагогічна думка, 2016. — 448 с. +24. Биков В. Ю. Сучасні завдання інформатизації освіти [Електронний ре- +сурс] // Інформаційні технології і засоби навчання. — 2010. — № 1 (15). — +Режим доступу: http://journal.iitta.gov.ua/index.php/itlt. +25. Кулицький С. П. Основи організації інформаційної діяльності у сфері +управління : навч. посіб. — К. : МАУП, 2002. — 224 с. +26. Пономаренко В. С., ЖуравльоваІ. В., Латишева І. Л. Інформаційні сис- +теми в управлінні персоналом / В. С. Пономаренко. — Харків : ХНЕУ, +2008. — 337 с. + +453 +27. Олійник В. В. Тендеції розвитку післядипломної освіти в умовах транс- +формації суспільства // Теорія і практика управління соціальними систе- +мами. — 2013. — № 1. — С. 56–66. +28. Авраменко В. С., Авраменко А. С. Проектування інформаційних систем : +навчальний посібник. — Черкаси : Черкаський національний університет +ім. Б. Хмельницького, 2017. — 434 с. +29. Перелік Національних стандартів України для створення, впровадження +та супроводження автоматизованих і інформаційних систем [Електро- +нний ресурс] / Національна бібліотека України імені І. В. Вернадсько- +го. — Режим доступу : http://nbuv.gov.ua/node/1469. +СИСТЕМНИЙ ПІДХІД ПРИ ОРГАНІЗАЦІЇ +НАВЧАЛЬНОГО ПРОЦЕСУ У ЗАКЛАДАХ +ВИЩОЇ ОСВІТИ З ЗАСТОСУВАННЯМ НОВИХ +ІНФОРМАЦІЙНИХ ТЕХНОЛОГІЙ +Воінова С. О. +Розглянуто виклики часу, що постали перед вищою освітою України, +та можливі шляхи вирішення поставлених ними завдань. Визначено акту- +альність використання нових методів навчання, що базуються на сучасних +інформаційних технологіях. Розглянуто філософсько-методологічні аспекти +використання інформаційних технологій в освітньому процесі. +Розкрито сутність системного підходу до навчального процесу у закладах +вищої освіти із застосуванням сучасних інформаційних технологій. Розгляну- +то етапи розвитку інформаційних технологій. Проаналізовано риси сучас- +ного етапу розвитку системи вищої освіти. Виділено зовнішні та внутрішні +фактори використання дистанційного навчання у системі освіти. +Розглянуто дистанційні освітні технології та електронне навчання як +основу дистанційного навчання. Виділено поняття та структуру дистан- +ційного курсу як важливого елемента системи дистанційного навчання. Від- +значено переваги та недоліки дистанційного очного та заочного навчання +перед традиційним. Особливу увагу приділено модульній технології навчання. +Розглянуто цілі, напрями, принципи інформатизації вищої освіти як пріори- +тетного напряму реформування вищої школи. +Висвітлено ресурс системного підходу до організації навчального процесу, +інтегрованого застосуванням нових інформаційних технологій у закладах ви- +щої освіти, що дозволяє усвідомлювати взаємозв’язок компонентів освітньої +системи та ефективно реалізовувати основні її функції. + +454 +The challenges of the time, faced by the higher education of Ukraine, and possi- +ble ways of solving the tasks set by them are considered. The relevance of using new +teaching methods based on modern information technologies is noted. Philosophical +and methodological aspects of the information technologies using in the educational +process are considered. +The essence of the systematic approach as applied to the educational process in +institutions of higher education using modern information technologies is disclosed. +The stages of information technologies development are considered. The features +of the present-day stage of development of the education system are analyzed. Ex- +ternal and internal factors of using distance learning in the education system are +highlighted. +The distance learning educational technologies and e-learning as the basis of +distance learning are considered. The concept and structure of a distance course +as an important element of a distance learning system are highlighted. The advan- +tages and disadvantages of the distance face-to-face teaching and the part-time +education over the traditional learning are noted. Particular attention is paid to +modular learning technology. The goals, directions, principles of informatization +of higher education as a priority direction of reforming higher education are con- +sidered. +The resource of a systematic approach to the organization of the educational +process, integrated by the use of new information technologies, in institutions of +higher education is highlighted. This resource as emphasized allows to understand +the relationship between the components of the educational system and effectively +implement its main functions. +Вища освіта в Україні має масовий характер. Згідно з аналітичною +інформацією Міністерства освіти і науки України, рівень охоплення +вищою освітою населення традиційного офіційного віку навчання є +високим — 82,7 %. За цим показником Україна у Глобальному інно- +ваційному індексі 2020 р. посіла 14-те місце зі 131 країни. Меншим є +охоплення у Німеччині (70,2 %, 28-ме місце), Польщі (67,8 %, 34-те) +та Великій Британії (60 %, 46-те місце) [1]. +В Україні високий рівень якісного складу викладачів закладів ви- +щої освіти. На початку 2019/1920 навчавльного року у загальній кіль- +кості викладачів університетів, інститутів, академій 47,3 % складали +доктори філософії / кандидати наук, 11,7 % — доктори наук, 31,1 % — +доценти, 9,3 % — професори. +В Україні мережа університетів — одна з найбільш щільних: на +1 млн населення припадає 6,7 університету. За останні п’ять років +кількість університетів, інститутів, академій зросла на 1,4 %. +Розвиток інфраструктури вищої освіти в Україні демонструє клю- +чову тенденцію: зростання чисельності університетів, академій й + +455 +інститутів, навчання в яких орієнтовано на більш ґрунтовну підго- +товку. Така тенденція стала наслідком, перш за все, змін у структурі +економіки країни, переходу до масової вищої освіти. Розвиненість і +регіональна розгалуженість мережі закладів вищої освіти України на- +дає можливість охоплення значної частини населення країни вищою +освітою з подальшим просуванням ціложиттєвої освіти та переквалі- +фікації. +Освіта наразі дещо відстає від загальної діджиталізації, і необхідно +докласти більше зусиль, щоб скористатися інструментами та сильни- +ми сторонами нових інформаційних технологій, одночасно вирішую- +чи проблеми щодо можливих зловживань, таких як кібервторгнення +та проблеми конфіденційності. +Завдання розвитку законодавства у сфері освіти окреслюються +Національною доктриною розвитку освіти, яка визначає систему +концептуальних ідей та поглядів на стратегію і основні напрямки роз- +витку освіти до 2025 р. [2; 3]. +У рамках підготовки звіту «Горизонт 2020» асоціацією EDUCAUSE +залучені експерти з різних країн світу окреслили ландшафт і визна- +чили найбільш впливові тенденції, що формують вищу освіту, викла- +дання та навчання [4]. Ключові тренди були ідентифіковані у рамках +п’яти категорій: соціальні, технологічні, економічні, вищої освіти та +політичні. Зокрема категорія «Технологічні» включає розвиток штуч- +ного інтелекту, формування цифрового навчального середовища на- +ступного покоління, проблеми аналітики даних та питання конфі- +денційності. Категорія «Вища освіта» включає альтернативні шляхи +до освіти, онлайн-освіту. +Згідно зі Стратегією розвитку вищої освіти в Україні на 2021–2031 +роки, в основу концептуальної моделі вищої освіти України має бути +покладений кібернетичний принцип необхідного розмаїття [1]. +Заклади вищої освіти мають створити власні або використовувати +вже існуючі онлайн-платформи для поширення знань у професійній +громаді, для професійної орієнтації тощо. +Актуальним є питання впровадження віртуальних університетів, +які можуть здійснювати підготовку за багатьма або окремими спе- +ціальностями, існувати як окрема онлайн-платформа або бути вір- +туальним дублером традиційного закладу вищої освіти. Віртуальні +університети орієнтовані на розширення доступу до вищої освіти +для різних категорій населення, включення до освітнього процесу +нетрадиційного контингенту (дорослі здобувачі вищої освіти, люди + +456 +протягом усього життя), підвищення кваліфікації, опанування додат- +кових навичок, актуалізацію знань та навичок, поширення кращих +навчальних практик. Освітні програми мають відрізнятися макси- +мальною гнучкістю, передбачати мікро- і нанокредитивні навчальні +дисципліни. Віртуальні університети стануть головним провайдером +екстернатної, неформальної та інформальної освіти. Форма навчан- +ня тут передбачається дистанційна [5]. +Як найважливішу операційну мету запропоновано впроваджен- +ня інноваційних інформаційних технологій і дистанційного навчан- +ня у вищій освіті. Як конкретні завдання для реалізації цієї мети +запропоновано створення індустрії інноваційних інформаційних +технологій та засобів навчання, що відповідають світовому науко- +во-технічному рівню; діджиталізація усіх процесів у системі вищої +освіти; унормування дистанційного навчання як форми здобуття +вищої освіти [1]. +Реформування освітньої галузі — це відповідь на суспільний запит, +адже саме освіта забезпечує якість людського капіталу, який є осно- +вою економічного розвитку країни. Упродовж 2020/2021 н. р. Мініс- +терством освіти і науки України було продовжено стратегічний курс +на реформування усіх сфер освіти. Водночас у 2019/2020 н. р. з огляду +на пандемію Covid-19 та запроваджені карантинні обмеження перед +системою освіти постали нові виклики, пов’язані з забезпеченням +неперервності освітнього процесу, спроможністю закладів усіх рівнів +освіти забезпечити якість і сталість здобуття освіти в умовах каран- +тинних обмежень, необхідністю розвитку дистанційної форми здо- +буття освіти. +Усе це спонукає посилювати складові реформи освітньої галу- +зі, пов’язані з діджиталізацією освітнього середовища, передусім +із забезпеченням закладів вищої освіти швидкісним доступом до +мережі Інтернет, а здобувачів вищої освіти і педагогічних праців- +ників — цифровими пристроями та електронними освітніми ре- +сурсами [6]. +Пандемія змусила все глобальне академічне співтовариство +звернутися до нових методів навчання, включаючи дистанційне та +онлайн-навчання. Аналіз вузівських практик показує, що в період +віддаленої роботи склалося кілька режимів організації освітньої ді- +яльності: асинхронний або заочний (здобувачі вищої освіти вивчають +матеріал у зручний для них час, відповідно до встановлених виклада- +чем термінів); синхронний (одночасна участь у занятті, наприклад, + +457 +у форматі вебінара); змішаний (поєднання синхронної та асинхрон- +ної взаємодії залежно від характеру педагогічних завдань). +Досвід останніх двох років показав широкі можливості викорис- +тання форматів та технологій дистанційної роботи для вирішення як +традиційних, так і нових завдань університетів. +Незалежно від цього в останні десятиріччя виникла нова проблема +розвитку системи освіти. Знання старіють кожні 3–5 років, а техно- +логічні знання — кожні 2–3 роки. Мине ще трохи часу і це буде 1,5–2 +роки, а необхідний обсяг знань для випускників освітніх закладів по- +двоюється кожні 3–4 роки. Якщо не змінювати освітніх технологій, +то якість підготовки фахівців об’єктивно відставатиме від вимог на +ринку праці. Засвоєння знань здобувачами вищої освіти за допомо- +гою інформаційних та комунікаційних технологій за найнижчими +оцінками є на 40–60 % швидшою або більшою в одиницю часу, ніж за +звичайними технологіями (за один і той же період надається більше +знань). +Одним із видів інновацій в організації вищої професійної освіти є +запровадження дистанційного навчання. +У закладах вищої освіти сьогодні навчається нове, єдине поки що +покоління, яке з перших днів життя стикається з інформаційними тех- +нологіями та мікропроцесорною технікою, зокрема комп’ютерами. +Цифрові пристрої для них є такми ж звичними, як телевізор або хо- +лодильник для старшого покоління. Для колективів закладів вищої +освіти немає більш нагального завдання, ніж пізнання культури, +психології, цінностей та змін, які очікує на це нове покоління. Ме- +режеве покоління обов’язково змінить сам спосіб виробництва, ство- +рить нову культуру праці. Представники нового покоління бажають +активно використовувати у навчанні мобільні пристрої (смартфони, +планшети, ноутбуки) та сервіси Інтернету, отже заклад вищої освіти +має бути технологічно готовий надати такі можливості новому поко- +лінню здобувачів вищої освіти [7]. +Можливість та необхідність використання інформаційних тех- +нологій у закладах вищої освіти не викликає сумніву. Застосування +мультимедійних програм, можливість візуалізації розрахунків, що +проводяться, дозволяють зробити навчання більш наочним, значною +мірою допомагають подолати традиційно надто формалізоване та +абстрактне викладання багатьох університетських навчальних кур- +сів. При цьому для багатьох дисциплін використання комп’ютерних +засобів необхідно пов’язувати з комп’ютерним моделюванням. За + +458 +багатьма розділами фундаментальних наук в Інтернеті накопичено +величезну кількість корисної інформації, яку необхідно шукати і сис- +тематизувати із застосуванням пошукових систем і використовувати +у процесі викладання. +Ефективне використання цих технологій потребує особливих +компетенцій викладачів, управлінців, здобувачів вищої освіти, а та- +кож ефективних та зручних технологічних рішень, особливої органі- +зації навчального процесу. Без цього не можна говорити про повно- +цінну освіту у дистанційному форматі. Саме заклади вищої освіти +покликані та мають найближчим часом стати колискою формування +нової інтернет-орієнтованої свідомості молодих людей. Саме заклади +вищої освіти мають забезпечити цей процес матеріально. Викладач у +своїй діяльності має орієнтуватися як на традиційні, так і на нетра- +диційні методи навчання. Головне — сформувати у здобувача вищої +освіти інтернет-орієнтований спосіб мислення, навчити викорис- +товувати інформацію для самоосвіти, підвищення кваліфікаційного +рівня, вирішення можливих виробничих проблем та завдань. +Практика використання інформаційних технологій в освітньому +процесі вищої школи свідчить про наявність протиріч між такими об- +ставинами: +– традиційними видами навчально-методичного забезпечення та +потребою практики в інноваційних формах застосування інформа- +ційних технологій у навчальному процесі закладів вищої освіти; +– процесом інформатизації освіти та відсутністю загального під- +ходу до використання інформаційних технологій при навчанні здо- +бувачів вищої освіти в сучасних освітніх установах; +– між пошуком та виявленням інформації, необхідної для органі- +зації навчального процесу та діджиталізованою інформацією, яка до- +зволяє застосовувати більш активні сучасні способи пошуку, сприй- +няття, обробки, використання та зберігання інформації; +– абсолютизацією структур та форм побудови навчально-мето- +дичних матеріалів для здобувачів вищої освіти та потребою практики +в їх інноваційних структурах з розширеними функціональними та ін- +формаційними можливостями. +Зазначені протиріччя сприяли пошуку шляхів застосування ін- +формаційних технологій у навчанні здобувачів вищої освіти на основі +системного підходу. +У сфері освіти інформаційні технології забезпечують збирання, +обробку, надання та публікацію даних, що належать до навчання, і + +459 +допомагають викладачам краще забезпечити навчальний процес не- +обхідними матеріалами, виявити прогалини, адаптувати зміст та пе- +дагогічні підходи до конкретної групи. +Цінність інформаційних технологій для розвитку навчальної ді- +яльності закладу вищої освіти полягає в такому: +– покращення якості навчання за допомогою більш повного ви- +користання доступної інформації, підвищення мотивації здобувачів +вищої освіти та творчої активності викладачів; +– впровадження нових освітніх технологій — розвиваюче та про- +ектне навчання, ділові ігри, візуалізація, імітаційне моделювання, +дистанційне навчання; +– інтеграція різних видів діяльності (навчальної, навчально-до- +слідницької, наукової); +– зменшення залежності здобувача вищої освіти від викладача; +– покращення оцінки навчальних досягнень на основі комп’ю- +терного тестування. +Інформаційні технології змінюють роль викладача, який з єдиного +носія знань перетворюється на навчального менеджера та наставни- +ка, спрямовуючи та контролюючи зусилля здобувачів вищої освіти +з освоєння певної програми — через індивідуальні завдання, визна- +чення відповідних навчальних ресурсів, створення спільних можли- +востей для навчання, а також надання свого розуміння матеріалу та +консультаційної підтримки як під час очного процесу, так і в навчаль- +них середовищах та віртуальній взаємодії. Викладач залишається, без- +умовно, ключовим, але все ж таки одним із учасників освітнього про- +цесу, з пультом біля проектора або за комп’ютером в інформаційному +сере довищі. Успіх нового підходу залежить від людського фактора та +готовності викладача увійти в віртуальні аудиторії та середовища. Ви- +кладач стане більшою мірою наставником, спрямовуватиме і навчати- +ме думати, досліджувати, вирішувати проблеми, а заклад вищої осві- +ти — готувати здобувача вищої освіти до реальної професійної кар’єри. +Для забезпечення належного реагування на виникаючі проблеми +заклади вищої освіти повинні зосередитися на якості, актуальності та +оперативності. +Освітня діяльність та підготовка здобувача вищої освіти є комп- +лексним поняттям, отже їхня ефективна реалізація повинна спирати- +ся на системний похід [8]. +Зміст поняття «якість освіти» у системі професійної підготов- +ки змінюється разом зі змістом цієї підготовки. Ці зміни викликані + +460 +такими причинами: по-перше, науково-технічними та інформацій- +ними змінами виробничих технологій; по-друге, падінням попиту +на некваліфіковану працю; по-третє, поширенням автоматизованих +систем управління виробничими процесами, тобто зміною у змісті +професій, що вимагає змін у змісті професійної підготовки, підви- +щення її якості, створення механізмів, що забезпечують її постійне +настроювання на вимоги ринку праці, що динамічно змінюються, +використання системного підходу при організації професійної під- +готовки. +У науковій літературі системний підхід — це методологічний на- +прям, який ставить завданням розробку принципів, методів і засобів +вивчення об’єктів, що являють собою системи. +Системний підхід, будучи елементом діалектичного методу в ціло- +му, є не тільки конкретизацією діалектико-матеріалістичного вчення +про загальний зв’язок явищ, але і однією зі сторін діалектико-матері- +алістичного вчення про розвиток. Принцип системності вимагає роз- +глядати всі явища у взаємозв’язку, у взаємодії. Таким чином, в осно- +ві системних досліджень лежить положення про діалектичну єдність +принципу системності та розвитку. +При системному підході виявляють та вивчають зв’язки та від- +носини між елементами (підсистемами) будь-якого об’єкта управ- +ління. Важливим моментом стає підпорядкування окремих, локаль- +них завдань окремих підсистем загальній кінцевій меті. При цьому +обов’язковою умовою є чітке формулювання єдиних цілей, завдань, а +потім визначення шляхів найефективнішого розв’язання як для сис- +теми в цілому, так і для окремих її елементів. +Система — це сукупність компонентів, що знаходяться у певних +відносинах і пов’язані один з одним, взаємодія яких породжує нову +якість, не властиву цим компонентам окремо. У системі існують еле- +менти (будь-які об’єкти) і певна структура як відносно стійкий спосіб +зв’язку елементів того чи іншого складного цілого. +Педагогічна система — це певна сукупність взаємопов’язаних за- +собів, методів та процесів, необхідних для створення організованого, +цілеспрямованого та спеціалізованого педагогічного впливу на фор- +мування особистості із заданими якостями [9]. +З позицій системного підходу у наведеному визначенні виділя- +ються такі внутрішні аспекти педагогічної системи: системно-ком- +понентний, системно-структурний, системно-функціональний та +системно-інтегративний. + +461 +Наявність структури — умова накопичення кількісних змін усе- +редині системи, що є необхідною передумовою для її подальшого +розвитку та перетворення. +Будь-яка система соціального порядку є активною і діяльною, що +проявляється у її функціях. У свою чергу, функції системи є інтегро- +ваним результатом певних дій компонентів, що її утворюють. По від- +ношенню до системи вони мають доцільний характер, інакше ком- +понент випадає із системи та стає стороннім тілом для неї. Зміни у +природі компонентів, у характері їхньої взаємодії викликають відпо- +відні зміни у функціях як самих компонентів, так і системи в цілому. +Отже, системний підхід — це не просто виділення системного об’єкта +суб’єктом пізнання, але й процедура його системного освоєння. Най- +більш продуктивним шляхом до цього є конструювання педагогічної +структури відповідно до потреб та цілей вищої освіти. +Основним завданням підходу, що розглядається, у вищій освіті +є побудова оптимальної моделі, яка поєднує освоєння теоретичних +знань і застосування їх у вирішенні практичних питань, що сприяє +формуванню професійних компетенцій у майбутнього спеціаліста. +Розглядаючи проблему професійної підготовки здобувачів вищої +освіти, її необхідно представляти як систему, до якої входять підсис- +теми, які підпорядковуються тим самим принципам, що і система: +цілісності, структуризації, множинності. Однією з підсистем про- +фесійної підготовки, яка є також системою, що має всі її власти- +вості, є навчальний процес. Він має певну цілісність, що дозволяє +розглядати одночасно систему як єдине ціле й як підсистему для ви- +щих рівнів. Структуризація дозволяє аналізувати елементи системи +та їхні взаємозв’язки у межах конкретної організаційної структури. +Множинність дозволяє використовувати безліч форм, засобів, мето- +дів для реалізації окремих елементів та системи в цілому. При цьому +навчальний процес має синергію (від грецької — «разом діючий»), це +пояснює більший сумарний ефект функціонування всіх складових +елементів системи порівняно із сумою дії кожного з елементів. +Застосування у педагогічній практиці навчання системного під- +ходу передбачає наявність взаємозв’язків між компонентами на- +вчального процесу, кожен з яких може функціонувати з максималь- +ною ефективністю, спираючись на внутрішні зв’язки в цій системі. +Зміст матеріалу, що вивчається, є одним із структурних компонентів +навчального процесу, засвоєння якого пов’язане з обраними метода- +ми, формами та засобами навчання. При цьому керує системою ви- + +462 +кладач, будучи по суті її компонентом. Від того, які технології будуть +використані викладачем, залежить ступінь ефективності функціону- +вання даної системи. +Сьогодні широко використовуються інформаційні текхнології, +які вбудовуються в усі компоненти навчального процесу, розробля- +ються та впроваджуються нові. +Системний підхід вимагає розгляду філософсько-методологічних +аспектів використання інформаційних технологій в освітньому про- +цесі. Такий аналіз спрямовано на обґрунтування загальних світогляд- +них установок у дослідженні різноманітних можливостей застосуван- +ня інформаційних технологій у сфері освіти [10]. +Інформаційні технології, втілені в обчислювальній техніці, в наші +дні глибоко проникають у структури людської діяльності, перетворю- +ють зміст і характер праці та навчання, по-новому ставлять проблеми +розвитку людського інтелекту та особистості, справляють серйозний +вплив на світогляд людей та ідеологічні концепції, породжують нові +способи та форми організації наукових досліджень. Ось чому соці- +ально-філософські та філософсько-методологічні аспекти розвитку +обчислювальної техніки, як результату розвитку інформаційних тех- +нологій, заслуговують на пильну увагу [11]. +Ця вимога відноситься до різних галузей наукових знань, у тому +числі і педагогічної науки, що відображає сутнісні характеристики +предметної області свого дослідження — педагогічної діяльності. +Інтеграція педагогіки з іншими суспільними, природничими, тех- +нічними науками — це провідна тенденція вдосконалення системи +науково-педагогічних знань. Зазначена тенденція проглядається і при +вивченні проблеми взаємодії людини з комп’ютером у сфері освіти, +яка за всієї своєї самостійності та важливості є, по суті, лише части- +ною більш загальної соціально-філософської проблеми «людина — +машина» — центральної проблеми сучасної науково-технічної ре- +волюції. При цьому категорія «машина» носить збірний характер, +позначаючи будь-які технічні пристрої, що використовуються як за- +сіб підвищення ефективності, доцільності людської діяльності. +В умовах прискорення соціально-економічного та науково-тех- +нічного прогресу, посилення уваги до комплексу питань, пов’язаних +із трактуванням ролі та місця людського фактора в інтенсифікації +суспільного виробництва, все більш актуальною є проблема прямого +та безпосереднього взаємозв’язку педагогічних та власне технічних +факторів. Цей взаємозв’язок знаходить своє відображення у процесі + +463 +взаємодії людини з мікропроцесорною, комп’ютерною технікою — +найвищим проявом технізації суспільно корисної людської діяльнос- +ті. Посилення взаємодії суспільних, природничих та технічних наук +підкреслює значущість системи філософських знань, які становлять +ядро інтегративних, міждисциплінарних форм пізнання і мають ви- +рішальне значення у розумінні процесу зближення наук про природу +та суспільство на розвиток техніки. +Безпосереднім методологічним орієнтиром взаємодії наук про лю- +дину і техніку служить філософський принцип загального зв’язку та +взаємозалежності предметів та явищ об’єктивної дійсності, на якому +базується системний підхід. З діалектико-матеріалістичної точки зору, +здатність речей, об’єктів, явищ, процесів, часто якісно глибоко різ- +них, до різноманітних взаємодій є проявом принципу матеріальної єд- +ності світу, що стверджує наявність законів, які поширюються на різ- +ні за своєю природою об’єкти. Водночас діалектична логіка вимагає, +щоб поряд з констатацією принципових відмінностей між трудовою +діяльністю людини та функціонуванням різноманітних машин було +виявлено й об’єктивно існуючі аналоги між інтелектуальними та фі- +зичними процесами, що супроводжують трудову діяльність людини, +та процесами, що протікають у машинах. Більше того, життя вимагає +створення таких концепцій, які дозволили б розглядати людину і ма- +шину з єдиної позиції, яка аж ніяк не означає, що при цьому стира- +ються всякі якісні відмінності між людиною і роботом. «У строгому +сенсі слова, жодна машина, навіть найдосконаліша, не працює і не +може працювати. Вона лише є знаряддям праці, за допомогою якого +людина впливає на природу, змінюючи останню відповідно до зазда- +легідь поставленої мети. Яких чудових успіхів не досягла б техніка, які +б дивовижні автомати не створювалися, праця завжди була і залиша- +ється свідомою діяльністю людини, а людина — суб’єктом праці» [12]. +Інформаційні технології можна подати як сукупність трьох осно- +вних способів перетворення інформації: зберігання, обробки та пе- +редачі [13]. +Методами інформаційних технологій є методи обробки та переда- +чі інформації. +Засобами інформаційних технологій є технічні, програмні, інфор- +маційні та інші засоби, за допомогою яких реалізується ІТ. +Інформаційна технологія спрямована на доцільне використання +інформаційних ресурсів та забезпечення ними всіх елементів органі- +заційної структури. + +464 +Реалізація системного підходу в описі інформаційних технологій +передбачає використання принципу цілісності, відповідно до якого +при системному підході виділяються такі аспекти або підходи. +Сутнісний підхід полягає у розкритті сутності системи, якісної +специфіки, властивих їй системних якостей. Виявлення сутності сис- +теми — найскладніший етап пізнання суттєвих ознак інформаційної +технології, які відрізняють її від інших об’єктів та систем. +Аналіз наведених визначень понять «технологія» та «інформацій- +на технологія» дозволяє виділити ряд суттєвих ознак: +– процесний характер інформаційної технології — виявляється в +тому, що сутність технології пов’язана з перетворенням властивостей, +форми, змісту та іншої інформації, по-перше, і по-друге, з процесом +організації інформаційної технології; +– формалізований характер інформаційної технології — представ- +ляється у різних формалізованих формах: у вигляді проекту, алгорит- +мів та програм, різноманітних математичних моделей та ін.; +– орієнтація на практику — завдяки запитам практики інформа- +ційні процеси стали реалізовуватися у формі технологій; +– концентрація у собі наукових знань та досвіду реалізації інфор- +маційних процесів; +– отримання ефективності, досягнення кінцевого результату — +невід’ємні характеристики інформаційної технології. Головним кри- +терієм соціальної ефективності інформаційної технології є вільний +час людини. Інформаційна технологія забезпечує економію витрат +праці, енергії, ресурсів; +– забезпечення заданого користувачем рівня якості реалізації ін- +формаційних процесів. +Елементний аспект передбачає опис складу системи, кількісну +та якісну характеристику частин, компонентів, їх координацію та + субординацію, пріоритетну (лідируючу) частину системи. +Засоби забезпечення інформаційних технологій представлені ме- +тодами, технічними засобами (апаратні засоби PC, оргтехніка та ін.), +алгоритмічними та програмними засобами, інформаційним та мето- +дичним забезпеченням, комп’ютерними мережами та телекомуніка- +ціями, персоналом та ін. +Функціональний підхід вимагає відповіді на такі питання. Які +внутрішні та зовнішні функції інформаційної технології як систе- +ми? Як ці функції дозволяють досягати цілі системи? Яка активність, +життєдіяльність системи? + +465 +Визначення функцій системи передбачає встановлення її мети. +Інформаційна технологія є цілеспрямованою системою. Основна +мета інформаційної технології полягає у формуванні якісного інфор- +маційного ресурсу (нової інформації, знань), необхідного для підви- +щення ефективності системи, в якій вона функціонує. Декомпозиція +загальної мети дозволяє побудувати дерево цілей, яке відбиває всі на- +прямки реалізації інформаційної технології. +Для досягнення цілей інформаційній технології необхідно вико- +нати певні функції. Головними з них є формування концептуальної +моделі інформаційної технології, перетворення даних, інформації та +знань (збір, обробка, зберігання, передача, розповсюдження та ін.) +та функції із забезпечення інформаційною технологією. Зовнішні +функції реалізуються для задоволення потреб у якісних і ефективних +інформаційних системах різноманітних елементів: держави, політич- +ного середовища, соціальної та виробничої сфери, науки, економіки, +технології та інших. +Структурний підхід дозволяє встановити внутрішню організацію +системи, способи взаємозв’язку елементів, компоненти у системі, її +структури. Виділені функції закріплюються у структурах, які є спосо- +бами взаємодії елементів у системі. +Функціональна структура технологічного інформаційного проце- +су задається логікою реалізації процедур перетворення інформації та +технологічними принципами. Конкретна інформаційна технологія +має вписуватися у відповідну організаційну структуру управління ін- +формаційною системою, технологічну систему. +Комунікативний підхід розкриває питання взаємодії системи із +зовнішнім середовищем шляхом визначення матеріальних, енерге- +тичних та інформаційних зв’язків. Цю властивість системи назива- +ють відкритістю [14]. +Властивість відкритості інформаційної системи проявляється у +взаємодії із зовнішнім середовищем шляхом постійного обміну з ним +енергією, речовиною та інформацією. Тут основне значення має ін- +формаційний аспект, хоча матеріальний та енергетичний обмін також +відіграють не останню роль у функціонуванні та розвитку технології. +Інформаційна технологія як відкрита система має такі характерні +властивості. +Перша — має властивість активності. Вона проявляється у ціле- +спрямованій взаємодії із зовнішнім середовищем для задоволення +своїх потреб. Активність інформаційної технології пов’язана з наяв- + +466 +ністю в ній ціленаправлених компонентів, головним елементом яких +є персонал. +Зростання активної ролі інформаційних технологій пов’язане зі +зміною характеру розвитку зовнішнього середовища та зі зростаю- +чою складністю взаємодії зі споживачем. Інформаційна технологія +(суб’єкт) за впливом на об’єкт має приводити його у той стан, який +найбільшою мірою допомагає досягати мети об’єкта, тобто носити +активний характер. Активність інформаційної технології передбачає +передусім розширення її дій та функцій у процесі свого функціону- +вання та розвитку. Тому активність інформаційної технології повинна +мати певну стійкість. +У ході практичної реалізації поставленої мети інформаційній тех- +нології необхідно керувати своєю діяльністю відповідно до змін зо- +внішнього середовища. Отже активність інформаційної технології +має передусім бути спрямованою на пізнання закономірностей роз- +витку зовнішнього середовища задля її подальшого активного впливу +на нього. +Важливим у використанні інформаційних технологій є облік +властивості гомеостатичності, яка забезпечує цілісність системи за +умов постійно змінного стану зовнішнього середовища. Тут слід за- +значити, що в різних станах довкілля істотні змінні системи залиша- +ються стабільними чи змінюються у заданих межах, чим забезпечу- +ють рівновагу із зовнішнім середовищем. Такий стан характеризує +систему як цілісність і не може бути приписаний жодній її частині +(підсистемі). +У практичному плані властивість відкритості інформаційної тех- +нології реалізовано у розробці концепції відкритих інформаційних +систем. Суть її коротко зводиться до такого: кожна відкрита інфор- +маційна система призначена для розв’язання двох завдань (обробки +та передачі даних) і складається з двох частин — прикладні процеси, +призначені для обробки даних і, насамперед, для задоволення потреб +користувачів; та область взаємодії, що забезпечує передачу даних між +прикладними процесами, розташованими у різних системах. Голо- +вну роль у розробці відкритих систем грає Міжнародна організація +зі стандартизації (International Organization for Standardization, ISO). +Вона розробляє стандарти взаємодії відкритих систем (Open Systems +Interconnection, OSI). +Інтегративний підхід виявляє системоутворюючі чинники, меха- +нізми забезпечення єдності системи, її цілісності. + +467 +Досліджуючи проблему цілісності, багато вчених дотримуються +різних поглядів на це поняття. Перший підхід до проблеми цілісності +пов’язують із наявністю у системи нових властивостей (неадитивнос- +ті, емерджентності, інтегральності тощо), які не притаманні її еле- +ментам. +Другий підхід акцентує увагу на автономності, цілісності системи +та протиставленості зовнішньому середовищу. +У третьому підході як критерій цілісності системи виділяють на- +явність певного ступеня впорядкованості, організованості елемен- +тів системи, взаємозв’язків та взаємодій, певної тісноти зв’язків; +наявність такого поєднання елементів (підсистем), властивостей та +зв’язків системи, яке найбільшою мірою відповідає її цілям функці- +онування та розвитку. Тут простежується тісний зв’язок властивості +цілісності з організованістю системи. Четвертий підхід поєднує пер- +ший і третій [15]. +Останнім часом у зв’язку з розвитком функціонального підходу +у науковому пізнанні розвивається погляд на проблему цілісності з +цих позицій. Виділення функціональної цілісності у пізнанні сис- +тем — ще один крок до вивчення цієї складної проблеми, що до- +зволяє враховувати властивість відкритості. Розглядаючи джерело +цілісності систем, необхідно враховувати зв’язки із зовнішнім сере- +довищем. +Інформаційна технологія дійсно володіє новими властивостями, +які виявляються внаслідок її функціонування та розвитку. Особли- +вий інтерес представляє поява серед нових властивостей таких, які не +характерні жодному з елементів системи, тобто інтегральних (емер- +джентних тощо) властивостей. +На думку багатьох фахівців, причиною виникнення системи ін- +тегральних властивостей є наявність різноманітних, стійких зв’язків +як усередині системи, так і з зовнішнім середовищем. Саме зв’язки +становлять той новий прихований доданок, який відрізняє ціле від +суми частин. +Нові властивості інформаційної технології можуть бути найрізно- +манітнішими. Для цілеспрямованих систем (якою і є інформаційна +технологія) важливе значення має виникнення нових властивостей, +пов’язаних з їх цільовим призначенням, тобто тих властивостей, які +визначають її якісну специфіку. +Інформаційна технологія як цілісна система у процесі свого функ- +ціонування та розвитку здатна на більше, ніж кожен із її ізольованих + +468 +елементів або підсистем. Така нова властивість систем у теорії органі- +зації одержала назву синергетичного ефекту. +Отже властивість цілісності інформаційної системи можна кон- +кретизувати і виразити через систему зв’язків між елементами та із +зовнішнім середовищем, з одного боку, та інтегративністю — з ін- +шого. З теорії систем відомо, що наявність зв’язків не є характерною +ознакою лише систем. Для забезпечення цілісності інформаційній +технології необхідно, щоб зв’язки між елементами мали стійкий ха- +рактер і серед них знаходилися системоутворюючі зв’язки. Роль сис- +темоутворюючих зв’язків грають зв’язку управління, організаційні, +функціональні, зворотні, технологічні та ін. +Історичний підхід визначає процеси виникнення системи, її ста- +новлення, функціонування, тенденції та перспективи розвитку. +Найбільший інтерес для наших завдань мають етапи розвитку ін- +формаційниї технологій, пов’язані з розвитком електронно-обчис- +лювальних машин. +1-й етап (до другої половини ХІХ ст.) — «ручні» технології: перо, +чорнильниця, книга, елементарні ручні засоби рахування. Комуніка- +ції здійснювалися шляхом доставки кінною поштою листів, пакетів, +депеш, у європейських країнах застосовувався механічний телеграф. +Основню метою технологій було подання та передача інформації +у потрібній формі. +2-й етап (кінець ХІХ ст. — 40-ві рр. ХХ ст.) — «механічні» техноло- +гії: друкарська машинка, арифмометр, телеграф, телефон, диктофон, +оснащена більш досконалими засобами доставки пошта. Основною +метою технологій було подання інформації у потрібній формі зручні- +шими засобами, скорочення витрат на компенсацію втрат та виправ- +лення спотворень. +3-й етап (40-ві — 60-ті рр. XX ст.) — «електричні» технології: перші +лампові електронно-обчислювальні машини і відповідне програмне +забезпечення, електричні друкарські машинки, телетайпи (телекси), +ксерокси, портативні диктофони. Організація доставки інформації +у заданий час. Акцент в інформаційних технологіях починає перемі- +щатися з форми подання інформації на формування її змісту. +4-й етап (70-ті рр. — середина 80-х рр.) — «електронні» техноло- +гії, основний інструментарій — великі електронно-обчислювальні +машини та створювані на їх базі автоматизовані системи управління +(АСУ) та інформаційно-пошукові системи, оснащені широким спек- +тром базових та спеціалізованих програмних комплексів. Центр ваги + +469 +технологій зміщується на формування змістовної складової інформа- +ції для управлінського середовища різних сфер громадського життя, +особливо на організацію аналітичної роботи. +5-й етап (з середини 80-х рр.) — «комп’ютерні» («нові») техноло- +гії, персональний комп’ютер із широким спектром стандартних та +замовлених програмних продуктів широкого призначення. Створен- +ня систем підтримки прийняття рішень на різних рівнях управління. +Системи мають вбудовані елементи аналізу та штучного інтелекту, +реалізуються на персональному комп’ютері та використовують мере- +жеві технології та телекомунікації для роботи в мережі. +6-й етап (з середини 90-х рр.) — «Internet/Intranet» («найновіт- +ніші») технології. Широко використовуються в різних областях на- +уки, техніки та бізнесу розподілені системи, глобальні, регіональні +та локальні комп’ютерні мережі. Розвивається електронна комерція. +Збільшення обсягів інформації призвело до створення технології +Data Mining (з англ.: видобуток даних) — автоматизований пошук +даних, заснований на аналізі великих масивів інформації. За мету бе- +реться ідентифікація тенденцій та патернів, яка за звичайного аналізу +неможлива. Для сегментації даних та оцінки ймовірності подальших +подій використовуються складні математичні алгоритми [16]. +Безперечним є твердження про початок переходу людської циві- +лізації в новий якісний стан — постіндустріальна чи інформаційна +культура приходить на зміну індустріальної, яка, у свою чергу, заміни- +ла в середні віки аграрну. Кожній стадії розвитку суспільства відпові- +дають свої форми та зміст процесу навчання нових поколінь, передачі +їм накопичених знань, навичок, традицій. +Аграрна цивілізація, яка існувала від первісного та рабовласниць- +кого суспільства до середини XV століття, породила менторську шко- +лу, засновану на усному спілкуванні, а потім на створенні та викорис- +танні рукописних конспектів лекцій та протоколів наукових дослідів. +Вона характеризувалася найвищою духовною близькістю вчителя та +учня, низьким рівнем безпеки даних. Інформаційні втрати були ката- +строфічними. Але за час існування менторської школи людство на- +громадило потенціал, що дозволив зробити прорив у індустріальне +суспільство, яке породило нові форми освітнього процесу — ремісни- +чу школу. Основою цього реформування стало книгодрукування, яке +розширило аудиторію користувачів і підвищило безпеку інформації, +вперше забезпечило масовий характер дистанційного навчання. Ре- +міснича школа, система міст-університетів насамперед задоволь- + +470 +няли потреби зростаючої промисловості. Аудиторне навантаження +професорів у розрахунку на одного студента знизилося. Зменшився +і світоглядний вплив викладача. І лише наприкінці ХХ століття нові +інформаційні, комунікаційні та насамперед комп’ютерні технології +перевернули уявлення про можливості інформаційного обміну. Це +сталося завдяки п’яти сторіччям передачі знань у рамках ремісничої +школи. +Новий етап розвитку системи освіти — етап виходу навчального +процесу за межі конкретного навчального закладу. Стають загаль- +нодоступними найкращі світові зразки викладання дисциплін, го- +тові курси, програми. Надійність систем дублювання та збереження +інформації стає абсолютною, як можливість віддаленого доступу до +невичерпних ресурсів світових бібліотечних фондів, інформаційних +баз даних, наукових результатів лідируючих лабораторій та інститутів +у всьому світі. Корінним чином змінюється і форма подачі навчаль- +ного матеріалу: стає ясно, що виникнення радіо, кіно і телебачення +стало не народженням самодостатніх засобів комунікації, а лише по- +передником синтетичних способів віддаленого впливу на людський +мозок за допомогою аудіо- і відеоінформації. Відбуваються зміни +і у сфері міжособистісних відносин: знижуються корпоративність та +колективізм навчальних груп, у масовому навчанні слабшають еле- +менти духовного спілкування та виховання. +Основними рисами розвитку такого типу освіти в інформаційно- +му суспільстві можна назвати такі. +1. Всесвітня інформаційна мережа — заміна письмового спілку- +вання електронною поштою, колективних усних дискусій — чатами, +відмова від поліграфічної форми підручників на користь електронних +версій. Роль, місце та функціональні обов’язки викладача змінюють- +ся. Він повинен не тільки володіти всіма цими технологіями, вміти +відбирати, оцінювати, застосовувати найцінніші освітні ресурси, але +й допомогти здобувачеві вищої освіти не потонути в інформаційному +океані. +2. Нові форми пред’явлення знань, умінь, навичок: інтерактивні +живі тексти, гіпертексти, аудіовізуальні засоби, комп’ютеризовані +практикуми — симулятори, віртуальні лабораторії. Тут викладач по- +винен як мінімум бути в змозі поставити завдання дизайнеру, про- +грамісту, аніматору при створенні таких методичних матеріалів та за- +стосувати вже створені професіоналами інтерактивні, мультимедійні +чи віртуальні посібники у своїй педагогічній області. + +471 +3. Пролонгований у часі характер. Технічні можливості надання +якісних освітніх послуг входять у суперечність із бажанням тривалого +безпосереднього спілкування вчитель — учень. Інформаційний пре- +синг засобів масової інформації та Інтернет повністю змінили харак- +тер, глибину та швидкість сприйняття зовнішніх подразників новими +поколіннями. Аудиторне навантаження знижується за прямими ме- +дичними показаннями. Спрощений варіант загальної вищої освіти +поширюється одночасно з інформаційною інфраструктурою. +У цих умовах потяг молоді до Інтернету треба використовувати +для грамотного, ввічливого та змістовного мережевого спілкуван- +ня. Необхідно розпочати підготовку педагогів, здатних застосовува- +ти найсучасніші інформаційні технології навчання, зберігаючи при +цьому той безцінний досвід, знання та методики викладання, які їх +носії мають передати їх новим поколінням. Також необхідно розви- +вати телекомунікаційну освітню інфраструктуру, випереджаючими +темпами розробляти навчально-методичне та апаратно-програмне +забезпечення для всіх форм очних занять, дублюючи його версії у ло- +кальному та дистанційному варіантах. +Особливу увагу необхідно приділити розробці освітніх серверів, +сайтів, інших інтернет-ресурсів, які здатні охопити максимально ши- +року аудиторію, створити та підтримувати єдиний освітній простір, +забезпечити державні стандарти. Поступово необхідно трансформу- +вати навчальні плани закладів вищої освіти у бік зменшення аудитор- +ного навантаження викладачів, зміщення центру ваги на дистанцій- +ні форми поза жорстким розкладом, самостійну роботу студентів за +консультаційної та методичної підтримки викладачів. +У перспективі слід прагнути до максимальної інтеграції провідних +закладів вищої освіти на основі уніфікованих освітніх стандартів, на- +дання загального мережевого сервісу за всіма формами навчального +процесу та єдиної рейтингової системи оцінки якості навчання. Оче- +видно, що це вимагає від усього суспільства створення розгалуженої +інфраструктури швидкого інформаційного обміну, заснованої на вза- +ємодоповнюючих нових інформаційних та телекомунікаційних тех- +нологіях [17]. +Серед нових інформаційних технологій можна назвати такі: штуч- +ний інтелект, нейрокомп’ютерна технологія, нейронні мережі, відео- +технологія, мультимедіатехнологія, об’єктно орієнтована технологія, +інтернет-технологія, віртуальна реальність та інші. Нові інформаційні +технології являють собою певні методики, що дозволяють на іншому, + +472 +новішому рівні вирішувати освітні та виховні завдання; здійснювати +прогноз та аналіз інформації; допомагати при прийнятті правильного +та ефективного рішення. +З їх допомогою здійснюються пошук, збирання інформації, її пере- +робка, зберігання, подання у доступному для здобувачів вищої освіти +вигляді, а також актуалізація інформації, що пов’язано з розвитком +науково-технічного прогресу, оновленням техніки та технологій, роз- +витком наукомістких виробництв. Масштабно використовувані циф- +рові навчально-методичні матеріали, у тому числі в мультимедійному +поданні, бездротові технології, презентаційне обладнання, мережеві +технології для доступу до ресурсів, впливають на інфрастурктуру ін- +формаційних технологій, на сервіси інформаційної системи закладу +вищої освіти [18]. +Використання інформаційних технологій у вищій освіті буде +найбільш успішно здійснюватися якщо: в освітньому просторі за- +кладу вищої освіти буде створено насичене мультисередовище, до +якого залучаються різні канали сприйняття інформації — тексто- +вої, візуальної, аудіоінформації, що дозволить інтенсифікувати на- +вчальний процес та готувати здобувача вищої освіти до майбутньої +роботи у професійній сфері, з урахуванням відомого останнім часом +посилення тенденції конвергенції сенсорних каналів сприйняття +інформації. +У сфері освіти, як і в усіх інших, сучасне використання інфор- +маційних технологій пов’язане з переходом до обробки, зберігання +та обміну інформацією у мережі. Інтернет став основою ХХІ ст. як +століття інформаційних технологій, будучи глобальною інформацій- +но-телекомунікаційною мережею, що пов’язує інформаційні систе- +ми та мережі електрозв’язку різних країн за допомогою глобального +адресного простору та надає можливість реалізації різних форм ко- +мунікації. +Інформаційні технології полегшують та спрощують процес на- +вчання і роблять його зручнішим і доступнішим, виконуючи при цьо- +му три взаємопов’язані між собою функції: діагностичну, навчальну +та виховну. +Реалізувати процес підвищення якості сучасної вищої освіти засо- +бами інформаційних технологій можна за допомогою управлінського +та вже згаданого системного підходів. +Суть управлінського підходу полягає у прийнятті управлінських +рішень із використанням цифрових технологій. + +473 +Системний підхід ґрунтується на організації взаємодії викладача +та студента як елементів єдиної вельми складної системи за допомо- +гою цифрових засобів навчання. +Можливості цифрових технологій дозволяють залучати до освіт- +нього процесу певного завкладу вищої освіти викладачів-практи- +ків, лекторів, учених, які перебувають за межами міста чи навіть +країни. +Останніми десятиліттями дистанційні освітні технології у світі на- +були інтенсивного розвитку. Настала епоха інформатизації освітньо- +го процесу. Сучасну фазу розвитку можна характеризувати як теле- +комунікаційну. Це — фаза спілкування, фаза трансферу інформації та +знань. Навчання та робота сьогодні — синоніми: професійні знання +старіють дуже швидко, тому потрібне їх постійне вдосконалення — це +і є відкрита освіта [19]. +Існують два види факторів використання дистанційного навчання +у системі вищої освіти: зовнішні та внутрішні фактори. +Зовнішні фактори. В інформаційному суспільстві пріоритетним +стає високий рівень освіченості його членів. Тільки високоосвічені +люди здатні ефективно використовувати інформацію як продуктив- +ний ресурс. Ефект «інформаційного вибуху» вимагає від кожного +члена суспільства постійного оновлення своїх знань. Людині недо- +статньо «освіти на все життя», їй необхідна «освіта протягом усього +життя». Навчання об’єктивно стає безперервним. Істотно змінюєть- +ся і характер процесу навчання. Ці питання є вельми актуальними у +масштабах всієї Земної кулі. ЮНЕСКО як провідна установа Органі- +зації Об’єднаних Націй, яка займається питаннями освіти, спільно зі +спеціалізованим Міжнародним інститутом планування освіти надає +країнам технічну підтримку у плануванні та аналізі політики в галузі +освіти. Інститут ЮНЕСКО з навчання протягом усього життя (life- +long learning education) відіграє ключову роль у підтримці держав-чле- +нів щодо розробки політики у цій галузі. +Термін «безперервна освіта» багатозначний. По-перше, безпе- +рервна освіта означає постійне, безперервне вдосконалення знань, +умінь, навичок людини, пов’язане з необхідністю бути актуальним +у сучасному середовищі (професійному, соціальному). По-друге, під +цим терміном розуміють систему поглядів на освітній процес загалом. +Ця система розглядає навчальну діяльність як невід’ємну та основну +складову способу життя в будь-якому віці; передбачає необхідність +добудови освітніх сходів новими сходинками, розрахованими на всі + +474 +періоди життя людини. По-третє, безперервна освіта передбачає по- +стійне збагачення творчого потенціалу особистості, розвиток людини +як творчої особистості. Безперервна освіта — процес цілісний, який +складається зі ступенів, що послідовно прямують один за одним, +спеціально організованої навчальної діяльності, яка створює людині +сприятливі умови для життя [20]. +Також необхідно відзначити важливість впровадження інформа- +ційних технологій у глобальному аспекті: +по-перше, інформаційні технології створюють нові можливості +для освіти, дають можливість охоплення широкого кола населення та +задовольняють потреби особистості у прагненні до знань, підвищенні +кваліфікації в обраній галузі та професійній діяльності; +по-друге, усувають бар’єри, пов’язані з доступом до необхідної ін- +формації, та скорочують витрати під час обміну інформацією; +по-третє, сприяють залученню в країну інвестиції та просуванню +прогресивних технологій у виробництві, управлінні, освіті; +по-четверте, інформаційні технології підвищують ефективність +економіки та суттєво прискорюють темпи глобалізації тощо. +Усе це робить подальше використання інформаційних технологій +вельми актуальним питанням та необхідною умовою успішного за- +стосування дистанційних технологій навчання. +Внутрішні фактори. Сучасні вимоги, продиктовані реформуван- +ням економіки та суспільства, карантинними обмеженнями, часті- +шими природними катаклізмами призвели до значного збільшення +ресурсомісткості навчального процесу. Надання освітніх послуг та +організації системи підвищення кваліфікації і перепідготовки кадрів +без урахування сучасних вимог та умов, що змінилися, призводить +до суттєвого обмеження зростання обсягу навчального континген- +ту, знижує доступність та ефективність освітніх послуг і, як наслідок, +звужує коло їх потенційних можливостей. +Для зниження ресурсомісткості навчального процесу, забезпе- +чення більшої доступності навчання в закладах вищої освіти, на- +вчальні технології повинні стати максимально ефективними, тобто +такими, що забезпечують високий рівень економічності навчального +процесу при вищій якості навчання. Необхідне широке застосуван- +ня інноваційних методів навчання, що інтенсифікують навчальний +процес. Все це можна досягти широким впровадженням у навчаль- +но-освітній процес сучасних педагогічних та новітніх інформацій- +них технологій. + +475 +Керуючись наведеним вище, можна виділити декілька основних +причин створення та впровадження технології дистанційного на- +вчання в системі освіти: +– розширення системи підвищення кваліфікації та перепідготов- +ки кадрів; +– підвищення вимог до якості освіти; +– необхідність широкого надання освітніх послуг особам з обме- +женими можливостями (інвалідам), соціальної адаптації; +– необхідність реалізації вимог до комфортності навчання та ви- +кладання за рахунок можливості як здобувача вищої освіти, так і ви- +кладача проводити процес навчання у зручний для себе час, у зруч- +ному місці та темпі. Нерегламентований відрізок часу на освоєння +курсу надає здобувачам вищої освіти можливість освоєння курсу за +менший або більший час у порівнянні з жорстко регламентованим за +часом традиційним курсом. Для викладача зменшується частка ауди- +торного навчального завантаження; +– створення конкурентного середовища в освіті між традиційною +і дистанційною освітою, що неодмінно стимулює підвищення якості +освіти. +Таким чином, новий, інформаційний етап розвитку світової сис- +теми освіти є об’єктивним і незворотнім. Використання інформацій- +них технологій у навчанні, що відповідають світовому рівню, — осно- +вний та ефективний шлях розвитку вітчизняної системи освіти [21]. +Дистанційне навчання має тривалу історію становлення, зазна- +ючи значних змін з часом: від навчання, яке проводилося за допо- +могою кореспонденції, до поступового використання аудіо- та відео- +матеріалів та, нарешті, перехід до активного впровадження у процес +навчання комп’ютерних технологій та Інтернету. Традиційно заро- +дження дистанційного навчання пов’язують зі становленням The +Open University у Великій Британії 1960-ті роки. +Дистанційне навчання є універсальною гуманістичною формою +навчання, що базується на використанні можливостей електронно- +го навчання та дистанційних освітніх технологій, які створюють для +здобувачів вищої освіти умови вибору освітніх дисциплін основної +та додаткової освіти, діалогового обміну з викладачем, при цьому +процес навчання не залежить від розташування слухача у просторі +та часі. +Дистанційні освітні технології — освітні технології, що реалізу- +ються із застосуванням інформаційних та телекомунікаційних техно- + +476 +логій при опосередкованій (на відстані) взаємодії студентів та педа- +гогічних працівників. Електронне навчання — організація освітньої +діяльності із застосуванням інформації, що міститься у базах даних, і +використовуваної під час реалізації освітніх програм та інформацій- +них технологій, які забезпечують її обробку, технічних засобів, а та- +кож інформаційно-телекомунікаційних мереж, які забезпечують пе- +редачу лініями зв’язку зазначеної інформації, взаємодію здобувачів +вищої освіти і педагогічних працівників. +Електронне навчання як самостійну форму навчання або складо- +ву дистанційного навчання можна розглядати як процес навчання та +викладання з використанням електронних технологій, який забез- +печує гнучкий доступ до навчальних ресурсів експертам, колегам, +освітнім сервісам та послугам, і розкриває потенціал комп’ютерних +технологій у можливості зробити навчання доступним у будь-який +час і в будь-якому місці. У світовому науковому співтоваристві ще +зовсім нещодавно склалася єдина точка зору на розуміння сутності +та особливостей навчання в електронному середовищі. Але ж фахівці +продовжують дискутувати на цю тему. +Одні дослідники вважають, що немає значної різниці між навчан- +ням в електронному середовищі та традиційними формами навчання +як на самому етапі навчання, так і на етапі отриманих у результаті на- +вчання знань. Але інші, яких на даний момент більшість, вважають, +що навчання в електронному середовищі є абсолютно новою пара- +дигмою освіти, яка формується на основі особливої культури навчан- +ня. Тому важливим елементом навчання в електронному сере довищі +стає його організація та методологія, які значно відрізняються від +традиційних форматів та методів навчання. +Сучасне електронне навчання включає в себе on-line навчання +(навчання за допомогою Інтернету), off-line навчання (навчання за +допомогою електронних носіїв, наприклад, мультимедійних ком- +пакт-дисків), m-learning (мобільне навчання за допомогою мобільних +телефонів, смартфонів, планшетів, ноутбуків та іншого, що дозволяє +також використовувати Інтернет). +Можливість створення повноцінного віртуального освітнього се- +редовища обумовлюється врахуванням таких положень: +1) акцент на залежності пізнання (та набуття знання) від соціаль- +ного контексту; +2) наявність тісного зв’язку між навчанням («дозріванням») та +розвитком, що передбачає необхідність пов’язувати (або вибирати) + +477 +ту чи іншу форму навчання залежно від рівня розвитку, потреб здо- +бувачів вищої освіти тощо; +3) необхідність розглядати здобувача вищої освіти як центральну +фігуру та елемент системи навчання; +4) ефективність спільнот, що навчаються, у яких соціальна, педа- +гогічна і когнітивна присутність забезпечують плідне середовище для +розвитку особистості та трансформації життєвих перспектив як тих, +хто навчає, так і тих, хто навчається. +Таким чином, електронне навчання є порівняно новою формою +навчання та сферою наукових досліджень. Електронне навчання яв- +ляє собою процес навчання та викладання з використанням елек- +тронних технологій, що забезпечує гнучкий доступ до навчальних +ресурсів, експертів, колег, навчальних сервісів і послуг і розкриває +потенціал комп’ютерних технологій у можливості зробити навчання +доступним у будь-який час і в будь-якому місці. В Україні сьогодні +активно розвивається тема електронного навчання, що підтверджу- +ється відкриттям нових порталів, присвячених цій темі, державних +програм. +Однак як результат впровадження електронного навчання в Укра- +їні необхідно не лише розглядати кількісні показники ефективності +його впровадження, а й аналізувати психологічні складові електрон- +ного навчання. Жодна з програм електронного навчання не буде +ефективною, якщо не враховано психологічний аспект, не створено +психологічних умов для електронного навчання, у тому числі й пси- +хологічних умов автентичності порозуміння учасників освітнього +процесу. +В Україні вже створено істотну основу майбутньої систе- +ми дистанцiйного навчання, як форми навчання з використан- +ням комп’ютер них і телекомунiкацiйних технологiй, якi забез- +печують iнтерактивну взаємодiю викладачiв та здобувачів вищої +освіти на рiзних етапах навчання i самостiйну роботу з матерiалами +iнформацiйної мережi [22]. +Сьогодні в нашій країні, як і в усьому світі, багато аспектів нашого +життя вже перенесено в мережу, що прискорює темпи розвитку ін- +формаційного суспільства. У сфері освіти достатньо довгий час, ще з +радянських часів існує заочна форма навчання студентів, але її мож- +ливості були дуже обмежені. Нові інформаційні технології, Інтернет +дають змогу зробити заочне навчання повноцінним та всеохоплю- +ючим і разом з очним навчанням забезпечити його цифровими за- + +478 +собами надання навчального матеріалу здобувачу вищої освіти; +цифровими засобами контролю успішності здобувача вищої освіти; +цифровими засобами консультації здобувача вищої освіти програ- +мою-викладачем; цифровими засобами інтерактивної співпраці ви- +кладача і здобувача вищої освіти; можливістю швидкого доповнення +курсу новою інформацією, коригування помилок та ін. +У наш час в умовах економічних відносин і жорсткої конкуренції +на ринку праці особливе значення мають знання, навички та досвід. +Фахівець XXI століття — це людина, яка вільно володіє сучасними +інформаційними технологіями, постійно підвищує і вдосконалює +свій професійний рівень. Набуття нових знань і навичок, прак- +тично корисних і застосовуваних у роботі в епоху інформаційного +суспільства, значно розширює можливості самореалізації і сприяє +кар’єрному росту. Проте однією з головних перешкод, що виникає +на шляху тих, хто бажає продовжити навчання (враховуючи, що +більшість з них вже працює), є брак часу. Більшість не має можли- +вості приїжджати кожного дня на заняття до навчального закладу. +Іншою значною перешкодою є відстань. Якщо навчальний заклад +розташований в іншому місті, часто відвідувати заняття також не- +зручно і дорого. +«Класична» заочна форма навчання часто не виправдовує свого +призначення. Знання, що отримує студент, часто є поверховими, а +самі заняття непродуктивними. Крім того, навчальний процес про- +довжується досить довго. +Дистанційна заочна освіта має такі переваги перед класичною: +– гнучкість — можливість викладення матеріалу курсу з ураху- +ванням підготовки, здібностей студентів. Це досягається створенням +альтернативних сайтів для одержання більш детальної або додаткової +інформації з незрозумілих тем, а також низки питань-підказок тощо; +– актуальність — можливість упровадження новітніх педагогіч- +них, психологічних, методичних розробок; +– зручність — можливість навчання у зручний час, у певному міс- +ці, здобуття освіти без відриву від основної роботи, відсутність обме- +жень у часі для засвоєння матеріалу; +– модульність — розбиття матеріалу на окремі функціонально +завершені теми, які вивчаються у міру засвоєння і відповідають зді- +бностям окремого студента або групи загалом; +– економічна ефективність — метод навчання дешевший, ніж +традиційні, завдяки ефективному використанню навчальних примі- + +479 +щень, полегшеному коригуванню електронних навчальних матеріа- +лів та мультидоступу до них; +– можливість одночасного використання великого обсягу на- +вчальної інформації будь-якою кількістю студентів; +– інтерактивність — активне спілкування між здобувачами вищої +освіти і викладачем, що значно посилює мотивацію до навчання, по- +ліпшує засвоєння матеріалу; +– більші можливості контролю якості навчання, які передбачають +проведення дискусій, чатів, використання самоконтролю, відсутність +психологічних бар’єрів; +– відсутність географічних кордонів для здобуття освіти. Різні +курси можна вивчати в різних навчальних закладах світу. +На Заході ця форма з’явилася вже досить давно і має велику по- +пулярність серед студентів через її економічні показники і навчальну +ефективність. Дистанційну форму навчання там називають, як вже +зазначалося, «освітою протягом усього життя» через те, що більшість +тих, хто навчається, — дорослі люди. Багато хто з них вже має вищу +освіту, проте через необхідність підвищення кваліфікації або розши- +рення сфери діяльності у багатьох виникає потреба швидко і якісно +засвоїти нові знання і набути навички роботи. Саме тоді оптималь- +ною формою може стати дистанційне навчання. +У системі дистанційного навчання виділено чотири типи суб’єкта: +1. Здобувач вищої освіти — той, хто навчається. +2. Тьютор (викладач) — той, хто навчає. +3. Організатор — той, хто планує навчальну діяльність, розробляє +програми навчання, займається розподіленням студентів за групами і +навчальним навантаженням на тьюторів, вирішує різні організаційні +питання. +4. Адміністратор — той, хто забезпечує стабільне функціонування +системи, вирішує технічні питання, слідкує за статистикою роботи +системи. +Важливим елементом дистанційного навчання є дистанційний +курс. Ще до початку навчання тьютори розробляють дистанційний +курс за своїми предметами. В процесі навчання курси можуть змі- +нюватися і доповнюватися. Кожний викладач має змогу сам вирішу- +вати, як буде виглядати дистанційний курс і які мультимедійні еле- +менти в ньому будуть застосовуватися. Міра і спосіб використання +комп’ютерних технологій при підготовці дистанційного курсу значно +впливають на ефективність його засвоєння. Світовий досвід показує, + +480 +що використання динамічних об’єктів для створення наочних моде- +лей процесів, адаптивне моделювання здобувача вищої освіти в бага- +тьох випадках значно підвищує навчальний ефект. +Курс розбивається на розділи, які потрібно проходити у визна- +чений час. За матеріалом розділів тьютори створюють і призначають +тести і завдання, які також потрібно вчасно проходити. Тьютор має +можливість призначати спеціальні перевірочні (граничні) тести за +відповідними розділами курсу. Тьютор може призначати завдання для +підгруп здобувачів вищої освіти, тоді завдання розв’язується колек- +тивно. +Взаємодія між суб’єктами системи дистанційного навчання здій- +снюється за допомогою системи індивідуальних гостьових книг, фо- +румів, чатів та електронної пошти. +Для організації дійсно ефективного навчального процесу дис- +танційного навчання необхідна систематична робота з сторінкою як +здобувача вищої освіти, так і тьютора майже кожного дня протягом +всього терміну навчання. +В інформаційному суспільстві в умовах колосального інформа- +ційного навантаження у сфері освіти системний підхід до організації +навчального процесу може бути реалізований через модульну техно- +логію навчання, яка повністю сумісна з сучасними інформаційно-ко- +мунікаційними технологіями [23]. +Модульне навчання — це така інструментальна форма організації +навчального процесу, коли здобувачі вищої освіти працюють із на- +вчальним середовищем, складеним з навчальних модулів, у режимі +активної самоосвіти за варіативними або індивідуальними освітніми +маршрутами. Технологія модульного навчання є одним з напрямків +індивідуалізованого навчання та дозволяє організувати процес само- +розвитку та самонавчання, регулювати темп навчання та зміст на- +вчального матеріалу. +Інформаційний навчальний матеріал у модульному навчанні має +бути організований у вигляді чіткої ієрархічної структури та нада- +ний здобувачам вищої освіти у всіх можливих кодах: графічному, +числовому, символічному та словесному. На цьому фундаменті фор- +мується цілісне системне сприйняття навчальної інформації. У мо- +дульному курсі має бути організовано інструментальне навчальне +середовище, що включає набір інформаційно-методичних матеріа- +лів та інтерактивних навчальних моделей для організації самостій- +них навчальних дій. + +481 +При цьому інформаційний навчальний гіперпростір є посередни- +ком між викладачем та здобувачем вищої освіти. Таке навчальне се- +редовище моделює діяльність педагога і забезпечує можливість орга- +нізації навчального процесу в режимі самонавчання, саморозвитку, +самоорганізації. Навички самоосвіти та самостійної роботи з різни- +ми джерелами інформації в інтерактивному навчальному середови- +щі є основою для розвитку здібностей до навчання. Таке навчання +побудоване на самомотивації, є розвиваючим та формує у здобувача +вищої освіти навички самоврядування навчальної діяльності. Тому +універсальні навчальні дії максимально ефективно та швидко фор- +муються у здобувачів вищої освіти саме у модульному освітньому +середовищі. +У циклі модульного навчання здобувачі вищої освіти організують +навчальну діяльність відповідно до поставлених особистих цілей, +використовуючи для цього необхідне інформаційно-методичне за- +безпечення та рекомендовані алгоритми навчальних дій. Вихідні ре- +зультати після вивчення чергового модуля стають вхідними під час +переходу до наступного циклу навчальної діяльності. При цьому про- +водиться коригування особистих навчальних цілей. +Поняття зворотного зв’язку є фундаментальним у кібернетиці. +Від якості зворотного зв’язку залежить ефективність управління +навчальним процесом. У кожному навчальному модулі канали зво- +ротного зв’язку можуть бути побудовані в кібернетичних системах +«здобувач вищої освіти — знання» та «викладач — здобувачі вищої +освіти». Функція зворотного зв’язку може бути вбудована в рей- +тингову електронну таблицю. При цьому здобувачі вищої освіти у +навчальному процесі за програмою модульного курсу мають мож- +ливість самостійно вимірювати обсяг навчальних дій, враховувати +результати самоконтролю на етапах сприйняття, обробки інформа- +ції та у процесі виконання вправ у режимі тренування. За підсумка- +ми цих записів з’являється можливість системного аналізу структу- +ри навчальних процесів. При цьому здобувачі вищої освіти вчаться +використовувати канал зворотного зв’язку, формують у себе нави- +чки самоврядування навчальним процесом і ці навички управління +автоматично переносяться на інші сфери життя (управління своїм +здоров’ям, емоційним станом, часом, грошовими потоками, ресур- +сами, іншими людьми та ін.). +У рейтинговій таблиці також має бути передбачена можливість +введення даних про результати виконання контрольних завдань для + +482 +визначення рівня засвоєння знань та вмінь здобувачів вищої освіти. +Це вже канал зворотного зв’язку для викладача. +При недостатності зворотних зв’язків між викладачем та здобува- +чами вищої освіти протягом семестру виникає взаємне нерозуміння +та погіршення якості навчання. Викладач повинен почути здобувачів +вищої освіти у разі виникнення складнощів сприйняття навчальної +інформації чи неприйняття методики викладання. Поняття прямих +та зворотних зв’язків можна співвіднести з вертикальною та горизон- +тальною комунікацією між учасниками навчального процесу у закла- +дах вищої освіти [24]. +У рамках навчального процесу закладу вищої освіти системи +«викладач — здобувач вищої освіти» передача інформації йде за +вертикальним принципом. Можливість горизонтальної передачі +з’являється у зв’язку з розвитком інтернет-технологій та соціальних +мереж. +Зворотній зв’язок від студентів можливий завдяки використанню +спеціалізованих ресурсів, де здобувачі вищої освіти виставляють сво- +їм викладачам оцінки за певними критеріями та пишуть відгуки. Все +це сприяє прозорості взаємин між викладачем та студентами та пере- +шкоджає зловживанням з боку викладачів. +При нерівномірності прямих та зворотних інформаційних потоків +викладач навчає здобувачів вищої освіти протягом семестру, а потім +організує проміжний контроль. Найчастіше при екзаменаційному +випробуванні здійснюється визначення рівня засвоєння інформації +як відповідність між змістом навчального матеріалу та його відтво- +ренням здобувачем вищої освіти. В результаті частіше визначається +ступінь запам’ятовування, але не розуміння здобувачами вищої осві- +ти змісту навчальної дисципліни. Вирішенням цієї проблеми може +бути зміна підходу до проміжного та підсумкового контролю, коли +питання до іспиту формулюються таким чином, щоб здобувач вищої +освіти продукував нове знання. +Системний аналіз навчальної діяльності проводиться на основі +даних самомоніторингу самостійних навчальних дій та вимірюван- +ня навчальних досягнень за результатами виконання контрольних +завдань. У результаті системного аналізу учні можуть отримати таку +інформацію: +– фактичні дані про структуру та обсяг самостійних навчальних +дій; +– дані про структуру витрат навчального часу; + +483 +– причинно-наслідкові зв’язки (навчальна діяльність — навчальні +результати); +– графічне відображення даних системного аналізу в вигляді гра- +фіків, діаграм. +Такий підхід до організації навчального процесу, побудований на +основі організації самостійних навчальних дій здобувачів вищої осві- +ти, забезпечує можливість формування та розвитку у них системи +універсальних навчальних дій. +Напрямки розвитку та вдосконалення електронних освітніх ре- +сурсів, сумісних з модульним та дистанційним навчанням, можуть +бути такими. +У модульному курсі має бути організовано системне інструмен- +тальне навчальне середовище, що включає набір інформаційно-мето- +дичних матеріалів та інтерактивних навчальних моделей для органі- +зації самостійних навчальних дій. Такий інформаційний навчальний +простір є посередником між викладачем та здобувачем вищої освіти, +який моделює діяльність педагога, що забезпечує можливість орга- +нізації навчального процесу в режимі самонавчання, саморозвитку, +самоорганізації. +Реалізація принципу системності означає, що навчальні модулі у +складі навчального курсу повинні включати цифрові освітні ресурси +в різних форматах та інтерактивні керуючі інструментальні засоби, +що забезпечують можливість організації повного навчального циклу, +реалізації всіх самостійних навчальних дій, необхідних для досягнен- +ня навчального результату. +У цьому навчальному циклі обов’язково має бути передбачено +таке: +– сприйняття та обробка інформації; +– тренування з метою формування навчання; +– контроль навчальних результатів; +– можливість самоаналізу та самоврядування навчальною діяль- +ністю. +В інструментальне навчальне середовище мають бути вбудовані +інтерактивні або друковані форми для моніторингу та системного +аналізу навчального процесу. +Необхідно, щоб інтерактивне навчальне середовище мало від- +криту модульну структуру та забезпечувало можливість зміни інтер- +фейсів, модифікації всіх компонентів системи, розширення функцій, +проектування різних варіантів освітніх маршрутів та ін. + +484 +Відкритість структури та інтерфейсу інструментального середови- +ща дозволяє організувати колективну творчість викладачів та здобу- +вачів вищої освіти. Це інноваційний підхід до впровадження методу +проектів у навчальний процес у закладах вищої освіти. +Реалізація повного навчального циклу на принципах системності +та модульності забезпечує створення повноцінного інтерактивного +навчально-методичного продукту як інструментального навчального +засобу, на основі застосування якого можливе впровадження елемен- +тів модульного навчання в освітній процес. +Комп’ютерні навчальні засоби, організовані на описаних прин- +ципах, забезпечують системне сприйняття здобувачами вищої освіти +змісту навчального курсу та сприяють розвитку у них системного мис- +лення, що є важливою метою в циклі навчання. На основі застосуван- +ня подібних інтерактивних програм можна побудувати навчальний +процес у режимі активної самоосвіти, саморозвитку, самоврядування. +Можна побудувати ефективніший навчальний процес, якщо +комп’ютерна навчальна програма безпосередньо взаємодіятиме зі +здобувачами вищої освіти і виконуватиме функції інтерактивного +тренажера. +Модульний підхід до побудови навчального середовища дає мож- +ливість організувати колективну творчу діяльність здобувачів вищої +освіти та за їх допомогою поступово наповнювати освітніми ресурса- +ми структури навчальних модулів. При цьому в модульному навчаль- +ному процесі автоматично реалізується можливість застосування +методу проектів у навчальний процес. Після розробки ієрархічного +графа — структури навчального модуля — викладач має можливість +на цій основі підготувати велику кількість технічних завдань на роз- +робку міні-проектів та подати їх у формі навчальних завдань різного +рівня складності. +Метод проекту освітньої технології, що розвивається, будується на +активній освітній діяльності здобувачів вищої освіти, а не на пасивне +сприйняття інформації. Проектування освітніх ресурсів організова- +но на сприйняття і самостійній обробці навчальної інформації, саме +тому метод проектів сприяє формуванню у здобувачів вищої освіти +системи універсальних навчальних дій, оскільки тільки в цій освітній +технології забезпечений творчий системний підход до організації са- +мостійних навчальних дій. +Використання системного підходу до освіти передбачає вдоскона- +лення процесів на всіх рівнях навчання. + +485 +За нестачі системного підходу у закладі вищої освіти спеціаліст +формується стихійно, часто відсутня самоідентифікація майбутньо- +го спеціаліста. Тому профорієнтацію необхідно продовжувати під час +навчання (при проведенні лекційних та практичних занять), інакше +виникає безцільність навчання. +Під час навчання здобувачів вищої освіти на молодших курсах +важливо дати їм правильний напрямок — «навчити вчитися». Необ- +хідно розділити два поняття: «навчання» та «вчення». +Навчання — це конкретніша і краще опрацьована сфера діяльнос- +ті, і спрямоване воно на здобувачів вищої освіти з боку викладачів. +Це методики навчання та підходи до організації навчального процесу. +Методика вчення — це мало формалізована галузь і її можна від- +нести до мистецтва. +Виходом тут може бути спільна з викладачем діяльність із виро- +блення методики вчення. При розробці методики навчання для здо- +бувачів вищої освіти, які не володіють методикою вчення, потрібно +врахувати таке: завдання мають бути гранично конкретними, дуже +докладними та адресними, тобто для кожного здобувача вищої осві- +ти необхідно виділяти завдання, яке необхідно виконати в певний +термін. +В результаті ефективної роботи закладу вищої освіти, узгодженої +роботи викладача та здобувача вищої освіти, взаємодії здобувачів ви- +щої освіти між собою у процесі навчання формуються чотири види +інтелекту, якими володіє людина: фізичний інтелект (або інтелект +тіла), ментальний інтелект, емоційний інтелект та духовний інтелект, +і освітні технології повинні бути спрямовані на розвиток всіх видів +інтелекту. +Потрібно визнати, що нинішні випускники наповнені інформа- +цією, але не знають, як її застосувати на практиці. +Для досягнення високих результатів в освітній системі необхідний +повний системний взаємозв’язок усіх етапів навчання у закладі вищої +освіти. +В основі підготовки хороших фахівців має бути викладач, який ін- +тегрує весь процес навчання (випускна кафедра, завідувач кафедри +або гарант освітньої програми) — від прийому до закладу вищої освіти +до працевлаштування випускника та подальшого його супроводу (на- +приклад, підвищення кваліфікації у процесі кар’єрного зростання). +Важливо відзначити, що універсального інструменту оцінки рівня +діджиталізації освіти бути не може, якість освітнього процесу зали- + +486 +шається незмінною в умовах формування компетентнісного підходу +до підготовки професіонала. +Завдяки новим інформаційним технологіям застосовуються інтер- +активні методи навчання, можливе індивідуальне, диференційоване, +різнорівневе навчання. Різноманітні і засоби навчання, що застосо- +вуються у навчальному процесі: це інтерактивні дошки, комп’ютери, +проектори, програмні продукти, додатки. У професійній підготовці +інформаційні технології проникли не тільки в область теоретично- +го навчання, а й у сферу практики, а також в область оцінки знань і +умінь здобувачів вищої освіти. +Інформаційні технології у вищому навчальному закладі дозволя- +ють найбільш ефективно організувати діяльність людей (навчальний +процес) та доступ до цифрових даних. Виходячи з цього в будь-якому +закладі вищої освіти можна виділити три основні компоненти ІТ- +рішень, між якими існує тісний взаємозв’язок, — це люди, процеси +та дані. З погляду управління, від того, наскільки добре вирішені та +організовані процеси, забезпечений зв’язок людей та даних, багато в +чому залежить успішна діяльність закладу вищої освіти [7]. +Істотний вплив на впровадження нових інформаційних техноло- +гій здійснюють сучасні інформаційні технологічні тенденції, основні +з яких такі: +– віртуалізація та «хмарні» технології; +– розширення використання сервісорієнтованих архітектур; +– впровадження мобільних пристроїв та рішень на корпоратив- +ному рівні для доступу до ресурсів та виконання корпоративних до- +датків; +– посилення диференціації користувацьких переваг; +– візуалізація, вебінари та відеоконференцзв’язок [25]. +Одним із важливих шляхів забезпечення ефективного функціо- +нування освітньої системи при впровадженні нових інформаційних +технологій у навчальний процес у закладах вищої освіти є створен- +ня та використання електронних навчально-методичних комплексів. +Усі документи у складі цього інформаційного комп’ютерного продук- +ту — мультимедійні, у них завжди присутні елементи інтерактивності, +вони можуть бути оформлені в вигляді набору веб-сторінок. Електро- +нні навчальні комплекси можуть бути використані на лекційних за- +няттях (показ відеозаписів, інтерактивних моделей та анімацій), під +час проведення віртуальних лабораторних робіт, атестації та само- +стійної роботи здобувачів вищої освіти. Таким чином, електронний + +487 +навчально-методичний комплекс — це програмний мультимедіапро- +дукт навчального призначення, що забезпечує безперервність та по- +вноту дидактичного циклу процесу навчання та містить організаційні +та систематизовані теоретичні, практичні, контролюючі матеріали, +побудовані на принципах системного підходу, інтерактивності, ін- +формаційної відкритості, дистанційності процедур оцінки знань. +Системний підхід при організації навчального процесу у закладі +вищої освіти з використанням нових інформаційних технологій за- +безпечує проведення інформатизації закладу вищої освіти як здій- +снення комплексу заходів, спрямованих на покращення його діяль- +ності як системи засобами інформаційних технологій [26]. +Щоб підвищити ефективність роботи закладу вищої освіти, по- +трібно комплексно впливати на систему в цілому — стратегію, мере- +жеву інфраструктуру, організаційну структуру, систему управління, +систему мотивації до праці, корпоративну культуру. Для вирішення +завдання інформатизації закладу вищої освіти необхідно створити +його єдину електронну систему, яка б дозволила управляти знаннями, +що забезпечило б розвиток інновацій, збільшення продуктивності +праці шляхом скорочення часу пошуку потрібного рішення в управ- +лінні та обсягу виконаних робіт, підвищення компетентності персо- +налу. В результаті користувачі отримають доступ до високоякісної +інформації, а самі рішення в галузі інформаційних технологій будуть +так вплетені в основні ділові процеси закладу вищої освіти, що персо- +нал і здобувачі вищої освіти вже не зможуть обходитися без сервісів, +що надаються інформаційним середовищем. При цьому підвищуєть- +ся ефективність виконання персоналом його посадових обов’язків, +підвищується якість навчання здобувачів вищої освіти, що робить +інвестиції в інформаційні технології економічно виправданими [7]. +ІТ-місія закладу вищої освіти має бути базою для формування +ІТ-стратегії та створення системи всередині ІТ-стандартів закладів +вищої освіти. Під ІТ-стратегією розуміють формалізовану систему +принципів, на основі яких формуються концепція інформатизації, +основні вимоги та план розвитку інформаційних технологій у закладі +вищої осіти. Стратегія забезпечує системний підхід до інформатизації +та узгодження з пріоритетами розвитку закладу вищої освіти в цілому. +Основні стратегічні цілі інформатизації: +– забезпечити гідне положення закладу вищої освіти серед інших +у галузі інформаційних технологій; +– розвинути нові форми та покращити якість освітніх послуг; + +488 +— підвищити віддачу від застосування інформаційних технологій в +управлінні закладом вищої освіти та у навчальному процесі на основі +узгодження бізнес-стратегії зі стратегією інформатизації, а також шля- +хом оптимізації інвестиційних, організаційних та технологічних рішень; +– знизити сукупну вартість володіння ІТ-ресурсами за рахунок +покращення керованості ресурсами; +– підвищити ефективність управління закладом вищої освіти та +покращити якість інформаційних сервісів, а також їх доступність для +користувачів на основі моделі єдиної інформаційної системи закладу +вищої освіти; +– знизити можливості для зловживання навчального персона- +лу щодо здобувачів вищої освіти та адміністративно-управлінського +персоналу щодо викладачів та співробітників на основі впроваджен- +ня систем комп’ютерного тестування, електронного документообігу, +контролю за виконанням управлінських рішень, регламентованого +доступу до управлінської та навчальної інформації; +– підвищити економічну ефективність застосування інформацій- +них технологій у вищому навчальному закладі [27]. +До основних напрямів інформатизації можна віднести такі: +– ІТ-інфраструктура: обладнання, лінії та канали передачі даних, +обчислювальна мережа, системне програмне забезпечення, бездро- +товий доступ до ресурсів; +– ІТ-рішення: комплексні проекти на основі інформаційнихз тех- +нологій, інформаційні системи та сервіси, інформаційні середовища, +геоінформаційні технології; +– методологія застосування інформаційних технологій: інформа- +ційні моделі бізнес-процесів у закладі вищої освіти, модель єдиної +інформаційної системи, методика оцінки ефективності застосування +інформаційних технологій, основні показники застосування інфор- +маційних технологій, узгоджені з ключовими показниками резуль- +тативності діяльності закладу вищої освіти, корпоративний стандарт +на порядок розробки, впровадження та застосування інформаційних +технологій у закладі вищої освіти, положення та регламенти; +– ІТ-служба: оргструктура, управління, взаємовідносини з інши- +ми підрозділами [28]. +До основних принципів інформатизації слід віднести: +– розвиток інфраструктури інформаційних технологій закладу ви- +щої освіти як окремої хмари з віртуалізацією не лише серверів, а й +клієнтів; + +489 +– розвиток інформаційного середовища на основі концепції інте- +грації ресурсів та автоматизації бізнес-процесів; +– постійне вдосконалення процесів, що реалізуються ІТ-службою; +– постійне вдосконалення використання ІТ на основі оцінки +ефективності їх застосування у закладі вищої освіти; +– фінансування інформаційних технологій визначається прийня- +тими стратегічними завданнями розвитку закладу вищої освіти; +– політика безпеки інформаційного середовища будується на +основі принципу розумної необхідності; +– розвиток процедур забезпечення якості корпоративних даних [7]. +Усі заходи, створені задля реалізації ІТ-стратегії, можна інтегру- +вати у єдиний проект створення єдиної електронної системи, ядром +якої є формування єдиної інформаційної системи закладу вищої осві- +ти. Процес формування єдиної інформаційної системи закладу вищої +освіти включає комплекс заходів із впровадження в усі сфери діяль- +ності закладу вищої освіти інформаційних технологій як сукупності +програмно-технічних засобів обчислювальної техніки, а також при- +йомів, способів та методів їх застосування під час виконання функцій +збирання, зберігання, обробки, передачі та використання інформації. +Можна виділити такі основні завдання, виконання яких спрямо- +ване на формування єдиної інформаційної системи закладу вищої +освіти: +– формування організаційної структури інформатизації; +– створення інформаційної інфраструктури закладу вищої освіти +та автоматизація її управління; +– інформатизація процесів управління закладом вищої освіти, зо- +крема фінансами; +– інформатизація навчального процесу; +– інформатизація наукових досліджень та проектів; +– підвищення рівня компетентності персоналу у сфері інформа- +ційних технологій [29]. +При створенні єдиної інформаційної системи закладу вищої осві- +ти слід забезпечувати розумний обсяг інновацій як у навчальній, так і +в управлінській діяльності. Створення та організація єдиної інформа- +ційної системи закладу вищої освіти — складне організаційне та тех- +нологічне завдання, що обумовлює доцільність поетапної розробки +системи: розв’язання задачі отримання на кожному етапі закінченого +продукту, який послідовно модифікуватиметься та нарощуватиметь- +ся від етапу до етапу. Взаємне ув’язування зазначених підсистем та + +490 +інтеграція даних досягається на основі організаційної, функціональ- +ної, технічної програмної та інформаційно-лінгвістичної сумісності. +Тільки на такій основі може бути забезпечене стійке функціонування +єдиної інформаційної системи вищої освіти. +Інформатизація вищої освіти в Україні є одним із пріоритетних +напрямків реформування вищої школи. На шляху інформатизації на- +вчального процесу важливим є створення, впровадження та розвиток +комп’ютерно орієнтованого освітнього середовища на основі нових +інформаційних технологій, систем, мереж та ресурсів. +Це — комплекс перетворень, пов’язаних із насиченням освітньої +системи інформаційною продукцією, інформаційними засобами, що +ґрунтуються на мікропроцесорній техніці, та новими інформаційни- +ми технологіями при всебічному використанні можливостей систем- +ного підходу як методологічної бази. +Ресурс системного підходу, інтегрованого застосуванням нових +інформаційних технологій у процесі професійної підготовки, дозво- +ляє організаторам та учасникам навчального процесу чітко усвідом- +лювати взаємозв’язок усіх компонентів освітньої системи та більш +ефективно реалізовувати основні її функції: організацію, керівни- +цтво, контроль. +СПИСОК ВИКОРИСТАНОЇ ЛІТЕРАТУРИ +1. 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Режим доступу: https://evansys.com/ articles/ +pedagogika-i-psikhologiya-nauchnye-prioritety-uchyenykh-sbornik- +nauchnykh-trudov-po-itoga +m-mezhdunar/sektsiya-6-teoriya-i-metodika- +professionalnogo-obrazovaniya/obrazovanie-na-protya zhenii-vsey-zhizni-ili- +pogovorim-o-nepreryvnom-professionalnom-obrazovanii/. Дата звернення: +груд. 6, 2021. +21. Лабуз Л. С., Мазаева Л. Н. Информационные технологии в высшем про- +фессиональном образовании: проблемы и перспективы. Концепт. 2016. +Т. 37. С. 90–95 [Електронний ресурс]. Режим доступу: http://e-koncept. +ru/2016/56791.htm. Дата звернення: груд. 6, 2021. +22. Гладуш В. А., Лисенко Г. І. Педагогіка вищої школи: теорія, практика, іс- +торія. Дніпро: Акцент, 2014 [Електронний ресурс]. Режим доступу: https:// +studbooks.net/70164/pedagogika/ +informatsionnye_tehnologii_obucheniya. +Дата звернення: груд. 6, 2021. +23. Вараксин Г. С. Ситемный подход к организации учебного процесса. ИКТ +в образовании. Пермь, 2021 [Електронний ресурс]. Режим доступу: https:// +www.ikt-school.com/. Дата звернення: груд. 6, 2021. +24. Левкин Г. Г., Колычев Н. М. Системный подход в организации деятель- +ности преподавателей вуза. Профессиональное образование в современном +мире. 2015. № 1(16). С. 77–89 [Електронний ресурс]. Режим доступу: +https://www.sibran.ru/upload/iblock/eb7/eb7f96c451a03cdf252aee81223cd61 +f.pdf. Дата звернення: груд. 6, 2021. +25. Хонин Г. А., Семченко В. В. Использование информационных техноло- +гий обучения в учебном процессе вуза. Профессиональное образование в +современном мире. 2014. № 3(14). С. 148–156 [Електронний ресурс]. Ре- +жим +доступу: +https://www.sibran.ru/upload/iblock/156/15684701862f643 +bc7dee584f03a92b3.pdf. Дата звернення: груд. 6, 2021. +26. Левкин Г. Г., Левкин Е. А. Инновационная модель образовательного про- +цесса в вузе. Киев: Наука и просвещение, 2011. +27. Симак Р. С., Левкин Г. Г. Организация обучения в вузе с помощью ин- +формационных технологий. Социальные технологии. 2012. № 4. С. 373– +377 [Електронний ресурс]. Режим доступу: http://files.informio.ru/files/ + +493 +main/documents/2016/06/Simak_R_S.-omgups.pdf. Дата звернення: груд. +6, 2021. +28. Сачанюк-Кавецька Н., Прозор О. Організація контролю навчальних +досягнень студентів за допомогою вітоматизаваних систем тестування. +Фізико-математична освіта. 2020. Ч. 1. № 3(25). С. 87–93 [Електрон- +ний ресурс]. Режим доступу: https://fmo-journal.fizmatsspu.sumy.ua/ +journals/2020-v3–25–1/2020_3–25-sachanuk-kavets-ka_fmo.pdf. Дата звер- +нення: груд. 6, 2021. +29. Польгун К. В. Організаційні засади створення електронного освітнього +середовища закладу вищої освіти на базі платформи MOODLE. Фізико- +математична освіта. 2020. Ч. 1. № 3(25). С. 68–73 [Електронний ресурс]. +Режим доступу: https://fmo-journal.fizmatsspu.sumy.ua/journals/2020-v3– +25–1/2020_3–25-Polhun_FMO. pdf. Дата звернення: груд. 6, 2021. + +494 +Розділ IV +ПРОЕКТУВАННЯ ІНФОРМАЦІЙНИХ СИСТЕМ +І ПРОГРАМНИХ КОМПЛЕКСІВ +UKRVECTŌRĒS ТА VHEALTH: +ІНТЕЛЕКТУАЛЬНІ СЕРВІСИ ПІДТРИМКИ ДИСТАНЦІЙНОЇ +МЕДИЧНОЇ РЕАБІЛІТАЦІЙНОЇ ДОПОМОГИ +Величко В. Ю., Малахов К. С. +Методологія реабілітаційних заходів в умовах пандемії має ряд суттєвих +особливостей, пов’язаних з непередбачуваністю і високою швидкістю виник- +нення проблем високої складності, обмеженістю спілкування між реабіліто- +логом і пацієнтом, необхідністю високої реактивності прийняття рішень +і їх відповідністю, масштабністю процесу і пов’язаною з нею необхідністю +використання масштабованих операційних засобів тощо. Одним з ефектив- +них рішень в наданні медичної реабілітаційної допомоги є дистанційна па- +цієнтцентрична реабілітація, яка потребує online-засобів теледіагностики, +телеметрії і втручання з орієнтацією на можливості пацієнта, розвинутої +Internet-взаємодії, інтелектуальних інформаційних технологій і сервісів, +ефективних методів когнітивної підтримки в системі «реабілітолог — па- +цієнт — мультидисциплінарна команда», статистичної обробки великих +об’ємів інформації тощо. Звідси поряд з традиційними засобами реабілітації +у складі системи Трансдисциплінарної інтелектуальної інформаційно-ана- +літичної системи супроводження процесів реабілітації при пандемії TISP +з’явилася Smart-система телемедичного супроводження реабілітаційних за- +ходів. В поєднанні з інтелектуальними дистанційними засобами біологічного +зворотного зв’язку і ефективними мініатюрними приладами теледіагности- +ки, телеметрії і відновлення такі системи мають великі перспективи, про +що свідчить також і світовий досвід. Мета дослідження полягала в розробці +формальної моделі, програмної реалізації та методологічних засад засто- +сування сервісів дистанційної пацієнтцентричної Smart-системи надання +медичної реабілітаційної допомоги пацієнтам при пандемії, зокрема нової +коронавірусної хвороби COVID-19. Світове сучасне та загальноприйняте ви- +значення поняття Телереабілітація або E-реабілітація — це комплекс реабі- +літаційних вправ і навчальних програм, які надаються пацієнту дистанцій- +но за допомогою телекомунікаційних комп’ютерних технологій переважно +на амбулаторному етапі лікування. Бурхливий розвиток телереабілітації у +світі та набуття цим напрямком медицини трансдисциплінарних зв’язків + +495 +з різноманітними предметними галузями, що виходять за рамки сучасної +парадигми E-здоров’я, призвів до появи найсучаснішого різновиду реабіліта- +ції — Гібридна Е-реабілітація. Цей різновид E-реабілітаціі складається з +ряду фундаментальних методів, підходів та технологій: телекомунікаційні +технології, телеметрія, вбудовані системи та мініатюрні «розумні» прилади +для носіння, біологічний зворотний зв’язок, віртуальні особисті помічники, +методи, технології та програмні застосунки на основі штучного інтелек- +ту для обробки великих баз даних. Розроблено формальну модель, програмну +реалізацію та методологічні засади застосування сервісів (UkrVectōrēs та +vHealth) дистанційної пацієнтцентричної Smart-системи надання медичної +реабілітаційної допомоги пацієнтам при пандемії, зокрема, нової коронаві- +русної хвороби COVID-19. +The methodology of rehabilitation measures in a pandemic has several signif- +icant features associated with the unpredictability and high rate of emergence of +problems of high complexity, limited communication between the therapist and the +patient, the need for high responsiveness of decision-making and their compliance, +the scale of the process and the associated need to use scalable operating tools, etc. +One of the most effective solutions in medical rehabilitation assistance is remote +patient/personal-centered rehabilitation. It requires online telediagnostic tools, +telemetry and interventions focused on the patient’s capabilities, developed In- +ternet interaction, intelligent information technologies, and services. Patient/per- +sonal-centered rehabilitation also needs effective methods in the “Physical ther- +apist — Patient — Multidisciplinary team” system, statistical processing of large +volumes of data, etc. Therefore, along with the traditional means of rehabilitation, +as part of the “Transdisciplinary intelligent information and analytical system for +the rehabilitation processes support in a pandemic (TISP)” the Smart-system for +remote support of rehabilitation activities and services appeared. Combined with +intelligent remote biofeedback devices and effective miniature telediagnostics, te- +lemetry and recovery devices, such systems hold great promise, as evidenced by +world experience as well. Objective of the research was to develop a formal model, +software implementation, and methodological foundations for the use of services +of a remote patient/personal-centered Smart-system for providing medical reha- +bilitation assistance to patients in a pandemic, in particular, the new coronavirus +disease COVID-19. The world modern and generally accepted definition of the +concept of Telerehabilitation or E-rehabilitation is a complex of rehabilitation ex- +ercises and training programs that are provided to the patient remotely using tele- +communication computer technologies, mainly at the outpatient stage of treatment. +The rapid development of telerehabilitation in the world and the acquisition by this +direction of medicine of transdisciplinary connections with various subject areas +that go beyond the modern paradigm of E-health, led to the emergence of the most +modern type of rehabilitation — Hybrid E-rehabilitation. This type of E-reha- +bilitation consists of a number of the following fundamental methods, approaches +and technologies: telecommunication technologies, telemetry, embedded systems + +496 +and miniature smart wearable devices, biofeedback, virtual personal assistants, +methods, technologies and software artificial intelligence applications for big data +processing. +The formal model, software implementation, and methodological foundations +for the use of services (UkrVectōrēs, vHealth) of a remote patient/personal-cen- +tered Smart-system for providing medical rehabilitation assistance to patients in +a pandemic, in particular, the new coronavirus disease COVID-19, have been de- +veloped. +Перелік скорочень +API — Application Programming Interface +CBOW — Continous bag of words +DWIM — Do What I Mean +PMI — Pointwise mutual information +SPA — Single-page application +SVD — Singular value decomposition +TISP — Трансдисциплінарна інтелектуальна інформаційно-аналі- +тична система супроводження процесів реабілітації при пандемії +БЗЗ — Біологічний зворотний зв’язок +БК — Біла книга з фізичної та реабілітаційної медицини в Європі +ЗПМ — Зростаючі пірамідальні мережі +МІС — медична інформаційна система +МКФ — Міжнародна класифікація функціонування, обмеження +життєдіяльності та здоров’я +НФДУ — Національний фонд досліджень України +ПЗ — Програмне забезпечення +ФРМ — Фізична і реабілітаційна медицина +ШІ — Штучний інтелект +1. Теоретичні засади методик мовного (дистрибутивно-семантично- +го) моделювання в математичній лінгвістиці. Сучасний етап розвитку +штучного інтелекту (ШІ) характеризують як вибух у сфері можливос- +тей та перспектив упровадження технологій та інструментів ШІ. Очі- +кується трансформація цілих галузей промисловості на основі цього +впровадження [1]. +Такі складні процеси не можуть базуватися тільки на розумінні +та застосуванні інструментів ШІ як засобів стимулювання інновацій +чи забезпечення збільшення прибутків. Потрібно розуміти також і +обмеження не лише технологічні, а й організаційні. Технології ШІ +та розроблені інструменти ґрунтуються на певних моделях, алгорит- +мах та їхніх програмних реалізаціях. Якщо результат роботи таких + +497 +інструментів — це певне передбачення, рекомендація чи рішення, +що впливає на суспільство, то потрібна додаткова інформація для +безпечного використання цих інструментів. Користувач повинен ро- +зуміти, на основі чого чи радше чому алгоритм дав такий результат, +які чинники і як вплинули на результат. На основі цього формуєть- +ся довіра до результатів, але потрібно подивитися всередину «чорної +скриньки» [2]. +Природна мова завжди була предметом досліджень в ШІ, а протя- +гом останніх років доволі успішно створювали технології, які забез- +печують опрацювання, автоматичне розуміння та ґенерацію тексту +[1]. Аналіз реального впровадження та використання цих технологій +у промисловості засвідчив, що їх застосовують насамперед для тек- +стової аналітики (81 %), аналітики соціальних мереж (46 %), а також +у створенні чат-ботів (англ. Chatbot) для взаємодії з клієнтами (40 %), +розумних помічників (23 %) та класифікації документів (30 %). Під +час використання технологій опрацювання природної мови по- +трібно розв’язувати проблеми побудови таксономій та виконання +тренувань у машинному навчанні, які необхідні для реалізації біль- +шості сучасних алгоритмів. Проблема у створенні систем на основі +машинного навчання полягає в необхідності забезпечити потрібний +обсяг даних для тренування та їхню якість, особливо коли йдеться +про навчання з учителем. Побудова таксономій вимагає встановлен- +ня ієрархічних взаємозв’язків між одиницями інформації. Залежно +від галузі, де така таксономія застосовується, взаємозв’язки можуть +змінюватися. +Спосіб представлення слова у вхідних даних та в моделях мови +все ще залишається важливим у більшості завдань опрацювання +природної мови. Донедавна в системах опрацювання природної +мови слова кодували рядками умовно довільних символів, а корисну +інформацію щодо подібності та відмінності між словами не завжди +використовували. +Векторні моделі відомі та їх використовують в опрацюванні +природної мови з 50-х років минулого століття. Розроблені протя- +гом останніх років алгоритми, методи та засоби побудови вектор- +них представлень — це, з наукової позиції, подальший розвиток +дистрибутивної семантики, а з позиції практичного застосування +інструмент, який використовують для розв’язання завдань видо- +бування іменованих сутностей, маркування семантичних ролей, +автоматичного реферування, встановлення взаємозв’язків між сло- + +498 +вами, у системах питання — відповідь тощо. Векторні моделі — це +вже загальноприйнятий метод як представлення одиниць мови, так +і обчислення семантичної подібності між ними [3]. Широке вико- +ристання векторних представлень для розв’язання завдань з опра- +цювання природної мови вимагає розуміння цих інструментів, їхніх +можливостей та обмежень. Вивченням теоретичних та практичних +засад векторного моделювання природної мови займається дослід- +ницька область — дистрибутивна семантика — це галузь матема- +тичної (або обчислювальної) лінгвістики, метою якої є кількісне +оцінювання семантичної подібності та категоризація мовознавчих +елементів на основі властивостей їх розподілу у великих вибірках +мовних даних. +1.1. Поняття векторного представлення — Word Embbedings. Век- +торне представлення, або подання/вкладання (англ. Word embedding +/ Distributed word represintation) — це техніка, яка розглядає слова як +вектори, відносна схожість між якими корелює з семантичною по- +дібністю. Воно є одним із найуспішніших прикладів застосування +навчання без учителя (англ. Unsupervised learning). Векторні представ- +лення — техніка для опрацювання природної мови, альтернативна до +традиційної, яка дозволяє відображати сутності (слова, словосполу- +чення, терміни) зі словника на вектори дійсних чисел в малому щодо +розміру словника просторі, а подібність між векторами корелює з се- +мантичною подібністю між сутностями [1]. +Значення сутностей, які трапляються (вживаються) в подібних +контекстах, мають тенденцію до подібності. Такий зміст має форму- +лювання (так звана дистрибутивна гіпотеза), яке запропонували у 50-х +роках минулого століття Зелліґ Саббеттай Гарріс (1954) та Джон Руперт +Фірт (1957), коли розвинулися дистрибутивні методи, в яких значення +сутності (в даному випадку сутністю є слово) обчислюється з розподі- +лу сутностей навколо нього. Сутність в такому разі представляється як +вектор (масив чисел), котрий обчислюється в певний спосіб [3]. +Словник слів за такого підходу — це не множина слів, які пред- +ставлені рядком символів із відповідним індексом, а множина векто- +рів у просторі. Додавання нового слова в такий словник — це не про- +сто додавання нового рядка, а складніший процес; звідси походить +термін Word embedding — вбудовування (вкладання) сутності (слова) +у векторний простір. Окреме слово проходить процес відображення з +власного багатовимірного простору його контекстів у векторний про- +стір малого розміру. + +499 +У найпростішому випадку дистрибутивну модель значення сло- +ва, або просто вектор слова, можна побудувати на основі того, як +часто воно трапляється разом з іншими словами. Зручним спосо- +бом представлення такої інформації є матриця (англ. Co-occurrence +matrix). Така матриця матиме однакову кількість рядків і стовпців. У +комірках матриці будуть числа, які визначають, скільки разів слово, +якому відповідає рядок матриці, зустрічається разом зі словом, яко- +му відповідає стовпець матриці, в корпусі текстів. Числові значення +обчислюють на основі оброблення корпусу текстів. Можна пораху- +вати, скільки разів слова зустрічаються разом у документі чи тексті +або його частині (параграф, абзац), але переважно використовують +контекстне вікно певного розміру. Наприклад, в таблиці 1 зображено +контекстне вікно для п’яти слів із фраґмента корпусу проблеми по- +етики творчого доробку Олеся Гончара. Розмір цього контекстного +вікна становить 11 слів (центральне слово та по п’ять слів перед та +після нього). +Таблиця 1 +Контекстне вікно сутностей (слів) +Не можу ж я забути про +товариша +по роботі, в значній мірі вчителя +не подумай, що гумор і +собрата +по стремлінню +Посідаю посаду +редактора +групової стінгазети молодий +журналіст +В одній групі зі мною Столяренко +пам’ятаєш, торік з комуніста баба +приїжджала +Багато пройшло +часу +відтоді як я тобі послав листа +В таблиці 2 подано відповідний фраґмент матриці, яка представ- +ляє спільне вживання слів у корпусі проблеми поетики творчого до- +робку Олеся Гончара. +Таблиця 2 +Фраґмент матриці, яка представляє спільне вживання сутностей (слів) +у корпусі текстів +... +собрата +... +посаду +журналіст +Столяренко +... +товариша +3 +1 +2 +3 +собрата +0 +1 +1 +2 +редактора +1 +3 +3 +2 +Столяренко +2 +2 +0 +0 +часу +1 +0 +0 +1 + +500 +Фраґмент матриці демонструє певну подібність між словами «со- +брата» та «товариша», оскільки слово «Столяренко» трапляється в +контекстних вікнах цих слів. Особливу увагу потрібно звернути на те, +що більшість значень у цьому фраґменті — нулі й ця тенденція збері- +гається для всієї матриці. Отже, довжина вектора для кожного слова +буде дорівнювати розміру словника корпусу текстів і більшість еле- +ментів цього вектора будуть нулями. У фраґменті корпусу проблеми +поетики творчого доробку Олеся Гончара розмір словника становить +15 000 сутностей — слів, а якщо брати національні корпуси текстів, то +це значення збільшиться до десятків мільйонів. На практиці такі век- +тори використовувати складно не тільки через їхню розрідженість, а +й через те, що абсолютні значення частоти є не надто інформатив- +ною мірою спільного вживання слів [3]. На практиці використовують +міру на основі поточкової взаємної інформації (англ. Pointwise mutual +information, PMI) або позитивної PMI (англ. Positive PPMI) та їхніх ва- +ріантів, що дозволяє записати в комірки матриці значення, які вка- +зують, як часто два слова зустрічаються разом порівняно з тим, коли +їх можна побачити незалежно одне від одного. Побудовані векторні +представлення слів дозволяють оцінити їхню подібність на основі зі- +ставлення їхніх векторів. Мірі подібності векторів відповідає косинус +кута між векторами, і ця міра відома як косинусна подібність (англ. +Cosine similarity). На рисунку 1 наведено вектори для слів «журна- +ліст» та «собрат», та позначено кут між ними. Що менший кут між +векторами, то більше значення має косинус цього кута, і слова, яким +відповідають ці вектори, вважають більш подібними. Косинусна по- +дібність може набувати значення в діапазоні від –1 до 1: якщо зна- +чення дорівнює –1, то вектори протилежні; 1 — вектори збігаються +(повна ідентичність контекстів); 0 — вектори ортогональні (відсутні +схожі контексти). Відомі та використовуються й інші міри оцінки по- +дібності, але міра на основі косинуса кута між векторами набула най- +більшого поширення. +Значний розмір векторів та їхня розрідженість обмежують їхнє +практичне використання. Для зменшення розмірності векторів і +кількості нульових елементів у векторі, тобто для ущільнення векто- +ра, розроблені окремі групи методів. Класичний метод, який вико- +ристовують для зменшення розмірності векторів — це сингулярний +розклад матриці (англ. Singular value decomposition, SVD). Застосуван- +ня цього методу дозволяє зменшити розмір векторів до значень від +500 до 5000, але цей метод потребує виконання значної кількості до- + +501 +даткових обчислень, і для деяких завдань обсяг обчислень стає спів- +мірний із використанням повної PPMI матриці [3]. + +Рис. 1. Представлення векторів слів у двовимірному просторі +Вектори слів, які одержані в такий спосіб, представляють смис- +лову та синтаксичну інформацію, але при цьому лишається багато +проблем. Зокрема такі: значний розмір матриці ( +6 +6 +10 +10 +> +× +) та її роз- +рідженість; складність внесення змін (додавання нових слів призво- +дить до збільшення розміру матриці та повторного обчислення її еле- +ментів); висока обчислювальна вартість виконання SVD. +Одним з головних обмежень використання слів (векторних моде- +лей слів у цілому) є те, що слова з кількома значеннями об’єднуються +в єдине представлення (єдиний вектор в семантичному просторі). +Іншими словами, багатозначність та омонімія не обробляються на- +лежним чином. Наприклад, в реченні «The club I tried yesterday was +great!» не ясно, який сенс має термін «club»: «багатошаровий бутер- +брод», «бейсбольний клуб», «молитовня», «ключка для гри в гольф», +чи будь-який інший сенс, який може мати слово «club». Необхідність +розміщення декількох сенсів на слово в різних векторах (багатосенсо- +ві вкладення, англ. Multi-sense embeddings) стале мотивацією для роз- +ділення односенсових вкладень на багатосенсові. +1.2. Методика та засіб мовного моделювання Word2vec. Альтерна- +тивний підхід, який останніми роками бурхливо розвивається, перед- +бачає використання нейронних мереж для моделювання природної +мови. Модель мови на основі нейронної мережі дозволяє замість об- +числення та зберігання величезних обсягів даних передбачати сут- +ності — слова контексту для заданого слова і в процесі прогнозуван- +ня одержувати щільні вектори слів. Word2vec — це найбільш відома + +peakTop +3 +2 +XypHanicT +co6paT +2 +3 +4 +5 TOBapWW502 +й популярна технологія (набір методик та алгоритмів), що її побу- +дував на основі такого підходу Томаш Міколов 2013 року та описав +тео ретичну і практичну частини у [4; 5]. Рисунок 2 ілюструє основну +ідею Word2vec. Дано корпус текстів значного обсягу, і кожне слово зі +словника цього корпусу представлене як вектор. Під час перегляду +всіх текстів корпусу для кожної з позицій слова в реченні розгляда- +ють центральне слово (поточна позиція) та слово контексту. На осно- +ві подібності між векторами центрального слова та слова контексту +обчислюють імовірність слова контексту для заданого центрального +слова. Так само за заданими словами контексту обчислюють імовір- +ність центрального слова. Основним завданням є підбір для слів та- +ких векторних представлень, які максимізують ці ймовірності. + +Рис. 2. Схема опрацювання корпусу текстів у Word2vec +Потрібно зауважити, що приймаються такі припущення: тексти +в корпусі незалежні між собою; кожне слово залежить тільки від слів +свого контексту; слова контексту незалежні одне від одного. Остан- +нє припущення вважають недоліком технології Word2vec, оскільки не +розглядаються відмінності в імовірності слова, якщо воно трапляються +перед центральним словом і якщо це слово після центрального слова. +Прогнозування відбувається з використанням нейронної мережі. +Здійснюється тренування простої нейронної мережі прямого поши- +рення (англ. Feedforward Neural Networks) з одним прихованим шаром, +але насправді мережу використовують з іншою метою. Метою трену- +вання є отримання вагових коефіцієнтів прихованого шару, і ці кое- +фіцієнти — це і є вектори слів. +У Word2vec реалізовано описаний вище підхід за допомогою мо- +делей CBOW (англ. Continous bag of words, CBOW) та skip-gram [4; 6]. +Skip-gram модель дозволяє отримати два окремі вектори для кож- +ного слова: вектор для слова, як центрального слова контекстного вік- +на та вектор для цього самого слова, як слова контексту. Ці вектори +формують дві матриці: матрицю слів та матрицю контекстів, які ви- + +KOpIIyC TeKCTiB (KOHTeKCTHe BiKHO = 5) +Hap cJiB +JIHCTa +TBOTO +olepKaB +TpariyHMM + 3BiTOM JIMCTa, TBOrO; JIИCTa, OepKaB +JIИCTa +TBOTO +oepxaB +TpariyHMM +3BiTOM TBOrO, JIicTa; TBOrO, OⅡepKaB; TBOrO, 3 +OepKaB, JIMcTa; oepKaB, TBoro; oIepKaB, 3; +JIИCTa +TBOTO +epKaB +TpariyHMM +3BiTOM +3 +oepKaB, TpariyHMM +JIHCTa +TBOTO +oepKaB +3 +TpariHMM +3BiTOM +3, JIHCTa; 3, JIHCTa; 3, TpariYHИM; 3, 3BiTOM503 +користовують для розв’язання завдання прогнозування. Кожен рядок +матриці слів — це вектор для слова зі словника слів корпусу текстів, а +в матриці слів контексту вектором для цього ж слова буде відповідний +стовпчик. За послідовного перегляду слів корпусу для кожного зі слів +модель skip-gram дозволяє передбачити всі слова контекстного вікна, +в якому поточне слово є центральним. Кожен такий прогноз мож- +на розглядати як визначення ймовірності спільного вживання цих +двох слів. Обчислення цієї ймовірності полягає в пошуку скалярно- +го добутку двох векторів: вектора центрального слова і вектора слова +контексту. Що більше значення скалярного добутку між векторами, +то більш подібні вони між собою. Оскільки нормований скалярний +добуток між векторами — це косинус кута між векторами, то його й +використовують як міру подібності. Щоб зі скалярного добутку векто- +рів одержати ймовірність, використовують нормовану експоненційну +функцію softmax. Отже, модель skip-gram дозволяє обчислити ймовір- +ність появи разом двох слів за допомогою знаходження скалярного +добутку між векторами цих слів та перетворення його на ймовірність +за допомогою нормованої експоненційної функції [7]. Описаний під- +хід має великий недолік: функція softmax потребує обчислення ска- +лярного добутку вектора кожного слова зі словника зі всіма вектора- +ми інших слів словника. За використання корпусів належного обсягу +зробити це безпосередньо практично неможливо. Модель CBOW, на +відміну від skip-gram, дозволяє передбачити поточне центральне слово +контекстного вікна на основі слів, які його оточують. +Вектори слів і контекстів формують за допомогою навчання без +вчителя через максимізацію подібності між вектором поточного слова +і векторами його сусідів та мінімізацію подібності з векторами інших +слів. Для розв’язання завдання прогнозування, яке було розгляну- +то вище, ймовірність слова обчислюється як відношення скалярно- +го добутку між вектором слова і вектором слова контексту до суми +скалярних добутків векторів усіх слів. Замість знаходження величез- +ної кількості скалярних добутків для обчислення знаменника в skip- +gram використовують варіант skip-gram з неґативною вибіркою (англ. +Negative sampling), в якому знаменник обчислюється наближено [8]. +На етапі тренування під час перегляду слів з корпусу для кожно- +го слова вибирають слова з контексту як позитивні приклади, а для +кожного позитивного прикладу вибирають також певну кількість +прикладів шуму або неґативних прикладів — слів, які не є сусідами +поточного слова. Зокрема, якщо прийняти, що кількість неґативних + +504 +прикладів дорівнює двом, то для кожної з пар слово — слово контек- +сту буде добрано по два слова шуму для кожного зі слів контексту. На- +приклад, під час перегляду слів з наступного прикладу в таблиці 3 для +поточного слова «вклали» буде дібрано шість неґативних прикладів +за умови, що контекстне вікно буде містити ще два слова зліва і два +слова справа від цього слова. +Процес навчання починається з матрицями, значення в яких ви- +падково зґенеровані. Під час проходження по корпусу зміни значень +у цих матрицях повинні забезпечити отримання такого вектора цен- +трального слова, щоб його скалярний добуток з вектором кожного зі +слів контексту був якнайбільшим. Додатково до цього потрібно, щоб +вектори слів шуму мали малі значення скалярного добутку з вектором +поточного слова. У такий спосіб відбувається ґенерація векторів. Ре- +зультатом після тренування є вектори, які представляють семантичну +та синтаксичну інформацію про слова. +Таблиця 3 +Формування неґативної вибірки слів +Корпус +одержав я листа твого, прочитав і думав над ним +цілий вечір; мені пригадався такий факт +Словник +одержав, я, листа, твого, прочитав, думав, цілий, +вечір, мені, пригадався, факт +Пари слово — кон- +текст +одержав (листа, твого, я) — одержав, листа; одержав, +твого; одержав, я листа (твого, одержав, я, прочи- +тав) — твого, одержав; прочитав, листа; одержав, я; я, +прочитав +Неґативна вибірка +одержав, вечір; одержав, пригадався; твого, мені … +Перевага техніки word2vec полягає в тому, що вона забезпечує ви- +соку ефективність обчислень. Програмний код є у вільному доступі, +моделі швидко та ефективно тренуються, доступні вже готові вектор- +ні представлення слів для багатьох мов. +Відомі такі реалізації методів та алгоритмів для побудови вектор- +них представлень: +– Ориґінальна реалізація Word2vec; мова реалізації C; доступна +для завантаження за посиланням [5]; +– Medallia/Word2VecJava, мова реалізації Java; доступна для заван- +таження за посиланням [9]; +– Spark MLLib Word2Vec; мова реалізації Java, доступна для заван- +таження за посиланням [10]; + +505 +– Бібліотека Gensim Word2vec, FastText, мова реалізації Python, +доступна для завантаження за посиланням [11]; +– Google’s TensorFlow Word2vec; мова реалізації Python; доступна +для завантаження за посиланням [12]; +– Бібліотека FastText; мова реалізації С++, доступна для заванта- +ження за посиланням [13]. +1.3. Методика та засіб мовного моделювання fastText. Створена ла- +бораторією досліджень ШІ Фейсбук (англ. Facebook’s AI Research lab, +FAIR) бібліотека fastText — ще один серйозний крок у розвитку моде- +лей дистрибутивної семантики природної мови (для навчання вкла- +день слів та класифікації тексту). В її розробці взяв участь Томаш Мі- +колов, вже знайомий нам по Word2vec. Алгоритм fastText ґрунтується +на працях [14, 15]. Для векторизації слів використовуються одночас- +но алгоритм skip-gram, алгоритм неґативної вибірки Negative sampling +та алгоритм безперервного мішка CBOW. +До основної моделі Word2Vec додана модель так званих символь- +них n-грам. Кожне слово представляється композицією декількох +послідовностей символів певної довжини. Наприклад, слово they в +залежності від гіперпараметрів може складатися з th, he, ey, the, hey. +По суті, вектор слова — це сума всіх його n-грам. +Для отримання вектора слова для слова +tw в даному набо- +рі документів вводиться функція оцінки +( +) +, +t +t +s w w +. Вона обчис- +лює суму символів n-грам, помножених на навколишнє слово +{ +} +..., +2, +1, +1, +2,... +c +t +t +t +t +w +w +w +w +w +∈ +− +− ++ ++ + слова +tw . Кількість контекстних +слів +tw задається як довжина вікна виведення skip-gram. Skip-gram вер- +сія fastText розраховує умовну ймовірність [14] +( +) +( +) +( +) +, +, +1 +| +, +t +c +t +c +s w w +c +t +N +s w w +i +e +p w +w +e += += +∑ + +замінивши результат скалярного множення між +T +c +t +u v на ( +) +, +t +t +s w w +. Не- +хай G словник n-грам і +{ +} +1,..., +tG +G +⊂ + це масив символьних n-грам для +слова +tw . Тоді результат [14] ( +) +, +t +T +t +c +g +c +g G +s w w +z c +∈ += ∑ + визначається для кож- +ного контекстного слова +c +w . Замість унітарно-кодованого слова век- +тора набір символів n-грам прогнозує контекстне слово у fastText. Усі +вектори +gz де +t +g +G +∈ + є символьними вкладеннями n-грам слова +tw . +Їх набір будує представлення/вкладення слова +tv . Через те, що за- +гальний набір n-грам для великого корпусу дуже великий, хешована +версія символів n-грам використовується як вхідна інформація. + +506 +Точність fastText у завданнях обробки природної мови, таких як +семантичний аналіз або класифікація за тегами, одна з найвищих се- +ред найсучасніших методів. +1.4. Відмінності моделей fastText та Word2vec. Модель fastText є по- +дальшим розвитком технології Word2vec, яка також дозволяє будува- +ти векторні представлення. FastText ґрунтується на моделі skip-gram, +яка реалізована в Word2vec. Основна відмінність моделі fastText від +Word2vec полягає в тому, що в Word2vec кожне слово в корпусі розгля- +дають окремо, як атомарний об’єкт, для якого будується вектор. У мо- +делі fastText кожне слово розглядають як сукупність n-грам символів +цього слова. Отже, вектор слова будується через суму векторів n-грам, +з яких складається слово. Наприклад, при заданому мінімальному +розмірі n-грами 3 і найбільшому розмірі n-грами 5, вектор слова «то- +вариш» буде складатися з суми векторів таких n-грам: «^то», «тов», +«ова», «вар», «ари», «иш^», «^тов», «това», «овар», «вари», «риш^», +«^това», «товар», «овари», «ариш^». +Модель fastText дозволяє, на відміну від моделі Word2vec: +• Ґенерувати кращі вектори слів для слів, які рідко вживані. На- +віть якщо слово нечасто трапляється в корпусі, то n-грами, з яких +воно складається, можна побачити частіше як частини інших слів, +що дозволяє зґенерувати кращий вектор. Якщо вектор будується за +допомогою Word2vec, то рідковживане слово (наприклад, 5 випадків +уживання в корпусі) має меншу кількість сусідів порівняно зі словом, +що трапляється частіше. В останнього є більше слів у контекстному +вікні, а це забезпечує побудову кращого вектора для цього слова. +• Будувати вектори для слів, які не трапляються в корпусі. Вектор +для такого слова буде складатися з n-грам символів, які є частинами +інших слів, що наявні в корпусі. +• Будувати вектори слів для мов із багатою морфологією. Вико- +ристання n-грам дозволить отримати точніші вектори для всієї мор- +фологічної парадигми слова. +За умови використання моделі fastText велике значення має добір +параметрів, зокрема мінімального й максимального розміру n-грам, +бо це впливає на розмір корпусу. Оскільки побудова векторів слів від- +бувається за допомогою тренування на рівні n-грам, то збільшуються +витрати часу порівняно з Word2vec. +1.5. Застосування прогностичних моделей дистрибутивної семан- +тики. Сучасні векторні моделі дозволяють обчислити семантичну +подібність між словами, реченнями чи документами, і саме на цих + +507 +можливостях ґрунтується їхнє використання для розв’язання завдань +опрацювання природної мови. Прогностичні моделі дистрибутивної +семантики використовуються безпосередньо для вирішення широ- +кого кола завдань, пов’язаних з семантичним моделюванням текстів +природною мовою, а саме: +– виявлення семантичної близькості слів, словосполучень, тек- +стів; +– розпізнавання іменованих сутностей; +– морфологічний аналіз слів; +– автоматична класифікація/кластеризація слів, словосполучень, +текстів за ступенем їх семантичної близькості; +– автоматична генерація тезаурусів і двомовних словників; +– вирішення лексичної неоднозначності; +– розширення запитів за допомогою асоціативних зв’язків; +– визначення тематики тексту; +– класифікація/кластеризація текстових документів для інформа- +ційного пошуку; +– отримання знань з неструктурованих джерел (текстових доку- +ментів); +– автоматична побудова семантичних карт довільних предметних +областей; +– визначення тональності текстів та висловлювань; +– моделювання селекційних обмежень слів. +Також із використанням векторних представлень вирішують за- +вдання ґенерації текстів, машинного перекладу, виявлення парафраз, +моделювання текстів. +Серед останніх відомих застосувань векторних представлень по- +трібно відзначити роботи [16; 17], в яких векторні моделі використо- +вують для розв’язання завдань машинного перекладу. У роботах по- +казано, як можна побудувати перекладний (англ. Bilingual dictionary) +двомовний словник без використання паралельних корпусів текстів. +Такий словник будують через вирівнювання векторних просторів за +допомогою навчання без учителя. Для дванадцяти мовних пар розро- +блено словники досить високої якості, точність яких для окремих пар +становить понад 60 %. Також указано, що штучно отримані словники +успішно враховують багатозначність слів мовних пар. Векторні про- +стори вирівнюють за допомогою пошуку відображення між незалеж- +ними векторними моделями для двох мов. Схематично цей процес +автори роботи ілюструють так, як наведено на рисунку 3. + +508 + +Рис. 3. Схема вирівнювання векторних просторів + +(A) +(B) +(C) +(D) +cat +X +profondd +gatto +car +auto +cat +WX +WX +deep509 +Вирівнювання здійснюється між двома векторними просторами, +які побудовані на основі моделі fastText із використанням Вікіпедії, +як корпусу для тренування (A). Для побудови перекладних словників +використовують тільки 200000 векторів найчастотніших слів. Кожне +слово представлено на рисунку 3 точкою, а її розмір вказує на частоту +слова в корпусі. Далі здійснюють пошук матриці повороту W, яка по- +передньо вирівнює два простори (В). Здійснюють пошук залежності, +яка «притягує» слова з високою частотою вживання в корпусі, що до- +зволяє покращити вирівнювання (С). Знайдене відображення та до- +даткова метрика дає можливість здійснювати переклад слів (D). +Серед перекладних словників, які побудовані за допомогою век- +торних представлень, доступні також і українсько-англійський та +англо-український словники. Обсяг цих словників становить 40722 +та 47912 пар слів відповідно. Оскільки в такий спосіб перекладні +словники ще не укладали, то для оцінки їхньої якості потрібно про- +вести додаткові дослідження. Попередній аналіз було здійснено за +допомогою перевірки наявності слів з цих словників у словнику +проєкту ВЕСУМ — Великий електронний словник української мови +[18]. Встановлено, що 30,7 % (12512) слів українсько-англійсько- +го словника відсутні у словнику ВЕСУМ, а для англо-українського +словника ця частка збільшується до 48 % (19633). Такі результати +частково можна пояснити наявністю в українсько-англійському та +англо-українському словниках значної кількості власних назв, які +записані з малої літери. +2. Розробка мережевого засобу (Веб-сервісу) використання дис- +трибутивно-семантичних моделей векторного представлення сутностей +природної мови — UkrVectōrēs. Мережевий засіб UkrVectōrēs обчислює +семантичні відношення між сутностями української мови в рамках +обраної дистрибутивно-семантичної моделі векторного представлен- +ня сутностей. UkrVectōrēs — це інструмент дистрибутивного аналізу +природної мови — це метод дослідження природної мови, заснова- +ний на вивченні середовища (дистрибуції, розподілу) окремих сут- +ностей у тексті, та не використовує відомостей про повне лексичне +або граматичне значення цих сутностей. В загальному випадку дис- +трибутивний аналіз використовує, базується та досліджує сутності +природної мови, такі як слова або словосполучення. +В рамках даного методу до текстів природною мовою застосову- +ється впорядкований набір універсальних процедур, що дозволяє +виділити основні одиниці мови (фонеми, морфеми, слова, словоспо- + +510 +лучення), провести їх класифікацію та встановити відносини семан- +тичної схожості між ними. +2.1. Призначення та функції мережевого засобу UkrVectōrēs. Мере- +жевий засіб UkrVectōrēs (у вигляді веб-сервісу з API (англ. Application +programming interface, API)) — це інструмент, який дозволяє досліджу- +вати семантичні відношення між словами в рамках прогностичних +моделей дистрибутивної семантики, з використанням програмної +бібліотеки з відкритим вихідним кодом для обробки та математич- +ного моделювання природної мови gensim [11; 19–21] (яка включає +інтерфейс прикладного програмування для роботи з алгоритмами +Word2vec, fastText та інші). +Можна образно назвати Мережевий засіб UkrVectōrēs «семантич- +ним калькулятором». Користувач може вибрати одну або кілька з ре- +тельно підготовлених прогностичних моделей дистрибутивної семан- +тики (або використати свою модель векторного представлення для +слів української мови), навчених на різних корпусах текстів, зокрема +таких наборів даних (англ. Dataset): +– проблеми поетики творчого доробку Олеся Гончара; +– художня література; +– книга «Серце віддаю дітям» Василя Сухомлинського. +Мережевий засіб UkrVectōrēs охоплює такі елементи дистрибутив- +но-семантичного аналізу: +• обчислення семантичної схожості/близькості між парами слів у +рамках обраної прогностичної моделі дистрибутивної семантики; +• знаходження слова, найближчого до заданого (з можливістю філь- +трації за алфавітом і коефіцієнтом косинусної схожості/близькості) в +рамках обраної прогностичної моделі дистрибутивної семантики (об- +числення семантичних асоціатів). Коефіцієнт косинусної близькості +слів може приймати значення в проміжку [–1...1]. Якщо коефіцієнт +косинусної схожості/близькості сутностей — слів приймає значення в +проміжку [–1...0,5], — це свідчить про відсутність схожих контекстів в +наборі даних та найменшу семантичну близькість слів. Якщо коефіці- +єнт косинусної схожості/близькості сутностей — слів приймає значен- +ня в проміжку [0,5...1], — це свідчить про наявність схожих контекстів +у наборі даних та більшу семантичну близькість слів. Чим більше кое- +фіцієнт косинусної схожості/близькості наближається до 1, тим більша +семантична близькість слів та більше схожих контекстів в наборі даних; +• виконання над векторами слів алгебраїчних операцій (додаван- +ня, віднімання, пошук центру лексичного кластера і відстаней до + +511 +цього центру) в рамках обраної прогностичної моделі дистрибутивної +семантики; +• генерування семантичної карти (з використанням програмно- +го інструментарію з відкритим початковим кодом TensorFlow [12], а +саме — TensorBoard [22]) відношень між словами (це дозволяє вияв- +ляти семантичні кластери або тестувати гіпотези на таких кластерах); +• отримання вектора (у вигляді масиву чисел) та його візуалізація +для заданого слова в рамках обраної прогностичної моделі дистрибу- +тивної семантики; +• вибір зі списку та завантаження для подальшого використання +прогностичної моделі дистрибутивної семантики; +• використання інших прогностичних моделей дистрибутивної +семантики, які вільно поширюються, за допомоги налаштування +конфігураційного файлу. +2.2. Програмні залежності мережевого засобу UkrVectōrēs. +– Python 3.8.6 [23] — інтерпретатор та стандартні бібліотеки; +– gensim [11; 19–21] — програмна бібліотека з відкритим вихідним +кодом для передової обробки та математичного моделювання при- +родної мови; +– Flask [24] — мікрофреймворк для веб-додатків; +– Flask-CORS [25] — розширення Flask для обробки спільного +використання ресурсів з різних джерел (англ. Cross-Origin Resource +Sharing, CORS); +– uWSGI [26] — веб-сервер і сервер веб-додатків, спочатку реа- +лізований для запуску додатків Python через протокол WSGI (і його +бінарний варіант uwsgi); +– Pandas [27] — програмна бібліотека, написана для мови програ- +мування Python для маніпулювання даними та їхнього аналізу. Вона +зокрема пропонує структури даних та операції для маніпулювання +чисельними таблицями та часовими рядами; +– nginx [28] — вільний веб-сервер і проксі-сервер; +– Angular [29] — написаний на TypeScript front-end фреймворк з +відкритим кодом для розробки односторінкових застосунків (англ. +Single-page application, SPA). В програмній інженерії терміни front-end +та back-end розрізняють за принципом розділення відповідальнос- +ті між рівнем представлення та рівнем доступу до даних відповідно. +Front-end — це інтерфейс для взаємодії між користувачем і back-end. +Front-end та back-end можуть бути розподілені між однією або кілько- +ма системами. В програмній архітектурі може бути багато рівнів між + +512 +апаратним забезпеченням та кінцевим користувачем. Кожен з цих +рівнів може мати як front-end, так і back-end. Front — це абстракція, +спрощення базового компонента через надання користувачу зручно- +го інтерфейсу взаємодію з SPA. +2.3. Архітектурна організація мережевого засобу UkrVectōrēs +2.3.1. Опис прикладного програмного інтерфейсу веб-сервісів (back- +end API) мережевого засобу UkrVectōrēs. Розробнику доступні сервіси +через кінцеві точки API (англ. API endpoints), наведені в таблиці 4. +Таблиця 4 +Кінцеві точки API мережевого засобу UkrVectōrēs +Кінцева точка API +Сервіс +Метод http-запиту +S1 host [:port] +/api/word2vec/ +similarity +обчислення семантичної +схожості/близькості між +парами слів у рамках об- +раної дистрибутивно-се- +мантичної моделі +POST +S2 host [:port] +/api/word2vec/similar +обчислення семантичних +асоціатів для заданого +слова у рамках обраної +дистрибутивно-семантич- +ної моделі +POST +S3 host [:port] +/api/word2vec/center +обчислення центру лек- +сичного кластера слів у +рамках обраної дистрибу- +тивно-семантичної моделі +POST +S4 host [:port] +/api/models +визначення списку доступ- +них для використання дис- +трибутивно-семантичних +моделей +GET +S5 host [:port]/ +графічного інтерфейсу ко- +ристувача односторінково- +го застосунку UkrVectōrēs +GET +S1 — сервіс обчислення семантичної схожості/близькості між па- +рами слів у рамках обраної дистрибутивно-семантичної моделі. +Опис вхідних даних. +Вхідними даними має бути JSON-структура, яка містить текстові +поля word_1, word_2 та числове поле model. Повна JSON-схема вхід- +них даних сервісу обчислення семантичної схожості/близькості між +парами слів у рамках обраної дистрибутивно-семантичної моделі на- + +513 +ведена на рисунку 4. Використовується метод http-запиту POST. При- +клад POST запиту до кінцевої точки сервісу S1 на мові програмування +JavaScript з використанням Fetch API [30] наведено на рисунку 5. +Опис вихідних даних. +Вихідними даними є спеціалізована JSON-структура, яка містить +числове поле similarity, що відповідає коефіцієнту косинусної схожос- +ті/близькості. Повна JSON-схема вихідних даних сервісу обчислення +семантичної схожості/близькості між парами слів у рамках обраної +дистрибутивно-семантичної моделі наведена на рисунку 6. +S2 — сервіс обчислення семантичних асоціатів для заданого слова +в рамках обраної дистрибутивно-семантичної моделі. +Опис вхідних даних. +Вхідними даними має бути JSON-структура, яка містить текстове +поле word та числове поле model. Повна JSON-схема вхідних даних +сервісу обчислення семантичних асоціатів для заданого слова в рам- +ках обраної дистрибутивно-семантичної моделі наведена на рисун- +ку 7. Використовується метод http-запиту POST. Приклад POST за- +питу до кінцевої точки сервісу S2 на мові програмування JavaScript +з використанням Fetch API [30] наведено на рисунку 8. +Опис вихідних даних. +Вихідними даними є спеціалізована JSON-структура, яка містить +поле similar, котре представляє собою масив масивів (елементи маси- +ву містять текстове та числове поле) семантичних асоціатів та коефі- +цієнта косинусної схожості/близькості для заданого слова в рамках +обраної дистрибутивно-семантичної моделі. Повна JSON-схема ви- +хідних даних сервісу обчислення семантичних асоціатів для заданого +слова в рамках обраної дистрибутивно-семантичної моделі наведена +на рисунку 9. +S3 — сервіс обчислення центру лексичного кластера слів у рамках +обраної дистрибутивно-семантичної моделі. +Опис вхідних даних. +Вхідними даними має бути JSON-структура, яка містить поле +words (представляє собою масив текстових елементів) та числове поле +model. Повна JSON-схема вхідних даних сервісу обчислення центру +лексичного кластера слів у рамках обраної дистрибутивно-семан- +тичної моделі наведена на рисунку 10. Використовується метод http- +запиту POST. Приклад POST запиту до кінцевої точки сервісу S3 на +мові програмування JavaScript з використанням Fetch API [30] наве- +дено на рисунку 11. + +514 + +Рисунок 4 – JSON-схема вхідних даних сервісу обчислення семантичної схожості/близькості між +парами слів + + +{ + "$schema": "http://json-schema.org/draft-07/schema", + "$id": "http://example.com/example.json", + "type": "object", + "title": "The root schema", + "description": “Схема вхідних даних сервісу обчислення семантичної схожості/близькості між парами +слів +в рамках обраної дистрибутивно-семантичної моделі.", + "default": {}, + "examples": [ + { + "word_1": "Гончар", + "word_2": "письменик", + "model": 0 + } + ], + "required": [ + "word_1", + "word_2", + "model" + ], + "properties": { + "word_1": { + "$id": "#/properties/word_1", + "type": "string", + "title": "The word_1 schema", + "description": “Лема слова для порівняння в рамках обраної дистрибутивно-семантичної моделі.”, + "default": "", + "examples": [ + "Гончар" + ] + }, + "word_2": { + "$id": "#/properties/word_2", + "type": "string", + "title": "The word_2 schema", + "description": "Лема слова для порівняння в рамках обраної дистрибутивно-семантичної моделі.", + "default": "", + "examples": [ + "письменик" + ] + }, + "model": { + "$id": "#/properties/model", + "type": "integer", + "title": "The model schema", + "description": “Індекс обраної дистрибутивно-семантичної моделі. Індекс моделей міститься +в конфігураційному файлі config.models.simple.json”, + "default": 0, + "examples": [ + 0 + ] + } + }, + "additionalProperties": true +} + +Рис. 4. JSON-схема вхідних даних сервісу обчислення семантичної схожості/ +близькості між парами слів + +515 + +Рисунок 5 – Приклад POST-запиту до кінцевої точки сервісу S1 + +Рисунок 6 – JSON-схема вихідних даних сервісу обчислення семантичної схожості/близькості між +парами слів + + +var myHeaders = new Headers(); +myHeaders.append("Content-Type", "application/json"); + +var raw = JSON.stringify({"word_1": "Гончар", "word_2": "письменик", "model": 0}); + +var requestOptions = { + method: 'POST', + headers: myHeaders, + body: raw, + redirect: 'follow' +}; + +fetch("host[:port]/api/word2vec/similarity", requestOptions) + .then(response => response.text()) + .then(result => console.log(result)) + .catch(error => console.log('error', error)); +var formData = new FormData(); +var fileField = document.querySelector('input[type="file"]'); +{ + "$schema": "http://json-schema.org/draft-07/schema", + "$id": "http://example.com/example.json", + "type": "object", + "title": "The root schema", + "description": "Схема вихідних даних сервісу обчислення семантичної схожості/близькості між парами +слів +в рамках обраної дистрибутивно-семантичної моделі.", + "default": {}, + "examples": [ + { + "similarity": 0.939421488228 + } + ], + "required": [ + "similarity" + ], + "properties": { + "similarity": { + "$id": "#/properties/similarity", + "type": "number", + "title": "The similarity schema", + "description": “Коефіцієнт косинусної схожості/близькості між парами слів +в рамках обраної дистрибутивно-семантичної моделі.", + "default": 0.0, + "examples": [ + 0.939421488228 + ] + } + }, + "additionalProperties": true +} + +Рис. 5. Приклад POST-запиту до кінцевої точки сервісу S1 + +Рисунок 5 – Приклад POST-запиту до кінцевої точки сервісу S1 + +Рисунок 6 – JSON-схема вихідних даних сервісу обчислення семантичної схожості/близькості між +парами слів + + +var myHeaders = new Headers(); +myHeaders.append("Content-Type", "application/json"); + +var raw = JSON.stringify({"word_1": "Гончар", "word_2": "письменик", "model": 0}); + +var requestOptions = { + method: 'POST', + headers: myHeaders, + body: raw, + redirect: 'follow' +}; + +fetch("host[:port]/api/word2vec/similarity", requestOptions) + .then(response => response.text()) + .then(result => console.log(result)) + .catch(error => console.log('error', error)); +var formData = new FormData(); +var fileField = document.querySelector('input[type="file"]'); +{ + "$schema": "http://json-schema.org/draft-07/schema", + "$id": "http://example.com/example.json", + "type": "object", + "title": "The root schema", + "description": "Схема вихідних даних сервісу обчислення семантичної схожості/близькості між парами +слів +в рамках обраної дистрибутивно-семантичної моделі.", + "default": {}, + "examples": [ + { + "similarity": 0.939421488228 + } + ], + "required": [ + "similarity" + ], + "properties": { + "similarity": { + "$id": "#/properties/similarity", + "type": "number", + "title": "The similarity schema", + "description": “Коефіцієнт косинусної схожості/близькості між парами слів +в рамках обраної дистрибутивно-семантичної моделі.", + "default": 0.0, + "examples": [ + 0.939421488228 + ] + } + }, + "additionalProperties": true +} + +Рис. 6. JSON-схема вихідних даних сервісу обчислення семантичної схожос- +ті/близькості між парами слів + +516 + +Рисунок 7 – JSON-схема вхідних даних сервісу обчислення семантичних асоціатів для заданого слова + + +{ + "$schema": "http://json-schema.org/draft-07/schema", + "$id": "http://example.com/example.json", + "type": "object", + "title": "The root schema", + "description": “Схема вхідних сервісу обчислення семантичних асоціатів для заданого слова +в рамках обраної дистрибутивно-семантичної моделі.", + "default": {}, + "examples": [ + { + "word": "Гончар", + "model": 0 + } + ], + "required": [ + "word", + "model" + ], + "properties": { + "word": { + "$id": "#/properties/word", + "type": "string", + "title": "The word schema", + "description": "Лема слова для пошуку семантичних асоціатів +в рамках обраної дистрибутивно-семантичної моделі.", + "default": "", + "examples": [ + "Гончар" + ] + }, + "model": { + "$id": "#/properties/model", + "type": "integer", + "title": "The model schema", + "description": "Індекс обраної дистрибутивно-семантичної моделі. Індекс моделей міститься +в конфігураційному файлі config.models.simple.json.", + "default": 0, + "examples": [ + 0 + ] + } + }, + "additionalProperties": true +} + +Рис. 7. JSON-схема вхідних даних сервісу обчислення семантичних асоціатів +для заданого слова +Опис вихідних даних. +Вихідними даними є спеціалізована JSON-структура, яка містить +поле center, котре представляє собою масив масивів (елементи масиву +містять текстове та числове поле) семантичних асоціатів центру лек- +сичного кластера слів та коефіцієнта косинусної схожості/близькості +до центру лексичного кластера слів в рамках обраної дистрибутивно- +семантичної моделі. Повна JSON-схема вихідних даних сервісу об- +числення центру лексичного кластера слів в рамках обраної дистри- +бутивно-семантичної моделі наведена на рисунку 12. + +517 + +Рисунок 8 – Приклад POST-запиту до кінцевої точки сервісу S2 + + +var myHeaders = new Headers(); +myHeaders.append("Content-Type", "application/json"); + +var raw = JSON.stringify({"word": "Гончар", "model": 0}); + +var requestOptions = { + method: 'POST', + headers: myHeaders, + body: raw, + redirect: 'follow' +}; + +fetch("host[:port]/api/word2vec/similar", requestOptions) + .then(response => response.text()) + .then(result => console.log(result)) + .catch(error => console.log('error', error)); +var formData = new FormData(); +var fileField = document.querySelector('input[type="file"]'); + +Рис. 8. Приклад POST-запиту до кінцевої точки сервісу S2 +S4 — сервіс визначення списку доступних для використання дис- +трибутивно-семантичних моделей. +Опис вхідних даних. +Вхідними даними має бути звичайний пустий метод http-запиту +GET. Приклад GET запиту до кінцевої точки сервісу S4 на мові про- +грамування JavaScript з використанням Fetch API [30] наведено на +рисунку 13. +Опис вихідних даних. +Вихідними даними є спеціалізована JSON-структура. Повна JSON- +схема вихідних даних сервісу визначення списку доступних для вико- +ристання дистрибутивно-семантичних моделей наведена в додатку d1. +S5 — сервіс графічного інтерфейсу користувача односторінкового +застосунку UkrVectōrēs. За замовчуванням сервіс графічного інтер- +фейсу користувача мережевого засобу UkrVectōrēs доступний через +метод http-запиту GET на відповідний порт за відповідною адресою +хоста. Графічний інтерфейс користувача односторінкового застосун- +ку UkrVectōrēs розробляється окремо, використовуючи розроблені +сервіси через кінцеві точки API та в залежності від предметної області +і вирішуваних задач. +2.3.2. Графічний інтерфейс користувача односторінкового застосун- +ку UkrVectōrēs. Розглянемо методику роботи користувача з графічним +інтерфейсом односторінкового застосунку UkrVectōrēs, зокрема ви- +користання таких функцій (елементів) дистрибутивно-семантичного +аналізу текстів природної мови. + +518 + +Рисунок 9 – JSON-схема вихідних даних сервісу обчислення семантичних асоціатів для заданого +слова + + +{ + "$schema": "http://json-schema.org/draft-07/schema", "$id": "http://example.com/example.json", "type": +"object", "title": "The root schema", "description": “Схема вихідних даних сервісу обчислення семантичних +асоціатів для заданого слова в рамках обраної дистрибутивно-семантичної моделі.”, + "examples": [ + { + "similar": [ [ + "український", 0.9999048709869385 + ] ] } + ], + "required": [ + "similar" + ], + "properties": { + "similar": { + "$id": "#/properties/similar", "type": "array", "title": "The similar schema", "description": “Масив масивів +(елементи масиву містять текстове та числове поле) семантичних асоціатів та коефіцієнту косинусної +схожості/близькості для заданого слова в рамках обраної дистрибутивно-семантичної моделі.", + "examples": [ + [ [ + "український", 0.9999048709869385 + ] ] ], + "items": { + "$id": "#/properties/similar/items", + "anyOf": [ + { + "$id": "#/properties/similar/items/anyOf/0", + "type": "array", + "title": "The first anyOf schema", + "examples": [ + [ + "український", 0.9999048709869385 + ] + ], + "items": { + "$id": "#/properties/similar/items/anyOf/0/items", + "anyOf": [ + { + "$id": "#/properties/similar/items/anyOf/0/items/anyOf/0", + "type": "string", "title": "The first anyOf schema", + "description": “Лема семантичного асоціату для заданого слова в рамках обраної +дистрибутивно-семантичної моделі.”, + "examples": [ + "український" + ] + }, + { + "$id": "#/properties/similar/items/anyOf/0/items/anyOf/1", + "type": "number", "title": "The second anyOf schema", "description": "Коефіцієнт +косинусної схожості/близькості семантичного асоціату до заданого слова в рамках обраної дистрибутивно- +семантичної моделі.", + "examples": [ + 0.9999048709869385 + ] } ] } } ] } } }, +} + +Рис. 9. JSON-схема вихідних даних сервісу обчислення семантичних асоціа- +тів для заданого слова + +519 + +Рисунок 10 – JSON-схема вхідних даних обчислення центру лексичного кластера слів + + +{ + "$schema": "http://json-schema.org/draft-07/schema", + "$id": "http://example.com/example.json", + "type": "object", + "title": "The root schema", + "description": “Схема вхідних даних обчислення центру лексичного кластера лем слів в рамках обраної +дистрибутивно-семантичної моделі.", + "default": {}, + "examples": [ + { + "words": [ + "Олесь", + "Гончар", + "письменник" + ], + "model": 0 + } + ], + "required": [ + "words", + "model" + ], + "properties": { + "words": { + "$id": "#/properties/words", + "type": "array", + "title": "The words schema", + "description": “Масив текстових елементів (лем слів) для обчислення центру їх лексичного кластера +в рамках обраної дистрибутивно-семантичної моделі.”, + "default": [], + "examples": [ + [ + "Олесь", + "Гончар" + ] + ], + "model": { + "$id": "#/properties/model", + "type": "integer", + "title": "The model schema", + "description": "Індекс обраної дистрибутивно-семантичної моделі. Індекс моделей міститься в +конфігураційному файлі config.models.simple.json.", + "default": 0, + "examples": [ + 0 + ] } } +} + +Рис. 10. JSON-схема вхідних даних обчислення центру лексичного кластера +слів +Обчислення семантичних асоціатів для заданого слова в рамках об- +раної дистрибутивно-семантичної моделі. Для використання цієї +функції необхідно: +Запустити графічний інтерфейс односторінкового застосунку +UkrVectōrēs з використанням актуальної версії веб-браузера Google +Chrome, Mozilla Firefox або Microsoft Edge. Для цього в адрес- + +520 +ному рядку веб-браузера потрібно вписати посилання: https:// +ukrvectores.ai-service.ml/ (посилання може відрізнятися, це зале- +жить від особливостей розгортання мережевого засобу UkrVectōrēs) +та в головному меню обрати режим роботи «Семантичні асоціати» +(рисунок 14); + +Рисунок 11 – Приклад POST-запиту до кінцевої точки сервісу S3 + +Рисунок 13 – Приклад GET-запиту до кінцевої точки сервісу S4 + + +var myHeaders = new Headers(); +myHeaders.append("Content-Type", "application/json"); + +var raw = JSON.stringify({"words”: "Олесь", "Гончар", "письменник", "model": 0}); + +var requestOptions = { + method: 'POST', + headers: myHeaders, + body: raw, + redirect: 'follow' +}; + +fetch("host[:port]/api/word2vec/center”, requestOptions) + .then(response => response.text()) + .then(result => console.log(result)) + .catch(error => console.log('error', error)); +var formData = new FormData(); +var fileField = document.querySelector('input[type="file"]'); +var requestOptions = { + method: 'GET', + redirect: 'follow' +}; + +fetch("host[:port]/api/word2vec/models", requestOptions) + .then(response => response.text()) + .then(result => console.log(result)) + .catch(error => console.log('error', error)); + +Рис. 11. Приклад POST-запиту до кінцевої точки сервісу S3 + +Рисунок 11 – Приклад POST-запиту до кінцевої точки сервісу S3 + +Рисунок 13 – Приклад GET-запиту до кінцевої точки сервісу S4 + + +var myHeaders = new Headers(); +myHeaders.append("Content-Type", "application/json"); + +var raw = JSON.stringify({"words”: "Олесь", "Гончар", "письменник", "model": 0}); + +var requestOptions = { + method: 'POST', + headers: myHeaders, + body: raw, + redirect: 'follow' +}; + +fetch("host[:port]/api/word2vec/center”, requestOptions) + .then(response => response.text()) + .then(result => console.log(result)) + .catch(error => console.log('error', error)); +var formData = new FormData(); +var fileField = document.querySelector('input[type="file"]'); +var requestOptions = { + method: 'GET', + redirect: 'follow' +}; + +fetch("host[:port]/api/word2vec/models", requestOptions) + .then(response => response.text()) + .then(result => console.log(result)) + .catch(error => console.log('error', error)); + +Рис. 13. Приклад GET-запиту до кінцевої точки сервісу S4 +За допомогою випадаючого списку компонента select під назвою +«Моделі» (рисунок 15) обрати бажану дистрибутивно-семантичну +модель, в рамках якої буде проводитися обчислення семантичних +асоціатів (в загальному випадку, за замовчуванням, використовується +нейронна векторна модель представлення слів «Олесь Гончар» (з ви- +користанням набору даних — проблеми поетики творчого доробку +Олеся Гончара), алгоритм word2vec word embeddings розмірністю +500d. Сутність — слово, лематизовано, приведено до нижнього регі- +стру. Параметри word2vec: -size 500 -negative 5 -window 5 -threads 24 +-min_count 10 -iter 20); + +521 + +Рисунок 12 – JSON-схема вихідних даних сервісу обчислення центру лексичного кластера слів +{ + "$schema": "http://json-schema.org/draft-07/schema", + "$id": "http://example.com/example.json", + "type": "object", + "title": "The root schema", + "description": “Cхема вихідних даних сервісу обчислення центру лексичного кластера слів в рамках +обраної дистрибутивно-семантичної моделі.", + "default": {}, + "examples": [ + { + "center": [ + [ + "український", + 0.8037014603614807 + ] + ] + } + ], + "required": [ + "center" + ], + "properties": { + "center": { + "$id": "#/properties/center", + "type": "array", + "title": "The center schema", + "description": "Масив масивів (елементи масиву містять текстове та числове поле) семантичних +асоціатів центру лексичного кластера слів та коефіцієнту косинусної схожості/близькості до центру +лексичного кластера слів в рамках обраної дистрибутивно-семантичної моделі.", + "default": [], + "examples": [ + [ + [ + "український", + 0.8037014603614807 + ] + ] + ], + ] + } + } + ] + } + } + } +} + +Рис. 12. JSON-схема вихідних даних сервісу обчислення центру лексичного +кластера слів +В полі компонента intput під назвою «Введіть лему слова» вкажіть +бажану лему слова, до якого треба обчислити семантичні асоціати +(наприклад — Гончар, як наведено на рисунку 14), та натисніть клаві- +шу «Enter» або кнопку «Обчислити»; + +522 + +Рис. 14. Графічний інтерфейс односторінкового застосунку UkrVectōrēs (режим роботи «Семантичні асоціати») + +.. +UkrVectores ++× +8 +C仓 +①178.128.245.158:7777/processing/terms?model=0 +☆ +三 +Moneni: +CeMaHTWYHi acouiaT +LeHTp neKcMyHoro KnacTepa +CeMaHTWYHa 6nW3bkicTb +CeMaHTWyHa KapTa +Npo npoekT +honchar.lowercased.lemmatized.word2vec.FINAL.500dv +O6YMCneHHA CeMaHTWYHMX acOuiaTiB AA OAHOcniBHMX CyTHOCTei +BukopwcToByeTbcAHeipoHHaBekTopHaMoneJbpeAcTaBneHHAcniBOnecbToHyap》(3BWkopwcTaHHAMHa6opyAaHMx-npo6neMMnoeTWKWTBopyoroAopo6kyOnecA +FoHyapa),anropWTM word2vec word embeddings po3MipHicTIo 50Od.CyTHicTb-cnoBo,JeMaTM3oBaHo,npwBeAeHo o HMHboro perwcTpy.lapaMeTpM word2vec: -size500 +-negative 5 -window 5 -threads 24 -min_count 10 -iter 20. +BBeaiTb JeMy choBa +ToHyap +Filter +CeMaHTW4HiacouiaTW +CyTHicTb +KocMHycHa6nM3bKicTb +yKpaiHCbKwi +0.9999048709869385 +NMCbMeHHMK +0.9999011158943176 +TeKCT +0.9999009370803833 +XyAOKHiN +0.9999009370803833 +KHWra +0.9998990297317505 +0.9998986721038818 +UkrVectores, ykpaiHa 2020523 + +Рис. 15. Графічний інтерфейс односторінкового застосунку UkrVectōrēs (режим роботи «Семантичні асоціати», ком- +понент select під назвою «Моделі») + +.. +UkrVectores ++× +8 +①178.128.245.158:7777/processing/terms?model=0 +☆ +三 +Moneni: +CeMaHTWYHi acouiaTM +LeHTp neKcWyHoro KacTepa +CeMaHTWYHa 6nW3bkicTb +CeMaHTWyHa KapTa +Npo npoekT +honchar.lowercased.lemmatized.word2vec.FINAL.50od +fiction.lowercased.lemmatized.word2vec.300d +O6YMCeHHACeMaHTMYHMXaCOLiaTiBAJAOAHOCniBHM +BukopwcToByeTbcAHeipoHHaBekTopHaMoneJbpeAcTaBneHHAcniBOnecbToHyap》(3BWkopwcTaHHAMHa6opyAaHMx-npo6neMMnoeTWKWTBopyoroAopo6kyOnecA +FoHyapa),ajropWTM word2vec word embeddingspo3MipHicTio500d.CyTHicTb-cnoBo,neMaTW3oBaHo,npwBeAeHoo HM>KHboro perwcTpy.apaMeTpw word2vec: -size 500 +-negative 5 -window 5 -threads 24 -min_count 10 -iter 20. +BBeaiTb JeMy choBa +ToHyap +Filter +CeMaHTW4HiacouiaTW +CyTHicTb +KocMHycHa6nM3bKicTb +yKpaiHCbKwi +0.9999048709869385 +NMCbMeHHMK +0.9999011158943176 +TeKCT +0.9999009370803833 +XyAOKHiN +0.9999009370803833 +KHWra +0.9998990297317505 +0.9998986721038818 +UkrVectores, YkpaiHa 2020524 +1. На екрані (рисунок 14) відобразяться семантичні асоціати (за +замовчуванням відображаються перші 100 асоціатів за зменшенням +коефіцієнта косинусної схожості/близькості) для заданої леми сло- +ва «Гончар» в рамках обраної дистрибутивно-семантичної моделі +«Олесь Гончар»; +2. Використовуючи елемент «Сутність», користувач може обрати +відображення семантичних асоціатів за абеткою (рисунок 16); +3. Використовуючи елемент «Косинусна близькість», користувач +може обрати відображення семантичних асоціатів за коефіцієнтом +косинусної схожості/близькості (за збільшенням або за зменшенням) +(рисунок 17). +Обчислення семантичної схожості/близькості між парами слів у +рамках обраної дистрибутивно-семантичної моделі. Для використан- +ня цієї функції необхідно: +1. Запустити графічний інтерфейс односторінкового застосун- +ку UkrVectōrēs з використанням актуальної версії веб-браузера +Google Chrome, Mozilla Firefox або Microsoft Edge. Для цьо- +го в адресному рядку веб-браузера потрібно вписати посилання: +https://ukrvectores.ai-service.ml/ (посилання може відрізнятися, це за- +лежить від особливостей розгортання мережевого засобу UkrVectōrēs) +та в головному меню обрати режим роботи «Семантична близькість» +(рисунок 18); +2. За допомогою випадаючого списку компонента select під назвою +«Моделі» (рисунок 19) обрати бажану дистрибутивно-семантичну +модель, в рамках якої буде проводитися обчислення семантичної +схожості/близькості між парами слів — коефіцієнта косинусної схо- +жості/близькості (в загальному випадку, за замовчуванням, викорис- +товується нейронна векторна модель представлення слів «Олесь Гон- +чар» (з використанням набору даних — проблеми поетики творчого +доробку Олеся Гончара), алгоритм word2vec word embeddings розмір- +ністю 500d. Сутність — слово, лематизовано, приведено до нижнього +регістру. Параметри word2vec: -size 500 -negative 5 -window 5 -threads +24 -min_count 10 -iter 20); +3. В полях компонентів intput під назвами «Введіть лему слова +для порівняння» вкажіть бажані леми слів, між якими треба об- +числити семантичну схожість/близькість — коефіцієнта косинус- +ної схожості/близькості (наприклад — Гончар та письменник, як +наведено на рисунку 18) та натисніть клавішу «Enter» або кнопку +«Обчислити»; + +525 +4. На екрані (рисунок 18) відобразиться коефіцієнт косинусної +схожості/близькості для заданих лем слів «Гончар» та «письмен- +ник» в рамках обраної дистрибутивно-семантичної моделі «Олесь +Гончар»; +Обчислення центру лексичного кластера лем слів в рамках обраної +дистрибутивно-семантичної моделі. Для використання цієї функції +необхідно: +1. Запустити графічний інтерфейс односторінкового застосун- +ку UkrVectōrēs з використанням актуальної версії веб-браузера +Google Chrome, Mozilla Firefox або Microsoft Edge. Для цьо- +го в адресному рядку веб-браузера потрібно вписати посилання: +https://ukrvectores.ai-service.ml/ (посилання може відрізнятися, це за- +лежить від особливостей розгортання мережевого засобу UkrVectōrēs) +та в головному меню обрати режим роботи «Центр лексичного клас- +тера» (рисунок 20); +2. За допомогою випадаючого списку компонента select під назвою +«Моделі» (рисунок 21) обрати бажану дистрибутивно-семантичну +модель, в рамках якої буде проводитися обчислення центра лексич- +ного кластера (в загальному випадку, за замовчуванням, використо- +вується нейронна векторна модель представлення слів «Олесь Гон- +чар» (з використанням набору даних — проблеми поетики творчого +доробку Олеся Гончара), алгоритм word2vec word embeddings розмір- +ністю 500d. Сутність — слово, лематизовано, приведено до нижнього +регістру. Параметри word2vec: -size 500 -negative 5 -window 5 -threads +24 -min_count 10 -iter 20); +3. В полі компонента intput під назвою «Введіть леми слів через +пробіл» вкажіть бажані леми слів через пробіл, центр лексичного +кластера яких необхідно обчислити (наприклад — «Гончар письмен- +ник герой», як наведено на рисунку 20) та натисніть клавішу «Enter» +або кнопку «Обчислити»; +4. На екрані (рисунок 20) відобразяться леми слів, що формують +центр лексичного кластера заданих лем слів (за замовчуванням відо- +бражаються перші 100 асоціатів за зменшенням коефіцієнта косинус- +ної схожості/близькості до центру лексичного кластера) для заданої +леми слова «Гончар» в рамках обраної дистрибутивно-семантичної +моделі «Олесь Гончар»; +5. Використовуючи елемент «Сутність», користувач може обрати +відображення семантичних асоціатів, що формують центр лексично- +го кластера заданих лем слів, за абеткою (рисунок 22); + +526 + +Рис. 16. Графічний інтерфейс односторінкового застосунку UkrVectōrēs (режим роботи «Семантичні асоціати», еле- +мент «Сутність») + +UkrVectores +8 +①178.128.245.158:7777/processing/terms?model=0 +☆ +Moneni: +CeMaHTWYHi acouiaTM +LeHTp neKcWyHoro KnacTepa +CeMaHTWYHa 6nW3bkicTb +CeMaHTWyHa KapTa +Npo npoekT +honchar.lowercased.lemmatized.word2vec.FINAL.5oodv +O6YMCneHHA CeMaHTWYHMXacOuiaTiBAAOAHOcniBHMXCyTHOCTei +BukopwcToByeTbcAHeipoHHaBekTopHaMoneJbpeAcTaBneHHAcniBOnecboHyap》(3BWkopwcTaHHAMHa6opyAaHMX-npo6neMMnoeTWKMTBopyoroAopo6kyOnecA +FoHyapa),anropWTM word2vec word embeddings po3MipHicTIo 50Od.CyTHicTb -cnoBo,JeMaTM3oBaHo,npWBeAeHo ^o HMKHboro perwcTpy.lapaMeTpM word2vec: -size 500 +-negative 5 -window 5 -threads 24 -min_count 10 -iter 20. +BBeaiTb JeMy choBa +ToHyap +Filter +CeMaHTWyHiacouiaTW +CyTHicTb 个 +KocMHycHa 6nM3bKicTb +aBTOp +0.9998944997787476 +aKTyani3yBaTW +0.9998907446861267 +0.9998903274536133 +0.9998981952667236 +Bep6ani3oBaHwM +0.9998841285705566 +BECHAHMM +0.9998844861984253 +UkrVectores, YkpaiHa 2020527 + +Рис. 17. Графічний інтерфейс односторінкового застосунку UkrVectōrēs (режим роботи «Семантичні асоціати», еле- +мент «Косинусна близькість») + +... +UkrVectores ++ +8 +①178.128.245.158:7777/processing/terms?model=0 +☆ +三 +Moneni: +CeMaHTWYHi acouiaTM +LeHTp neKcWyHoro KnacTepa +CeMaHTWYHa 6nW3bkicTb +CeMaHTWyHa KapTa +Npo npoekT +honchar.lowercased.lemmatized.word2vec.FINAL.5oodv +O6YMCneHHA CeMaHTWYHMXacOuiaTiBAAOAHOcniBHMXCyTHOCTei +BukopwcToByeTbcAHeipoHHaBekTopHaMoneJbpeAcTaBneHHAcniBOnecboHyap》(3BWkopwcTaHHAMHa6opyAaHMX-npo6neMMnoeTWKMTBopyoroAopo6kyOnecA +FoHyapa),anropWTM word2vec word embeddings po3MipHicTIo 50Od.CyTHicTb -cnoBo,JeMaTW3oBaHo,npWBeAeHo ^o HMKHboro perwcTpy.lapaMeTpM word2vec: -size 500 +-negative 5 -window 5 -threads 24-min_count 10 -iter 20. +BBeaiTb JeMy choBa +ToHyap +Filter +CeMaHTW4HiacouiaTW +CyTHicTb +KocMHycHa6nM3bKicTb个 +cnpaB>KHiN +0.999883770942688 +Bep6aniaoBaHwi +0.9998841285705566 +KpaiHa +0.9998841285705566 +0.999884307384491 +OAHHMKOBM +0.999884307384491 +npocTopui +0.9998843669891357 +UkrVectores, ykpaiHa 2020528 + +Рис. 18. Графічний інтерфейс односторінкового застосунку UkrVectōrēs (режим роботи «Семантична близькість») + +UkrVectores +8 +C仓 +①178.128.245.158:7777/processing/similarity?model=0 +目☆ +三 +CeMaHTWyHa 6nW3bKicTb +Moneni: +CeMaHTWYHi acouiaTM +LeHTpneKcWyHoroKnacTepa +CeMaHTWyHa KapTa +Npo npoekT +honchar.lowercased.lemmatized.word2vec.FINAL.500dv +O6YMCeHHACeMaHTWYHOi6nM3bKOCTiOAHOCniBHMXCyTHOCTe +CepBic o6yWcnIOe ceMaHTMyHi BiAHOWeHHA MiK cnOBaMMyKpaiHCbKOlOMOBOlO BpaMKaxo6paHoiMoAeni. +3HayeHHA O np6nM3HO O3Hayae, Wo y LMX cniB HeMae cxOKMX KOHTeKcTiB iix 3HayeHHA He NOB's3aHi oAMH 3OAHMM.3HayeHHA 1, HaBnaKW, cBiAYMTb npo nOBHy +iAeHTW4HicTbix KOHTeKCTiB i, OTKe, npo 6nW3bKicTb 3HayeHHA. +FoHyapa),aropWTM word2vecwordembeddingspo3MipHicTo 500Od.CyTHicTb-cnoBo,neMaTW3oBaHo,npWBeAeHo^o HW>KHboropercTpy.apaMeTpW word2vec:-size 500 +-negative 5 -window 5 -threads 24 -min_count 10 -iter 20. +BBeAiTb JeMy hOBa AnS nopiBHRHHg +BBeAiTb NIeMy chOBa ANg nOopiBHAHHA +dehHoJ +WCbMeHHMK +KocMHycHa6nM3bkicTb: +0.9999011158943176 +UkrVectores, ykpaiHa 2020529 + +Рис. 19. Графічний інтерфейс односторінкового застосунку UkrVectōrēs (режим роботи «Семантична близькість», +компонент select під назвою «Моделі») + +UkrVectores +8 +C仓 +①178.128.245.158:7777/processing/similarity?model=0 +目☆ +三 +Moneni: +CeMaHTWHi acouiaTM +LeHTpneKcwyHoroKnacTepa +CeMaHTWyHa 6nW3bkicTb +CeMaHTWyHa KapTa +Npo npoekT +honchar.lowercased.lemmatized.word2vec.FINAL.500d +fiction.lowercased.lemmatized.word2vec.300d +O6YMCeHHACeMaHTMWYHOi6nM3bKOCTiOAHOCniBHWX +CepBic o6yWcnIOe ceMaHTMyHi BiAHOWeHHA MiK cnOBaMMyKpaiHCbKOlOMOBOlO BpaMKaxo6paHoiMoAeni. +KOcMHycHa 6M3bKicTb Mix BeKTOpaMM ABOx cniB i MOKe npwiMaT 3HayeHHA B npOMiKKy [-1... 1] (Ha npaKTWLi yacTO BMKOpWcTOByIOTbcA TinbKM 3HayeHHA BMWe O). +3HayeHHOnpW6nW3Ho o3Hayae,WoyMX cniBHeMae cxOKMXKOHTeKcTiB iix 3HayeHHA HenoB'3aHioAMH3OAHWM.3HayeHH1,HaBnaKW,cBinYWTbnpoOBHy +iAeHTW4HicTbix KOHTeKCTiB i, OTKe, npo 6nW3bKicTb 3HayeHHA. +FoHyapa),anropwTM word2vec word embeddings po3MipHicTio 500d.CyTHicTb-cJoBo,JeMaTW3oBaHo,npBeneHo o HM>kHboro perwcTpy.apaMeTpM word2vec:-size500 +-negative 5 -window 5 -threads 24 -min_count 10 -iter 20. +BBeAiTb JeMy chOBa Ang nopiBHSHHA +BBeAiTb NIeMy chOBa ANg nopiBHAHHA +dehHoJ +MCbMeHHMK +KocWHyCHa6nW3bKicTb: +0.9999011158943176 +UkrVectores, YkpaiHa 2020530 + +Рис. 20. Графічний інтерфейс односторінкового застосунку UkrVectōrēs (режим роботи «Центр лексичного кластера») + +... +UkrVectores +8 +C仓 +①178.128.245.158:7777/processing/term?model=0 +☆ +三 +Moneni: +CeMaHTWYHi acouiaTM +LeHTp neKcwYHoro KnacTepa +CeMaHTWYHa 6nW3bkicTb +CeMaHTWyHa KapTa +Npo npoekT +honchar.lowercased.lemmatized.word2vec.FINAL.50odv +O6yMcneHHALeHTpyJeKCWyHOroKJacTepaOAHOcniBHWXCyTHOcTei +CepBico6yMcnroeLeHTpJekcWyHoroKnacTepacniByKpaiHcbKoroMoBoroBpaMKaxo6paHoiMoqeni +BukopwcToByeTbcAHeipoHHaBekTopHaMoneJbpeAcTaBneHHAcniBOnecboHyap》(3BMkopwcTaHHAMHa6opyAaHMX-npo6neMMnoeTWKMTBopyoroAopo6kyOnecA +FoHyapa),anropWTM word2vec word embeddings po3MipHicTIo 50Od.CyTHicTb -cnoBo,JeMaTM3oBaHo,npWBeAeHo ^o HMKHboro perwcTpy.lapaMeTpM word2vec: -size 500 +-negative 5 -window 5 -threads 24 -min_count 10 -iter 20. +BBeaiTb neMH cnis 4epe3 npo6in +ToHyapnMCbMeHHMKrepoi +Filter +LeHTpJeKcW4HoroKnacTepa +CyTHicTb +KocMHycHa6nM3bKicTb +aBTop +0.9999430179595947 +XyAOKHin +0.9999415874481201 +0.9999398589134216 +yKpaiHCbKwi +0.9999394416809082 +KOHTeKCT +0.999937891960144 +CTaBaTW +0.9999368190765381 +UkrVectores, YkpaiHa 2020531 + +Рис. 21. Графічний інтерфейс односторінкового застосунку UkrVectōrēs (режим роботи «Центр лексичного класте- +ра», компонент select під назвою «Моделі») + +... +UkrVectorés +×+ +8 +①178.128.245.158:7777/processing/term?model=0 +☆ +三 +Moneni: +CeMaHTWYHi acouiaTM +LeHTp nekcwyHoro KnacTepa +CeMaHTWYHa 6nW3bkicTb +CeMaHTWyHa KapTa +Npo npoekT +honchar.lowercased.lemmatized.word2vec.FINAL.50od +fiction.lowercased.lemmatized.word2vec.300d +O6yMcneHHA LeHTpy JeKcWyHoro KnacTepa OAHocniBHI +CepBico6yMcnroeLeHTpJekcWyHoroKnacTepacniByKpaiHcbKoroMoBoroBpaMKaxo6paHoiMoqeni +BukopwcToByeTbcAHeipoHHaBekTopHaMoneJbpeAcTaBneHHAcniBOnecbToHyap》(3BWkopwcTaHHAMHa6opyAaHMx-npo6neMMnoeTWKWTBopyoroAopo6kyOnecA +FoHyapa),ajropWTM word2vec word embeddingspo3MipHicTio500d.CyTHicTb-cnoBo,neMaTW3oBaHo,npwBeAeHoo HM>KHboro perwcTpy.apaMeTpw word2vec: -size 500 +-negative 5 -window 5-threads 24-min_count 10 -iter 20. +BBeaiTb neMH cnis 4epe3 npo6in +ToHyap nMcbMeHHMKrepoi +Filter +LeHTpJeKcM4HoroKacTepa +CyTHicTb +KocMHycHa6nM3bKicTb +aBTOp +0.9999430179595947 +XYyAOKHiN +0.9999415874481201 +0.9999398589134216 +yKpaiHCbKwi +0.9999394416809082 +KOHTeKCT +0.999937891960144 +CTaBaTW +0.9999368190765381 +UkrVectores, YkpaiHa 2020532 + +Рис. 22. Графічний інтерфейс односторінкового застосунку UkrVectōrēs (режим роботи «Центр лексичного кластера» +елемент «Сутність») + +.. +UkrVectores ++× +8 +①178.128.245.158:7777/processing/term?model=0 +☆ +三 +CeMaHTWyHa 6nW3bkicTb +Moneni: +CeMaHTWYHi acouiaTM +LeHTpneKcHyHoroKnacTepa +CeMaHTWyHa KapTa +Npo npoekT +honchar.lowercased.lemmatized.word2vec.FINAL.5oodv +O6yMcneHHALeHTpyJeKCWyHOroKJacTepaOAHOcniBHWXCyTHOcTei +BukopwcToByeTbcAHeipoHHaBekTopHaMoneJbpeAcTaBneHHAcniBOnecboHyap》(3BWkopwcTaHHAMHa6opyAaHMX-npo6neMMnoeTWKMTBopyoroAopo6kyOnecA +FoHyapa),anropWTM word2vec word embeddings po3MipHicTIo 50Od.CyTHicTb -cnoBo,JeMaTW3oBaHo,npWBeAeHo ^o HMKHboro perwcTpy.lapaMeTpM word2vec: -size 500 +-negative 5 -window 5-threads 24-min_count 10 -iter 20. +BBeaiTb neMH cnis 4epe3 npo6in +ToHyapnMCbMeHHMKrepoi +Filter +LeHTpJekcwyHoroKnacTepa +CyTHicTb 个 +KocMHycHa 6nM3bKicTb +aBTOp +0.9999430179595947 +aKTyani3yBaTW +0.99992835521698 +0.9999275207519531 +BaMBMi +0.9999312162399292 +0.9999337196350098 +Bep6ani3oBaHwM +0.9999262094497681 +UkrVectores, YkpaiHa 2020533 + +Рис. 23. Графічний інтерфейс односторінкового застосунку UkrVectōrēs (режим роботи «Центр лексичного класте- +ра», елемент «Косинусна близькість») + +... +UkrVectores +8 +①178.128.245.158:7777/processing/term?model=0 +☆ +三 +CeMaHTWyHa 6nw3bkicTb +Moneni: +CeMaHTWYHi acouiaTM +LeHTp neKcwYHoro KnacTepa +CeMaHTWyHa KapTa +Npo npoekT +honchar.lowercased.lemmatized.word2vec.FINAL.50odv +O6yMcneHHALeHTpyJeKCWyHOroKJacTepaOAHOcniBHWXCyTHOcTei +BukopwcToByeTbcAHeipoHHaBekTopHaMoneJbpeAcTaBneHHAcniBOnecboHyap》(3BWkopwcTaHHAMHa6opyAaHMX-npo6neMMnoeTWKMTBopyoroAopo6kyOnecA +FoHyapa),anropWTM word2vec word embeddings po3MipHicTIo 50Od.CyTHicTb -cnoBo,JeMaTM3oBaHo,npWBeAeHo ^o HMKHboro perwcTpy.lapaMeTpM word2vec: -size 500 +-negative 5 -window 5 -threads 24 -min_count 10 -iter 20. +BBeaiTb neMH cnis 4epe3 npo6in +ToHyapnMCbMeHHMKrepoi +Filter +LeHTpJeKcW4HoroKnacTepa +CyTHicTb +KocMHycHa6nM3bKicTb +aBTop +0.9999430179595947 +XyAOKHin +0.9999415874481201 +0.9999398589134216 +yKpaiHCbKwi +0.9999394416809082 +KOHTeKCT +0.999937891960144 +CTaBaTW +0.9999368190765381 +UkrVectores, YkpaiHa 2020534 +6. Використовуючи елемент «Косинусна близькість», користувач +може обрати відображення семантичних асоціатів, що формують +центр лексичного кластера заданих лем слів, за коефіцієнтом ко- +синусної схожості/близькості (за збільшенням або за зменшенням) +(рисунок 23). +Генерування семантичних карт (з використанням програмного ін- +струментарію з відкритим початковим кодом TensorFlow [12], а саме — +TensorBoard [22]) відношень між словами в рамках обраної дистрибу- +тивно-семантичної моделі. Для використання цієї функції необхідно: +1. Запустити графічний інтерфейс односторінкового застосун- +ку UkrVectōrēs з використанням актуальної версії веб-браузера +Google Chrome, Mozilla Firefox або Microsoft Edge. Для цьо- +го в адресному рядку веб-браузера потрібно вписати посилання: +https://ukrvectores.ai-service.ml/ (посилання може відрізнятися, це за- +лежить від особливостей розгортання мережевого засобу UkrVectōrēs) +та в головному меню обрати режим роботи «Семантична карта» (ри- +сунок 24); +2. За допомогою випадаючого списку компонента select під назвою +«Моделі» (рисунок 24) обрати бажану дистрибутивно-семантичну +модель, в рамках якої буде проводитися обчислення центра лексич- +ного кластера (в загальному випадку, за замовчуванням, використо- +вується нейронна векторна модель представлення слів «Олесь Гон- +чар» (з використанням набору даних — проблеми поетики творчого +доробку Олеся Гончара), алгоритм word2vec word embeddings розмір- +ністю 500d. Сутність — слово, лематизовано, приведено до нижнього +регістру. Параметри word2vec: -size 500 -negative 5 -window 5 -threads +24 -min_count 10 -iter 20); +3. Документація користувача використання інструментарію візуа- +лізації TensorBoard доступна за посиланням [22]. Приклад візуалізації +семантичних асоціатів леми слова «Гончар» наведено на рисунку 25. +2.4. Методика тренування дистрибутивно-семантичної моделі век- +торного представлення сутностей (з використанням набору даних — +проблеми поетики творчого доробку Олеся Гончара). Загальна методика +тренування дистрибутивно-семантичних моделей векторного пред- +ставлення сутностей (слів) дана у вигляді структури конвеєра (англ. +Pipeline) обробки наборів даних (електронних текстових документів), +що містять тексти природною мовою (рисунок 26), та складається +з таких етапів та компонентів: +1. Технологія формування електронного корпусу текстів; + +535 + +Рис. 24. Графічний інтерфейс односторінкового застосунку UkrVectōrēs (режим роботи «Семантична карта») + +UkrVectores +8 +①178.128.245.158:7777/processing/semantic-map?model=0 +☆ +← +C +三 +Moneni: +CeMaHTWHi acouiaTM +LeHTp neKcWYHoro KnacTepa +CeMaHTW4Ha 6nW3bkicTb +CeMaHTWYHa KapTa +Npo npoekT +honchar.lowercased.lemmatized.word2vec.FINAL.500d +EmbeddingProjector +? +# +DATA +[4 +A +Points:808Dimension:500 +Show All +Isolate 63 +Clear +Data +points +selection +1 tensor found +? +by +Honchar small +Search +* +label +Edit by +label +Tag selection as +peo7 +Publish +Download +Label + Sphereize data ? +Checkpoint: +Metadata: +Odf06d4ef229467edc8cafc7e0b84c20/ra +6aec263aefe8caa3763610eeacb8e7c6e0 +honchar-small-metadata.tsv +UMAP +T-SNE +PCA +CUSTOM +Component #1 +Component#2 +Component #3 +PCAis approximate. +Total variance described: 5.0% +BOOKMARKS (0) +UkrVectores, ykpaiHa 2020536 + +Рис. 25. Графічний інтерфейс односторінкового застосунку UkrVectōrēs (режим роботи «Семантична карта», візуалі- +зація семантичних асоціатів леми слова «Гончар») + +... +UkrVectorés +8 +< +C仓 +178.128.245.158:7777/processing/semantic-map?model=0 +☆ +三 +CeMaHTWYHi acouiaTM +Moneni: +LeHTp eKcWyHoro KnacTepa +CeMaHTW4Ha 6nW3bkicTb +CeMaHTWyHa KapTa +Npo npoekT +honchar.lowercased.lemmatized.word2vec.FINAL.500d +EmbeddingProjector +? +# +DATA +A +I Points: 808|Dimension: 500|Selected 101 points +Show All +Isolate 101 +Clear +Data +points +selection +1 tensor found +? +by +Honchar small +couiokynbTypHMi +roH4ap +Search +label +Edit by +nHCbMeHHMK +label +Tag selection as +label roHyap +pea/iaM +neighbors? +1000 +PeKMM +peo7 +Publish +Download +Label +distance +COSINE +EUCLIDEAN + sphereize data ? +Ma/na +Checkpoint: +Nearest points in the original space: +-roHyap +BMCH +HOBOK +Metadata: +_cninKyBaHH +AHinpo +KMA +0.810 +Odf06d4ef229467edc8cafc7e0b84c20/ra +C/OB +6aec263aefe8caa3763610eeacb8e7c6e0: +cTala +0.810 +honchar-small-metadata.tsv +onecA +MaTepian +Ayx +XKynMHCbKMi +0.814 +KMi +PO3BMTOK +Becenka +0.815 +UMAP +T-SNE +PCA +CKnaAHMA +nepeAM +0.835 +CUSTOM +ranwy +BMXOAMTM +ynopaA +0.844 +niaroT KynbTypHMA +CycninbHMi +0.850 +KHMra +CycninbHHA +Y +ykpaiHCbKHA +nWiHKM +0.852 +Component#1 +Component#2 +niAroT +0.855 +WeByeHKa +0.857 +Component #3 +AHinpo +0.866 +BinbHWi +0.879 +PCA is approximate. +Total variance described: 5.0% +BOOKMARKS (0) +UkrVectores, YkpaiHa 2020537 +2. Технологія попередньої лінгвістичної обробки електронного +корпусу текстів; +3. Технологія тренування/навчання прогностичних моделей дис- +трибутивної семантики; +4. Технологія опрацювання прогностичних моделей дистрибутив- +ної семантики; +5. Джерела текстових документів та корпусів текстів (аналогові +тексти, мережа Інтернет, корпуси текстів Wikipedia, електронні ко- +лекції ТД, БД та ін.); +6. Електронний корпус текстів; +7. Анотований корпус текстів — лінгвістичний корпус текстів; +8. Прогностична модель дистрибутивної семантики — модель век- +торного представлення сутностей (слів). +7 +1 +2 +3 +8 +5 +6 +4 + +Рис. 26. Структура конвеєра узагальненої методики навчання прогностичних +моделей дистрибутивної семантики +Технологія формування електронного корпусу текстів (рисунок 26, +елемент 1). Електронний корпус текстів в загальному випадку зазви- +чай формується на основі (рисунок 26, елемент 5) загальнодоступного +і достатньо об’ємного корпусу текстів статей Wikipedia (актуальні вер- +сії корпусу текстів Wikipedia доступні на сервері Wikimedia, що збері- +гає повні архіви — дампи різних проектів Wikipedia foundation [31]), +з використанням програмної бібліотеки gensim [21] — програмне за- +безпечення з відкритим початковим кодом для векторного моделю- +вання та тематичного моделювання, а саме її модулю gensim.corpora. +wikicorpus (дозволяє побудувати електронний корпус текстів з дампів +бази даних Wikipedia або інших MediaWiki ресурсів). Результатом за- +стосування технології формування електронного корпусу текстів є — +електронний корпус текстів (рисунок 26, елемент 6) представлений в +текстовому форматі. + +538 +Технологія попередньої лінгвістичної обробки електронного корпусу +текстів (рисунок 26, елемент 2). Конвеєр попередньої лінгвістичної +обробки електронного корпусу текстів складається з таких компо- +нентів: +– Лексичний аналіз (елементи лексичного аналізу) — токені- +зація (англ. Tokenizing) — в загальному випадку це процес пере- +творення послідовності символів у послідовність токенів: деком- +позиція тексту в послідовність речень та декомпозиція речень в +послідовність токенів (заздалегідь визначеної категорії) — слів +(категорія — слово, словосполучення, термін), знаків пунктуації, +пробілів тощо. +– Граматичний аналіз (елементи граматичного аналізу) — розміт- +ка тексту частинами мови (англ. POS tagging, Part-of-speech tagging) — +в загальному випадку це процес присвоєння синтаксичної категорії +кожному з токенів. +– Морфологічний аналіз (елементи морфологічного аналізу) — +в загальному випадку це процес лематизації — представлення слів +у початковій словниковій формі. Лематизація значно скоротить +словник і збільшить зв’язність текстів при побудові векторного +представлення слів. +– Синтаксичний аналіз (елементи синтаксичного аналізу) — пар- +синг та чанкінг (англ. Shallow parsing, англ. Chunking) — в загальному +випадку це процес аналізу речень, який спочатку визначає їх складові +частини (іменники, дієслова, прикметники тощо), а потім зв’язує їх +з одиницями вищого порядку, які мають дискретні граматичні зна- +чення (іменні групи або фрази, групи дієслів тощо). +Всі етапи конвеєра попередньої лінгвістичної обробки електрон- +ного корпусу текстів, зокрема українською мовою, виконуються за +допомоги вільного програмного інструментарію обробки природної +мови — LanguageTool API NLP UK [32] та проєктів відкритої спіль- +ноти фахівців у галузі комп’ютерної обробки текстів (програмістів, +лінгвістів, дослідників) — lang-uk [33]. +Результатом застосування технології попередньої лінгвістичної +обробки електронного корпусу текстів є анотований корпус текстів — +лінгвістичний корпус текстів (рисунок 26, елемент 7), представлений +у текстовому форматі. +Технологія тренування/навчання прогностичних моделей дистри- +бутивної семантики. Найпоширенішим програмним інструментом/ +технологією, що використовується для навчання прогностичних мо- + +539 +делей дистрибутивної семантики — векторного представлення слів, +є — word2vec. Бібліотека gensim надає досить багато засобів для ефек- +тивного використання та дослідження векторних представлень слів, +в тому числі і word2vec. +Результати тренування моделей визначають якість векторних +представлень і залежать від параметрів тренування, які може зада- +вати користувач. До таких основних параметрів належать: власне +корпус текстів; алгоритм тренування skip-gram чи CBOW; розмір век- +торів; максимальний розмір контекстного вікна; мінімальна частота +слова, яке буде враховано; параметр для зменшення впливу високо- +частотних слів; модель для тренування — ієрархічний softmax (англ. +Hierarchical softmax) або неґативні вибірки (англ. Negative sampling); +кількість неґативних прикладів; кількість ітерацій (англ. Epochs) на- +вчання; кількість виділених потоків для навчання. +Результатом застосування технології тренування/навчання про- +гностичних моделей дистрибутивної семантики є — дистрибутивно- +семантична модель представлення сутностей (рисунок 26, елемент 8). +Для мережевого засобу UkrVectōrēs було розроблено (навчено) де- +кілька прогностичних моделей дистрибутивної семантики, зокрема +модель — «Олесь Гончар», з використанням набору даних невеликого +(обмеженого) обсягу — «проблеми поетики творчого доробку Олеся +Гончара». Початковий код програмного інструментарію навчання +прогностичних моделей дистрибутивної семантики (програмна бі- +бліотека gensim, алгоритм word2vec), зокрема моделі «Олесь Гончар» +наведено в додатку d2. Відмінною рисою навчання дистрибутивно- +семантичних моделей на текстових наборах даних невеликого обся- +гу є спеціалізований набір параметрів, застосування яких дозволяє +отримати якісні векторні представлення сутностей. Нижче наведено +набір параметрів для навчання моделі «Олесь Гончар»: + алгоритм тренування — skip-gram; + розмір векторів — 500; + максимальний розмір контекстного вікна — 5; + мінімальна частота слова, яке буде враховано — 10; + модель для тренування — неґативна вибірка (англ. Negative +sampling); + кількість ітерацій (англ. Epochs) навчання — 20; + кількість виділених потоків для навчання — максимальна; + параметр для зменшення впливу високочастотних слів — 1e-5; + інші параметри — за замовчуванням. + +540 +Оцінка векторних представлень. Дослідження векторних пред- +ставлень дають можливість зрозуміти характер результатів за ви- +явленою подібністю між словами, але питання оцінки векторних +представлень з позиції їхньої якості для розв’язання практичних за- +вдань залишається не тільки актуальним, але і гостро дискусійним. +Загалом розрізняють два підходи до оцінки векторних представ- +лень слів: на основі внутрішніх оцінок та на основі зовнішніх оці- +нок. Використання зовнішніх оцінок передбачає оцінювання якості +векторних представлень на основі результатів їхнього застосування +для розв’язання реальних завдань. Наприклад, якщо вдалий добір +параметрів під час побудови векторного представлення спричинив +збільшення точності аналізу тональності тексту, то якість цього век- +торного представлення вважається вищою. Внутрішнє оцінювання +базується на використанні спеціальних тестових наборів (тести ана- +логій — вирази виду «A до B як C до D») та вручну промаркованих +даних. +Технологія опрацювання прогностичних моделей дистрибутивної +семантики. В загальному випадку для розробки програмних засобів +дистрибутивного аналізу (або опрацювання прогностичних моделей +дистрибутивної семантики) використовують API бібліотеки gensim та +реалізують такі функції: знаходження схожих векторів слів для векто- +ра заданого слова на основі обчислення косинусної подібності (англ. +Cosine similarity) між вектором указаного слова та векторами всіх ін- +ших слів моделі; знаходження схожих векторів слів на основі множи- +ни позитивних та неґативних слів, які будуть мати відповідний вплив +на виявлення схожості між векторами слів; знайдені схожі вектори +слів на основі множини позитивних та неґативних слів можуть де- +монструвати наявність упереджень та стереотипів, які зберігаються +в моделях; знайдені схожі вектори слів на основі множини позитив- +них та неґативних слів можуть ілюструвати асоціативні зв’язки між +словами; знайдені схожі вектори слів на основі множини позитивних +та неґативних слів можуть демонструвати також і граматичні зв’язки; +знаходження косинусної відстані (англ. Cosine distance) між вектором +слова та вектором іншого слова; знаходження слова, яке не трапля- +ється разом з іншими словами із вказаного переліку; знаходження +слова в переліку, яке найбільш подібне до вказаного слова; знахо- +дження всіх слів у моделі, які ближчі до вказаного слова, ніж інше +вказане слово; обчислення відстані між словами (англ. Word mover’s +distance) двох документів. + +541 +3. Розробка моделі розгортання мережевого засобу UkrVectōrēs +3.1. Інструментарій для управління ізольованими Linux-контейнерами +Docker +Docker [34] — інструмент з відкритим сирцевим кодом, який ав- +томатизує розгортання застосунку у середовищах, що підтримують +контейнеризацію. Docker допомагає викладати код швидше, швидше +тестувати, швидше викладати додатки і зменшити час між написан- +ням і запуском коду. Docker робить це за допомогою легкої платфор- +ми контейнерної віртуалізації, використовуючи процеси й утиліти, +які допомагають керувати і викладати програми. У своєму ядрі Docker +дозволяє запускати практично будь-який додаток, безпечно ізольова- +ний в контейнері. Безпечна ізоляція дозволяє запускати на одному +хості багато контейнерів одночасно. +Переваги Docker: + пришвидшення процесу розробки; + зручна інкапсуляція застосунку; + однакова поведінка на локальній машині, а також dev/staging/ +production серверах; + простий і чіткий моніторинг; + зручність масштабування. +Термінологія Docker-інструментарію: + Контейнер (Container) — запущений екземпляр, що інкапсулює +необхідне ПЗ. Контейнери завжди створюються з образу і можуть на- +давати порти та дисковий простір для взаємодії з іншими контейне- +рами чи/та зовнішнім ПЗ. Контейнери можна з легкістю знищити/ +видалити та створити знову. Контейнери не зберігають стан. + Образ (Image) — базовий елемент кожного контейнера. При +створенні образу кожен крок кешується і може бути використаний +повторно (копіювання під час запису). Час на збірку залежить від са- +мого образу. З іншого боку, контейнери можна одразу запустити з об- +разу. + Порт (Port) — TCP/UDP порт у звичному розумінні. Для спро- +щення припустимо, що порти можуть бути відкриті для зовніш- +нього ПЗ (доступні з хостової ОС) або підключатися до інших кон- +тейнерів (тобто доступні лише з цих контейнерів та невидимі для +іншого ПЗ). + Volume можна вважати спільною текою. Volume ініціалізується +при створенні контейнера і призначений для збереження даних, не- +залежно від життєвого циклу контейнера. + +542 + Registry (Сховище) — сервер, що зберігає образи Docker. Ми мо- +жемо порівняти його з Github: витягуєте образ зі сховища, щоб роз- +горнути його локально, а потім відправляєте локально зібрані образи +до віддаленого сховища. + Docker Hub [35] — сховище з веб-інтерфейсом від Docker Inc. +Зберігає багато Docker-образів з різним ПЗ. Docker Hub — джерело +«офіційних» образів Docker, створених його командою або у співпра- +ці з іншими компаніями (але це не обов’язково образи від офіційних +виробників ПЗ). Якщо ви зареєстровані, можна переглянути перелік +потенційних вразливостей таких образів. Доступні платні та безкош- +товні облікові записи. Для безкоштовного облікового запису можна +створювати один приватний образ та безліч публічних. + Docker Store [36] — сервіс дуже подібний до Docker Hub. Це май- +данчик з рейтингами, відгуками тощо. +Архітектура Docker. +Docker складається з двох головних компонентів: + Docker: платформа віртуалізації з відкритим кодом; + Docker Hub: платформа-як-сервіс для поширення і управління +Docker контейнерами. +Docker використовує архітектуру клієнт — сервер. Docker-клієнт +спілкується з доменом Docker, який бере на себе створення, запуск, +розподіл контейнерів. Обидва, клієнт і сервер, можуть працювати на +одній системі, також можна підключити клієнт до віддаленого домена +docker. Клієнт і сервер спілкуються через сокет або через RESTful API. +Користувач не взаємодіє з сервером напряму, а використовує для +цього клієнт. Docker-клієнт — головний інтерфейс до Docker системи. +Він отримує команди від користувача і взаємодіє з docker-доменом. +Щоб розуміти, з чого складається Docker, потрібно знати про три +його компоненти: + образи (images); + реєстр (registries); + контейнери. +Docker-образ — це read-only шаблон. Наприклад, образ може міс- +тити операційну систему Ubuntu з Apache і додатком на ній. Образи +використовуються для створення контейнерів. Docker дозволяє лег- +ко створювати нові образи, оновлювати існуючі, або можна заван- +тажити образи, створені іншими людьми. Образи — це компонента +збірки Docker-а. Docker-реєстр зберігає образи. Є публічні і приватні +реєстри, з яких можна скачати або завантажити образи. Публічний + +543 +Docker-реєстр — це Docker Hub. Там зберігається величезна колекція +образів. Образи можуть бути створені вами або можна використову- +вати образи, створені іншими користувачами. Реєстри — це компо- +нента поширення. +Контейнери схожі на директорії. У контейнерах міститься все, +що потрібно для роботи програми. Кожен контейнер створюється з +образу. Контейнери можуть бути створені, запущені, зупинені, пе- +ренесені або видалені. Кожен контейнер ізольований і є безпечною +платформою для додатка. Контейнери — це компонента роботи. Ви- +ходячи з цих трьох компонентів в Docker можна: + створювати образи, в яких знаходяться додатки; + створювати контейнери з образів, для запуску додатків; + розповсюджувати через Docker Hub або інший реєстр образів. +Принцип роботи Docker. +Отже образ — це read-only шаблон, з якого створюється контейнер. +Кожен образ складається з набору рівнів. Docker використовує union +file system для поєднання цих рівнів в один образ. Union file system до- +зволяє файлам і директоріям з різних файлових систем (різних гілок) +прозоро накладатися, створюючи когерентну файлову систему. +Одна з причин, з якої Docker легкий — це використання таких +рівнів. Коли змінюється образ, наприклад, проходить оновлення до- +датку, створюється новий рівень. Так, без заміни всього образу або +його перезібрання, як вам можливо доведеться зробити з віртуальною +машиною, тільки рівень додається або оновлюється. І вам не потріб- +но роздавати весь новий образ, публікується тільки оновлення, що +дозволяє поширювати образи простіше і швидше. +В основі кожного образу знаходиться базовий образ. Наприклад, +ubuntu, базовий образ Ubuntu, або Fedora, базовий образ дистрибу- +тива Fedora. Так само можна використовувати готові образи як базу +для створення нових образів. Наприклад, образ apache можна вико- +ристовувати як базовий образ для веб-додатків. Docker зазвичай бере +образи з реєстру Docker Hub. +Docker образи можуть створитися з цих базових образів, кроки +опису для створення цих образів називаються інструкціями. Кожна ін- +струкція створює новий образ або рівень. Інструкціями будуть такі дії: + запуск команди; + додавання файлу або директорії; + створення змінної оточення; + вказівки, що запускати, коли запускається контейнер цього способу. + +544 +Ці інструкції зберігаються в файлі Dockerfile. Docker зчитує цей +Dockerfile, коли збирається образ, виконує ці інструкції і повертає +кінцевий образ. +Реєстр — це сховище Docker образів. Після створення образу ви +можете опублікувати його на публічному реєстрі Docker Hub або на +вашому особистому реєстрі. За допомогою Docker-клієнта ви мо- +жете шукати вже опубліковані образи і завантажувати їх на машину +з Docker для створення контейнерів. +Docker Hub надає публічні і приватні сховища образів. Пошук і +скачування образів з публічних сховищ доступні для всіх. Вміст при- +ватних сховищ не попадає в результат пошуку. І тільки ви і ваші корис- +тувачі можуть отримувати ці образи і створювати з них контейнери. +Принцип роботи контейнера. +Контейнер складається з операційної системи, призначених для +користувача файлів і метаданих. Відомо, що кожен контейнер ство- +рюється з образу. Цей образ говорить Docker’у, що знаходиться в кон- +тейнері, який процес запустити, коли запускається контейнер та інші +конфігураційні дані. Docker-образ доступний тільки для читання. +Коли Docker запускає контейнер, він створює рівень для читання / +запису зверху образу (використовуючи union file system, як було за- +значено раніше), в якому може бути запущено додаток. +Або за допомогою програми Docker, або за допомогою RESTful +API, Docker-клієнт говорить Docker-домену запустити контейнер. +$ sudo docker run -i -t ubuntu /bin/bash +Давайте розберемося з цією командою. Клієнт запускається за до- +помогою команди Docker, з опцією run, яка говорить, що буде запу- +щений новий контейнер. Мінімальними вимогами для запуску кон- +тейнера є такі атрибути: + який образ використовувати для створення контейнера. У нашо- +му випадку ubuntu; + команду яку ви хочете запустити, коли контейнер буде запуще- +ний. У нашому випадку /bin/bash. +Після запуску цієї команди Docker по порядку робить наступне: + завантажує образ ubuntu: Docker перевіряє наявність образу +ubuntu на локальній машині, і якщо його немає — то викачує його +з Docker Hub. Якщо ж образ є, то використовує його для створення +контейнера; + створює контейнер: коли образ отриманий, Docker використо- +вує його для створення контейнера; + +545 + ініціалізує файлову систему і монтує read-only рівень: контейнер +створений у файлової системі і read-only рівень доданий образ; + ініціалізує мережу/міст: створює мережевий інтерфейс, який до- +зволяє Docker’у спілкуватися хост машиною; + установка IP адреси: знаходить і задає адресу; + запускає вказаний процес: запускає програму; + обробляє та видає вихід додатку: підключається і залоговує стан- +дартний вхід, вихід і потік помилок додатку, щоб можна було відслід- +ковувати, як працює програма. +Тепер у вас є робочий контейнер. Ви можете управляти своїм кон- +тейнером, взаємодіяти з вашим додатком. Коли вирішите зупинити +додаток, видаліть контейнер. +Технології, використані у Docker. +Докер написаний на мові Go і використовує деякі можливості +ядра Linux, щоб реалізувати наведений вище функціонал. +Docker використовує технологію namespaces для організації ізо- +льованих робочих просторів, які називаються контейнерами. Коли +запускається контейнер, Docker створює набір просторів імен для +даного контейнера. Це створює ізольований рівень, кожен контей- +нер запущений у своєму просторі імен, і не має доступу до зовнішньої +системи. +Список деяких просторів імен, які використовує Docker: + pid: для ізоляції процесу; + net: для управління мережевими інтерфейсами; + ipc: для управління IPC ресурсами (ICP: InterProccess Commu- +nication); + mnt: для управління точками монтування; + utc: для ізолювання ядра і контролю генерації версій (UTC: Unix +timesharing system). +Control groups (контрольні групи). Docker також використовує +технологію cgroups або контрольні групи. Ключ до роботи додатка в +ізоляції, надання додатку тільки тих ресурсів, які йому потрібні. Це +гарантує, що контейнери будуть добре співіснувати. Контрольні гру- +пи дозволяють розділяти доступні ресурси заліза і, якщо необхідно, +встановлювати межі і обмеження. Наприклад, обмежити можливу +кількість пам’яті, що використовується контейнером. +Union File Sysem або UnionFS — це файлова система, яка працює, +створюючи рівні, що робить її дуже легкою і швидкою. Docker вико- +ристовує UnionFS для створення блоків, з яких будується контейнер. + +546 +Docker може використовувати кілька варіантів UnionFS включаючи: +AUFS, btrfs, vfs і DeviceMapper. +Docker поєднує ці компоненти в обгортку, яку ми називаємо фор- +матом контейнера. Формат, який використовується за умовчанням, +називається libcontainer. Так само Docker підтримує традиційний +формат контейнерів в Linux з допомогою LXC. В майбутньому Docker +можливо буде підтримувати інші формати контейнерів. Наприклад, +інтегруючись з BSD Jails або Solaris Zones. +3.2. Компіляція, збірка та розгортання мережевого засобу UkrVectōrēs +(з GitHub репозиторію) в середовищі UNIX-подібних операційних сис- +тем Linux +Системні вимоги: + мінімальні апаратні ресурси: x86–64 сумісний процесор з такто- +вою частотою 1 ГГц; оперативна пам’ять: 4 Гб; місце на жорсткому +диску: 20 Гб; +UNIX-подібна операційна система Linux (при тестуванні, компі- +ляції, збірці та розгортанні мережевого засобу UkrVectōrēs використо- +вувались дистрибутиви Ubuntu Server 18.04 LTS x86–64 та Alpine Linux +3.9.4 x86–64); +Git розподілена система керування версіями файлів та спільної +роботи; +Docker CE інструментарій для управління ізольованими Linux/ +Windows-контейнерами; +швидкісне підключення до мережі Інтернет. +Компіляція, збірка та розгортання мережевого засобу UkrVectōrēs +в середовищі UNIX-подібних операційних систем Linux складається +з таких етапів: +Клонування початкового коду програми UkrVectōrēs з git- +репозиторію [37] сервісу GitHub за посиланням https://github.com/ +malakhovks/docsim. Цей етап можна виконати, використовуючи таку +команду: +$ git clone https://github.com/malakhovks/docsim.git. +Або клонувати початковий код програми UkrVectōrēs з git- +репозиторію [37] сервісу GitHub з конкретної гілки/тега використо- +вуючи таку команду: +$ git clone --depth=1 --branch= , +де tag_name — ім’я гілки/тега; +repo_url — https-адреса приватного репозиторію з параметрами +авторизації. + +547 +Приклад: +$ git clone --depth=1 --branch=develop https://Velychko-Vitalii:ae9c2fa2 +d73fbbb0bd0a5ffa746f1df59036815c@github.com/malakhovks/docsim.git. +Або отримати реліз у вигляді архіву (початковий код програми +UkrVectōrēs) у розробника, розпакувати його та перейти до наступ- +ного етапу. +1. Перехід в діректорію docsim: +$ cd docsim. +2. Перехід в гілку, яку потрібно використовувати для компіляції/ +збірки, командою git checkout: +$ git checkout , +де branch_name — ім’я гілки; +git-репозиторій програми docsim має дві основні гілки: develop та +master. +Гілка master містить стабільний початковий код програми docsim. +Гілка develop містить робочий початковий код програми docsim. +Приклад: +$ git checkout master. +Створення ізольованого застосунку Docker, так званого Docker +image з файлу Dockerfile: +$ docker build. — t , +де: image name — ім’я ізольованого застосунку Docker image. +Приклад: +$ docker build. — t docsim_image. +Створення ізольованого застосунку docsim_image може зайняти +тривалий час в залежності від потужностей апаратного забезпечен- +ня. Повна документація по командах Docker доступна за посиланням +[38]. +3. Запуск створеного ізольованого застосунку docsim_image в кон- +тейнері docsim: +$ docker run --restart always --name docsim -d -p 80:80 docsim_image. +Команда Docker run з параметром --restart always дозволяє авто- +матично перезапускати при перезавантаженні операційної системи, +що дозволяє досягти безперебійної роботи сервісу. +Основні команди керування Docker-контейнером: + docker attach docsim — побачити вихід консолі контейнера +docsim; + docker stop docsim — зупинити контейнер docsim; + docker start docsim — відновити роботу (старт) контейнера docsim; + +548 + docker rm docsim — видалення контейнера docsim (перед вида- +ленням контейнера його потрібно зупинити); +Деякі корисні параметри для запуску Docker-контейнера: + --name — дає контейнеру ім’я, яке можна знайти у виводі коман- +ди docker ps; + -p 80:80 — публікує порт 80. Другий номер 80 після двокрапки +повідомляє, який порт сервер nginx слухає всередині контейнера; +–d — запускає контейнер, від’єднаний від терміналу. Потім жур- +нали можна переглядати за допомогою команди журналів Docker +docker logs; +–t — щоб бачити консольний вихід Docker-контейнера; +–-restart on-failure — автоматичний перезапуск невдалих контей- +нерів. Перезапускає контейнер, якщо він вийде з ладу через помилку, +яка виявляється як ненульовий код виходу; +–-restart always — завжди перезапускає контейнер, якщо він зу- +пиняється. Якщо контейнер зупинено вручну, він перезапускається +лише тоді, коли служба Docker перезапускається або сам контейнер +перезапускається вручну. +3.3. Компіляція, збірка та розгортання мережевого засобу UkrVectōrēs +(з GitHub репозиторію) в середовищі програми віртуалізації для опера- +ційних систем VirtualBox. +Системні вимоги: +мінімальні апаратні ресурси: x86–64 сумісний процесор з такто- +вою частотою 2 ГГц; оперативна пам’ять: 4 Гб; місце на жорсткому +диску: 20 Гб; +x86–64 сумісна UNIX-подібна операційна система Linux; x86–64 +сумісна операційна система Microsoft Windows 7 Service Pack 1 або но- +віша; +VirtualBox [39] програма віртуалізації для операційних систем вер- +сії VirtualBox 6.0.8 або новіша; +віртуальна машина з UNIX-подібною операційною системою +Linux (при тестуванні, компіляції, збірці та розгортанні мереже- +вого засобу UkrVectōrēs використовувались дистрибутиви Ubuntu +Server 18.04 LTS x86–64 та Alpine Linux 3.9.4 x86–64), яка вклю- +чає таке встановлене програмне забезпечення: Git-розподілена +система керування версіями файлів та спільної роботи; Docker +CE інструментарій для управління ізольованими Linux/Windows- +контейнерами; +швидкісне підключення до мережі Інтернет; + +549 +віртуальна машина — модель обчислювальної машини, створена +шляхом віртуалізації обчислювальних ресурсів: процесора, оператив- +ної пам’яті, пристроїв зберігання та вводу і виводу інформації. Вір- +туальна машина на відміну від програми емуляції конкретного при- +строю забезпечує повну емуляцію фізичної машини чи середовища +виконання (для програми). +VirtualBox — програма для створення віртуальних машин, що на- +лежить Oracle Corporation. Ця програма є в вільному доступі та під- +тримується основними операційними системами Linux, FreeBSD, Mac +OS X, OS/2 Warp, Microsoft Windows, які підтримують роботу гостьових +операційних систем FreeBSD, Linux, OpenBSD, OS/2 Warp, Windows +і Solaris. +Ключові можливості. + кросплатформовість; + модульність; + жива міграція; + підтримка USB 2.0, коли пристрої хост-машини стають доступ- +ними для гостьових ОС (лише в пропрієтарній версії); + підтримка 64-бітних гостьових систем (починаючи з версії 2.0), +навіть на 32-бітних хост-системах (починаючи з версії 2.1, для цього +потрібна підтримка технології віртуалізації процесором); + підтримка SMP на стороні гостьової системи (починаючи з версії +3.0, для цього потрібна підтримка технології віртуалізації процесором); + вбудований RDP-сервер, а також підтримка клієнтських USB- +пристроїв поверх протоколу RDP (лише в пропрієтарній версії); + експериментальна +підтримка +апаратного +3D-прискорення +(OpenGL, DirectX 8/9 (з використанням коду wine) (лише в 32-бітних +Windows XP и Vista), для гостьових DOS/Windows 3.x/95/98/ME під- +тримка апаратного 3D-прискорення не передбачена; + підтримка образів жорстких дисків VMDK (VMware) и VHD +(Microsoft Virtual PC), включаючи snapshots (починаючи з версії 2.1); + підтримка iSCSI (лише в пропрієтарній версії); + підтримка віртуалізації аудіопристроїв (емуляція AC97 або +SoundBlaster 16 на вибір); + підтримка різноманітних видів мережевої взаємодії (NAT, Host +Networking via Bridged, Internal); + підтримка ланцюжка збережених станів віртуальної машини +(snapshots), до яких можна повернутися з будь-якого стану гостьової +системи; + +550 + підтримка Shared Folders для простого обміну файлами між хос- +товою та гостьовою системами (для гостьових систем Windows 2000 і +новіше, Linux та Solaris); + підтримка інтеграції робочих столів (seamless mode) хостової та +гостьової ОС; + є можливість вибору мови інтерфейса (підтримується й україно- +мовний інтерфейс). +Компіляція, збірка та розгортання мережевого засобу UkrVectōrēs +(з git-репозиторію [37]) в середовищі програми віртуалізації для опе- +раційних систем VirtualBox складається з таких етапів. +Створення віртуальної машини з операційною системою Alpine +Linux 3.9.4 x86–64 або новішою, згідно з настановами користувача, +наведеними на офіційному сайті VirtualBox [39] nf, використовуючи +відео-туторіали. Встановити апаратні ресурси для віртуальної маши- +ни згідно з прогнозованим навантаженням на сервіс UkrVectōrēs. +Встановлення Git та Docker CE в середовиші віртуальної машини +з операційною системою Alpine Linux 3.9.4 x86–64 згідно з настанова- +ми користувача, наведеними на офіційному сайті wiki-документації +wiki.alpinelinux.org. +Клонування початкового коду програми UkrVectōrēs з git- +репозиторію [37] сервісу GitHub за посиланням https://github.com/ +malakhovks/docsim. Цей етап можна виконати, використовуючи ко- +манду: +$ git clone https://github.com/malakhovks/docsim.git. +Або клонувати початковий код програми UkrVectōrēs з git- +репозиторію [37] сервісу GitHub з конкретної гілки/тега використо- +вуючи команду: +$ git clone --depth=1 --branch= , +де tag_name — ім’я гілки/тега; +repo_url — https-адреса приватного репозиторію з параметрами +авторизації. +Приклад: +$ git clone --depth=1 --branch=develop https://Velychko-Vitalii:ae9c2fa2 +d73fbbb0bd0a5ffa746f1df59036815c@github.com/malakhovks/docsim.git. +Або отримати реліз у вигляді архіву (початковий код програми +UkrVectōrēs) у розробника, розпакувати його та перейти до наступ- +ного етапу. +1. Перехід в директорію docsim: +$ cd docsim. + +551 +2. Перехід в гілку, яку потрібно використовувати для компіляції/ +збірки, командою git checkout: +$ git checkout , +де branch_name — ім’я гілки; +git-репозиторій програми UkrVectōrēs має дві основні гілки: +develop та master. +Гілка master містить стабільний початковий код програми +UkrVectōrēs. +Гілка develop містить робочий початковий код програми +UkrVectōrēs. +Приклад: +$ git checkout master. +Створення ізольованого застосунку Docker, так званого docker +image з файлу Dockerfile: +$ docker build. — t , +де image name — ім’я ізольованого застосунку docker image. +Приклад: +$ docker build. — t docsim_image. +Створення ізольованого застосунку docsim_image може зайняти +тривалий час в залежності від потужностей апаратного забезпечення. +Повна документація по командах Docker доступна за посиланням [38]. +3. Запуск створеного ізольованого застосунку docsim_image в кон- +тейнері docsim: +$ docker run --restart always --name docsim -d -p 80:80 docsim_image. +Команда docker run з параметром --restart always дозволяє автома- +тично перезапускати при перезавантаженні операційної системи, що +дозволяє досягти безперебійної роботи сервісу. +4. Електронна бібліотека медіа-файлів підсистеми телереабілітації +TISP — сервіс vHealth. +Практична реалізація і впровадження алгоритмів та технологій, +що входять в застосунок UkrVectōrēs, інтегрована у веб-сервіс vHealth, +зокрема інтелектуальна інформаційно-пошукова підсистема vHealth +повністю працює з використанням алгоритмів та технологій дистри- +бутивно-семантичного аналізу UkrVectōrēs. +Першочергові виклики постали перед системою медичної реабілі- +тації в Україні. До особливо важливих завдань відноситься, у першу +чергу, реабілітація хворих, які одужали від COVID-19. Цей факт добре +усвідомлюється як суспільством, так і керівництвом МОЗ України, +яке наразі створює спеціальну робочу групу з цієї проблеми. + +552 +Україна має систему лікувально-профілактичних закладів, при- +значених для психологічної та фізичної реабілітації військовослуж- +бовців, в яких використовуються сучасні технології реабілітації. Од- +нак довготривала реабілітація в таких центрах доступна далеко не +всім. Тому застосування технології телереабілітації хворих з посттрав- +матичним стресовим розладом та подібними розладами, в поєднанні +з засобами об’єктивного контролю функціонального стану є вкрай +важливим. +Роботи виконуються на перетині робіт за проектами Національ- +ного фонду досліджень України, які мають назву «Трансдисциплінар- +на інтелектуальна інформаційно-аналітична система супроводження +процесів реабілітації при пандемії (ТІSР)» 2020–2020 рр. та «Розроб- +ка хмарної платформи пацієнтцентричної телереабілітації онколо- +гічних хворих на основі математичного моделювання» 2022–2023 рр. +Особливістю систем є те, що вони базується на знанняорієнтованій +технології, онтологічному інжинірингу і трансдисциплінарній пара- +дигмі. Когнітивні сервіси системи реалізують структуризацію і кла- +сифікацію інформації, синтезують необхідні документи на основі +семантичного аналізу, виявляють характерні властивості інформа- +ційних процесів і забезпечують підтримку прийняття рішень на всіх +етапах їх життєвого циклу. +Методологія реабілітаційних заходів в умовах пандемії має ряд +суттєвих особливостей, пов’язаних з непередбачуваністю і високою +швидкістю виникнення (на відміну від звичайної ситуації) проблем +високої складності, обмеженістю спілкування між реабілітологом і +пацієнтом, необхідністю високої реактивності прийняття рішень і їх +відповідністю, масштабністю процесу, і пов’язаною з нею необхідніс- +тю використання масштабованих операційних засобів тощо. Одним +з ефективних рішень в наданні медичної реабілітаційної допомоги +є дистанційна пацієнтцентрична реабілітація, яка потребує online- +засобів теледіагностики, телеметрії і втручання з орієнтацією на мож- +ливості пацієнта, розвинутої Internet-взаємодії, інтелектуальних ін- +формаційних технологій і сервісів, ефективних методів когнітивної +підтримки в системі «Реабілітолог — пацієнт — мультидисциплінарна +команда», статистичної обробки великих об’ємів інформації (зокре- +ма даних анкетування та телеметрії) з виділенням достовірних знань +тощо. Звідси поряд з традиційними засобами реабілітації в процесі +реалізації проєкту «Трансдисциплінарна інтелектуальна інформаційно- +аналітична система супроводження процесів реабілітації при пандемії + +553 +(TISP)» [40], що переміг у конкурсі «Наука для безпеки людини та +суспільства» Національного фонду досліджень України (НФДУ) [41] +й отримав грантове фінансування, у складі системи TISP, з’явилася +Smart-система телемедичного супроводження реабілітаційних заходів +[42]. В поєднанні з інтелектуальними дистанційними засобами біо- +логічного зворотного зв’язку [43] і ефективними мініатюрними при- +ладами (англ. Embedded systems, Wearable devices) теледіагностики [40; +44], телеметрії і відновлення такі системи мають великі перспективи, +про що свідчить також і світовий досвід. +Smart-система телемедичного супроводження реабілітаційних за- +ходів — це комплексна, інтегрована, пацієнтцентрична інформацій- +на підсистема TISP надання медичної допомоги, вирішення різних +клініко-організаційних та науково-дослідних задач у галузі реабілі- +таційної медицини (консультації; дистанційний нагляд і супрово- +дження реабілітаційних процесів та заходів; виявлення, класифіка- +ція, прогнозування та вивчення знань; дослідження та огляд нових +предметних галузей), з використанням засобів дистанційного зв’язку, +елементів технологій штучного інтелекту, зокрема онтологічного ін- +жинірингу [45 – 48] та машинного навчання [49]. +Електронна бібліотека медіа-файлів підсистеми телереабілітації +TISP — сервіс vHealth — це розподілена інформаційна система, що +дозволяє зберігати, використовувати та розповсюджувати (функ- +ція шерингу) різнорідні колекції електронних документів (відео- та +аудіо контент) довільних предметних галузей, для дистанційного на- +вчання пацієнтів і їх родичів, зокрема реабілітаційному комплексу +вправ та заходів. +Реабілітація людей, що одужали від COVID-19, є безумовно вкрай +важливою соціальною проблемою. Цей факт вже добре розуміється +міжнародною лікарською спільнотою. У той же час доступність реа- +білітаційних заходів у різних країнах дуже різна. В країнах з розвине- +ною страховою медициною процес реабілітації в відповідних спеці- +алізованих центрах доступний багатьом. На жаль, в Україні ситуація +інша — потреби пацієнтів в амбулаторних реабілітаційних послугах +набагато перевищують наявні ресурси, що вимагає пошуку альтер- +нативних рішень і підключення сучасних і передових технологій для +підтримки пацієнтів. Тому є велика потреба у використанні нового +сучасного напрямку відновлювальної медицини — телереабілітації. +Світове сучасне та загальноприйняте визначення поняття Телереа- +білітація або E-реабілітація (англ. E-rehabilitation) [44] — це комплекс + +554 +реабілітаційних вправ і навчальних програм, які надаються пацієнту +дистанційно за допомогою телекомунікаційних комп’ютерних тех- +нологій переважно на амбулаторному етапі лікування. Сенс цього +сучасного напряму у тому, що пацієнт самостійно, як правило, у до- +машніх умовах виконує програми відновлювального лікування на ам- +булаторному етапі під дистанційним контролем і керівництвом ліка- +ря-спеціаліста. Телереабілітація має супроводжуватися відповідним +програмним забезпеченням, яке дозволяє спеціалісту з реабілітації, +що спостерігає пацієнта в стаціонарі, швидко скласти індивідуальний +комплекс вправ для самостійних занять у відеоформаті. Цей комп- +лекс має коригуватися в залежності від динаміки відновлення. Таким +чином пацієнти мають змогу продовжувати структуровану програму +домашньої реабілітації, розроблену на стаціонарному етапі. Пацієнти +отримують зворотний зв’язок від вже знайомих фахівців, відзнача- +ються результати, досягнуті за минулий період, ставляться нові, ак- +туальні для пацієнта завдання, здійснюється об’єктивний контроль +відповідних функцій. Все це, безумовно, покращує і підтримує моти- +вацію пацієнта та забезпечує значно більшу ефективність амбулатор- +ного етапу реабілітації. +Телереабілітація є втіленням відразу декількох сучасних техно- +логічних трендів. По-перше, телереабілітація неможлива без влас- +не телекомунікаційних технологій. По-друге, вона потребує засто- +сування спеціалізованих для реабілітації медичних інформаційних +систем. Ці системи потрібні як для адміністрування пацієнтів, так, +і це є найголовніше, для створення низки реабілітаційних доку- +ментів відповідно до структури реабілітаційного циклу, наприклад, +індивідуального реабілітаційного плану, категоріального профілю, +реабілітаційного прогнозу тощо. По-третє, важливою частиною те- +лереабілітаційних технологій є функціональне оцінювання стану +пацієнтів у домашніх умовах з використанням мініатюрних при- +ладів та сучасних алгоритмів оцінювання даних у відповідності з +тенденцією, яка англійською називається point-of-care testing, що у +вільному перекладі означає медичний тест, який здійснюється без- +посередньо в місці знаходження пацієнта, поза офісом лікаря. Наре- +шті, телереабілітація неможлива без активного залучення пацієнта +до процесу прийняття рішень щодо його діагностики та лікування. +Це є однією з основних тенденцій сучасної медицини, яка була під- +тримана в тому числі і на рівні законодавчих ініціатив у системі охо- +рони здоров’я України. + +555 +Бурхливий розвиток телереабілітації у світі та набуття цим на- +прямком медицини трансдисциплінарних зв’язків з різнома- +нітними предметними галузями, що виходять за рамки сучасної +парадигми E-здоров’я (англ. E-health), призвів до появи найсучас- +нішого різновиду реабілітації — гібридна Е-реабілітація (англ. Hybrid +E-rehabilitation) [50]. +Гібридна Е-реабілітація складається з ряду фундаментальних ме- +тодів, підходів та технологій: +– Телекомунікаційні технології — надання реабілітаційних послуг +через телекомунікаційні мережі та Інтернет. Крім того, це дозволяє +пацієнтам дистанційно взаємодіяти з провайдерами та може вико- +ристовуватися як для оцінки пацієнтів, так і для проведення терапії. +– Насичені Інтернет-застосунки (англ. Rich Internet application). +Перш за все це медичні інформаційні системи (МІС). МІС — це все- +бічна, інтегрована інформаційна система, призначена для управління +всіма аспектами роботи медичної установи (зокрема поліклініки, лі- +карні або реабілітаційного центру), такими, як медичні, адміністра- +тивні, фінансові та юридичні питання з відповідною обробкою/обмі- +ном даних (зокрема з реєстрами центральної бази даних електронної +системи охорони здоров’я України [51]). +– Телеметрія — сукупність методів, підходів та технологій, що да- +ють змогу проводити дистанційне вимірювання, збір, передачу та об- +робку інформації про показники діяльності (фізіологічні параметри) +організму пацієнта (зокрема при виконанні реабілітаційного комп- +лексу вправ та заходів в реальному часі). +– Вбудовані системи (англ. Embedded systems) та мініатюрні «розум- +ні» прилади для носіння (англ. Wearable devices, Wearables). Такі при- +строї для носіння можуть бути для загального використання, і в цьому +випадку вони є лише особливим прикладом мобільних комп’ютерів. +В якості альтернативи вони можуть бути призначені для спеціальних +цілей, таких як фітнес-трекери або медичні пристрої. Вони можуть +включати спеціальні датчики та сенсори, такі як акселерометри, мо- +нітори серцевого ритму, або більш просунуті, електрокардіограма, +монітори насичення крові киснем та датчики контролю артеріально- +го тиску; +– Біологічний зворотний зв’язок (БЗЗ, англ. Biofeedback). Технології +БЗЗ [43] включають в себе комплекс дослідницьких, немедичних, фі- +зіологічних, профілактичних і лікувальних процедур, в ході яких лю- +дині за допомогою зовнішньої ланцюга зворотного зв’язку, організо- + +556 +ваного переважно за допомогою мікропроцесорної або комп’ютерної +техніки, пред’являється інформація про стан і зміни тих чи інших +власних фізіологічних процесів. БЗЗ-процедура полягає в безперерв- +ному моніторингу в режимі реального часу певних фізіологічних по- +казників і свідомому управлінні ними за допомогою мультимедійних, +ігрових та інших прийомів у заданій області значень. Таким чином +протягом курсу БЗЗ-сеансів можливо посилити або послабити даний +фізіологічний показник, а отже, рівень тонічної активації тієї регуля- +торної системи, чию активність показник відображає. +– Інтелектуальні/віртуальні особисті помічники (англ. Intelligent/ +Virtual personal assistant). Це програмні агенти, що можуть надавати +персональну інформацію, виконувати завдання та послуги для окре- +мої особи. Сучасні програмні агенти класу інтелектуальних/віртуаль- +них особистих помічників можуть взаємодіяти між собою задля вико- +нання певного класу завдань. Взаємодія з такими помічниками з боку +людини зазвичай відбувається за допомогою голосу або тексту. Іноді +стосовно віртуальних помічників з текстовим інтерфейсом застосо- +вують термін «чат-бот». Зокрема в рамках проєкту та системи TISP +розроблено універсальну діалогову підсистему [52] (імплементовано +в рамках предметної галузі «Фізична і реабілітаційна медицина» — +ФРМ) у формах веб-застосунку та віртуального співрозмовника у +сервісі «Telegram». Розроблена діалогова підсистема TISP використо- +вує елементи онтологічного інжинірингу, зокрема онтологічне пред- +ставлення «Білої книги з фізичної та реабілітаційної медицини в Єв- +ропі» (БК, англ. The White Book of Physical and Rehabilitation Medicine in +Europe) [53] та Міжнародну класифікацію функціонування, обмежен- +ня життєдіяльності та здоров’я» (МКФ, англ. International Classification +of Functioning, Disability and Health, ICF) [54]. +– Методи, технології та програмні застосунки на основі штучного +інтелекту для обробки великих даних (англ. Big data) з метою отри- +мання знань та вирішення аналітичних завдань [55]. Для виявлення +та отримання знань та вирішення основних аналітичних завдань, та- +ких як класифікація, діагностика чи прогнозування, ми використо- +вуємо метод під назвою «Зростаючі пірамідальні мережі» [55] (ЗПМ, +англ. Growing pyramidal networks, GPN). Результатом навчання є зако- +номірність у вигляді логічної функції (функції алгебри логік). ЗПМ +належить до класу статистичних методів. Інтелектуальний інформа- +ційний пошук також базується на використанні прогностичних моде- +лей дистрибутивної семантики [49]. + +557 +4.1. Призначення та функції мережевого засобу vHealth. +Одним із основних завдань та призначень сервісу vHealth є ін- +теграція інформаційних ресурсів і ефективна навігація в них. Ін- +теграція інформаційних ресурсів — це їхнє об’єднання з метою +використання різної інформації зі збереженням її властивостей, осо- +бливостей представлення і можливостей її обробляти. Об’єднання +ресурсів може відбуватися як фізично, так і віртуально. Але при +цьому таке об’єднання повинно забезпечувати користувачу сприй- +няття необхідної інформації як єдиного інформаційного простору: +електронна бібліотека повинна забезпечити роботу з базами даних і +високу ефективність інформаційних пошуків. Ефективна навігація в +електронній бібліотеці — це можливість користувача знаходити ін- +формацію, яка його цікавить, в усьому доступному інформаційному +просторі з найбільшою повнотою і точністю при найменших затра- +тах зусиль. Для вирішення цієї задачі сервіс vHealth використовує +інтелектуальний пошук на основі прогностичних моделей дистрибу- +тивної семантики. +Сервіс «Електронна бібліотека vHealth» має такі функціональні +можливості: +• повний контроль над медіаконтентом та даними користувачів; +• підтримка декількох робочих процесів публікації контенту (ре- +жиму доступу): загальнодоступний контент (public), приватний кон- +тент (private), контент, що не входить до жодного списку та доступ- +ний тільки за посиланням (unlisted); +• підтримка декількох медіаформатів (медіатипів) даних: аудіо- +контент, відеоконтент та в майбутньому планується підтримка тек- +стових документів pdf, docx; +• можливість каталогізації об’єктів контенту і різних їхніх +об’єднань (категорії та теги); +• обмін медіаконтентом з використанням спільного доступу до +окремих медіаресурсів, списків відтворення (плейлистів), категорій, +тегів. Автоматична генерація коду для вставки медіаконтенту на зо- +внішній Web-ресурс; +• інтелектуальний інформаційний пошук в реальному часі на +основі прогностичних моделей дистрибутивної семантики (лексич- +ний, символьний та атрибутний пошук); +• функція формування списків відтворення (плейлистів) медіа- +контенту із налаштуванням робочих процесів публікації контенту +(режиму доступу); + +558 +• сучасний дизайн графічного інтерфейсу користувача з підтрим- +кою світлої та темної тем оформлення; +• функція розширеного адміністрування користувачами з вико- +ристанням окремої панелі адміністратора сервісу; +• функції соціальної мережі: можливість додавати коментарі, впо- +добання (лайки та дизлайки) та завантаження медіаконтенту на ло- +кальний диск; +• наявність профілів кодування медіаконтенту: для кількох роз- +ширень (240p, 360p, 480p, 720p, 1080p) та декількох профілів кодуван- +ня (h264, h265, vp9); +• функція адаптивної потокової передачі медіаконтенту: можливо +використання протоколу HLS; +• підтримка багатомовних файлів субтитрів для відеоконтенту; +• функція поступового завантаження медіаконтенту (так званий +сhunked file upload); +• протоколювання сеансу роботи користувача із системою з мож- +ливістю переходу в кожний з раніше існуючих станів системи; +• маніпулювання зі структурою опису об’єкта медіаконтенту; +• підтримка апарату гіпертекстових і гіпермедійних зв’язків, +що забезпечує користувачу оперативний перехід від об’єкта чи де- +якого його елемента до іншого взаємопов’язаного з ним об’єкта чи +елемента. +4.2. Програмні залежності мережевого засобу vHealth. +– Python 3.8.6 — інтерпретатор та стандартні бібліотеки; +– gensim — програмна бібліотека з відкритим вихідним кодом для +передової обробки та математичного моделювання природної мови; +– Django 3.1.6 — високорівневий відкритий Python-фреймворк +(програмний каркас) для розробки веб-систем; +– PostgreSQL 12 — об’єктно-реляційна система керування базами +даних; +– React 16.13.1 — відкрита JavaScript бібліотека для створення гра- +фічних інтерфейсів користувача, зокрема для Web-застосунків; +– Video.js — відкрита JavaScript бібліотека, веб-відеопрогравач; +– uWSGI — веб-сервер і сервер веб-додатків, спочатку реалізова- +ний для запуску додатків Python через протокол WSGI (і його бінар- +ний варіант uwsgi); +– Celery 5.0.2 — є асинхронною чергою з відкритим кодом або +чергою задач, яка базується на розподіленому передаванні повідом- +лень; + +559 +– Redis 6.2.1 — розподілене сховище пар ключ — значення, які +зберігаються в оперативній пам’яті, з можливістю забезпечувати дов- +говічність зберігання за бажанням користувача; +– nginx — вільний веб-сервер і проксі-сервер; +– Fine Uploader — відкрита JavaScript бібліотека для завантаження +файлів. +4.3. Графічний інтерфейс користувача мережевого засобу vHealth. +За основу побудови графічного інтерфейсу користувача мереже- +вого засобу vHealth було взято інтерфейс популярної медіаплатформи +Youtube, який є еталоном для систем розповсюдження медіаконтенту. +Під час розробки графічного інтерфейсу користувача мережевого за- +собу vHealth було дотримано одну з найважливіших вимог до сучас- +ного графічного інтерфейсу програмної системи — концепцію «роби +те, що я маю на увазі» або DWIM (англ. Do What I Mean). Тому система +працює передбачувано, щоб користувач заздалегідь інтуїтивно розу- +мів, яку дію виконає програма після отримання його команди. Це +значно полегшує взаємодію користувача з системою та не потребує +розробки додаткових методик та настанов користувачу для взаємодії +з графічним інтерфейсом програмної системи. +Розглянемо основні елементи графічного інтерфейсу користувача +мережевого засобу vHealth (рисунок 27): +– центральна частина інтерфейсу містить весь медіаконтент, до- +ступний для користувача відповідно до його профілю. Медіаконтент +(за замовчуванням) розподілено за категоріями: +– частина інтерфейсу зліва містить пункти головного меню мере- +жевого засобу vHealth, зокрема пункти: «Завантажити» (функція за- +вантаження нового медіаконтенту); «Мої файли» (функція перегляду +завантаженого медіаконтенту в профілі користувача); «Мої плейлис- +ти» (формування списків відтворення — плейлистів медіа-контенту +із налаштуванням робочих процесів публікації контенту); «Історія» +(функція перегляду списку медіаконтенту, що було вже переглянуто); +«Персонал» (функція перегляду всіх користувачів сервісу vHealth); +«Категорії» та «Теги» (функція каталогізації об’єктів медіа-контенту +та різних їхніх об’єднань); +– графічний інтерфейс профілю (облікового запису) користувача +наведено на рисунку 28. Користувач має доступ до персонального ме- +діаконтенту та має змогу редагувати графічний інтерфейс свого про- +філю та кожен об’єкт медіаконтенту. Також є доступ до сторінки зі +списками відтворення (плейлистами) користувача (рисунок 29). + +560 + +Рис. 27. Графічний інтерфейс користувача мережевого засобу vHealth (головна сторінка) + + * +60 +O /ynl += +vHealth +Nowyx +Tonoe +almedeeH +Pesounxg +onoeoro +4 02 +5.2± +Creeopi +COVID-1 +Nepcosan +3anaram +D +Molpain +tlo Hoeoro +- +Mo nneinient +Icnopis +4 02 +5.2h +2 12 +V10.13 +527 +Wio anonofanv +COVID-1930 +opceas) +fnicnenodexas +TISP +cepelcy +ponpocx +@561 + +Рис. 28. Графічний інтерфейс користувача мережевого засобу vHealth (сторінка профілю користувача) + +O B -nyn/eibrsymt.ve/s +vHealth +Nowy +fonoed +ABOUT ME +MY'MEDIA +MY PLAYUSTSQ, +Hagaie +Uploads +Pecosexi +WIVMd +PEANYBATY +PEANYBAT +FEAAYIATH +PGWYBATM +up soeoro +Ten +F +Kareropll + >7 +4 c2 + 74 +ts 40 1 +Nepcosan +TISF +3aaaam +D +Moipaint +Moinneanicte +YTPOROA +saxoxisePM +5.27 +C36 +leropis +01.43 +D:45] +uepotouson +exa +12 views -5 r +25 vews + 6 +ponpocxt +PEIYSAT +REANYSA +PEIWYSATW +PAYSATM +PEWYSATW562 + +Рис. 29. Графічний інтерфейс користувача мережевого засобу vHealth (сторінка профілю користувача зі списками +відтворення (плейлистами) + +NneinicT-vHealth +8 +一 +凸 +X +个 +O B https://e-library.ml/playlists/vnuZm180Tu += +vHealth +owyk +Q +FonoBHa +NopaaM nikapy Wono xapyyBaHH9 (nicng noB'93aHMx 3 coVID-19 3axBopioBaHb) +Haikpae +6:39 +Kupwno MaaxoB +PeKOMeHAaui +0 +山o HoBoro +3axBoploBaHb. +3:30 +Terw +KupwnoManaxoB +PLAY ALL +国 +Kateropii +Pea6iniTaiq nicg COVID-19 +BnpaBW (nicn noB'g3aHMx 3 COVID-19 3axBoprOBaHb).4acTVHa 2 +NepcoHan +KupunoManaxoB +5 media · Created on 23 April 2021 ++K +3aBaHTaKWTW +Nopaan nikapg BianoBinHo pekoMeHAauin BOO3 Wono +3axBoploBaHb. +D +Moi painn +niATpMMK Ang caMocTiMHoi peaGiniTauii nicng +13:19 +KnpunoManaxoB +noB'93aHИX 3COVID-193axBoprOBaHb +Moi nneMnicTM +BnpaBW (nicn noB'g3aHMXx 3 COVID-19 3axBoprOBaHb).4acTVHa 1 +admin +EDIT +IcTopiq +5:28 +KupwnoManaxoB +? +ponpoeKT +YMOBИ +KOHTaKTИ563 + +Рис. 30. Графічний інтерфейс користувача мережевого засобу vHealth (сторінка авторизації облікового запису ко- +ристувача) + ++ +8 +X +Ca +08 +ps.e-library.ml. +☆ +vHealth +Nowyk +YBIИTM +FonoBHa +Haikpawe +PekOMeHAaLIi +！ +o HoBoro +YBiiTW: +Terw +IM' kopvcTyBaya abo e-mail +国 +Kateropir +Naponb: +nepcoHan +quodeu +ICTopig +3a6ynw naponb? +? +Npo npocKT +@ +KOHTaKTW +malakhovks.github.io564 +Технологія компіляції, збірки, розгортання та більш детальний +опис початкового коду мережевого засобу vHealth, а також методи- +ка роботи користувача з графічним інтерфейсом застосунку vHealth +буде наведено у фінальному звіті по проєкту «Трансдисциплінарна +інтелектуальна інформаційно-аналітична система супроводження +процесів реабілітації при пандемії (ТІSР)». +Актуальна версія сервісу vHealth доступна за посиланням: https:// +vhealth.ai-service.ml/ +Для початку роботи з сервісом vHealth необхідно бути авторизова- +ним користувачем (увійти), тому було створено обліковий запис для +демонстрації роботи сервісу. Авторизуватися можна, використавши +логін та пароль облікового запису демонстраційного профілю (рису- +нок 30): +Ім’я користувача (логін): demouser +Пароль: JyMyuC6nMdD494T +За посиланням: https://vhealth.ai-service.ml/accounts/login/ +Результати і висновки +1. Систематизовано теоретичні засади методик мовного (дистри- +бутивно-семантичного) моделювання в математичній лінгвістиці. +2. Розроблено методику тренування дистрибутивно-семантичної +моделі векторного представлення сутностей. +3. Розроблено програмну реалізацію сервісів Smart-системи теле- +медичного супроводження реабілітаційних заходів, зокрема електрон- +ної бібліотеки медіафайлів підсистеми телереабілітації TISP — сервіс +vHealth та електронного засобу для дослідження, моделювання та ви- +вчення довільних предметних галузей — сервіс UkrVectōrēs. +4. Розроблено моделі розгортання мережевих засобів UkrVectōrēs +та vHealth. +5. Розроблено опис прикладного програмного інтерфейсу веб- +сервісів (back-end API) мережевого засобу UkrVectōrēs. +6. Визначено поняття гібридна Е-реабілітація та його фундамен- +тальні основи. +Перспективи подальших досліджень. +У подальшій роботі планується впровадження в практику +комп’ютерних програм для оптимізації затрат часу фахівцями мульти- +дисциплінарної команди при застосуванні МКФ в реабілітації онко- +логічних хворих (зокрема на рак молочної залози). Також планують- +ся подальші дослідження у визначенні та застосуванні ефективних +математичних методів аналізу великих об’ємів даних, моделювання + +565 + + + + + + + + + + + + + + + + + +і побудови сценаріїв прогнозування й оптимізації усього комплексу + +реабілітаційних + +процедур + +і + +їх + +маршрутизації + +з + +використанням + +вже + +апробованих + +у + +колективі + +системних + +засобів, + +технологій + +та + +досвіду + +розробки реабілітаційних комплексів. +Подяки + + +Дослідження виконано при підтримці гранту НФДУ на перетині + +робіт + +за + +проектами, + +які + +мають + +назву + +«Трансдисциплінарна + +інтелек- + +туальна + +інформаційно-аналітична + +система + +супроводження + +процесів + +реабілітації при пандемії (ТІSР)» 2020–2020 рр. та «Розробка хмарної + +платформи пацієнтцентричної телереабілітації онкологічних хворих + +на + +основі + +математичного + +моделювання» + +2022–2023 + +рр. + +на + +базі + +Ін- + +ституту кібернетики ім. + +В. + +М. + +Глушкова Національної академії наук + +України, м. + +Київ, Україна. + + +Окрему подяку автори висловлюють Щурову Олександру Сергійо- + +вичу, молодшому науковому співробітнику відділу мікропроцесорної + +техніки № + +205 Інституту кібернетики ім. + +В. + +М. + +Глушкова НАН Украї- + +ни та фахівцю з Front-end web-розробки за вагомий вклад в розробку + +мережевих + +засобів + +UkrVectōrēs + +та + +vHealth, + +зокрема + +Front-end + +частин + +застосунків. + + +Особливу + +подяку + +автори + +висловлюють + +науковому + +керівнику + +— + +Палагіну Олександру Васильовичу, академіку Національної академії + +наук України, доктору технічних наук, професору, заслуженому вина- + +хіднику України, заступнику директора з наукової роботи Інституту + +кібернетики ім. + +В. + +М. + +Глушкова НАН України, завідувачу відділу мі- + +кропроцесорної техніки № + +205. +Науково-практичний вклад авторів + + +Величко + +Віталій + +Юрійович. + +Розділи: + +Теоретичні + +засади + +методик + +мовного + +(дистрибутивно-семантичного) + +моделювання + +в + +матема- + +тичній лінгвістиці; + +Розробка моделі + +розгортання мережевого засобу + +UkrVectōrēs. + + +Малахов + +Кирило + +Сергійович. + +Розділи: + +Розробка + +мережевого + +засо- + +бу (веб-сервісу) використання дистрибутивно-семантичних моделей + +векторного представлення сутностей природної мови + +— UkrVectōrēs; +Електронна + +бібліотека + +медіафайлів + +підсистеми + +телереабілітації + +TISP + +— сервіс vHealth. +Ця книга присвячується моєму синові, +Марку Кириловичу Малахову. + +566 +СПИСОК ВИКОРИСТАНОЇ ЛІТЕРАТУРИ +1. 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P. 5—13. + +570 +Додаток d1 +JSON-схема вихідних даних сервісу визначення списку доступних для викорис- +тання дистрибутивно-семантичних моделей +{ + +«$schema»: «http://json-schema.org/draft-07/schema», + +«$id»: «http://example.com/example.json», + +«type»: «object», + +«title»: «The root schema», + +“description”: «Cхема вихідних даних сервісу визначення списку доступ- +них для використання дистрибутивно-семантичних моделей.», + +«default»: {}, + +«examples»: [ + + +{ + + + +«models»: { + + + + +«word2vec»: [ + + + + + +{ + + + + + + +«description»: «Використовується нейронна вектор- +на модель представлення слів «Олесь Гончар» (з використанням набору +даних — проблеми поетики творчого доробку Олеся Гончара), алгоритм +word2vec word embeddings розмірністю 500d. Сутність — слово, лематизова- +но, приведено до нижнього регистру. Параметри word2vec: -size 500 -negative +5 -window 5 -threads 24 -min_count 10 -iter 20.», + + + + + + +«name»: «honchar.lowercased.lemmatized.word2vec. +FINAL. 500d», + + + + + + +«link»: «», + + + + + + +«language»: «ua», + + + + + + +«index»: 0 + + + + + +} + + + + +] + + + +} + + +} + +], + +«required»: [ + + +«models» + +], + +«properties»: { + + +«models»: { + + + +«$id»: «#/properties/models», + + + +«type»: «object», + + + +«title»: «The models schema», + + + +«description»: «An explanation about the purpose of this instance.», + + + +«default»: {}, + +571 + + + +«examples»: [ + + + + +{ + + + + + +«word2vec»: [ + + + + + + +{ + + + + + + + +«description»: «Використовується нейронна век- +торна модель представлення слів «Олесь Гончар» (з використанням набору +даних — проблеми поетики творчого доробку Олеся Гончара), алгоритм +word2vec word embeddings розмірністю 500d. Сутність — слово, лематизова- +но, приведено до нижнього регистру. Параметри word2vec: -size 500 -negative +5 -window 5 -threads 24 -min_count 10 -iter 20.», + + + + + + + +«name»: «honchar.lowercased.lemmatized.word2vec. + + + + + + + +FINAL. 500d», + + + + + + + +«link»: «», + + + + + + + +«language»: «ua», + + + + + + + +«index»: 0 + + + + + + +} + + + + + +] + + + + +} + + + +], + + + +«required»: [ + + + + +«word2vec» + + + +], + + + +«properties»: { + + + + +«word2vec»: { + + + + + +«$id»: «#/properties/models/properties/word2vec», + + + + + +«type»: «array», + + + + + +«title»: «The word2vec schema», + + + + + +«description»: «An explanation about the purpose of this +instance.», + + + + + +«default»: [], + + + + + +«examples»: [ + + + + + + +[ + + + + + + + +{ + + + + + + + + +«description»: «Використовується нейронна +векторна модель представлення слів «Олесь Гончар» (з використанням на- +бору даних — проблеми поетики творчого доробку Олеся Гончара), алгоритм +word2vec word embeddings розмірністю 500d. Сутність — слово, лематизова- +но, приведено до нижнього регистру. Параметри word2vec: -size 500 -negative +5 -window 5 -threads 24 -min_count 10 -iter 20.», + + + + + + + + +«name»: «honchar.lowercased.lemmatized. + + + + + + + + + +word2vec.FINAL. 500d», + + + + + + + + +«link»: «», + + + + + + + + +«language»: «ua», + +572 + + + + + + + + +«index»: 0 + + + + + + + +} + + + + + + +] + + + + + +], + + + + + +«additionalItems»: true, + + + + + +«items»: { + + + + + + +«$id»: «#/properties/models/properties/word2vec/items», + + + + + + +«anyOf»: [ + + + + + + + +{ + + + + + + + + +«$id»: «#/properties/models/properties/word2vec/ +items/anyOf/0», + + + + + + + + +«type»: «object», + + + + + + + + +«title»: «The first anyOf schema», + + + + + + + + +«description»: «An explanation about the purpose of +this instance.», + + + + + + + + +«default»: {}, + + + + + + + + +«examples»: [ + + + + + + + + + +{ + + + + + + + + + + +«description»: «Використовується не- +йронна векторна модель представлення слів «Олесь Гончар» (з використан- +ням набору даних — проблеми поетики творчого доробку Олеся Гончара), +алгоритм word2vec word embeddings розмірністю 500d. Сутність — слово, +лематизовано, приведено до нижнього регистру. Параметри word2vec: -size +500 -negative 5 -window 5 -threads 24 -min_count 10 -iter 20.», + + + + + + + + + + +«name»: «honchar.lowercased.lemmatized. +word2vec.FINAL. 500d», + + + + + + + + + + +«link»: «», + + + + + + + + + + +«language»: «ua», + + + + + + + + + + +«index»: 0 + + + + + + + + + +} + + + + + + + + +], + + + + + + + + +«required»: [ + + + + + + + + + +«description», + + + + + + + + + +«name», + + + + + + + + + +«link», + + + + + + + + + +«language», + + + + + + + + + +«index» + + + + + + + + +], + + + + + + + + +«properties»: { + + + + + + + + + +«description»: { + + + + + + + + + + +«$id»: «#/properties/models/properties/ +word2vec/items/anyOf/0/properties/description», + + + + + + + + + + +«type»: «string», + +573 + + + + + + + + + + +«title»: «The description schema», + + + + + + + + + + +«description»: «An explanation about the +purpose of this instance.», + + + + + + + + + + +«default»: «», + + + + + + + + + + +«examples»: [ + + + + + + + + + + + +«Використовується нейронна век- +торна модель представлення слів «Олесь Гончар» (з використанням набору +даних — проблеми поетики творчого доробку Олеся Гончара), алгоритм +word2vec word embeddings розмірністю 500d. Сутність — слово, лематизова- +но, приведено до нижнього регистру. Параметри word2vec: -size 500 -negative +5 -window 5 -threads 24 -min_count 10 -iter 20.» + + + + + + + + + + +] + + + + + + + + + +}, + + + + + + + + + +«name»: { + + + + + + + + + + +«$id»: «#/properties/models/properties/ +word2vec/items/anyOf/0/properties/name», + + + + + + + + + + +«type»: «string», + + + + + + + + + + +«title»: «The name schema», + + + + + + + + + + +«description»: «An explanation about the +purpose of this instance.», + + + + + + + + + + +«default»: «», + + + + + + + + + + +«examples»: [ + + + + + + + + + + + +«honchar.lowercased.lemmatized. +word2vec.FINAL. 500d» + + + + + + + + + + +] + + + + + + + + + +}, + + + + + + + + + +«link»: { + + + + + + + + + + +«$id»: «#/properties/models/properties/ +word2vec/items/anyOf/0/properties/link», + + + + + + + + + + +«type»: «string», + + + + + + + + + + +«title»: «The link schema», + + + + + + + + + + +«description»: «An explanation about the +purpose of this instance.», + + + + + + + + + + +«default»: «», + + + + + + + + + + +«examples»: [ + + + + + + + + + + + +«» + + + + + + + + + + +] + + + + + + + + + +}, + + + + + + + + + +«language»: { + + + + + + + + + + +«$id»: «#/properties/models/properties/ +word2vec/items/anyOf/0/properties/language», + + + + + + + + + + +«type»: «string», + + + + + + + + + + +«title»: «The language schema», + +574 + + + + + + + + + + +«description»: «An explanation about the +purpose of this instance.», + + + + + + + + + + +«default»: «», + + + + + + + + + + +«examples»: [ + + + + + + + + + + + +«ua» + + + + + + + + + + +] + + + + + + + + + +}, + + + + + + + + + +«index»: { + + + + + + + + + + +«$id»: «#/properties/models/properties/ +word2vec/items/anyOf/0/properties/index», + + + + + + + + + + +«type»: «integer», + + + + + + + + + + +«title»: «The index schema», + + + + + + + + + + +«description»: «An explanation about the +purpose of this instance.», + + + + + + + + + + +«default»: 0, + + + + + + + + + + +«examples»: [ + + + + + + + + + + + +0 + + + + + + + + + + +] + + + + + + + + + +} + + + + + + + + +}, + + + + + + + + +«additionalProperties»: true + + + + + + + +} + + + + + + +] + + + + + +} + + + + +} + + + +}, + + + +«additionalProperties»: true + + +} + +}, + +«additionalProperties»: true +} + +575 +Додаток d2 +Початковий код програмного інструментарію навчання +прогностичних моделей дистрибутивної семантики +(програмна бібліотека gensim, алгоритм word2vec) +from __future__ import unicode_literals +import multiprocessing, time +from gensim.models import Word2Vec +from gensim.models import Word2Vec as WV_model +from gensim.models.word2vec import LineSentence +from gensim import utils +class MyCorpus(object): + +”””An interator that yields sentences (lists of str).””” + +def __iter__(self): + + +corpus_path = ’./dataset/honchar/extracted_lemmatized.txt’ + + +for line in open(corpus_path): + + + +# assume there’s one document per line, tokens separated by whitespace + + + +yield utils.simple_preprocess(line) +# inp = “extracted.txt” +sentences = MyCorpus() +out_model = “../models/honchar.lowercased.lemmatized.word2vec.500d” +size = 500 # size is the dimensionality of the feature vectors. +window = 5 # window is the maximum distance between the current and predicted +word within a sentence. +sg = 1 # By default (sg=0), CBOW is used. Otherwise (sg=1), skip-gram is employed. +# cbow_mean = 1 # cbow_mean = if 0, use the sum of the context word vectors. If 1 +(default), use the mean. Only applies when cbow is used. +sample = 1e-5 # sample = threshold for configuring which higher-frequency words are +randomly downsampled; default is 1e-3, useful range is (0, 1e-5). + +576 +negativeSampling = 5 # negative = if > 0, negative sampling will be used, the int for +negative specifies how many “noise words” should be drawn (usually between 5–20). +Default is 5. If set to 0, no negative samping is used. +hs = 0 # hs = if 1, hierarchical softmax will be used for model training. If set to 0 +(default), and negative is non-zero, negative sampling will be used. +iter = 20 +min_count = 10 +workers = multiprocessing.cpu_count() +start = time.time() +# model = Word2Vec(LineSentence(inp), sg = sg, size = size, window = window, +workers = workers, negative = negativeSampling, iter = iter, min_count = min_count, +hs = hs, sample = sample) +model = Word2Vec(sentences = sentences, sg = sg, size = size, window = window, +workers = workers, negative = negativeSampling, iter = iter, min_count = min_ +count, hs = hs, sample = sample) +# trim unneeded model memory = use (much) less RAM +model.init_sims(replace=True) +print(time.time()-start) +sim = model.wv.similarity(’гончар’, ’лист’) +print(sim) +s = model.wv.most_similar(’гончар’) +print(s) +m = model.wv.most_similar(’герой’) +print(m) +lc = model.wv.most_similar(positive= [’гончар’, ’герой’]) +print(lc) +model.save(out_model) + +577 +FUNDAMENTALS OF COMPUTER ECHOLOCATION +IN DISTRIBUTER STRUCTURES +Khoshaba O. M. +У роботі запропоновано основи комп’ютерної ехолокації в розподілених +структурах на основі генерації та аналізу затримок повернутих сигналів різ- +ної частоти для виявлення структурно-функціональних порушень. +Показано класифікацію моделей впливу навантаження та обробки да- +них на основі детермінованих та ймовірнісних методів дослідження. Описано +приклади використання комп’ютерної ехолокації в розподілених структу- +рах. Представлено етапи дослідження розподілених структур за допомогою +комп’ютерної ехолокації. +The paper proposes the basics of computer echolocation in distributed structures +based on the generation and analysis of delays of reflected signals of different fre- +quencies to detect structural and functional disorders. +The classification of models of loading impact and data processing based on +deterministic and probabilistic research methods is shown. Examples of the use of +computer echolocation in distributed structures are described. The stages of research +of distributed structures using computer echolocation are presented. +1. Basic concepts and definitions. Computer echolocation is a method +for generating and analyzing delays of reflected signals of different frequen- +cies to detect structural and functional disorders in computer systems or +distributed structures. +The use of computer echolocation makes it possible to move to a higher, +qualitative level in obtaining information about the structural and function- +al features of distributed systems and diagnosing their violations, which can +manifest themselves both at earlier and later stages of the operation of cor- +porate software and hardware systems. +Computer echolocation can diagnose structural and functional disor- +ders in distributed systems by assessing the amplitude and frequency spectra +of signals obtained due to loading effects on the objects of study by comput- +er echolocation. +The importance of conducting echolocation studies is increasing since +the developed infrastructure of an organization can consist of heteroge- +neous software and hardware complexes and devices where it is possible to +determine abnormal areas of their functioning. +Computer echolocation is based on using the sent and reflected signals +from the research object. + +578 +The use of computer echolocation is based on repeating sequences of +stages that are aimed at studying the process of loading effects and data pro- +cessing, selecting the parameters of the reference (required) trajectory of the +loading effect on the research object, forming, cleaning (eliminating noise +and distortion) and analyzing the signal. +The main stages of research of distributed structures using computer +echolocation include the following. +1. Formation of a reference model of the trajectory of the load action. +2. Determination of the main parameters of the trajectory of the load +action. +3. Preparation for signal shaping, sampling definition. +4. We are working on generating a signal, sending a signal, receiving, and +shaping a reflected signal. +The stages of carrying out echolocation works are closely related to the +use of subjects and objects of research. +As shown in Table 1, there are operations on the subjects of the study of +computer echolocation. Operations used at the top level concerning the tra- +jectory of loading actions are abbreviated as CRUD and mean the following. +C (create) — the operation of creating a trajectory with specific param- +eters in the form of an analog or discrete signal. +R (read) — operation of reading the parameters of the trajectory, which +it can perform by displaying the required parameters. Also, such an opera- +tion can carry out the output of several types of trajectories. +Table 1 +Comparative characteristics of the levels of subjects of echolocation research +Specifications +Upper level +Lower level +Research subject +Load trajectory +Signal +Level feature +Abstract +Physical +The nature of the use of +methods +Deterministic research +methods +Probabilistic research +methods +Operations on research +subjects +CRUD operations +Sampling operations +U (update) — the operation of adding a trajectory to the scenario of load +action, since it is possible to combine several trajectories. +D (delete) — operation of deleting the added trajectory from the scenar- +io of the load action. Such an operation can be carried out based on the in- +put of the trajectory parameters or the identification number of the created +or added trajectory. + +579 +It is convenient to perform the above operations at the stage of formal- +izing the task of the load action or when working with a database, where the +parameters of the load action are processed. +2. Classification of models of the process of exposure to load and data +processing. Load impact and data processing models describe the processes +occurring in distributed structures. This can describe these processes using +deterministic (Fig. 1) and probabilistic models (Fig. 2). In turn, each of the +listed groups of deterministic and probabilistic models is divided into sever- +al categories that differ in the nature and characteristics of their use. Let’s +consider each group and category of models separately. + +Fig. 1. Classification of deterministic models of trajectories of the loading action of +the process of loading action and data processing +2.1. Features of deterministic models of loading effects. Deterministic mod- +els directly describe the processes of loading actions themselves. The model +of the process of loading influence is deterministic (or non-random) when it +is possible to describe its exact prediction (behavior) over any period of time. + +Deterministic models +of trajectories of load +impact +Bythe natureof +periodicity +Periodic +Non-periodic +Bythe nature of +Harmonic +/aperiodic/ +datarepresentation +Polyharmonic +Analog +Digital +Discrete580 + +Fig. 2. Harmonic (or sinusoidal) functions that are used in the group of periodic +trajectories of loading effects +The deterministic model of the load action and data processing (MLI) +process is expressed by the following relationship: +MLI = F(t,z,ω,...,A,B,C,...), +where t, z, w,… are independent arguments (time, spatial coordinate, fre- +quency, etc.); +A, B, C… — trajectory parameters. +Using a deterministic model, the values of the trajectory of the load ac- +tion are a priori known since they can be quite accurately determined (cal- +culated) at an arbitrary moment in time on the numerical axis or at a point +in space. +The physical meaning of the trajectory of the load action is that it is a +reference function that contains information about the number of requests +created at certain points in time to the object of study. +2.2. Category of models of the nature of periodicity in trajectories of load- +ing action. In the category of models of periodicity nature, two groups in the +load action trajectories can be distinguished, which correspond to periodic +and non-periodic functions (Fig. 1). +In the periodic trajectories of the loading effects group, we include har- +monic and polyharmonic functions. For periodic functions, the general +condition is satisfied, under which the trajectory of the load impact (TrLI, +the trajectory of load impact) takes the form: +TrLI(t) = TrLI(t + kT), +where k = 1, 2, 3,... — any integer; +T — period, which is a finite length of time. +2.2.1. Harmonic paths of loading action. Consider the harmonic trajec- +tories of the loading action. Let us define the parameters of the trajectory +of the loading action as amplitude, frequency, and phase shift, which will + +y(t)= A.sin[wo-t + +Wot+Φ +0581 +determine the general characteristics of the process of loading actions and +data processing. +Then, let us designate the following information parameters of the load +acts as a signal as follows: +A — signal amplitude (in units of measurement); +fо — cyclic frequency (in hertz); +ωо = 2πfо — angular frequency (in radians); +ϕ and φ are the initial phase angles (in radians). +In this case, the period of one swing will be: +T = 1/fо = 2π/ωо. +This relationship also shows the relationship between cyclic and angular +frequency. +If we take the group of harmonic (or sinusoidal) functions of the trajec- +tory of loading actions as signals, then we describe the following relation- +ships (Fig. 2): +TrLI(t) = A⋅sin (2πfо t+φ) = A⋅sin (ωо t+φ), +or +TrLI(t) = A⋅cos (ωо t+ϕ), +where A, fo, ωo, φ, ϕ are constants that can play the role of information pa- +rameters of the signal. +We should also note that for ϕ = φ-π / 2, the sine and cosine functions +will describe the same signal. The signal’s frequency spectrum can be rep- +resented (Fig. 3) by its amplitude and initial phase value of the frequency fо +(at t = 0). + + +Signal coordinates +Signal frequency +Fig. 3. The trajectory of the loading effect in the form of a harmonic signal and the +spectrum of its amplitude + +2 +AAA +0 +- +-2 +0 +20 +40 +601 +- +1 +- +1 +- +- +1 +- +- +- +1 +- +- +-F +- +- +- +- +1 +- +- +1 +- +1 +- +1 +- +1 +0 +0 +0.1 +0,2 +0,3 +0.4 +0,5582 +2.2.2. Polyharmonic paths of loading action. The polyharmonic trajecto- +ries of the loading action are a set of trajectories and are described as follows: +( ) +( +) +1 +0 +2 +N +LI +n +n +n +n +Tr +t +A sin +f t +− += += +π ++ ϕ +∑ +, +or directly by function +TrLI(t) = y(t ± kTp), +where k = 1,2,3,..., +Tr is the period of one complete signal oscillation for the function y(t), +set for one period. +The value fp = 1 / Tp is defined as the fundamental oscillation frequency. +At the same time, polyharmonic trajectories of loading actions, which +are represented by signals, consisting of the sum of a certain constant com- +ponent (fo = 0) and an arbitrary (in the limit — infinite) number of harmonic +components with arbitrary values of the amplitudes An and phases ϕn, with +periods that are multiples of the period of the fundamental frequency fp. +Thus, on the period of the fundamental frequency fp, which is equal to +or multiples of the minimum frequency of harmonics, multiple periods of +all harmonics can fit. This creates a repetition rate for the signal. +The frequency spectrum of polyharmonic signals is discrete. In this re- +gard, there is another mathematical representation of the signal, which is +described in the form of spectra (or Fourier series). +For example, consider the representation of a periodic function (Fig. 4), +obtained by summing the constant component (the frequency of the con- +stant component is 0) and three harmonic oscillations with different values +of the frequency and the initial phase of the oscillations. + + + +Temporary model +Amplitude spectrum +Phase spectrum +Fig. 4. Model of the trajectory of the loading action +The formula gives the mathematical description of the signal: +( ) +( +) +3 +0 +2 +LI +n +n +n +n +r +t +A cos +f t += += +π ++ φ +∑ +, + +0.1 +0.2 +0.3 +0.4 +0.500 +D +2 +0 +0 +40 +80 +1200.25 +0.5 +0.75 +-1 +0 +4080120583 +where Ak = {5, 3, 4, 7} — amplitude of harmonics; +fk = {0, 40, 80, 120} — frequency in hertz; +ϕk = {0, -0.4, -0.6, -0.8} is the initial phase angle of the harmonic in +radians; +k = 0,1,2,3 is the number of periods. +The fundamental frequency of the signal is 40 Hz. +The frequency representation of the trajectory of the load action (in the +form of a signal spectrum) is shown in Fig. 4 (b). Also, the frequency repre- +sentation of the periodic signal TrLI (t) is determined, limited by the number +of spectrum harmonics. +It should note that a periodic signal of any arbitrary shape can be repre- +sented as a sum of harmonic oscillations with frequencies that are multiples +of the fundamental frequency: +fр = 1 / Tr. +To do this, it is enough to expand one period of the signal in a Fourier se- +ries in terms of trigonometric functions of sine and cosine with a frequency +step equal to the fundamental frequency of oscillations Δf = fp: +( ) +( +) +0 +2 +2 +K +k +k +k +Tr t +a cos +k ft +b sin +k ft += += +π Δ + +π Δ +∑ +, +( +) +( ) +( +) +( ) +0 +0 +0 +1/ +, +2 / +2 +, +T +T +k +a +T +Tr t dt a +T +Tr t cos +k ftdt += += +π Δ +∫ +∫ + +( +) +( ) +0 +2 / +2 +. +T +kb +T +Tr t sin +k ftdt += +π Δ +∫ + +The number of terms of the Fourier series K = kmax is usually limited +by the maximum frequencies fmax of harmonic components in the signals +so that fmax < K · fp. +However, for signals with discontinuities and jumps, fmax → ∞ exists. In +this case, the number of members of the series is limited by the permissible +error of approximation of the function TrLI(t). +Single frequency cosine and sine harmonics can be combined and de- +composed in a more compact form as follows: +( ) +( +) +0 +2 +, +K +k +k +k +Tr t +Tr cos +k ft += += +π Δ − ϕ +∑ +, +k +Tr = +, +( +) +/ +k +k +k +arctg b +a +ϕ = +. + +584 +There is also a representation of a rectangular periodic signal (meander) +in an amplitude Fourier series in the frequency domain. For example, in +fig. 5, the trajectory of the loading action in the form of a rectangular peri- +odic signal, where the depicted signal is even concerning t = 0, does not have +sinus harmonics, and all values of ϕk for this signal model are equal to zero. +a) Time model +b) Amplitude spectrum +Fig. 5. Model of the trajectory of the load acting in the form of a rectangular periodic +signal +The input parameters of the polyharmonic trajectory of the loading ac- +tion can be: +– specific features of the waveform (swing from minimum to maximum, +abnormal deviation from the mean, etc.); +– some parameters of signal harmonics. +For example, for rectangular pulses, the input parameters can be pulse +repetition period, pulse duration, pulse duty ratio (i.e., the ratio of the pe- +riod to duration). +When analyzing complex periodic signals, the input parameters can also be: +– the current average value (AC) for a specific time, for example, for +some time: +( ) +1/ +t T +C +t +A +T +Tr t dt ++ += +∫ +, +– constant component (CC) of one period: +( ) +0 +1/ +T +C +C +T Tr t dt += +∫ +, + +x(t) +0 +0 +200 +400 +600 +8002 +(X585 +– average rectified (AR) value: +( ) +0 +1/ +T +R +A +T +Tr t dt += +∫ +. +2.3. Models of the category of representation of the trajectory data of +loading actions. Models of the data presentation category describe processes +based on trajectories in cases where they can represent the values of load +actions as functions or signals: +– analog, in which there is no quantization; +– discrete, in which quantizations are used only on the time scale; +– digital, in which quantizations are used on all scales. +In this case, a signal can be understood as a physical or abstract process +that contains information. +To the analog representation of the trajectory of the load, action belongs +to such a continuous line, which has a set of values determined at each mo- +ment relative to the time axis (Fig. 6). + +Fig. 6. Analog representation of the trajectory of the loading action +The values of the analog trajectory of the loading action (Fig. 6) are ar- +bitrary at each moment. Therefore, such a trajectory can be represented as a +continuous function (depending on time or on a variable) or as a piecewise +continuous function of time. +The analog values of the trajectory of the loading action can have an in- +finite number of values within certain limits. They are continuous, and their +values cannot change abruptly. +The analog form of the trajectory of the load action is written as x(t), +where t is a specific moment in time. + +0 +T586 +Such an imaginary line belongs to the discrete representation of the tra- +jectory of the load action, at which there are many values only at specific +points in time (Fig. 7). + +Fig. 7. Discrete representation of the trajectory of the loading action +Thus, the discrete representation of the trajectory of the load action +takes on specific values only at certain moments of sampling. That is, the +imaginary line is not continuous, in contrast to the analog representation of +the trajectory of the load action. So, in fig. 7 shows an example of the for- +mation of such a discrete representation of the trajectory of the load action +with an interval (or step) of sampling T. +When using a discrete representation of the trajectory of the loading ac- +tion, it is necessary to pay attention to the following provisions: +– for this type of representation, quantization is performed only at sam- +pling intervals along the time scale, but not the values of the trajectory of the +load action themselves; +– for this type of presentation, it is possible to use uniform and non-uni- +form intervals, which are located on the timeline. +The digital representation of the trajectory of the load action takes only +fixed values (Fig. 8), which are located in the time axis with a certain inter- +val (step). +Fig. 8 shows an example of the formation of a digital representation of +the trajectory of the load acting on the basis of an analog one. In this case, it +is necessary to pay attention to the fact that the values of digital representa- +tion cannot take intermediate values. +Thus, the digital representation of the trajectory of the load action is +such a discrete representation in which quantization occurs not only in the +time scale, but also in the level of values. + +-3T +-2T +-T +0 +T +2T +3T587 + +Fig. 8. Digital representation of the trajectory of the loading action +These can widely use such a representation of the trajectory of the load +action in solving several problems. This representation of the load impact +trajectory is especially in demand when using controllers or other comput- +ing devices to solve several modeling problems based on Boolean algebra. +3. Probabilistic models of the process of loading effects and data processing +3.1. Features of using probabilistic models. Random (probabilistic) mod- +els describe data processing processes due to loading effects on the research +object. A data processing model describes the statistical characteristics of +a random process by specifying various laws of a probability distribution, +correlation function, spectral density, etc. +4. An example of using the trajectory of the loading effect based on the fre- +quency of sounding musical notes in octaves. There is a table of the frequency +of sounding musical notes in octaves. It is sometimes convenient to use this +table to design the load path. +For example, the A note for the first octave (A) has a frequency of 440.00 +hertz, the C# for the second octave is 554.37 hertz, and the E for the second +octave (E) is 659.26 hertz. Let’s round off the values of the proposed notes +and get the following values: +A = 440 Hz; +C# = 550 Hz; +E = 660 Hz. +Let’s write the program code for Matlab: +where the cyclic frequency will be: +fc = 440; + +-3T +-2T +-T +0 +T +2T +3T588 + +Fig. 9. Classification of probabilistic models of the process of loading impact and +data processing +the sampling rate will be: +fs = 8000; +the time interval within the period will be: +dt = 1/fs; +the constant component (Ak) will be equal to: +Ak = 2.5. +Next, we create a vector of time t, which will have values from 0 to 0.1 +seconds with a step of 1.25 * 10–4: +t = 0: dt: 0.1. +Next, we create a cosine wave as follows: +Tr = Ak + cos (2 * pi * fc * t). + +Probabilistic +/random/ models +oftheprocessofload +impact and +dataprocessing +Bythe natureof +static +Bythenatureof +stationary +Static +Non-stationary +Dynamic +Stationary589 +Consider the graph of the trajectory of the load action (Fig. 10): +plot (t, Tr) + +Fig. 10. Graph of the trajectory of the loading effect for the signal of the note A of +the first octave +5. Research structure of the distributed system using computer echoloca- +tion. The study of distributed structures using computer echolocation has +several functional components (Fig. 12): a load generator (or benchmark), +a load balancer, a monitoring system, modules, and nodes. +Let’s consider the main components of a distributed structure. Bench- +mark is a structural component of the research structure of the load balanc- +er, which is necessary for the generation of request flows that are executed +according to a specific trajectory. +A module is a structural component of the research structure of a load +balancer. Its main functions include: +– processing and exchange of synchronous request flows; +– synchronization of requests between the pool and the load balancer. +The pool is a structural component of the research structure of the load +balancer, which is necessary for: +– storage of request flows; + +3.5 +2.5 +1.5 +0.01 +0.02 +0.03 +0.04 +0.05 +0.06 +0.07 +0.08 +0.09 +0.1590 + а) + b) +Fig. 11. Graph of the trajectory of the loading effect for a signal of three notes: +a) presentation of individual signals b) presentation of the sum of three signals + +3.5 +2.5 +X 0.007125 +Y2.20596 +X0.00975 +1.58225 +1.5 +0.002 +0.004 +0.006 +0.008 +0.013.4 +3.2 +3 +2.8 +2.6 +2.4 +2.2 +2 +1.8 +1.6 +2 +8 +10 +12 +14 +×10°3591 + +Fig. 12. Research structure of the distributed system. +– synchronization of request flows between the benchmark and the load +balancer module. +In this load balancer research system, the pool is a dynamic bottleneck. +A distributed system node is a structural component of a load balancer. +Its primary function is to implement request flows created by the bench- +mark in a specific scenario. Request flows are transferred to a distributed +system node using a module. +The monitoring system of the research system is a structural component +of the load balancer, which is necessary for measuring the performance of +benchmarks, the pool of the load balancer, modules, and communication +channels. +In this research structure of the load balancer, measuring the dynamics of +changes in the bottleneck is based on the observation points. The structure +can set observation points of the monitoring system of the research structure +for a specific time interval of the process or the occurrence of some event. +Also, communication channels play an essential role in the work of the +research structure of the load balancer. Communication channels are struc- +tural formations necessary to transfer requests to the main components of +the load balancer. +The communication channels can transfer synchronous and asynchro- +nous request flows in communication channels. + +- +- +- +- +1 +2 +Z +nodes +1 +- +Benchmarks +1 +[00. +system +us +P +1 +- +ibuted +- +Asynch +- +- +I +- +Distril +/ +M +I Load Balancer +- +-592 +6. Comparative characteristics of evaluations of the work of distributed +systems. Comparative characteristics of the assessments of the work of dis- +tributed systems are based on the assumption of the static and dynamic na- +ture of the processes carried out in such structures. To solve the problems of +determining the estimates of the operation of nodes in the literature, models +of parallel and distributed structures are proposed based on reference algo- +rithms for solving problems [1–4]. +In this regard, the determination of the estimates of the work of +nodes, which is based on the model of a parallel system, uses a reference +sequential algorithm for solving some problem A by an application in +time T [2, 4]. In this case, the acceleration estimate is used, which is +defined as: +0 / +S +T +T += +, +where T0 is the time to solve reference problem A by the application on one +device (node) using the fastest sequential algorithm. +Acceleration S shows how many times the node can reduce the time for +solving a problem by an application by using a parallel structure [3]. +The next assessment of the work of applications on nodes in parallel +structures is efficiency, which is usually defined [1, 3] as: +0 +/ +/ +E +S +nT +nT += +. +The described model of application operation on a parallel structure is +simple for calculating scores. However, in this model, the values of their +estimates are determined only after the solution of the problem, when the +total time T is known. In addition, the model requires knowledge of the +time of solving the problem by the best of the set of sequential algorithms T0 +on one node on a parallel structure. +A different approach to using similar models for job appraisals has +distributed structures due to two aspects. First, due to their heteroge- +neity, the nodes in distributed structures can have different values for +evaluating the performance of applications since these nodes have differ- +ent computing resources. Secondly, nodes in distributed structures may +be unavailable at certain intervals throughout the solution of the entire +problem. +Consider one of the models for distributed structures applications, which +is characterized by the presence of a schedule and is defined as: +( ) +{ +} +: +0,1 +ih t +→ +R +. + +593 +Moreover, hi (t) = 1 if the application on the node at time t is available +for solving problem A. Otherwise, if hi (t) = 0, then the application on the +node at time t is unavailable. +The performance estimates for applications on a distributed structure +assume different relationships. So, for a model with a distributed structure +schedule, the efficiency assessment takes the form [5]: +( ) +( ) +t +T A +E +T A += +, +where T(A) is the reference time for solving problem A. +The reference time T(A) means the time for solving problem A by the +i-th application at the node using the fastest sequential algorithm, where +T(A)> 0. +Also, for applications on a distributed structure, such additional esti- +mates are introduced as [5,6]: the performance of the reference system and +the complexity of the task. Calculation of the reference system performance +(A, t) [5–7] is necessary to calculate T(A). +The reference performance of the structure i(A, t) is called [7] the per- +formance of the i-th node of a distributed system when solving problem A: +( ) +( ) +( ) +i +i +L A +A +T +A +π += +, +where L(A) is a function of the complexity of the task execution by an appli- +cation on a distributed structure. +The function complexity of task execution L(A) is defined on a certain +set of tasks and expresses a priori knowledge of its complexity: +( ): +L A ++ +Λ → R . +For example, an estimate of the number of elementary operations, cal- +culated using complexity theory [8–10], can be referred to as the function +of the complexity of task execution L (A) by an application on a distributed +structure. +To solve the problems of determining the estimates of the operation of +nodes in parallel and distributed structures, a model with a schedule is in- +troduced, which describes the concept of the reference performance of the +structure as the sum of the reference performance of the nodes [7]: +1 +( , ) +( ) ( ) +( ( ), ( )) +n +i +i +i +A t +A h t +A h t += +π += +π += π +∑ + + +, + +594 +where with full availability of applications on nodes +( ) +1 +ih t ≡ during the +solution of the problem and with the same reference performance, where +( ) +0 +i A +π += π , the reference performance of the distributed structure will +coincide with the reference performance of the parallel structure since the +condition +0 +n⋅π will be satisfied. +At the same time, a model with a schedule for solving problems from a +set is called a set: +( ), ( ) +A h t +ℜ =< π +> + + +. +For a model with a schedule, the reference time for solving problem A is +called the value ( ) +T A [5–7], which is determined by the following relation: +( ) +( +) +0 +: +, +t +t +Т А +mint +A +d += += +π +τ +τ +∫ +. +In general, the acceleration rates for a parallel structure are defined as +the ratio of the time it takes to solve a problem by an application at one node +to the time it takes to solve a problem on the entire system. In a distributed +structure with a schedule, the resources of the nodes can be different. There- +fore, it is incorrect to introduce the concept of acceleration to applications +in a distributed structure in the same way since it is unclear which node to +calculate the acceleration parameter itself. Based on this, a more general +concept of relative acceleration is introduced, which is defined as follows: +( +) +1 +1 +2 +2 +, +T +S R R +T += +. +This relation shows the estimate of the acceleration S for a model with +a schedule R1 relative to another system R2 as the ratio of their time to solve +problem A on applications in a distributed structure. +Also, for a model with a schedule, it is customary to estimate the accel- +eration S for each node of the distributed structure as follows: +( +) +1 +1 +2 +2 +, +T +S R R +T += +. +This relation shows the estimate of the acceleration Si for the i-th appli- +cation on the node as the ratio of the reference time for solving problem A +to the time for solving the same problem in a distributed structure based on +a model with a schedule. +Conclusions. The paper proposes the basics of computer echolocation in +distributed structures based on the generation and analysis of delays of reflect- +ed different frequency signals to detect structural and functional disorders. + +595 +The classification of models of loading and data processing based on de- +termined and probabilistic research methods is shown. Examples of the use +of computer echolocation in distributed structures are described. +The comparative characteristic of levels of subjects of echolocation re- +search is described. +The stages of research of distributed structures with the help of computer +echolocation are given. +REFERENCES +1. Афанасьев А. П., Посыпкин М. А., Хританков А. С. Аналитическая мо- +дель оценки производительности распределенных систем // Программ- +ные продукты и системы. — 2009. — № 4. — С. 60–64. +2. Хританков А. С. Математическая модель характеристик производитель- +ности распределенных вычислительных систем // Труды 50-й научной +конференции МФТИ. — 2007. — С. 86–88. +3. Хританков A. C. 0 характеристиках производительности распределенных +систем // Труды 51-й научной конференции МФТИ. — 2008. +4. Хританков А. С. Модели и алгоритмы распределения нагрузки. Алгорит- +мы на основе сетей СМО //Информационные технологии и вычисли- +тельные системы. — 2009. — № 3. — С. 33–48. +5. Посыпкин М. А., Хританков А. С. О понятии ускорения и эффективно- +сти в распределенных системах // Труды Всероссийской научной конфе- +ренции «Научный сервис в сети Интернет: решение больших задач». — +2008. — С. 149–155. +6. Хританков А. С. Оценка эффективности распределенных систем при +решении задач переменного размера. // Научно-технический вестник +СПбГУ ИТМО. — 2010. — № 2(66). — С. 66–71. +7. Посыпкин М. А., Хританков А. С. О понятии производительности в рас- +пределенных вычислительных системах // Труды ИСА РАН. — 2008. — +Т. 32. — С. 26–32. +8. J. L. Balc´azar, J. D´ıaz, and J. Gabarr´o. Structural Complexity II. Vol. 22. +EATCS Monographs on Theoretical Computer Science. Springer, 1990. +[Електронний ресурс] / електронні дані — Режим доступу: http://dx.doi. +org/10.1007/978–3–642–75357–2. +9. J. L. Balc´azar, J. Dґıaz, and J. Gabarr´o. Structural Complexity I, Second Edi- +tion. Texts in Theoretical Computer Science. An EATCS Series. Springer, 1995. +[Електронний ресурс] / електронні дані — Режим доступу: http://dx.doi. +org/10.1007/978–3–642–79235–9. +10. O. Goldreich. P, NP, and NP-Completeness: The Basics of Complexity Theory. +Cambridge University Press, 2010. + +596 +ЗАСТОСУВАННЯ МАТЕМАТИЧНИХ МОДЕЛЕЙ +ТА ПРОГРАМНОГО ЗАБЕЗПЕЧЕННЯ ДЛЯ ПРОЕКТУВАННЯ +НОВИХ ХАРЧОВИХ ПРОДУКТІВ +Котлик С. В., Соколова О. П. +У роботі показано необхідність вживання людиною кисломолочних +продуктів (сирів), показано їх переваги та користь, що вони приносять. +До складу сирів входять різні тваринні жири, однак сучасні технології +дозволяють замінювати тваринні жири рослинними. При цьому виникає +необхідність застосовувати рослинні олії в такій пропорції, щоб одер- +жання в суміші жирів НЖК, МНЖК, ПНЖК було близьким до співвід- +ношень, які рекомендовані теорією раціонального харчування. Для цього +були проведені відповідні експерименти, результати їх оброблені за до- +помогою методів регресійно-кореляційного аналізу, отримані адекватні +математичні моделі. Для цього складено комп’ютерну програму, яка ви- +користовує власну базу даних та метод випадкового пошуку для оптимі- +зації функцій. Програма була перевірена для деякої вибірки експеримен- +тальних даних, результати добре співвідносяться з реальними цифрами. +Також були отримані математичні моделі гомогенізації емульсій при ви- +робництві кисломолочного сиру з використанням купажів соняшникової +та оливкової олій. Для визначення оптимальних режимів гомогенізації +були побудовані математичні моделі залежності стійкості емульсії та +відстою жирової фази від температурі та тиску. Для їх використання +також розроблено програмний додаток, проведено його перевірку, надано +рекомендації щодо використання. В цілому розроблена програма дає в руки +користувача-технолога інструмент, яким він може користуватися для +розрахунку рецептури нових сортів кисломолочних продуктів з додаван- +ням рослинних олій, не проводячи фізичних експериментів, досліджуючи +властивості продукту на комп’ютері на підставі розроблених матема- +тичних моделей. +The paper shows the need for a person to consume fermented milk products +(cheeses), shows their advantages and the benefits that they bring. The compo- +sition of cheeses includes various animal fats, but modern technologies make it +possible to replace animal fats with vegetable ones. In this case, it becomes neces- +sary to use vegetable oils in such a proportion that the production of SFA, MUFA, +PUFA in a mixture of fats is close to the ratios recommended by the theory of ra- +tional nutrition. For this, appropriate experiments were carried out, their results +were processed using regression-correlation analysis, and adequate mathemati- +cal models were obtained. To do this, a computer application has been compiled +that uses its own database and a random search method to optimize functions. +The program has been tested for some sample of experimental data, the results are + +597 +in good agreement with real numbers. Mathematical models of emulsion homoge- +nization in the production of cheese were also obtained using blends of sunflower +and olive oils. To determine the optimal modes of homogenization, mathematical +models of the dependence of the stability of the emulsion and the settling of the +fat phase on temperature and pressure were built. For their use, a software ap- +plication was also developed, it was tested, and recommendations for use were +given. In general, the developed program gives the user-technologist a tool that +he can use to calculate the formulation of new varieties of fermented milk prod- +ucts with the addition of vegetable oils, without conducting physical experiments, +examining the properties of the product on a computer based on the developed +mathematical models. +Постановка проблеми. Одне з найважливіших завдань із покра- +щення структури харчування населення — збільшення продуктів +масового споживання з високою харчовою та біологічною цінністю. +Сучасне харчування має не лише задовольняти фізіологічні потреби +організму людини в харчових речовинах та енергії, а й виконувати +профілактичні та лікувальні функції та, звичайно, бути абсолютно +безпечними. +Розробка продуктів харчування із заданими якісними характерис- +тиками можлива за допомогою математичного моделювання їхнього +рецептурного складу. Завдання моделювання полягає в обґрунтова- +ному кількісному підборі основної сировини та збагачувальних доба- +вок, що у сукупності забезпечує формування необхідних органолеп- +тичних та фізико-хімічних властивостей готового продукту із заданим +рівнем споживчої та енергетичної цінності. При комп’ютерному мо- +делюванні з’являється можливість оптимізації певних властивостей +продукту, що розробляється, за встановленим критерієм (або крите- +ріями) без використання дорогих експериментальних досліджень. Ця +методологія дозволяє створювати продукти з певним вмістом білка, +жиру, вуглеводів, вітамінів, харчових волокон, амінокислот, міне- +ральних та інших речовин [8; 9; 16; 21; 47]. +Сьогодні поняття «проектування» продуктів включає в себе роз- +робку моделей, що представляють математичні залежності, які ві- +дображають всі зміни одного або декількох ключових параметрів. +При цьому необхідно проводити оптимізацію вибору і співвідношен- +ня вихідних компонентів для отримання рецептури, яка за кількісним +вмістом і якісним складом максимально відповідає заданій формулі +збалансованого харчування, відповідає заданим вимогам і володіє ви- +сокими споживчими властивостями [22; 40; 46]. + +598 +Розробка і виробництво нових продуктів заданої якості і складу в +умовах сучасного розвитку науки і техніки (в першу чергу комп’ютерів +і програмного забезпечення) вимагають застосування відповідного +математичного апарату і високопродуктивного комп’ютерного об- +ладнання. +Пошук і розробка ефективних чисельних методів, математичних +моделей, алгоритмів і реалізація новітніх інформаційних технологій +у вигляді комплексів проблемно-орієнтованих програм для вирішен- +ня задач оптимізації та проведення обчислювальних експериментів є +актуальними для різних сфер виробничої діяльності, в тому числі при +створенні нових харчових продуктів. +Створення таких ефективних рецептур в даний час базується на +проведенні необхідних натурних експериментів, обробки результатів +за допомогою методів регресійно-кореляційного аналізу, побудови +адекватної математичної моделі, розробки відповідного програмно- +го забезпечення і проведення комплексних розрахунків. Такий під- +хід дозволяє заощадити матеріальні засоби і отримати інструмент для +розрахунку рецептури створення нових продуктів із заданими влас- +тивостями [21]. +Виходячи зі сказаного, саме розширення можливостей оптиміза- +ційних програмних засобів дозволить вийти на якісно новий рівень +в розробці нових видів харчових продуктів із заданим хімічним скла- +дом, споживчими і технологічними характеристиками. Проектуван- +ня харчових продуктів оптимального складу методами математично- +го моделювання дозволить знизити фінансові та часові витрати на +розробку продуктів харчування, до яких відносяться і різні кисломо- +лочні продукти, в тому числі сири, своєчасно реагувати на зміну по- +треб людського організму в умовах техногенного суспільства і суттєво +розширити асортимент продукції функціонального, лікувально-про- +філактичного та лікувально-терапевтичного призначення, спрямова- +них на харчування окремих груп населення [23]. +Майже у всіх лікувальних меню, що пропонуються лікарями, +одним з перших значаться усі молочні та кисломолочні продукти, +насамперед сир. Але він корисний і здоровим людям будь-якого +віку. Сир є концентратом молочного білка і деяких інших скла- +дових частин молока. Важливість білка в нашому житті загально- +відома: це той матеріал, з якого будуються всі клітини організму, +ферменти, а також іммунні тіла, завдяки яким організм отримує +стійкість до захворювань. Організм людини отримує білки разом + +599 +з їжею, розщеплює їх до амінокислот і з цих своєрідних цеглинок +будує молекули нових білків, властивих тільки нашому організму. +Для цього йому необхідний набір з 20 амінокислот. Основним по- +стачальником саме цих амінокислот і служить сир. Поряд з білками +для нормальної життєдіяльності організму необхідні і мінеральні +речовини, найважливіші з яких — з’єднання кальцію і фосфору. +Саме останні складають основу кісткової тканини і зубів. До речі, +цим і пояснюється той факт, що в період формування, росту орга- +нізму діти та підлітки потребують додаткові кількості кальцію. Слід +додати, що через насиченість кальцієм молочні продукти є неза- +мінним при туберкульозі, переламах кісток, захворюваннях крово- +творного апарату, рахіті. +Сирні продукти — це продукти, що виробляються сквашу- +ванням молока або вершків чистими культурами молочнокислих +бактерій. Деякі сирні продукти отримують в результаті тільки мо- +лочнокислого бродіння; при цьому утворюється досить щільний, +однорідний згусток з вираженим кисломолочним смаком. Сирні +продукти мають велике значення в харчуванні людини завдяки лі- +кувальним і дієтичним властивостям, приємному смаку, легкій за- +своюваності [42]. +До складу сиру входить 14–17 % білків, до 18 % жиру, 2,4–2,8 % +молочного цукру. Він багатий на кальцій, фосфор, залізо, магній — +речовини, необхідні для росту і правильного розвитку молодого ор- +ганізму. Сир і вироби з нього дуже поживні, оскільки містять багато +білків і жиру. Білки сиру частково пов’язані з солями фосфору і каль- +цію. Це сприяє кращому їх перетравлюванню в шлунку і кишечнику. +Тому сир добре засвоюється організмом. +Вживання сиру і сирних виробів сприяє правильному обміну ре- +човин в організмі, підтримці на певному рівні осмотичного тиску. +Мінеральні речовини беруть участь в кісткоутворенні, харчуванні +нирвової системи та сприяють підвищенню рівня гемоглобіну в кро- +ві. Сир містить різноманітні вітаміни груп А, В, С, D і багато інших. +До складу сирів входять також різні тваринні жири, однак сучасні +технології дозволяють замінювати тваринні жири рослинними [38; +42–44]. +Це збільшує термін зберігання продукту, знижує вартість, покра- +щує споживчі якості, рятує від шкідливого холестерину. Але продукт +виходить лише за умови використання якісних фракцій, а не їх деше- +вих замінників. + +600 +Заміна тваринних жирів рослинними найчастіше зустрічається у +молочній промисловості. Сучасні жирові системи, в яких заміна до +30–50 % молочного жиру на рослинні жири дозволяє виробити ком- +біновану олію, сметану, сир, морозиво, кефір, сирні вироби, які за +смаковими якостями та консистенцією практично не відрізняються +від традиційних продуктів зі 100 %-м молочним жиром. +Відповідно до концепції збалансованого харчування для нормаль- +ної життєдіяльності людини необхідно надходження до організму +адекватної кількості енергії та основних харчових речовин, а також +дотримання строго певних співвідношень між багатьма факторами +харчування — білками, жирами, вуглеводами та іншими компонен- +тами [9; 10; 38]. +При проектуванні складу кисломолочних продуктів, що мають +комплексний сировинний вид, слід врахувати, що застосування рос- +линної сировини, що має підвищену біологічну цінність, дозволяє +отримувати композиції, які характеризуються поліпшеним вітамін- +ним, мінеральним, вуглеводним і амінокислотним складом у порів- +нянні з окремо взятими компонентами, при цьому можливо більш +тонке керування процесом формування продуктів. +При виробництві продуктів на молочній основі, які відповідають +вимогам раціонального харчування, необхідним етапом є обґрунту- +вання молочно-жирової основи та підбір інгредієнтів, які б сприяли +корегуванню її складу, обґрунтування жирнокислотного складу обра- +них фізіологічних добавок [22; 43]. +Робота присвячена розробці програмного забезпечення для ство- +рення та оптимізації рецептур сирних виробів з використанням ку- +пажів рослинних олій шляхом математичного моделювання різних +складових та їх співвідношень. +Аналіз розробки аналогічних комп’ютерних програм. В основному +запропоновані постановки моделей оптимізації рецептур зводяться +до задач лінійного програмування, в яких в якості цільової функції ви- +ступають вимоги мінімальної вартості суміші, максимального виходу +якогось одного компонента, необхідності утримання компонентів не +менше певної величини, деякий адитивний критерій, який об’єднує +кілька критеріїв з різними ваговими коефіцієнтами. У більшості пу- +блікацій дослідження завершується на етапі побудови математичної +моделі з поясненням очікуваного результату їх застосування. Можна +перерахувати поодинокі спроби реалізувати запропоновані постанов- +ки розробки рецептур харчових продуктів на практиці за допомогою + +601 +комп’ютерних програм, хоча такий підхід є логічним і раціональним +[8; 16; 25; 26; 34–37]. +Дослідження з розробки комп’ютерних програм для розрахунку +рецептур нових продуктів в основному ведуться в контексті реалі- +зації математичних моделей, створених за результатами експери- +ментів. +Існують різні програмні продукти для автоматизованого розрахун- +ку рецептур. Однією з найбільш поширених програм для розрахунку +рецептур є MS Excel. При використанні цього програмного продукту +необхідні для обчислення дані, а також розрахункові формули зано- +сяться у відповідні комірки електронної таблиці. Недоліком викорис- +тання MS Excel є відсутність можливості автоматизованого введення +вхідних даних і розрахункових залежностей [6; 9; 25]. +Існуючі спеціалізовані пакети програм для проектування рецеп- +тур продуктів харчування діляться на два класи: програми в складі +автоматизованих систем управління виробництвом і спеціалізовані +програми, призначені для виконання разових розрахунків стосовно +певних видів продовольчих продуктів. Для спеціалізованих пакетів +програм, що працюють у складі математичного забезпечення авто- +матизованих систем управління виробництвом, характерна надмірно +висока вартість, їх впровадження висуває підвищені вимоги до рівня +комп’ютерної підготовки персоналу харчових підприємств. До не- +доліків спеціалізованих програм для проектування рецептур можна +віднести обмеженість відомостей з альтернативних сировинних ін- +гредієнтів, прив’язку до офісних програм загального призначення і +конкретних видів продовольчих продуктів, а також недостатньо ви- +сокий рівень захисту інтелектуальної власності. Загальним недоліком +існуючих програмних продуктів, які застосовуються для проектуван- +ня рецептур, є відсутність підсистеми (модуля) оптимізації рецептури +за сукупністю критеріїв харчової, біологічної та енергетичної ціннос- +ті [9; 16; 22; 25]. +Спеціалізований програмний комплекс «Etalon» [37] призна- +чений для проектування багатокомпонентних рецептур продуктів +загального призначення, а також спеціалізованих продуктів, відпо- +відних за складом фізіологічним потребам організму з урахуванням +віку, патології, фізичних станів і навантажень, навколишнього се- +редовища, призначених для дитячого, дієтичного, функціонального +харчування, вагітних і жінок, що годують, спецконтингенту. Засто- +сування програми в значній мірі дозволяє забезпечити впорядкова- + +602 +ну роботу з даними і розробити продукт із заданими властивостями. +Програмний комплекс складається з таких частин: 1) інформаційна +база даних, в якій зберігається інформація про нутрієнтний склад +харчової сировини і фізіологічні норми харчування різних соціаль- +них груп населення; 2) спеціалізована база даних, розроблена для +підвищення ефективності функціонування алгоритму моделювання +рецептур харчових продуктів; 3) система управління інформацій- +ною базою даних. Інформаційна база даних розроблена в середови- +щі Microsoft SQL Server 2000 на моделі «клієнт / сервер» і включає +кілька взаємопов’язаних таблиць. Спеціалізована база даних побу- +дована в програмному середовищі Microsoft Access 2002. Програма +призначена для розрахунку й оптимізації рецептур м’ясних виробів. +До недоліків цього програмного продукту слід віднести обов’язкову +наявність на робочому комп’ютері Microsoft SQL Server і Microsoft +Access. +Програма «Розробка рецептур композицій з рослинної сировини» +[36] дозволяє відповідно до сучасних принципів створення здорових +продуктів харчування розробити рецептури харчових концентратів +підвищеної біологічної цінності на плодоовочевій основі. Завдання +необхідних параметрів еталонного продукту дозволяє отримати ре- +цептури зі збалансованим співвідношенням макроелементів і отри- +мати максимально повне забезпечення добової потреби людини у ві- +тамінах і мінеральних речовинах. +Generic 2.0 — програма Кубанського державного технологічного +університету — призначена для автоматизованого проектування і +розрахунку багатокомпонентних рецептур продуктів функціональ- +ного харчування. Цей програмний продукт призначений для розра- +хунку й оптимізації рецептур м’ясних, рослинних і молочних виро- +бів [34]. +Вищевказані програмні продукти не враховують специфіку роз- +рахунку багатофазних рецептур кондитерських виробів. На сайті +http://ttk.telenet.ru/index.htm представлений програмний комплекс +«Система розрахунків для громадського харчування», що включає +розробку промислових рецептур на кондитерські вироби. Недоліка- +ми комплексу є відсутність автономності програмного забезпечення +і, як наслідок, недостатній захист права інтелектуальної власності +користувача. +На сайті http://www.es-nsk.ru/programmi.html представлені розро- +блені компанією «Експерт Софт» комп’ютерні програми для техноло- + +603 +гів підприємств харчової промисловості та громадського харчування. +Найбільший інтерес представляють програми: «Технолог-кулінар», +«Технолог-кондитер», «Технолог-хлібопекар». Програма «Технолог- +кулінар» розроблена для впровадження елементів системи якос- +ті і безпеки на підприємствах індустрії харчування. Функціональні +можливості програми дозволяють повністю автоматизувати розроб- +ку технологічної документації на всіх основних етапах виробництва +кулінарної продукції: при вхідному контролі якості сировини, при +виробництві кулінарної продукції і при зберіганні та реалізації кулі- +нарної продукції. +Основним недоліком перерахованих програмних комплексів є +відсутність специфіки моделей тієї чи іншої якості для розрахунків +рецептур. Програм розрахунків режимів виробництв сирних виробів +у відкритому доступі дуже мало. +Опис експериментальної частини досліджень жирнокислотного +складу емульсії. При виробництві продуктів на молочній основі, які +відповідають вимогам раціонального харчування, необхідним етапом +є обґрунтування молочно-жирової основи та підбір інгредієнтів, які +б сприяли корегуванню її складу, обґрунтування жирнокислотного +складу обраних фізіологічних добавок [23; 41; 42; 46; 47]. +Відповідно вимогам раціонального харчування співвідношення +між білком : жиром : вуглеводами повинно складати 1,0 : 1,2 : 4,6, +а співвідношення НЖК : МНЖК : ПНЖК має певні особливості і +повинно становити 0,3 : 0,6 : 0,1. Всі природні жири, в тому числі +і жир молока, не задовольняють усім цим вимогам, тому одним із +завдань розробки нових молочних продуктів є правильна оцінка (з +точки зору збалансованості) жирнокислотного складу сировини з +метою наступного його корегування і забезпечення оптимального +жирнокислотного складу готового продукту. Для цього необхідно +збільшити кількість рослинного жиру по відношенню до тварин- +ного, щоб досягти необхідного співвідношення жирних кислот +[22; 23]. +У зв’язку з цим виникає необхідність вибору жирової добавки у +вигляді рослинної олії, для чого було розглянуто жирнокислотний +склад олій, які традиційно використовуються у молочній промисло- +вості. Такими оліями є соняшникова, соєва та оливкова. Жирнокис- +лотний склад перерахованих олій наведено у таблиці 1. +Для наближення складу основи для виробництва продуктів, що +відповідають вимогам раціонального харчування, необхідно значно + +604 +підвищити вміст ПНЖК і МНЖК. Кількість НЖК повинна залиша- +тись майже такою ж. Як видно із даних, наведених в табл. 1, для ко- +регування співвідношення між жирними кислотами доцільно вико- +ристовувати оливкову олію, яка є основним постачальником МНЖК +і соняшникову як джерело ПНЖК. +Таблиця 1 +Жирнокислотний склад рослинних олій +Показники +Соняшникова +олія +Соєва олія +Оливкова олія +Сумарний вміст ліпідів, % +99,9 +99,9 +99,8 +Тригліцериди +99,2 +99,2 +99,0 +Фосфоліпіди +0 +0 +0 +В-ситостерин +0,57 +0,30 +0,30 +Холестерин +0 +0 +0 +Жирні кислоти, % +94,9 +94,4 +94,7 +Насичені: +Пальмітинова +Стеаринова +Арахідонова +13,3 +11,10 +2,20 +0 +13,9 +10,3 +3,5 +0 +15,75 +12,9 +2,5 +0,35 +Мононенасичені: +Олеїнова +Пальмітолеїнова +Гадолеїнова +24,0 +24,0 +– +– +19,8 +19,8 +– +– +66,9 +64,7 +1,55 +0,50 +Поліненасичені: +Лінолева +Ліноленова +57,6 +57,0 +0,6 +61,2 +50,60 +10,30 +12,10 +12,0 +0 +НЖК:МНЖК:ПНЖК +1,0:1,8:4,3 +1,0:1,4:4,4 +1,3:5,5:1,0 +Внесення у продукти рослинних олій дозволить збагатити їх не +лише цінними МНЖК та ПНЖК, а й важливими вітамінами-анти- +оксидантами, зокрема жиророзчинним вітаміном Е та токоферола- +ми. Ці біоантиоксиданти, які присутні в оліях, проявляють в організ- +мі людини протиракову дію, стимулюють функцію серцевого м’яза, є +стабілізаторами біологічних мембран. +З точки зору харчової і біологічної цінності, а також антиокси- +дантного статусу доцільним є використання суміші оливкової та со- +няшникової олій для нормалізації молочної суміші за масовою част- +кою жиру. +Завдання дослідження полягає в тому, щоб підібрати таке співвідно- +шення оливкової та соняшникової олій у суміші, щоб склад кислот НЖК : + +605 +МНЖК : ПНЖК якомога ближче підходив до співвідношення 0,3 : 0,6 : +0,1, визначеного теорією раціонального харчування. +Для отримання математичної моделі кисломолочного продук- +ту (жирнокислотного модуля молочно-жирової основи) на кафедрі +ХХтаЕ Одеського національного технологічного університету, під +керівництвом доцента Шарахматової Т. Є. були проведені відповідні +експерименти, в яких вміст оливкової та соняшникової олій зміню- +вали від 5 до 95 % (з інтервалом у 5 %) від загальної масової частки +жиру у суміші, яка становить 1,6 %. Результати моделювання жирно- +кислотного модуля молочно-жирової основи наведено у табл. 2. +За результатами експериментів, наведених у таблиці 2, зроблено +висновок про те, що при співвідношенні між соняшниковою та олив- +ковою олією 0,4:0,6, досягається максимальне наближення у спів- +відношенні між НЖК:МНЖК:ПНЖК. Крім того, оливкова олія зо- +всім не має холестерину, що дуже суттєво для продуктів харчування, +оскільки надлишок холестерину у продуктах харчування недопусти- +мий. Отже часткова заміна молочного жиру сумішшю рослинних олій +покращує збалансованість жирнокислотного складу молочно-жиро- +вої суміші. +Проте створення математичної моделі емульсії з соняшникової та +оливкової олій, відповідного програмного забезпечення та проведен- +ня розрахунків з урахуванням процедур оптимізації функцій дозволяє +покращити ці результати. +Для більш детальних розрахунків ефективності такої суміші не- +обхідно побудувати таку математичну модель залежності співвідно- +шення НЖК:МНЖК:ПНЖК від вмісту оливкової та соняшникової +олій, яка б допомогла наблизити отримане співвідношення до 0,3 : +0,6 : 0,1. +Опис експериментальної частини досліджень режимів гомогені- +зації емульсій різного хімічного складу. Для промислового застосу- +вання емульсій необхідно піддавати їх подальшому ефективному +диспергуванню за допомогою спеціального обладнання — гомоге- +нізаторів клапанного типу, які широко застосовуються у молочній +промисловості і дають змогу одержувати дрібнодисперсні стійкі +жирові емульсії прямого типу. На сьогоднішній день в молочній +промисловості гомогенізація є єдиним способом утворення стійкої +емульсії, в тому числі і з рослинними оліями. Тому слід уточнити +технологічні режими процесу гомогенізації емульсій визначеного +хімічного складу [30; 38]. + +606 +Таблиця 2 +Жирнокислотний склад емульсії з соняшниковою та оливковою оліями +Соняш- +никова +олія +Олив- +кова +олія +Вміст жирних кислот в 100 г +олії +Сумарний +вміст жир- +них кислот +Вміст жирних кислот в 100 г +продукту +НЖК +МНЖК +ПНЖК +НЖК +МНЖК +ПНЖК +0,05 +0,95 +18,95195 +68,66605 +12,44605 +100,0641 +1,52272809 +5,517095785 +0,27600175 +0,1 +0,9 +21,2729 +66,6881 +12,1151 +100,0761 +1,75589966 +5,504543916 +0,31899094 +0,15 +0,85 +23,59385 +64,71015 +11,78415 +100,0882 +2,00216817 +5,491287025 +0,36460818 +0,20 +0,8 +25,9148 +62,7322 +11,4532 +100,1002 +2,26266895 +5,477263996 +0,41310204 +0,25 +0,75 +28,23575 +60,75425 +11,12225 +100,1123 +2,53867248 +5,462406438 +0,46475349 +0,3 +0,7 +30,5567 +58,7763 +10,7913 +100,1243 +2,83160509 +5,446637569 +0,51988131 +0,35 +0,65 +32,87765 +56,79835 +10,46035 +100,1364 +3,14307361 +5,429870893 +0,57884868 +0,4 +0,6 +35,1986 +54,8204 +10,1294 +100,1484 +3,47489486 +5,412008609 +0,6420712 +0,45 +0,55 +37,51955 +52,84245 +9,79845 +100,1605 +3,82913114 +5,3929397 +0,71002669 +0,5 +0,5 +39,8405 +50,8645 +9,4675 +100,1725 +4,208133 +5,3725376 +0,78326731 +0,55 +0,45 +42,16145 +48,88655 +9,13655 +100,1846 +4,61459194 +5,350657524 +0,86243456 +0,6 +0,4 +44,4824 +46,9086 +8,8056 +100,1966 +5,05160353 +5,327132734 +0,94827814 +0,65 +0,35 +46,80335 +44,93065 +8,47465 +100,2087 +5,52274725 +5,301770575 +1,04167979 +0,7 +0,3 +49,1243 +42,9527 +8,1437 +100,2207 +6,03218439 +5,274347041 +1,14368363 +0,75 +0,25 +51,44525 +40,97475 +7,81275 +100,2328 +6,58478129 +5,244600173 +1,25553542 +0,8 +0,2 +53,7662 +38,9968 +7,4818 +100,2448 +7,18626534 +5,212221658 +1,37873364 +0,85 +0,15 +56,08715 +37,01885 +7,15085 +100,2569 +7,84342421 +5,176846109 +1,51509704 +0,9 +0,1 +58,4081 +35,0409 +6,8199 +100,2689 +8,56436311 +5,138037215 +1,66685502 +0,95 +0,05 +60,72905 +33,06295 +6,48895 +100,281 +9,3588408 +5,095269651 +1,83677046 + +607 +Для обґрунтування режимів механічного оброблення емульсій різ- +ного хімічного складу їх піддівали гомогенізації при тиску у межах від +7 до 15 МПа та температурі від 55 до 70 °C, що є загальноприйнятими +режимами для молочної промисловості. Раціональні режими гомо- +генізації визначали за стійкістю емульсії (Y, %) та відстоєм жирової +фази (v, %). При цьому стійкість емульсії повинна бути максималь- +ною (100 %), відстій жирової фази повинний бути мінімальним. +Результати експериментальних досліджень наведено в табл. 3. +Аналізуючи наведені дані, бачимо, що з підвищенням гомогенізації +відстій жирової фази зменшується. Це пов’язано з тим, що при ра- +діусі жирових кульок менше 0,5 мкм в гомогенізованій суміші при +тиску 12–15 МПа таких кульок абсолютна більшість, електричні +сили відштовхування перевищують ван-дер-вальсові сили притя- +гування, такі кульки не утворюють скупчення. Саме тому при ви- +сокому тиску гомогенізації спостерігається менший відстій жиро- +вої фази. Так при тиску 15 МПа відстій складає 0,6 % — 4,2 % від +загальної кількості жиру, при 12 МПа — 0,9–5,2 %, а при 7 МПа — +3,5–9,2 %. Таким чином найкращий тиск, обчислений емпіричним +шляхом, 12–15 МПа. +Таблиця 3 +Фізичні характеристики гомогенізованих емульсій +Тиск, +МПа +Температура, °C +55 +60 +65 +70 +Y, % +v, % +Y, % +v, % +Y, % +v, % +Y, % +v, % +Олія соняшникова +7 +98,5 +8,3 +98,8 +7,6 +99,1 +4,9 +99,3 +3,4 +10 +100,0 +6,1 +100,0 +5,2 +100,0 +3,8 +100,0 +2,0 +12 +4,4 +3,1 +1,5 +0,9 +15 +3,8 +2,6 +1,0 +0,6 +Олія оливкова +7 +98,6 +8,6 +98,7 +7,8 +99,2 +4,9 +99,6 +3,6 +10 +100,0 +6,4 +100,0 +5,5 +100,0 +3,7 +100,0 +2,4 +12 +4,8 +3,4 +1,6 +0,9 +15 +3,7 +2,8 +0,9 +0,8 +Купаж (олія соняшникова+олія оливкова) +7 +98,1 +9,2 +98,4 +7,7 +99,0 +5,0 +99,3 +3,5 +10 +98,3 +6,9 +100,0 +5,3 +100,0 +3,6 +100,0 +2,1 +12 +98,6 +5,2 +3,2 +1,5 +0,9 +15 +98,8 +4,2 +2,8 +1,0 +0,6 + +608 +Емпіричним шляхом встановлюють гранично допустимі коефі- +цієнти відстою, при значеннях вище яких якість продукту недопус- +тима. +Результати розрахунків коефіцієнта відстою відповідно до суміші +з масовою часткою жиру 1,6 % наведені в табл. 4. +Таблиця 4 +Коефіцієнт відстою для суміші з масовою часткою жиру 1,6 % +Тиск гомогенізації, МПа +Коефіцієнт відстою +7 +0,224 +10 +0,194 +12 +0,176 +15 +0,170 +Аналізуючи дані таблиці, помітно, що зі збільшенням кількості +рослинного жиру в суміші коефіцієнт відстою збільшується. Най- +більш оптимальний тиск гомогенізації суміші 12 МПа та 15 МПа. +При такому тиску коефіцієнт відстою жирової фази найменший і ста- +новить при 12 МПа — 0,176, при 15 МПа — 0,170 відповідно. +Отже, за результатами експерименту, при гомогенізації соняшни- +кової та оливкової олій окремо достатнім режимом гомогенізації є +температура 55 °C при тиску 15 МПа. При гомогенізації купажу (со- +няшникова олія + оливкова олія) рекомендованим режимом гомоге- +нізації є температура 60 °C при тиску 12 МПа. При цьому стійкість +емульсії максимальна і становить 100 % і відстій жирової фази стано- +вить 2,8 %, що є достатнім для виробництва продукції з кисломолоч- +ного сиру. Подальше підвищення тиску та температури недоцільне, +тому що збільшуються енерговитрати на виробництво, за рахунок +чого значно зростає собівартість продукції. +Порівнюючи отримані дані по зміні стійкості емульсії, відстою +жирової фази, можна зробити висновок, що експериментальні дані +для тиску 12 МПа та 15 МПа майже не мають суттєвих відмінностей. +Стійкість емульсії складає 100 %, відстій жирової фази — 2,8–3,2 %. +Тому оптимальним тиском за результатами експерименту при вироб- +ництві кисломолочного сиру з використанням купажів рослинних +олій є 12 ± 0,5 МПа. +Завданням дослідження є побудова математичної моделі та побудо- +ва комп’ютерної програми для розрахунку режимів гомогенізації різного +хімічного складу емульсій при виробництві кисломолочного сиру з вико- + +609 +ристанням купажів рослинних олій (соняшникова олія + оливкова олія), +тобто знаходження оптимальних значень тиску та температури. +Методика складання математичних моделей. Для розробки нової +рецептури необхідно застосувати сучасний математичний апарат, по- +будувати математичну модель процесу, оптимізувати її та отримати +найкращі параметри. Математична модель має складатися за допо- +могою методів регресійно-кореляційного аналізу на основі натурних +експериментів [22; 33; 40; 44; 46]. +Сьогодні одним з важливих чинників підвищення ефективності та +якості досліджень є застосування ймовірнісно-статистичних методів +і комп’ютерів для створення математичних моделей різних процесів +і об’єктів. Їх застосування дозволяє від простих розрахунків і оцінок +перейти до нової стадії роботи — детального математичного моделю- +вання і дослідження складних реальних процесів і об’єктів. Статис- +тичні методи планування й обробки експерименту з використанням +комп’ютера дозволяють значно інтенсифікувати працю дослідника, +скоротити терміни і витрати на реальний фізичний експеримент, під- +вищити достовірність і якість висновків за результатами експеримен- +тів. Метою застосування таких методів є отримання математичної +моделі досліджуваного процесу, яка має описувати його досить по- +вно. Після отримання такої моделі з’являється можливість замінити +подальше експериментальне дослідження реального процесу аналі- +зом його математичної моделі, що, природно, різко знижує витрати +часу і матеріальних вкладень. Це дозволяє визначити оптимальні ре- +жими та інші характеристики технологічного процесу, конструктивні +параметри машини або апарату [15; 22; 23]. +У загальному випадку модель є тією або іншою формою відобра- +ження реальної дійсності. Надалі під моделлю будемо розуміти таку +формалізовану систему, яка, відображаючи і відтворюючи об’єкт до- +слідження, здатна заміщати його в розрахунках. +Критерії відповідності моделі об’єкта можуть бути різними. Най- +частіше таким критерієм є ступінь відхилення показника якості про- +цесу (вихідні характеристики, витрата енергії робочого агента, ви- +трати та ін.), виміряного безпосередньо на об’єкті, та отриманого +шляхом розрахунків знайденої математичної моделі z. +Іноді при складанні математичної моделі досліджуваного процесу +деякі параметри її можуть бути відомі заздалегідь, однак в загально- +му випадку об’єкт дослідження уявляється у вигляді «чорного ящика» +(кібернетичний термін), внутрішня структура якого невідома; на вхід + +610 +його діють вхідні впливу xi, i = 1,2,..., k (так звані «фактори», k — кіль- +кість факторів), а вихідні впливу y («відгуки») можуть вимірюватися +реєструючими приладами (рис.1). Якщо об’єкт має кілька відгуків, +вони можуть розглядатися незалежно один від одного, або входити в +розрахункову формулу з ваговими коефіцієнтами, тому в подальшому +будемо розглядати системи з одним виходом. +Методика складання математичних моделей. Для розробки нової рецептури необхідно +застосувати сучасний математичний апарат, побудувати математичну модуль процесу, оптимізувати +її і отримати найкращі параметри. Математична модель повинна складатися з допомогою методів +регресійно-кореляційного аналізу на основі натурних експериментів [22, 33, 40, 44, 46]. +В даний час одним з важливих чинників підвищення ефективності і якості досліджень є +застосування ймовірнісно-статистичних методів і комп'ютерів для створення математичних моделей +різних процесів і об'єктів. Їх застосування дозволяє від простих розрахунків і оцінок перейти до нової +стадії роботи - детальному математичному моделюванню і дослідженню складних реальних процесів +і об'єктів. Статистичні методи планування і обробки експерименту з використанням комп'ютера +дозволяють значно інтенсифікувати працю дослідника, скоротити терміни і витрати на реальний +фізичний експеримент, підвищити достовірність і якість висновків за результатами експериментів. +Метою застосування таких методів є отримання математичної моделі досліджуваного процесу, яка +повинна описувати його досить повно. Після отримання такої моделі з'являється можливість замінити +подальше експериментальне дослідження реального процесу аналізом його математичної моделі, що, +природно, різко знижує витрати по часу і матеріальним вкладенням. Це дозволяє визначити +оптимальні режими та інші характеристики технологічного процесу, конструктивні параметри +машини або апарату [15, 22, 23]. +У загальному випадку модель є тією або іншою формою відображення реальної дійсності. +Надалі під моделлю будемо розуміти таку формалізовану систему, яка, відображаючи і відтворюючи +об'єкт дослідження, здатна заміщати його в розрахунках. + Критерії відповідності моделі об'єкту можуть бути різними. Найчастіше таким критерієм є +ступінь відхилення показника якості процесу (вихідні характеристики, витрата енергії робочого +агента, витрати та ін.), виміряного безпосередньо на об'єкті у і отриманого шляхом розрахунків по +знайденої математичної моделі z. +Іноді при складанні математичної моделі досліджуваного процесу деякі параметри її можуть +бути відомі заздалегідь, однак в загальному випадку об'єкт дослідження представляється у вигляді +«чорного ящика» (кібернетичний термін), внутрішня структура якого невідома; на вхід його діють +вхідні впливу xi, i = 1,2, ..., k (так звані «фактори», k - кількість факторів), а вихідні впливу y +("відгуки") можуть вимірюватися реєструючими приладами (рис.1). Якщо об'єкт має кілька відгуків, +вони можуть розглядатися незалежно один від одного, або входити в розрахункову формулу з +ваговими коефіцієнтами, тому в подальшому будемо розглядати системи з одним виходом. + х1 +……….. y + хk + +Рисунок 1 - Представлення досліджуваного об'єкта у вигляді «чорного ящика» +Для знаходження математичної моделі зазвичай проводять експериментальні дослідження, які +встановлюють зв'язок між вхідними факторами, які впливають на перебіг процесу, і вихідними +параметрами процесу, які характеризують його властивості. Перші з них є незалежними і можуть +приймати довільні значення, другі – залежними [12, 22]. +Експеримент проводять пасивними і активними методамі. Під пасивними експериментами +розуміють отримання будь-яких даних без планування умов проведення опитів при випадковій зміні +вхідних факторів. Пасивні методи, хоча і прості в застосуванні, але не досить точні, а також +відрізняються складними методами обробки отриманих даних. Активний, заздалегідь спланований +експеримент, ставлять в тому випадку, якщо досліджуваний об'єкт допускає можливість зміни +вхідних факторів в необхідних межах. Методика зміни вхідних факторів в цьому випадку повинна +передбачати мінімізацію числа експериментів, застосування простих і найменш трудомістких методів +обробки отриманих результатів. Принципами створення ефективних планів проведення дослідів +займається спеціальний розділ математики - «планування експерименту» [12]. +Під математичною моделлю досліджуваного об'єкта на рис.1 будемо розуміти рівняння, що +зв'язує відгук і фактори + + + + y = f(х1, х2,…, хk) +(1) + + «Чорний ящик» +Рис. 1. Представлення досліджуваного об’єкта у вигляді «чорного ящика» +Для знаходження математичної моделі зазвичай проводять екс- +периментальні дослідження, які встановлюють зв’язок між вхідними +факторами, що впливають на перебіг процесу, і вихідними параме- +трами процесу, які характеризують його властивості. Перші з них є +незалежними і можуть приймати довільні значення, другі — залеж- +ними [12; 22]. +Експеримент проводять пасивними і активними методамі. Під па- +сивними експериментами розуміють отримання будь-яких даних без +планування умов проведення дослідів при випадковій зміні вхідних +факторів. Пасивні методи, хоча і прості в застосуванні, але не досить +точні, а також відрізняються складними методами обробки отрима- +них даних. Активний, заздалегідь спланований експеримент, став- +лять в тому випадку, якщо досліджуваний об’єкт допускає можливість +зміни вхідних факторів в необхідних межах. Методика зміни вхідних +факторів у цьому випадку має передбачати мінімізацію числа експе- +риментів, застосування простих і найменш трудомістких методів об- +робки отриманих результатів. Принципами створення ефективних +планів проведення дослідів займається спеціальний розділ математи- +ки — «планування експерименту» [12]. +Під математичною моделлю досліджуваного об’єкта на рис.1 буде- +мо розуміти рівняння, що пов’язує відгук і фактори + +y = f(х1, х2,…, хk). +(1) +Потрібно виразити аналітично (тобто у вигляді формули) за- +лежність між значеннями х і у, в результаті чого замість функції y = +f(х1, х2,…, хk) повинна вийти інша, апроксимуюча (тобто приблиз- +но описуюча) її функція z = ϕ(х1, х2,…, хk). Залежно від вимог, що + +611 +пред’являються до апроксимуючої функції, розрізняють два типи +апроксимації [6; 12]. +Апроксимація першого типу. Допускається, що результати експе- +рименту, зафіксовані в таблиці, є наближеними, мають деякі погріш- +ності. Це часто відбувається в реальних експериментах в силу недо- +сконалості застосовуваних при вимірах приладів. Завдання полягає +в тому, щоб вибрати таку апроксимуючу функцію з деякого класу +функцій, яка б з мінімальними відхиленнями відповідала результатам +експериментів. +Апроксимація другого типу. Передбачається, що результати екс- +перименту, зафіксовані в таблиці, є точними. Потрібно із заданого +класу вибрати таку функцію ϕ(х1, х2,…, хk), щоб для вузлів сітки х1, +х2,…, хn виконувалася строга рівність ϕ(х1, х2,…, хk) = y(х1, х2,…, хk). +Такий вид апроксимації називають інтерполяцією. Для вирішення +такого завдання часто використовують інтерполяційний многочлен +Лагранжа, поліноми Ньютона. Однак точність такого наближення +гарантована лише в невеликому інтервалі, для іншого проміжку по- +трібно заново обчислювати коефіцієнти інтерполяційної формули. +Надалі будемо вирішувати завдання апроксимації першого типу +як найбільш поширеної в інженерних задачах; іноді таке завдання на- +зивають також завданням знаходження емпіричної залежності. +Для складання математичної моделі за результатами експеримен- +тальних даних необхідно вирішення таких завдань: вибір виду аналі- +тичної формули; визначення її найкращих параметрів; доказ адекват- +ності отриманої моделі досліджуваного об’єкта. +Загальної теорії вибору виду емпіричної залежності не існує, +функцію вибирає дослідник виходячи з прогностичних здібностей, +специфіки завдання і характеру розташування на координатній пло- +щині точок, відповідних експериментальним даним. У деяких випад- +ках вибір виду емпіричної формули може бути проведений на основі +теоретичних уявлень про характер досліджуваної залежності або про +зміну вимірюваних величин. В інших випадках доводиться підбирати +формулу, порівнюючи графік, побудований за даними спостережень, +з типовими графіками залежностей, наведеними в довідковій літера- +турі. Деякі рекомендації щодо вибору виду емпіричної формули на- +ведені в [12]. +На практиці для знаходження параметрів емпіричної залежності +(після висунення гіпотези про її вигляд) використовують метод ви- +браних точок, метод середніх, метод найменших квадратів. Для чи- + +612 +сельних розрахунків коефіцієнтів регресійної формули нами буде ви- +користовуватися метод випадкового пошуку. +Для знаходження кривої, яка приблизно відповідає вихідної ін- +формації, необхідно виробити критерій. Назвемо відхиленням екс- +периментальної точки різницю між експериментальною ординатою +yi і тією, яка обчислена з теоретично знайденою функціональною за- +лежністю zi=ϕ(xi) (на рис. 2 розрахунковий графік залежності zi=ϕ(xi) +і відхилення показані суцільними лініями). +В якості сумарного критерію, що визначає отримане загальне від- +хилення, можна прийняти формулу квадратів відхилень: +2 +1 +( +) +n +i +i +i +y +z += +− +∑ +. +Метод апроксимації, в якому критерієм якості обрана показана +формула, називають методом найменших квадратів [5; 12; 16; 31]. +Основна мета регресійного аналізу полягає у визначенні аналітичної +форми зв’язку, в якій зміна результативної ознаки зумовлена впливом +однієї або декількох факторних ознак. +Рисунок 2 - Ілюстрація відхилень між уi і zi=φ (xi) +Завдання регресійного аналізу [12, 44]: +а) Встановлення форми залежності. Щодо характеру і форми залежності між явищами, +розрізняють позитивну лінійну і нелінійну, а також негативну лінійну і нелінійну регресію. +б) Визначення функції регресії у вигляді математичного рівняння того або іншого типу і +встановлення впливу вхідних змінних на залежну змінну. +в) Оцінка невідомих значень залежної змінної. За допомогою функції регресії можна відтворити +значення залежної змінної всередині інтервалу заданих значень (тобто вирішити задачу інтерполяції) +або оцінити перебіг процесу поза заданого інтервалу (тобто вирішити задачу екстраполяції). +Результат являє собою оцінку значення залежної змінної. +Нехай функціональна залежність між x і y має вигляд: +z = ( x , a , b , c , ...) +де a, b, c, …- невідомі параметри у формулі емпіричної залежності, які необхідно підібрати +(якщо функція zi =  (xi) має вигляд полінома, то шукану математичну модель об'єкта іноді +називають рівнянням регресії). Вираз +S (a , b, c, ...) = + +n +i 1 +[yi - (xi , a , b , c , ...)]2 + (2) +називають квадратичним відхиленням емпіричної формули від експериментальних даних. +У методі найменших квадратів параметри a, b, c,… підбирають таким чином, щоб мінімізувати +функцію (2), тобто знаходячи найменше сумарне відхилення розрахункових даних від +експериментальних. Для цього відповідно до правил класичної математики можна прирівняти нулю +приватні похідні від функції S (2) в невідомих параметрах a, b, c,…: +;0 + + + +a +S +;0 + + + +b +S +;0 + + + +c +S +……… .. + (3) +У розгорнутому вигляді систему (3) записують так: +……..  + +n +i 1 +2 [yi-(xi,a,b,c,…)]  ( - ((xi,a,b,c,…)) /a ) =0 + + +n +i 1 +2 [yi-(xi,a,b,c,…)]  ( - ((xi,a,b,c,…))/b ) =0 + +Рис. 2. Ілюстрація відхилень між уi і zi=φ (xi) +Завдання регресійного аналізу [12; 44]: +а) встановлення форми залежності. Щодо характеру і форми за- +лежності між явищами розрізняють позитивну лінійну і нелінійну, а +також негативну лінійну і нелінійну регресію; + +Y +Z=β(x) +y3 +Z3 +y1 +Z2 +y2 +Z1 +0 +X1 +X2 +X3 +x613 +б) визначення функції регресії у вигляді математичного рівняння +того або іншого типу і встановлення впливу вхідних змінних на за- +лежну змінну; +в) оцінка невідомих значень залежної змінної. За допомогою +функції регресії можна відтворити значення залежної змінної всере- +дині інтервалу заданих значень (тобто вирішити задачу інтерполяції) +або оцінити перебіг процесу поза заданим інтервалом (тобто виріши- +ти задачу екстраполяції). Результат являє собою оцінку значення за- +лежної змінної. +Нехай функціональна залежність між x і y має вигляд: +z =ϕ (x, a, b, c,...), +де a, b, c, … — невідомі параметри у формулі емпіричної залежності, +які необхідно підібрати (якщо функція zi = ϕ (xi) має вигляд поліно- +ма, то шукану математичну модель об’єкта іноді називають рівнян- +ням регресії). Вираз + +S (a, b, c,...) = +1 +n +i=∑ [yi – ϕ(xi, a, b, c,...)]2 +(2) +називають квадратичним відхиленням емпіричної формули від екс- +периментальних даних. +У методі найменших квадратів параметри a, b, c,… підбирають та- +ким чином, щоб мінімізувати функцію (2), тобто знаходячи наймен- +ше сумарне відхилення розрахункових даних від експериментальних. +Для цього відповідно до правил класичної математики можна при- +рівняти нулю окремі похідні від функції S (2) в невідомих параметрах +a, b, c,…: + +0; +S +a +∂ += +∂ + +0; +S +b +∂ += +∂ + +0; +S +c +∂ += +∂ + ……….. +(3) +У розгорнутому вигляді систему (3) записують так: + +…….. +1 +n +i=∑ 2 [yi-ϕ(xi,a,b,c,…)] ⋅ ( – (∂ϕ(xi,a,b,c,…)) /∂a) =0, + +1 +n +i=∑ 2 [yi-ϕ(xi,a,b,c,…)] ⋅ ( – (∂ϕ(xi,a,b,c,…))/∂b) =0, +(4) +................... +В отриманій системі число рівнянь дорівнює числу невідомих па- +раметрів. Вирішивши систему будь-яким відомим методом, знайдемо + +614 +значення параметрів a, b, c,.... Однак не можна забувати про труднощі +при реалізації методу найменших квадратів, які можуть бути викли- +кані такими причинами [2; 19; 31]: +1. Система (4) може бути несумісна. +2. Система (4) може вийти надзвичайно важкою для вирішення. +3. Система (4) може мати безліч рішень, в цьому випадку необхідно +додатково з’ясовувати, які з них відповідають мінімуму функції (2). +У загальному випадку методом найменших квадратів можна зна- +йти формули для обчислення параметрів будь-якої емпіричної фор- +мули, проте рішення системи (4) і пов’язані з її отриманням розра- +хунки можуть виявитися досить складними. +Для оцінки точності отриманої апроксимації можна застосовувати +середньоквадратичну помилку (чим менше ця величина, тим точніше +проведена апроксимація) + +2 +2 +1 +( +) +1 +n +i +i +i +y +z +n +k += +− +δ = +− +− +∑ +. +(5) +Це значення характеризує міру розсіювання фактичних значень +щодо розрахункових, отриманих за емпіричною формулою. Чим мен- +ше помилка Δ, тим краще отримана математична модель описує існу- +ючий зв’язок між відгуком і факторами. Варіюючи види функції (1) і +оцінюючи результати за допомогою середньоквадратичної помилки +(5), можна серед розглянутих емпіричних формул вибрати найкращу. +Приклади використання декількох емпіричних формул і розрахунків +(5) наведені в [5; 12; 31]. Однак слід ще перевірити, чи значимо отри- +мане рівняння регресії; при відсутності паралельних дослідів це про- +водиться за розрахунковим критерієм Фішера +2 +2 +y +rF +δ += +δ +, +де +2 +2 +1 +( +) +1 +n +i +s +i +y +y +y +n += +− +δ = +− +∑ + — дисперсія y щодо середнього ys; +ys — середнє значення y за експериментальними даними. +Розраховане рівняння регресії вважають надійним і адекватним +експериментальним даним, якщо виконується умова +Fr < Ft (α, ν1,ν2), +де ν1= n – 1, ν2= n – k – 1 — ступені свободи; + +615 +α — рівень значущості (у технічних розрахунках найчастіше ви- +користовують рівень значущості α = 0,05); +Ft (α, ν1,ν2) — табличний критерій Фішера. +Якщо виявиться, що умова Fr < Ft не виконується, то це означає, +що вид емпіричної залежності (1) обраний неправильно і необхідно +повторювати всі розрахунки спочатку. +Використання методів оптимізації. У розроблюваному додатку для +застосування методології найменших квадратів та оптимізації отри- +маних математичних моделей реалізовано метод випадкового пошуку. +Метод випадкового пошуку заснований на застосуванні послідов- +ностей випадкових чисел, за допомогою яких у сфері зміни незалеж- +них змінних проводиться вибірка випадкових точок або визначення +випадкових напрямків. Цей метод є прямим розвитком відомого ме- +тоду спроб і помилок, коли рішення шукається випадково і при удачі +приймається, а при невдачі відкидається, щоб негайно знову зверну- +тися до випадковості як до джерела можливостей. Така випадкова по- +ведінка розумно спирається на впевненість, що випадковість містить +у собі всі можливості, у тому числі й шукане рішення у всіх його ви- +падках [4; 20; 31]. +Метод випадкового пошуку при оптимальному проектуванні до- +зволяє порівняно невеликими витратами машинного часу визначити +екстремум функції великої кількості змінних. Перевагою цього ме- +тоду є те, що, крім необхідності існування в області єдиного локаль- +ного екстремуму, він не пред’являє істотних вимог ні до виду безлічі +параметрів, за якими відшукується оптимальне значення, ні до виду +залежностей, що пов’язують параметри, які вибираються з оптимі- +зуючим критерієм і обмеженнями. Він дозволяє знайти всі локальні +мінімуми функції від 10–20 змінних зі складним рельєфом. Він ко- +рисний і для дослідження функції з єдиним мінімумом. +Цей метод має дві переваги. По-перше, він придатний для будь- +якої цільової функції незалежно від того, є вона унімодальною чи ні. +По-друге, ймовірність успіху при спробах залежить від розмірності +аналізованого простору. Хоча цей метод не дозволяє безпосередньо +знайти оптимальне рішення, він створює відповідні передумови для +подальшого застосування інших методів пошуку. Тому його часто за- +стосовують у поєднанні з одним чи декількома методами інших типів. +Недолік методу полягає в тому, що треба заздалегідь задати об- +ласть, де вибираються випадкові точки. Якщо ми поставимо занадто +широку область, то її важче детально досліджувати, а якщо виберемо + +616 +занадто вузьку область, то багато локальних мінімумів можуть опи- +нитися поза нею. +Існують кілька методів випадкового пошуку, які схожі один на од- +ного і відрізняються лише кількома кроками чи умовами. +Найзагальніша ітераційна формула методів випадкового пошуку +має вигляд +1 +k +k +k +X +X ++ = ++ ξ , +де ε_(k) — n-вимірна випадкова величина. Імовірнісні розподіли цієї +випадкової величини, їх зміни у різних кроках методу визначають ме- +тод пошуку. Звичайно для випадкової величини ε_(k) ставляться спе- +цифічні вимоги. +Норма цієї векторної величини має бути обмеженою, щоб точка +X_(k+1) залишалася поблизу точки X_k. +Закони розподілу залежать від результатів подальших випробу- +вань (адаптація випадкового пошуку). +До найпростіших алгоритмів належать такі: +Алгоритм із парною пробою. У випадковому напрямку по обидва +боки вихідного стану X_k роблять пробні кроки X_(k)± Lk, де L — +дов жина пробного кроку. Обчислюють значення цільової функції у +цих точках. Робочий крок роблять у напрямі меншого значення ці- +льової функції. Характерною особливістю алгоритму є висока тен- +денція до «блукання». +Алгоритм із поверненням при невдалому кроці. Роблять крок у ви- +падковому напрямку. Якщо значення цільової функції у новій точці +більше, ніж у вихідної, тобто крок виявився невдалим, то поверта- +ються у вихідну точку. Після цього випадкові кроки повторюються. +Алгоритм найкращої проби. З вихідної точки роблять m випадко- +вих кроків і запам’ятовують той крок, який призвів до найменшого +значення цільової функції. Робочий крок роблять саме у цьому на- +прямку. +Оскільки у математичних моделях кількість змінних невелика, в +програмному забезпеченні для знаходження коефіцієнтів рівнянь ре- +гресії та мінімізації отриманих функцій реалізований метод з парною +пробою як найбільш універсальний і простий метод оптимізації. +Обґрунтування вибору мови програмування. Для реалізації обраних +алгоритмів практично потрібно побудувати програму на комп’ютері, +і тут центральне питання — вибір необхідної мови програмування. +Мова програмування — формальна знакова система, призначена для + +617 +запису комп’ютерних програм. Мова програмування визначає набір +лексичних, синтаксичних та семантичних правил, що задають зо- +внішній вигляд програми та дії, які виконає комп’ютер під її керуван- +ням [14; 32]. +Високорівнева мова програмування — мова програмування, роз- +роблена для швидкості та зручності використання програмістом. +Основна риса високорівневих мов — це абстракція, тобто введення +смислових конструкцій, що коротко описують такі структури да- +них та операції над ними, опис яких на машинному коді (або іншій +низькорівневій мові програмування) дуже довгий і складний для ро- +зуміння. +Так, високорівневі мови прагнуть не лише полегшити вирішення +складних програмних завдань, а й спростити портування програмно- +го забезпечення. Використання різноманітних трансляторів та інтер- +претаторів забезпечує зв’язок програм, написаних за допомогою мов +високого рівня, з різними операційними системами та обладнанням, +у той час як їхній вихідний код залишається, в ідеалі, незмінним. +Загалом мова називається безпечною, якщо програми на ній, які +можуть бути прийняті компілятором як правильно побудовані, в ди- +наміці ніколи не вийдуть за межі допустимої поведінки. Це не озна- +чає, що такі програми не містять помилок взагалі. Термін «хороша +поведінка програми» (англ. well behavior) означає, що навіть якщо +програма містить якийсь баг (зокрема логічну помилку), вона, про- +те, не здатна порушити цілісність даних і обрушитися. Хоча терміни +неформальні, безпека деяких мов (наприклад, Standard ML) матема- +тично доведена. Безпека інших (наприклад, Ada) була забезпечена +ad hoc-чином, без забезпечення концептуальної цілісності, що може +призвести до катастроф, якщо покластися на них у відповідальних за- +вданнях. +Мова C та її нащадок C++ є небезпечними. У програмах з ними +широко зустрічаються ситуації ослаблення типізації (приведення +типів) та її порушення (каламбур типізації), отже помилки доступу +до пам’яті є у них статистичною нормою (але крах програми настає +далеко не відразу, що утруднює пошук місця помилки у коді). Най- +потужніші системи статичного аналізу здатні виявляти трохи більше +70–80 % помилок, та їх використання дуже дороге фінансове. Досто- +вірно ж гарантувати безвідмовність програм цими мовами неможли- +во, не вдаючись до формальної верифікації, що ще дорожче та вима- +гає спеціальних знань [14]. + +618 +Сі має і безпечні нащадки, такі як Cyclone, C# або Rust. Мова Forth +не претендує на звання «безпечної», але, проте, на практиці існування +програм, здатних пошкодити дані, майже виключено, оскільки про- +грама, що містить потенційно небезпечну помилку, аварійно завер- +шується на першому ж тестовому запуску, примушуючи до корекції +вихідного коду. У співтоваристві Erlang прийнято підхід «let it crash», +також націлений на раннє виявлення помилок. +Програма компільованою мовою за допомогою спеціальної про- +грами компілятора перетворюється (компілюється) на набір інструк- +цій для даного типу процесора (машинний код) і далі записується +в модуль, який може бути запущений на виконання окремих про- +грам. Інакше кажучи, компілятор переводить вихідний текст програ- +ми з мови програмування високого рівня у двійкові коди інструкцій +процесора. +Якщо програма написана мовою, що інтерпретується, то інтер- +претатор безпосередньо виконує (інтерпретує) вихідний текст без +попереднього перекладу. При цьому програма залишається вихідною +мовою і може бути запущена без інтерпретатора. Можна сказати, що +процесор комп’ютера це інтерпретатор машинного коду. +Коротко кажучи, компілятор перекладає вихідний текст програми +на машинну мову відразу і повністю, створюючи при цьому окрему +програму, що виконується, а інтерпретатор виконує вихідний текст +прямо під час виконання програми [14; 28; 45]. +Поділ на компільовані та інтерпретовані мови є дещо умовним. +Так, для будь-якої традиційно компільованої мови, наприклад, +Паскаль, можна написати інтерпретатор. Крім того, більшість су- +часних «чистих» інтерпретаторів не виконують конструкції мови +безпосередньо, а компілюють їх у деяке високорівневе проміжне +уявлення (наприклад, з розіменуванням змінних та розкриттям ма- +кросів). +Для будь-якої інтерпретованої мови можна створити компіля- +тор — наприклад, мова Лісп спочатку інтерпретується, може компі- +люватися без будь-яких обмежень. Створюваний під час виконання +програми код може динамічно компілюватися. +Як правило, скомпільовані програми виконуються швидше і не +вимагають виконання додаткових програм, оскільки вже перекладе- +ні на машинну мову. Про те при кожній зміні тексту програми по- +трібна її перекомпіляція, що створює труднощі розробки. Крім того, +скомпільована програма може виконуватися тільки на тому ж типі + +619 +комп’ютерів і, як правило, під тією самою операційною системою, на +яку розрахували компілятор. Щоб створити файл для машини іншого +типу, потрібна нова компіляція. +Інтерпретовані мови мають деякі специфічні додаткові можли- +вості, крім того, програми на них можна запускати відразу ж після +зміни, що полегшує розробку. Програма, що інтерпретується, може +бути часто запущена на різних типах машин і операційних систем без +додаткових зусиль. +Однак програми, що інтерпретуються, виконуються помітно по- +вільніше, ніж компільовані, крім того, вони не можуть виконуватися +без додаткової програми-інтерпретатора. Приклади компільованих +мов: assembler, C++, Pascal. Приклади мов, що інтерпретуються: PHP, +JavaScript, Python. Деякі мови, наприклад, Java і C#, знаходяться між +компільованими та інтерпретованими [28; 32]. +Після аналізу застосовуваних алгоритмічних мов та особливостей +їх використання було прийнято рішення для програмування додатку +використовувати мову C# в силу її поширеності, універсальності та +відносної простоти. +Мова C#, розроблена компанією Microsoft (вона з’явилася в 2000 +році), одна з найпопулярніших сучасних мов програмування. Вона +затребувана на ринку розробки в різних країнах, C# застосовують під +час роботи з програмами для ПК, створення складних веб-сервісів +або мобільних додатків. Мова перетерпіла велику кількість оновлень +та нововведень. +C# — вкрай гнучка, потужна та універсальна алгоритмічна +мова. У сучасному вигляді С# здатна на дуже багато речей. Сьо- +годні вона не дарма займає лідируючі позиції в списках популяр- +них мов, тому що на її основі можливо будувати практично будь-які +проекти. +Крім того, після появи ігрового двигуна Unity мова набула додат- +кової сили на ринку. Тепер на її основі у зв’язці з мегапопулярним +двигуном Unity можна легко та швидко створювати ігри будь-якого +жанру та будь-якої складності. +Мова C# є об’єктно орієнтованою мовою програмування. Це +означає, що кожен файл являє собою певний клас. +Мова C# практично універсальна. Можна використовувати її для +створення будь-якого програмного забезпечення: просунутих біз- +нес-додатків, відеоігор, функціональних веб-додатків, програм для +Windows, macOS, мобільних програм для iOS та Android [18; 27; 28]. + +620 +Інструментарій C# дозволяє вирішувати широке коло завдань, +мова справді дуже потужна й універсальна. На цій мові розробляють: +• Програми для WEB. +• Різні ігрові програми. +• Програми платформ Андроїд або iOS. +• Програми для Windows. +На ній пишуть практично все, від невеликих веб-додатків до по- +тужних програмних систем, що поєднують у собі веб-структури, до- +датки для десктопів та мобільних пристроїв. Все це стало можливим +завдяки зручному Сі-подібному синтаксису, строгому структуруван- +ню, величезній кількості фреймворків та бібліотек (до кількох со- +тень). +Список можливостей розробки практично не має обмежень за- +вдяки найширшому набору інструментів та засобів. Звичайно, все +це можна реалізувати за допомогою інших мов, але деякі з них вузь- +коспеціалізовані, в інших доведеться використовувати додаткові ін- +струменти сторонніх розробників. У C# вирішення широкого кола +завдань можливо швидше, простіше і з меншими витратами часу та +ресурсів. +Розвиток об’єктноорієнтованого програмування та мережі Internet +сприяв появі нової технології програмування —.NET технології, що +дозволяє на єдиній платформі розробляти компоненти програм різ- +ними мовами програмування та забезпечити їхнє спільне виконання. +В рамках .NET технології запропоновано нову мову програмування +C#, засновану на мові С++, що перейняла з мови Java риси, які за- +безпечують створення безпечних програм. З урахуванням .NET тех- +нології мова С++ розширена новими можливостями і отримала на- +зву C++/CLI, з’явилася також мова J# — мова Java стосовно .NET +технології [45]. +Мова C# розроблена після мови Java. Вона не тільки успадкува- +ла найкраще з мови Java, але модифікувала її, надавши стрункість та +зручність використання, наприклад, таких конструкцій, як делегати +та події. Але, будучи відкритою і легкодоступною із сайту фірми Sun +Microsystems в Інтернеті, мова Java, мабуть, стала найпопулярнішою +мовою програмування у світі. Сайт фірми Sun Microsystems доступ- +ний програмістам усього світу. Доступність сайту об’єднала профе- +сійних програмістів, небайдужих до долі мови Java, сприяючи про- +суванню компонентноорієнтованого програмування цією мовою. +Запропонована фірмою Microsoft мова J#, що є варіантом мови Java + +621 +для .NET платформи, може використовувати (імпортувати — import) +як бібліотеку .NET Framework, і бібліотеку Java. +Коли говорять C#, часто мають на увазі технології платформи .NET +(Windows Forms, WPF, ASP.NET, Xamarin). І навпаки, коли говорять +.NET, нерідко мають на увазі C#. Проте, хоча ці поняття пов’язані, +ототожнювати їх не слід. Мова C# була створена спеціально для робо- +ти з фреймворком .NET, проте саме поняття .NET дещо ширше. +Фреймворк .NET є потужною платформою для створення додат- +ків. Можна виділити такі основні риси [45]: +• Підтримка кількох мов. Основою платформи є загальномовне +середовище виконання Common Language Runtime (CLR), завдяки +чому .NET підтримує кілька мов: поряд з C# це також VB.NET, C++, +F#, а також різні діалекти інших мов, прив’язані до .NET, наприклад, +Delphi.NET. При компіляції код будь-якої з цих мов компілюється +у складання загальною мовою CIL (Common Intermediate Language) — +свого роду асемблер платформи .NET. Тому за певних умов ми можемо +зробити окремі модулі однієї програми окремими мовами. +• Кросплатформність. .NET є платформою, що переноситься +(з деякими обмеженнями). Наприклад, остання версія платформи +на даний момент — .NET 6 підтримується на більшості сучасних ОС +Windows, MacOS, Linux. Використовуючи різні технології на плат- +формі .NET, можна розробляти програми мовою C# для різних плат- +форм — Windows, MacOS, Linux, Android, iOS, Tizen. +• Потужна бібліотека класів. .NET представляє єдину бібліотеку +класів, що підтримує всім мов. І яку б програму ми не збиралися пи- +сати на C# — текстовий редактор, чат або складний веб-сайт, — так +чи інакше ми використовуємо бібліотеку класів .NET. +• Різноманітність технологій. Загальномовне середовище вико- +нання CLR та базова бібліотека класів є основою цілого стеку тех- +нологій, які розробники можуть задіяти при побудові тих чи інших +додатків. Наприклад, для роботи з базами даних у цьому стеку техно- +логій призначено технології ADO.NET та Entity Framework Core. Для +побудови графічних програм з багатим насиченим інтерфейсом — +технологія WPF і WinUI, для створення більш простих графічних про- +грам — Windows Forms. Для розробки кросплатформових мобільних +та десктопних програм — Xamarin/MAUI. Для створення веб-сайтів +та веб-додатків — ASP.NET і т. д. До цього варто додати активний +Blazor — фреймворк, що розвивається і набирає популяність, який +працює поверх .NET і який дозволяє створювати веб-додатки як на + +622 +стороні сервера, так і на стороні клієнта. А в майбутньому підтримува- +тиме створення мобільних додатків і, можливо, десктоп-додатків. +• Продуктивність. Відповідно до ряду тестів веб-програми на +.NET 6 у ряді категорій сильно випереджають веб-програми, побудо- +вані за допомогою інших технологій. Програми на .NET 6 у принципі +відрізняються високою продуктивністю. +Також слід відзначити таку особливість мови C# і фреймворку +.NET, як автоматичне складання сміття. А це означає, що нам зде- +більшого не доведеться, на відміну від С++, дбати про звільнення +пам’яті. Вищезазначене загальномовне середовище CLR само викли- +че збирач сміття та очистить пам’ять. +Варто відзначити, що .NET тривалий час розвивався переважно +як платформа для Windows під назвою .NET Framework. У 2019 році +вийшла остання версія цієї платформи — .NET Framework 4.8. Вона +більше не розвивається. +З 2014 року Microsoft став розвивати альтернативну платформу — +.NET Core, яка вже призначалася для різних платформ і повинна +була увібрати в себе всі можливості застарілого .NET Framework і до- +дати нову функціональність. Потім Microsoft послідовно випустив +ряд версій цієї платформи: .NET Core 1, .NET Core 2, .NET Core 3, +.NET 5. І поточною версією є платформа .NET 6. Тому слід розріз- +няти .NET Framework, який призначений переважно для Windows, і +кроссплатформений .NET 6 (його будемо розглядати у зв’язці з C#). +Нерідко програму, створену на C#, називають керованим кодом +(managed code). Це означає, що ця програма створена на основі плат- +форми .NET і тому управляється загальномовним середовищем CLR, +яке завантажує програму і при необхідності очищає пам’ять. Але є +також програми, наприклад, створені мовою С++, які компілюють- +ся не у спільну мову CIL, як C#, VB.NET чи F#, а у звичайний ма- +шинний код. У цьому випадку .NET не керує програмою. У той же +час платформа .NET надає можливості для взаємодії з некерованим +кодом [27; 45]. +Вихідний код C# компілюється у програми або окремі зборки на +CIL з розширеннями dll, exe. У процесі запуску готової програми +виконується JIT-компіляція — це скорочення від Just-In-Time (про- +сто зараз). На виході буде машинний код, який передається на ви- +конання. +Для роботи програм на C# необхідно встановити та налаштувати +платформу .NET Framework. Вона поставляється повністю безкош- + +623 +товно, застосовується дуже широко, а тому проблем із пристроями +зазвичай не виникає. Платформа вбудована в інсталяційний пакет +Windows, при необхідності її також можна завантажити та поставити +окремо. Існують версії для Linux та MAC. +В рамках платформи до обробки коду, що виконується, підключа- +ється середовище CLR — єдиний об’єднаний набір бібліотек та кла- +сів, який був розроблений Microsoft і є реалізацією світового стандар- +ту Common Language Infrastructure (CLI). +Після роботи компілятора текст програми перекладається проміж- +ною мовою IL, яка «розуміє» CLI. IL і всі необхідні ресурси, включа- +ючи рядки та малюнки формату BMP, зберігаються на жорсткий диск +у вигляді файлу dll або exe. З таких файлів з проміжним кодом форму- +ється збірка програми, яка включає опис з повною інформацією про +всі важливі параметри роботи [14; 18]. +Безпосередньо при виконанні програми CLR звертається до скла- +дання та виконує дії залежно від отриманих відомостей. Якщо код +написаний правильно і проходить перевірку безпеки системи, про- +водиться компіляція з ІL в інструкції до машинних команд. Сере- +довище CLR одночасно виконує ще багато побічних функцій: +• видалення «програмного» сміття; +• робота з винятками; +• розподіл ресурсів; +• контроль типізації; +• керування версіями; +• типізація. +В результаті код C# вважається керованим, тобто він компілюєть- +ся у двійковий вигляд на власному пристрої з урахуванням особли- +востей встановленої системи. +С# популярний за рахунок своєї «простоти». Простоти для су- +часних програмістів і великих команд розробників, щоб ті могли в +стислий термін створювати функціональні та продуктивні програми. +Цьому сприяють нетипові конструкції мови та специфічний син- +таксис, що допомагає максимально органічно реалізувати намічені +функції. +На додаток до всіх переваг мова C# полегшує розробку програм- +них компонентів за допомогою кількох інноваційних конструкцій +мови: +• Інкапсульовані сигнатури методів, названі делегатами, включа- +ють оповіщення безпеки типів. + +624 +• Властивості служать акцесорами до змінних закритих елементів. +• Атрибути надають декларативні метадані щодо типів під час ви- +конання. +• Рядкові документаційні коментарі XML. +• Інтегрована мова запитів (LINQ) надає вбудовані можливості +запитів між джерелами даних. +Популярність мови — ще одна значима перевага. Багато шануваль- +ників C# сприяють її розвитку. Також це позитивно впливає на зрос- +тання кількості вакансій, пов’язаних з розробкою мовою Microsoft. +Програмісти, добре знайомі з С#, затребувані в індустрії, незважаючи +на їх кількість, що постійно збільшується. +Важливим достоїнством програми є можливість компіляції лише +необхідних нині частин програми. Якщо програма не звертається до +якоїсь частини коду, її компіляція не відбувається. У момент звернен- +ня виконується моментальна компіляція із CIL у машинний код [32]. +C# протягом тривалого часу впевнено лідирує у рейтингу найкра- +щих та найбільш затребуваних на ринку розробки мов. Спочатку ним +зацікавилися лише розробники, які пишуть програми під Windows. +Але в процесі розвитку C# «навчився» працювати на Mac, Linux, IoS +та Android. А після того, як код платформи відкрили для всіх бажаю- +чих, було знято практично всі можливі обмеження до застосування +C#. В результаті мова активно розвивається, застосовується все шир- +ше. Рекомендована до вивчення як одна з базових мов для розробни- +ків будь-якого профілю. +Компанія Microsoft приділяє значну увагу підтримці мови розроб- +ки, тому регулярно з’являються оновлення і доповнення, виправля- +ються виявлені баги в компіляторі, розширюються бібліотеки. Роз- +робники зацікавлені у популяризації інструменту та докладають до +цього багато зусиль. +Методика розрахунку коефіцієнтів математичної моделі жирнокис- +лотного складу емульсії. Як зазначалося вище, для наближення складу +сирного виробу до продуктів, що відповідають вимогам раціонально- +го харчування, необхідно додати суміш оливкової та соняшникової +олій. Однак при цьому також необхідно, щоб співвідношення кислот +НЖК : МНЖК : ПНЖК було максимально наближено до співвідно- +шення 0,3 : 0,6 : 0,1. Для моделювання залежності співвідношення +кислот від суміші олій будемо використовувати таблицю експери- +ментальних даних табл.1, перетворивши її у вигляді табл.5, відкинув- +ши проміжні дані. + +625 +Таблиця 5 +Вхідні дані для моделі співвідношення кислот +Соняшникова +олія +Оливкова +олія +Вміст жирних кислот в 100 г продукту +НЖК +МНЖК +ПНЖК +0,05 +0,95 +1,5227 +5,5171 +0,2760 +0,1 +0,9 +1,7559 +5,5045 +0,3190 +0,15 +0,85 +2,0022 +5,4913 +0,3646 +0,2 +0,8 +2,2627 +5,4773 +0,4131 +0,25 +0,75 +2,5387 +5,4624 +0,4648 +0,3 +0,7 +2,8316 +5,4466 +0,5199 +0,35 +0,65 +3,1431 +5,4299 +0,5788 +0,4 +0,6 +3,4749 +5,4120 +0,6421 +0,45 +0,55 +3,8291 +5,3929 +0,7100 +0,5 +0,5 +4,2081 +5,3725 +0,7833 +0,55 +0,45 +4,6146 +5,3507 +0,8624 +0,6 +0,4 +5,0516 +5,3271 +0,9483 +0,65 +0,35 +5,5227 +5,3018 +1,0417 +0,7 +0,3 +6,0322 +5,2743 +1,1437 +0,75 +0,25 +6,5848 +5,2446 +1,2555 +0,8 +0,2 +7,1863 +5,2122 +1,3787 +0,85 +0,15 +7,8434 +5,1768 +1,5151 +0,9 +0,1 +8,5644 +5,1380 +1,6669 +0,95 +0,05 +9,3588 +5,0953 +1,8368 +Для побудови та оптимізації математичної моделі раціонально ви- +брати єдиний критерій, який характеризуватиме отриманий результат. +Досить часто у цій якості вибирають адитивний критерій, до якого вхо- +дять з деякими ваговими коефіцієнтами як складові інші математичні +висловлювання. Однак в даному випадку це не можна використовува- +ти, тому що ми повинні отримати критерій, який показує ступінь на- +ближення відношення кислот до шуканого співвідношення 0,3 : 0,6 : 0,1, +визначеного теорією раціонального харчування. Для створення єдиного +критерію пропонується визначити «еталонні співвідношення» між чис- +лами 0,3, 0,6, 0,1 і порівнювати отримані пропорції з цім «еталоном». +Позначимо еталонні співвідношення (до яких будемо наближати- +ся при побудові моделі) як: +Y1= 0,3 : 0,6 = 0,5; + +Y2= 0,6 : 0,1 = 6; +(6) +Y3= 0,3 : 0,1 = 3. + +626 +Таблиця 6 +Розрахункові дані для моделі співвідношення кислот +Соняшни- +кова олія, li +Оливкова +олія, mi +Вміст жирних кислот в 100 г +продукту +НЖК/ +МНЖК, +T1i +МНЖК/ +ПНЖК, +T2i +НЖК/ +ПНЖК +T3i +Сумарне +відхилен- +ня, Fi +НЖК, ci +МНЖК, di +ПНЖК, ei +0,05 +0,95 +1,5227 +5,5171 +0,2760 +0,2760 +19,9894 +5,5171 +16,7304 +0,1 +0,9 +1,7559 +5,5045 +0,3190 +0,3190 +17,2561 +5,5045 +13,9417 +0,15 +0,85 +2,0022 +5,4913 +0,3646 +0,3646 +15,0608 +5,4913 +11,6875 +0,2 +0,8 +2,2627 +5,4773 +0,4131 +0,4131 +13,2589 +5,4773 +9,8230 +0,25 +0,75 +2,5387 +5,4624 +0,4648 +0,4648 +11,7533 +5,4624 +8,2510 +0,3 +0,7 +2,8316 +5,4466 +0,5199 +0,5199 +10,4767 +5,4466 +6,9432 +0,35 +0,65 +3,1431 +5,4299 +0,5788 +0,5788 +9,3805 +5,4299 +5,8892 +0,4 +0,6 +3,4749 +5,4120 +0,6421 +0,6421 +8,4290 +5,4120 +4,9831 +0,45 +0,55 +3,8291 +5,3929 +0,7100 +0,7100 +7,5954 +5,3929 +4,1984 +0,5 +0,5 +4,2081 +5,3725 +0,7833 +0,7833 +6,8591 +5,3725 +3,5149 +0,55 +0,45 +4,6146 +5,3507 +0,8624 +0,8624 +6,2041 +5,3507 +2,9172 +0,6 +0,4 +5,0516 +5,3271 +0,9483 +0,9483 +5,6177 +5,3271 +3,1577 +0,65 +0,35 +5,5227 +5,3018 +1,0417 +1,0417 +5,0896 +5,3018 +3,7538 +0,7 +0,3 +6,0322 +5,2743 +1,1437 +1,1437 +4,6117 +5,2743 +4,3063 +0,75 +0,25 +6,5848 +5,2446 +1,2555 +1,2555 +4,1772 +5,2446 +4,8230 +0,8 +0,2 +7,1863 +5,2122 +1,3787 +1,3787 +3,7804 +5,2122 +5,3105 +0,85 +0,15 +7,8434 +5,1768 +1,5151 +1,5151 +3,4168 +5,1768 +5,7751 +0,9 +0,1 +8,5644 +5,1380 +1,6669 +1,6669 +3,0825 +5,1380 +6,2224 +0,95 +0,05 +9,3588 +5,0953 +1,8368 +1,8368 +2,7740 +5,0953 +6,6580 + +627 +Позначимо також (табл. 6): +li — вміст соняшникової олії в і-му експерименті; +mi — вміст оливкової олії в і-му експерименті; +ci — вміст кислоти НЖК в і-му експерименті; +di — вміст кислоти МНЖК в і-му експерименті; +ei — вміст кислоти ПНЖК в і-му експерименті. +Визначимо також співвідношення кислот експериментальних да- +них НЖК/МНЖК, МНЖК/ПНЖК, НЖК/ПНЖК в i-му експери- +менті, як T1i, T2i, T3i: +1 +i +i +i +c +T +d += +; + +2 +i +i +i +d +T +e += +; +(7) +3 +i +i +i +c +T +e += +. +Розрахуємо T1i, T2i, T3i в експериментальних даних та занесемо до +таблиці 6. В якості критерію оптимальності відношення кислот бу- +демо використовувати розрахункову величину, представлену в остан- +ньому стовпці таблиці 4: + +Fi = | T1i – Y1| + | T2i – Y2| + | T3i – Y3|. +(8) +Очевидно, що чим менше показник F, тим ближче співвідношен- +ня кислот НЖК : МНЖК : ПНЖК до найбільш раціонального від- +ношення 0,3 : 0,6 : 0,1 (гіпотетично F може дорівнювати 0, тоді спів- +відношення рівні). +Для моделювання необхідно побудувати математичну модель за- +лежності F від l и m, шукатимемо її у вигляді полінома, як найбільш +універсальної функції. Обмежимося 4-м ступенем і шукатимемо мо- +дель у такому вигляді: +G (l, m) = a1l2+ a2m2 +a3l+ a4m+ a5lm+ a6+ a7l3+ a8m3+ a9l4+ a10m4. +(9) +Розраховуємо невідомі коефіцієнти ai за методикою найменших +квадратів з використанням методу випадкового пошуку в розробле- +ній програмі, отримуємо таку модель: + +G = 1,552162 + 0,589001l+ 0,955900m + + ++ 5,549843l3 + 17,483025m4. +(10) + +628 +Таким чином, розраховані коефіцієнти регресійної моделі такі: +a1= +0,000000 +a2= +0,000000 +a3= +0,589001 +a4= +0,955900 +a5= +0,000000 +a6= +1,552162 +a7= +5,549843 +a8= +0,000000 +a9= +0,000000 +a10= +17,483025 +Мінімізуючи отриману функцію, маємо такі значення: +l = 0,579062; +m = 0,420938. +При цьому значення критерію оптимальності дорівнюватиме +F = 2,8949, що добре корелює з експериментальними даними з табл. 2. +Методика розрахунку коефіцієнтів математичної моделі гомогеніза- +ції емульсій при виробництві кисломолочного сиру з використанням +купажів соняшникової та оливкової олій. +Як зазначалося вище, для визначення оптимальних режимів го- +могенізації необхідно побудувати математичні моделі залежності +стійкості емульсії та відстою жирової фази від температурі та тиску. +Розглянемо окремі залежність стійкості емульсії від температури та +тиску та залежність жирової фази від температури та тиску. Для зруч- +ності обробки вхідних даних під час створення математичної моде- +лі стійкості емульсії перетворимо таблицю 3, відкинувши проміжні +дані: +Для знаходження залежності стійкості емульсії від тиску та темпе- +ратури введемо такі позначення: +Di — значення стійкості емульсії в і-му експерименті; +xi — значення тиску в і-му експерименті; +yi — значення температури в і-му експерименті. +Шукатимемо математичну залежність у вигляді поліноміальної +функції +S = a1*x+ a2*y +a3*x2+ a4*y2+ a5xy+ a6+ a7*x3+ a8*y3+ a9*x4+ a10*y4. (11) + +629 +Таблиця 7 +Вибрані експериментальні дані для моделювання стійкості емульсії +Тиск, Мпа +Температура, С +Стійкість емульсії Y, % +7 +55 +98,1 +10 +55 +98,3 +12 +55 +98,6 +15 +55 +98,8 +7 +60 +98,4 +10 +60 +100 +12 +60 +100 +15 +60 +100 +7 +65 +99 +10 +65 +100 +12 +65 +100 +15 +65 +100 +7 +70 +99,3 +10 +70 +100 +12 +70 +100 +15 +70 +100 +Розраховуємо невідомі коефіцієнти ai за методикою найменших +квадратів: шукаємо мінімум функції + +( +) +( +) +( +) +2 +1 + +, + +, +min +n +i +i +i +i +i +S x +y +D x +y += +− +→ +∑ +. +(12) +Таблиця 8 +Розрахунок стійкості емульсії за математичною моделлю +Тиск, xi +Температура, yi +Стійкість +емульсії Di +Розрахунок S +Відхилення +7 +55 +98,1 +91,357 +6,743 +10 +55 +98,3 +101,393 +3,093 +12 +55 +98,6 +103,777 +5,177 +15 +55 +98,8 +94,798 +4,002 +7 +60 +98,4 +93,491 +4,909 +10 +60 +100 +103,526 +3,526 +12 +60 +100 +101,910 +1,910 +15 +60 +100 +96,931 +3,069 +7 +65 +99 +93,971 +5,029 +10 +65 +100 +104,006 +4,006 +12 +65 +100 +106,390 +6,390 + +630 +Закінчення табл. 8 +Тиск, xi +Температура, yi +Стійкість +емульсії Di +Розрахунок S +Відхилення +15 +65 +100 +97,411 +2,589 +7 +70 +99,3 +92,862 +6,438 +10 +70 +100 +102,897 +2,897 +12 +70 +100 +105,280 +5,280 +15 +70 +100 +96,301 +3,699 +Використовуючи метод випадкового пошуку в розробленій про- +грамі, отримуємо таку модель: + +S = –0,004666x–0,026530y+0,577439x2+0,076405y2–0,000010xy+ + ++1,550705–0,021941x3–0,001249y3 -0,000656x4 0,000005y4. +(13) +Таким чином, розраховані коефіцієнти регресійної моделі такі: +a1= +-0,004666 +a2= +-0,026530 +a3= +0,577439 +a4= +0,076405 +a5= +-0,000010 +a6= +1,550705 +a7= +-0,021941 +a8= +-0,001249 +a9= +-0,000656 +a10= +0,000005 +Для експериментальних даних розрахунок за цією математич- +ною моделлю призводить до таких результатів (табл. 8). В остан- +ньому стовпці показано відхилення експериментальних даних +від розрахункових, отриманих за побудованою математичною + моделлю. +Очевидно, що відхилення невеликі, тому побудованою моделлю +можна користуватися для розрахунку реальних значень стійкості +емульсії сирних виробів. +Також для визначення оптимальних режимів гомогенізації необ- +хідно побудувати математичну модель залежності відстою жирової +фази від температури та тиску. Для цього перетворимо таблицю 3 на +таку, відкинувши проміжні дані: + +631 +Таблиця 9 +Вибрані експериментальні дані до моделювання відстою жирової фази +Тиск, МПа +Температура, С +Відстій жирової фази v, % +7 +55 +9,2 +10 +55 +6,9 +12 +55 +5,2 +15 +55 +4,2 +7 +60 +7,7 +10 +60 +5,3 +12 +60 +3,4 +15 +60 +2,6 +7 +65 +5 +10 +65 +3,6 +12 +65 +1,5 +15 +65 +1 +7 +70 +3,5 +10 +70 +2,1 +12 +70 +0,9 +15 +70 +0,6 +За аналогією з попередніми розрахунками введемо позначення від- +стою жирової фази Vi (яке залежить від експериментальних даних xi — +значення тиску в і-му експерименті, yi — значення температури в і-му +експерименті) та будемо шукати математичну модель як функцію +G = a1*x+ a2*y +a3*x2+ a4*y2+ a5xy+ a6+ a7*x3+ a8*y3+ a9*x4+ a10*y4. (14) +Застосування розрахунків за методикою найменших квадратів, як +зазначено вище, дає таку модель: + +G = –0,004837x–0,027562y+0,005950x2+0,034753y2–0,000011xy+ + ++1,599765–0,008708x3–0,000901y3+0,000438x4+0,000006y4. (15) +Розраховані коефіцієнти регресійної моделі такі: +a1= +-0,004837 +a2= +-0,027562 +a3= +0,005950 +a4= +0,034753 +a5= +-0,000011 +a6= +1,599765 +a7= +-0,008708 + +632 +a8= +-0,000901 +a9= +0,000438 +a10= +0,000006 +Для експериментальних даних розрахунок за цією математичною мо- +деллю відстою жирової фази призводить до таких результатів (табл. 10). +В останньому стовпці показано відхилення експериментальних даних +від розрахункових, отриманих за побудованою математичною моделлю. +Відхилення експериментальних даних від розрахункових (остан- +ній стовпець таблиці 10) невеликі, тому знайдену математичну мо- +дель можна використовувати у роботах дослідників. +Використовуючи ці дві математичні моделі гомогенізації емульсій +різного хімічного складу, можна знайти оптимальні параметри про- +цесу гомогенізації таким чином: стійкість емульсії має бути макси- +мальною (100 %), відстій жирової фази має бути мінімальний. Роз- +рахунки за цими критеріями дають такі результати: тиск дорівнює +12 МПа, температура 60°C, при цьому стійкість емульсії дорівнює +100 %, відстій жирової фази 3,167 %. Ці дані добре корелюють з дани- +ми, отриманими іншим експериментальним шляхом. +Таблиця 10 +Розрахунок відстою жирової фази за математичною моделлю +Тиск, xi +Температура, yi +Відстій жирової +фази vi +Розрахунок Gi +Відхилення +7 +55 +9,2 +8,915 +0,285 +10 +55 +6,9 +6,809 +0,091 +12 +55 +5,2 +5,424 +0,224 +15 +55 +4,2 +4,639 +0,439 +7 +60 +7,7 +7,058 +0,642 +10 +60 +5,3 +4,953 +0,347 +12 +60 +3,4 +3,167 +0,233 +15 +60 +2,6 +2,782 +0,182 +7 +65 +5 +5,360 +0,360 +10 +65 +3,6 +3,254 +0,346 +12 +65 +1,5 +1,868 +0,368 +15 +65 +1 +1,084 +0,084 +7 +70 +3,5 +4,277 +0,777 +10 +70 +2,1 +2,171 +0,071 +12 +70 +0,9 +0,785 +0,115 +15 +70 +0,6 +0,000 +0,600 + +633 +Програмна підтримка дослідження. З метою розрахування опти- +мальної рецептури сирного виробу були проведені натурні експе- +рименти, на основі отриманих даних з яких будується математична +модель. Всі отримані дані потрібно структуровано зберігати для зруч- +ного доступу до них, саме тому використання бази даних є необхід- +ним. Приклад створено універсальною алгоритмічною мовою С# [18; +27; 28]. +Оскільки обсяг даних є невеликим, а доступ до них буде виключ- +но локальним, використання таких великих та потужних СУБД як +PostgreSQL або Oracle Database не є раціональним, тому враховуючи +вищезазначене найбільш оптимальним вибором стає SQLite, це лег- +ка вбудована СУБД що повністю задовольняє поставленим умовам, а +також є безкоштовною, тому її використання не потребує залучення +додаткових коштів. +SQLite — компактна СУБД, що вбудовується. Вихідний код бі- +бліотеки передано до загального використання. Слово «вбудований» +(embedded) означає, що SQLite не використовує парадигму клієнт — +сервер, тобто двигун SQLite не є окремо працюючим процесом, з яким +взаємодіє програма, а являє собою бібліотеку, з якою програма компо- +нується, і двигун стає складовою програми. Таким чином, як протокол +обміну використовуються виклики функцій (API) бібліотеки SQLite. +Такий підхід зменшує накладні витрати, час відгуку та спрощує про- +граму. SQLite зберігає всю базу даних (включаючи визначення, табли- +ці, індекси та дані) в єдиному стандартному файлі на тому комп’ютері, +на якому виконується програма. Простота реалізації досягається за +рахунок того, що перед початком виконання транзакції запису весь +файл, що зберігає базу даних, блокується; ACID-функції досягаються +у тому числі для створення файлу журналу [14; 17]. +Декілька процесів або потоків можуть одночасно без будь-яких +проблем читати дані з однієї бази. Запис до бази можна здійснити +лише у тому випадку, якщо жодних інших запитів на даний момент +не обслуговується; інакше спроба запису закінчується невдачею, й у +програму повертається код помилки. Іншим варіантом розвитку по- +дій є автоматичне повторення спроб запису протягом заданого інтер- +валу часу. +SQLite — це вбудована бібліотека, яка реалізує автономний, без- +серверний, нульової конфігурації механізм транзакції СУБД SQL. Це +база даних, яка налаштована на нуль. Це означає, що вам не потрібно +налаштовувати її у вашій системі. + +634 +SQLite не є автономним процесом, як інші бази даних, ви можете +пов’язати його статично або динамічно відповідно до вашої вимоги з +вашою програмою. SQLite безпосередньо звертається до своїх файлів +зберігання [8]. +Особливості SQLite: +• SQLite не вимагає окремого процесу сервера або системи для ро- +боти (без сервера). +• SQLite поставляється з нульовою конфігурацією, що означає +відсутність необхідності в налаштуванні або адмініструванні. +• Повна база даних SQLite зберігається в одному крос- +платформному диску. +• SQLite дуже маленька і легка, менше 400KiB повністю налашто- +вана або менше 250KiB з додатковими функціями. +• SQLite є автономною, що означає відсутність зовнішніх залеж- +ностей. +• Транзакції SQLite повністю сумісні з ACID, забезпечуючи без- +печний доступ до кількох процесів або потоків. +• SQLite підтримує більшість функцій мови запитів, знайдених у +стандарті SQL92 (SQL2). +• SQLite написана на ANSI-C і надає простий спосіб у викорис- +танні API. +• SQLite доступна у UNIX (Linux, Mac OS-X, Android, iOS) та +Windows (Win32, WinCE, WinRT). +СУБД SQLite багато в чому підтримує стандартний SQL. Діалект +мови SQL, що використовується в SQLite, за синтаксисом схожий +на той, який використовується в PostgreSQL. Однак SQLite накладає +низку специфічних особливостей на SQL. +Слід розрізняти саму SQLite як бібліотеку, що містить СУБД, і +базу даних як таку. За допомогою SQLite створюються бази даних, що +являють собою один кросплатформений текстовий файл. Файл бази +даних, на відміну SQLite, не вбудовується в додаток, не стає його час- +тиною, він існує окремо. Так можна створити базу даних, користую- +чись консольним sqlite3, після чого використовувати її у програмі за +допомогою бібліотеки SQLite мови програмування. При цьому файл +бази даних зберігається на локальній машині. +Програма, що включає SQLite, використовує її функціональність +за допомогою простих викликів функцій. Оскільки функції виклика- +ються в тому самому процесі, що працює програма, виклики працю- +ють швидше, ніж це було б у випадку міжпроцесної взаємодії. + +635 +Відхід від клієнт-серверної моделі зовсім не означає, що SQLite це +навчальна або урізана СУБД. Це означає лише специфіку її застосу- +вання в ролі компонента, що вбудовується. Існує безліч типів додат- +ків, від «записних книжок» до браузерів та операційних систем, що +потребують невеликих локальних баз даних. +Оскільки SQLite працює в рамках іншої програми, під час за- +пису файл бази даних блокується. Таким чином, записувати дані +можна лише послідовно. У той же час, читати базу можуть відра- +зу кілька процесів. SQLite — не найкращий вибір, якщо передба- +чаються часті звернення до БД на запис. Перелічені особливості +СУБД SQLite сприяють тому, що вона була використана для роз- +робки додатка. +На рис. 3 представлена схема бази даних SQLite, що використову- +ється для роботи додатку. + +Рис. 3. Схема бази даних додатку +Також нижче наводяться фрагменти опису таблиць бази даних: +Таблиця олій: + + +blend +blendExp +id +blendld +oill +ratio1 +id +oil2 +ratio2 +name +ratio +sat +oressure +munsat +temperature +punsat +sedExp +stabilityExp +blendld +blendld +sedPress +stabPress +sedTemp +stabTemp +sediment +stabilityCREATE +TABLE +"id" +INTEGER NOT NULL UNIOUE +"name" +TEXT NOT NULL, +PRIMARY KEY ("id" AUTOINCREMENT)636 +Таблиця сумішей: + +Таблиця експериментів жирнокислотного складу сумішей: + +Таблиця експериментів стійкості суміші: + +Таблиця експериментів відстою жирової фази: + +Опис основних процедур та функцій. Першочергово при запуску до- +датку перевіряється актуальність посилання на файл бази даних. +var db = Properties.Settings.Default.pathToDB; + +if (!File.Exists(db)) + + +MessageBox.Show («Файл бази даних відсутній, вкажіть нове +розташування файлу»); + +CREATE TABLE +"blend" +"id" +INTEGER NOT NULL UNIQUE, +"oill" +INTEGER, +"oi12" +INTEGER, +"ratio" +INTEGER, +"pressure" +INTEGER +"temperature" +INTEGER +FOREIGN KEY("oi11") +REFERENCES"oil"("id") +FOREIGN KEY ("oi12") +REFERENCES"oi1"("id") +PRIMARY KEY("id")CREATE +TABLE +"blendExp' +"blendId" +INTEGER NOT NULL, +"ratiol" +INTEGER NOT NULL, +"ratio2" +INTEGER NOT NULL, +"sat" +REAL NOT NULL, +"munsat" +REAL NOT NULL, +"punsat" +REAL NOT NULL, +FOREIGNKEY(blendId) +REFERENCES +"blend"("id")CREATE +TABLE +'stabil +ltyExp +"blendId" +INTEGER NOT NULL, +"stabPress" +INTEGER NOT NULL, +"stabTemp" +INTEGER NOT NULL, +"stability" +REAL, +FOREIGN KEY("blendId") +REFERENCES +"blend"("id")CREATE +TABLE +sedimentExp +"blendId" +INTEGER NOT NULL, +"sedPress" +INTEGER NOT NULL, +"sedTemp" +INTEGER NOT NULL, +"sediment" +REAL637 + + +using (OpenFileDialog dialog = new OpenFileDialog() {Filter = «Файл +бази даних (*.db)|*.db”}») + + + +dialog.ShowDialog(); + + + +if (string.IsNullOrEmpty(dialog.FileName) || !File.Exists(dialog.File- +Name)) + + + + +return; + + + +db = dialog.FileName; + + + +Properties.Settings.Default.Save(); + +else if(Path.GetExtension(db) != “.db”) + + +MessageBox.Show («Файл не є базою даних. Оберіть файл з +розширенням.db»); + + +using (OpenFileDialog dialog = new OpenFileDialog() {Filter = «Файл +бази даних (*.db)|*.db}») + + + +dialog.ShowDialog(); + + +if (string.IsNullOrEmpty(dialog.FileName) || !File.Exists(dialog.File- +Name)) + + + +return; + + + +db = dialog.FileName; + + + +Properties.Settings.Default.Save(); +У випадку недоступності файлу з тих чи інших причин буде від- +крито діалогове вікно системного файлового менеджеру з метою вка- +зування шляху до нового файлу, сам файл може знаходитись у будь- +якому місці. +public static DataTable select(string columns, string from) + +CheckConnection(); + +using (SQLiteDataAdapter adapter = new SQLiteDataAdapter(String.For- +mat(«select {0} from {1}», columns, from), connection)) + +using (var dataSet = new DataSet()) + + +adapter.Fill(dataSet); + + +return dataSet.Tables [0]; +Процедура запиту даних з таблиці приймає рядок назв потрібних +стовбців та назву таблиці, також є однойменна процедура з додатко- +вим параметром для вказування параметрів фільтрування даних. +public static void update(string table, string upd, string where) + +CheckConnection(); + +using (var cmd = new SQLiteCommand(String.Format(«update {0} set {1} +where {2}», table, upd, where), connection)) + + +cmd.ExecuteNonQuery(); + +638 +Процедура оновлення існуючих записів. +public static void delete(string from, string where) + +CheckConnection(); + +using (var cmd = new SQLiteCommand(String.Format(«delete from {0} where +{1}», from, where), connection)) + + +cmd.ExecuteNonQuery(); +Процедура видалення. Для відображення та роботи з даними БД +віконний додаток використовує елемент DataGridView. Далі наведено +процедури роботи з ними. +private void loadBlendExp() + +if (blendExp.Rows.Count != 0) + + +blendExp.Rows.Clear(); + +var rows = select(“rowid, ratio1,ratio2,sat,munsat,punsat”, “blendExp”, +$”blendId={selectedBlend.ItemArray [0]}”).Rows; + +if (rows.Count != 0) + + +foreach (DataRow row in rows) + + + +blendExp.Rows.Add(row.ItemArray); +Заповнення даних з таблиці експериментів складу суміші. +private void DataGridUserDeletingRow(object sender, DataGridViewRowCan- +celEventArgs e) + +var dg = (sender as DataGridView); + +string id = dg.Columns [0].Name.Contains(«row») ? «id» : «rowid»; + +delete(dg.Name, $»{id}={dg.Rows [e.Row.Index].Cells [0].Value}»); +Процедура видалення, оскільки всі таблиці посилаються на спіль- +ні процедури, в першу чергу, визначається, до якої таблиці адресова- +но запит, після чого вже виконується робота над вказаними запитами +private string cellValue; +private void DataGridCellBeginEdit(object sender, DataGridViewCellCancelEv- +entArgs e) + +var dg = (sender as DataGridView); + +cellValue = dg.Rows [e.RowIndex].Cells [e.ColumnIndex].Value.ToString(); +private void DataGridCellEndEdit(object sender, DataGridViewCellEventArgs e) + +var dg = (sender as DataGridView); + +string id = dg.Columns [0].Name.Contains(«row») ? «id» : «rowid»; + +if (dg.Rows [e.RowIndex].Cells [e.ColumnIndex].Value.ToString() != cellValue) + +639 + + +update(dg.Name, + + + +$»{dg.Columns [e.ColumnIndex].Name}=’{dg.Rows [e.RowIndex]. +Cells [e.ColumnIndex].Value}’», + + + +$»{id}={dg.Rows [e.RowIndex].Cells [0].Value}»); + + +if (dg.Name == «oil») + + + +FillCalcBlendCombo(); +Процедура редагування розбита на два етапи, спочатку зберігаєть- +ся поточне значення у редагованій комірці, яке потім перевіряєть- +ся на збіг з новим записом, це зроблено для уникнення перезапису, +якщо виклик редагування був випадковим. +Вибір суміші робиться шляхом обрання першого та другого ком- +понентів з двох випадаючих списків, черговість вибору неважлива, +вона збережена після додавання запису про нову суміш. Випадаючі +списки розміщені на трьох сторінках додатку та є синхронізованими, +немає потреби обирати компоненти на кожній сторінці. +private void FillCalcBlendCombo() + +var CB = blendCB1.ComboBox; + +var selected = CB. SelectedIndex == -1 ? CB. Items.Count : CB. SelectedIn- +dex; + +var DataSource = GetIdNamePairs(«oil»); + +CB. DataSource = DataSource; + +CB. ValueMember = «id»; + +CB. DisplayMember = «name»; + +CB. SelectedIndex = selected; + +CB = blendCB2.ComboBox; + +selected = CB. SelectedIndex == -1 ? CB. Items.Count : CB. SelectedIndex; + +CB. BindingContext = new BindingContext(); + +CB. DataSource = DataSource; + +CB. ValueMember = «id»; + +CB. DisplayMember = «name»; + +CB. SelectedIndex = selected; +Процедура заповнення випадаючих списків. +private void SynchronizeCB(ComboBox CB1, ComboBox CB2) + +CB1.DataSource = blendCB1.ComboBox.DataSource; + +CB1.ValueMember = «id»; + +CB1.DisplayMember = «name»; + +CB2.BindingContext = blendCB2.ComboBox.BindingContext; + +CB2.DataSource = blendCB2.ComboBox.DataSource; + +640 + +CB2.ValueMember = «id»; + +CB2.DisplayMember = «name»; +private void BindCB() + +SynchronizeCB(sedimentCB1.ComboBox, sedimentCB2.ComboBox); + +SynchronizeCB(stabilityCB1.ComboBox, stabilityCB2.ComboBox); + +(blend.Columns [1] as DataGridViewComboBoxColumn).DataSource = +blendCB1.ComboBox.DataSource; + +(blend.Columns [1] as DataGridViewComboBoxColumn).ValueMember = +«id»; + +(blend.Columns [1] as DataGridViewComboBoxColumn).DisplayMember = +«name»; + +(blend.Columns [2] as DataGridViewComboBoxColumn).DataSource = +blendCB2.ComboBox.DataSource; + +(blend.Columns [2] as DataGridViewComboBoxColumn).ValueMember = +«id»; + +(blend.Columns [2] as DataGridViewComboBoxColumn).DisplayMember = +«name»; +Процедура синхронізації випадаючих списків. +private void selectBlend() + +var CB1 = blendCB1.ComboBox; + +var CB2 = blendCB2.ComboBox; + +var s = select(«*», «blend», $»oil1={CB1.SelectedValue} and oil2={CB2. +SelectedValue} or oil1={CB2.SelectedValue} and oil2={CB1.SelectedValue}»); + +if (s.Rows.Count == 0) + + +using (var cmd = new SQLiteCommand($»insert into blend (oil1, oil2) +values (’{CB1.SelectedValue}’, ’{CB2.SelectedValue}’); SELECT last_insert_row- +id()», connection)) + + + +selectedBlend = select(«*», «blend», $»id={cmd.ExecuteScalar()}»). +Rows [0]; + + + +loadExp(); + +else +selectedBlend = s.Rows [0]; + +loadExp(); + +if (selectedBlend != null) + + +blendExp.Columns [1].HeaderText = selectedBlend.ItemArray [1]. +ToString() == CB1.SelectedValue.ToString() ? StringExtensions.FirstCharToUp- +per(CB1.Text) : StringExtensions.FirstCharToUpper(CB2.Text); + + +blendExp.Columns [2].HeaderText = selectedBlend.ItemArray [2]. +ToString() == CB2.SelectedValue.ToString() ? StringExtensions.FirstCharToUp- +per(CB2.Text) : StringExtensions.FirstCharToUpper(CB1.Text); + +641 +Процедура обрання суміші. Оскільки списки синхронізовані, про- +цедура завжди посилається на ті, що розташовані на першій сторінці. +Коди компонентів зчитуються та перевіряється наявність суміші з та- +кою комбінацією, якщо такого запису немає — буде створено новий +та отримано посилання на нього. +StringBuilder newValues = new StringBuilder(); + +var CB1 = blendCB1.ComboBox; + +var CB2 = blendCB2.ComboBox; + +if (CB1.SelectedValue == null) + + +if (CB1.Text != «») + + + +newValues.Append($»(’{CB1.Text}’),»); + + +if (CB2.SelectedValue == null) +if (CB2.Text != «») +newValues.Append($»(’{CB2.Text}’),»); +if (newValues.Length != 0) +insert(«oil», «name», newValues.Remove(newValues.Length — 1, 1).ToString()); +FillCalcBlendCombo(); +selectBlend(); +Списки передбачають можливість введення нових компонентів +не переходячи до вікна всіх записів. Не знайшовши ідентифікатора +компонентів, додаток автоматично збереже їх та суміш на їх основі. +Для додавання нових записів експериментів на кожній сторінці є +відповідні поля та кнопка підтвердження. +if (selectedBlend != null) + +var error = false; + +for (int i = 0; i < TS. Items.Count — 1; i += 2) + + +if (TS. Items [i].Text == «») + + +TS. Items [i].BackColor = Color.Red; + + +error = true; + +if (!error) + + +StringBuilder newValues = new StringBuilder(); + + +newValues.Append($»({selectedBlend.ItemArray [0]},»); + + +for (int i = 0; i < TS. Items.Count — 1; i += 2) + + +newValues.Append($»’{TS. Items [i].Text.Replace(’,’, ’.’)}’,»); + + +TS. Items [i].Text = «»; + + +newValues [newValues.Length — 1] = ’)’; + + +return (newValues.ToString()); + +else return null; +else return null; + +642 +var newValues = addExp((sender as ToolStripButton).Owner); + +if (newValues != null) + + +insert(«blendExp», «blendid, ratio1,ratio2,sat,munsat,punsat», newValues. +ToString()); + + +loadBlendExp(); +Процедура додавання результату експерименту спільна для всіх +вікон, спочатку отримується посилання на панель з елементами вве- +дення, потім перевіряється, чи обрана суміш, після чого процедура +зчитує наявні поля, перевіряє їх заповнення та додає новий запис. +Опис програмного додатка. Програмне забезпечення являє собою +віконний додаток з п’ятьма основними сторінками та вбудованою +системою управління базою даних. Розроблена програма може за- +стосовуватися не тільки для створення та оптимізації математичних +моделей сумішей при виробництві кисломолочних продуктів, але й +для будь-яких завдань, у яких необхідно знайти коефіцієнти рівняння +регресії за еспериментальними даними. Особливістю додатка є мож- +ливість визначення близькості одержуваних трьох величин до задано- +го співвідношення трьох еталонних чисел. +Основне вікно програми містить кілька вкладок, на які користу- +вач може переходити у процесі роботи над створенням математичних +моделей та їх оптимізацією, — «розрахунок суміші», «стійкість емуль- +сії», «відстій фази», «суміші», «олії» (рис. 4). Дві останні вкладки є до- +поміжними, в них заносяться і вибираються вихідні дані — назви олій +та ті олії, які будуть у суміші для подальших розрахунків. Хоча зараз +додаток використовується для оптимізації сумішей з соняшниковою +та оливковою оліями, в принципі він носить універсальний характер +і може застосовуватися і для інших інгредієнтів. +На рис. 4 представлений екран програми з відкритою вкладкою +для занесення та редагування інгредієнтів, що використовуються в +задачі, — олій. +На рис. 5 представлений фрагмент роботи додатка при виборі двох +олій, що беруть участь у подальших розрахунках, у цьому вікні також +можна заносити деякі вхідні характеристики суміші. Для початку ро- +боти необхідно обрати з випадаючих списків перший та другий ком- +понент суміші та підвердити вибір, натиснувши на кнопку. +При виборі олій можна скористатися табл.1, але в реальних роз- +рахунках будуть використовуватися соняшникова та оливкова олії. +У табл.1 наведено жирнокислотний склад різних рослинних олій од- + +643 +нак наступні міркування дозволяють вибрати з усього списку дві — +соняшникову та оливкову олії. + +Рис. 4. Екран роботи з вкладкою «олії» +Для наближення складу основи для виробництва продуктів, що +відповідають вимогам раціонального харчування необхідно значно +підвищити вміст ПНЖК і МНЖК. Кількість НЖК повинна залиша- +тись майже такою ж. Як видно із даних, наведених в табл. 1, для коре- +гування співвідношення між жирними кислотами доцільно викорис- +товувати оливкову олію, яка є основним постачальником МНЖК, і +соняшникову як джерело ПНЖК. + +CheeseProductModeller +口 +X +Po3paxyHok +CriikicTb +Biucrii +Cymimi +O.ri +cyMmimi +ey.lbcii +Ha3Ba +OJIMBROBOi +COHHIIHMKOBOi +paicoBoi644 + +Рис. 5. Екран роботи з вкладкою «суміші» +На рис. 6 показаний процес занесення експериментальних вхід- +них даних для створення математичної моделі емульсії з соняшни- +ковою та оливковою оліями. На цьому етапі необхідно ввести відсо- +ток участі в суміші кожної олії (соняшникова та оливкова), а також +отримані значення кислот НЖК, МНЖК, ПНЖК у 100 г кисломо- +лочного продукту (тобто занести дані з табл. 5). Результат занесення +експериментальних даних в «розрахунок суміші», представлений на +рис. 7. Внесені дані повністю відповідають табл. 5. Вкладка «розра- +хунок суміші» відповідає за перегляд, додавання, видалення та реда- +гування записів експериментальних даних й розрахунок на їх основі + +CheeseProductModeller +口 +X +Po3paxyHok +CriikicTb +Biucrii +Cymimi +O.rii +cymimi +eMyIbci +da3n +Oin 1 +Oia 2 +CHiBBinHOmeHHA +TucK, MIIa +Temeparypa, C +COHAMHKOBO +OJIMBOBOi +58 +12 +60 +OJIMBKOBOi +OJIMBKOBOi +paricoBoi +OJIMBEOBOI +parlcoBoi +COHHIHMROBOi +COHHIHMKOBOi +COHHIHMKOBOi645 +оптимального співвідношення олій в суміші для максимального на- +ближення їх жирнокислотного складу до еталонного. + +Рис. 6. Екран демонстрації занесення даних у вкладку «розрахунок суміші» +При цьому програма автоматично розраховує співвідношення +НЖК/МНЖК, МНЖК/ПНЖК, НЖК/ПНЖК за формулами (7), +а також інтегральний показник сумарного відхилення від заданого +співвідношення 0,3:0,6:0,1 за формулою (8) — рис. 8. Результати тако- +го розрахунку наведено у табл.6. Для додавання нових записів слід за- +повнити поля у нижній частині екрану та підвередити додаваня, після +чого таблиця автоматично оновиться і нові дані будуть виведені. + +CheeseProductModeller +口 +X +Po3paxyHok +CTiHkicTb +Biucrii +CyMii +O.rii +cyMimi +ey.lbcii +da3H +MoeJIFoBaHH cyMimi +OMBKOBOi +Ta +OJWBKOBO +OJMBKOBOi +Orial +Oix2 +HKK +MHKK +IHKK +HKK/ +CyMapHe +COHALHMKOBOi +pancoBoi +IIHKK +BiIXMJIeHHH +Po3paxyHoK lapaMeTpisMareMaTwyHoiMoeli +Po3paxyHOKHaikpaOro CIliBBinHomIeHHA646 + +Рис. 7. Результат занесення експериментальних даних у вкладку «розрахунок +суміші» +Для розрахунку параметрів математичної моделі необхідно на- +тиснути відповідну кнопку, після чого розрахункові величини будуть +відображені у таблиці, а також з’явиться вікно зі збереженою мате- +матичною моделлю та її коефіцієнтами. Розрахунок ведеться за алго- +ритмом випадкового пошуку (Монте-Карло), викладеним вище. При +цьому методом найменших квадратів вирішується завдання + +( +) +( +) +( +) +2 +1 + +, + +, +min, +n +i +i +i +i +i +G l +m +F l +m += +− +→ +∑ + +(16) + +CheeseProductModeller +一 +口 +X +Po3paxyHok +CriHkicTb +Biucrii +CyMii +Ori +cymimi +ey.lbcii +da3H +MoJeJIOBaHH cyMii +OJMBKOBOI +ra +COHALHMKOBOT +Oi +HKK/ +MHKK +HKK/ +CyMapHe +COHAMHKOBOi +OJIMBKOBOi +HKK +MHKK +IIHKK +MHKK +IIHKK +IIHKK +BXMJIeHH +5 +95 +1,523 +5,517 +0,276 +10 +90 +1.756 +5,505 +0.319 +15 +85 +2 +5.491 +0.365 +20 +80 +2.263 +5.426 +0.413 +25 +75 +2,539 +5,477 +0,465 +30 +70 +2,831 +5,447 +0,5199 +35 +65 +3,1431 +5,42999 +0.5788 +40 +60 +3,4749 +5,412 +0.6421 +45 +55 +3,8291 +5,3929 +0,71 +50 +50 +4,2081 +5.3725 +0,7833 +55 +45 +4,6146 +5,3507 +0.8624 +60 +40 +5.0516 +5,3271 +0.9483 +65 +35 +5,5227 +5.3018 +1.0417 +70 +30 +6,0322 +5.2743 +1,1437 +75 +25 +6,5848 +5.2446 +1.2555 +80 +20 +7,1863 +5.2122 +1.3787 +85 +15 +7.8434 +5,1768 +1.5151 +90 +10 +8,5644 +5.138 +1,6669 +95 +5 +9.3588 +5.0953 +1.8368 +Po3paxyHoKlapaMeipiBMareMaTvHoiMonei +Po3paxyHOKHaikpamOro ciBBinHOmeHHA647 + +Рис. 8. Автоматичний розрахунок інтегрального показника сумарного відхи- +лення +де значення G та F знаходяться за формулами (8) та (9). Для рівняння +регресії використовується поліноміальна функція як найбільш уні- +версальна функція (при цьому для зменшення кількості коефіцієн- +тів обмежуємося 4-м ступенем). Результати розрахунку коефіцієнтів +математичної моделі (9) за допомогою розробленої програми наведе- +но на рис. 9 та в моделі (10). Алгоритм випадкового пошуку (Монте- +Карло) в програмі використовує вбудовану функцію псеводвипадко- +вих чисел із дуже великим періодом повторення (можна вважати для +нашого завдання, що це нескінченний ряд випадкових нормованих + +CheeseProductModeller +口 +X +Po3paxyHok +CriikicTb +Bicrin +CyMinui +O.ri +cyMiui +eMy.lbci +da3H +MoJeJIFOBaHHA cyMii +OJMBKOBOi +o.i +HKK/ +MHKK +HKK/ +CyMapHe +COHAMHMKOBOi +OJIMBKOBOi +HKK +MHKK +IIHKK +MHKK +IIHKK +IIHKK +BXMJIeHH +5 +95 +1,523 +5,517 +0,276 +0.276 +19.989 +5,518 +16,731 +10 +90 +1.756 +5,505 +0.319 +0.319 +17,257 +5,505 +13,943 +15 +85 +2 +5.491 +0,365 +0,364 +15.044 +5,479 +11,659 +20 +80 +2,263 +5,426 +0.413 +0.417 +13,138 +5,479 +9.,7 +25 +75 +2,539 +5,477 +0,465 +0.464 +11,778 +5,46 +8,274 +30 +70 +2,831 +5,447 +0,5199 +0,52 +10.477 +5,445 +6,942 +35 +65 +3,1431 +5,42999 +0.5788 +0,579 +9,381 +5,43 +5,89 +40 +60 +3,4749 +5,412 +0,6421 +0.642 +8,429 +5,412 +4,983 +45 +55 +3,8291 +5,3929 +0,71 +0,71 +7,596 +5,393 +4,199 +50 +50 +4,2081 +5,3725 +0,7833 +0,783 +6,859 +5,372 +3,514 +55 +45 +4,6146 +5,3507 +0.8624 +0,862 +6.204 +5,351 +2,917 +60 +40 +5.0516 +5,3271 +0,9483 +0.948 +5,618 +5,327 +3,157 +65 +35 +5,5227 +5.3018 +1.0417 +1.042 +5.09 +5.302 +3,754 +70 +30 +6,0322 +5,2743 +1,1437 +1,144 +4,612 +5,274 +4,306 +75 +25 +6,5848 +5.2446 +1.2555 +1,256 +4,177 +5,245 +4,824 +80 +20 +7,1863 +5.2122 +1.3787 +1.379 +3,781 +5,212 +5,31 +85 +15 +7.8434 +5.1768 +1,5151 +1.515 +3,417 +5,177 +5,775 +90 +10 +8,5644 +5.138 +1,6669 +1,667 +3.082 +5,138 +6,223 +95 +5 +9,3588 +5.0953 +1.8368 +1.837 +2,774 +5,095 +6.658 ++ +Po3paxyHoKlapaMeTpiBMareMaTvHoiMonei +Po3paxyHoK Haikpamoro ciBBinHomeHHA648 +у діапазоні [0, 1] чисел). Для кожного кроку алгоритму застосовується +10 тисяч невдалих кроків, якщо не знаходиться точка з меншим зна- +ченням функції, крок зменшується вдвічі. Мінімальне знання кроку, +після якого алгоритм припиняє свою роботу, — 0,0001. + +Рис. 9. Результати розрахунку коефіцієнтів математичної моделі суміші олій +Для розрахунку найкращого співвідношення, використовуючи +отриману математичну модель, потрібно натиснути відповідну кноп- +ку, після чого вікно з ним з’явиться на екрані, а також буде збере- +жено для обраної суміші. Це досягається мінімізацією функції двох +змінних (10) за допомогою описаного алгоритму випадкового по- + +CheeseProductModleller +Po3paxyHoK +CriikicTb +Biucrii +CyMimi +O.ril +cyMii +eMy.Ibcil +a3H +MoeJIFOBaHH cyMiioJMBKoBoi +Ta COHAWHMKOBO +OJIi +HKK/ +COHHmHMKOBOi +OIMBKOBOi +HKK +MHKK +IIHKK +MHKK +HKK/ +CyMapHe +MHKK +IIHKK +IIHKK +BXMJIeHHH +5 +95 +1,523 +5,517 +0,276 +0.276 +19.989 +5.518 +16.731 +10 +90 +1,756 +5,505 +0.319 +0,319 +17,257 +5,505 +13,943 +15 +85 +2 +5,491 +0,365 +0,364 +15,044 +5,479 +11,659 +20 +80 +2,263 +5,426 +0.413 +0,417 +13,138 +5,479 +9.7 +25 +75 +2,539 +5,477 +0,465 +0.464 +11.778 +5.46 +8,274 +30 +70 +2,831 +5,447 +0,5199 +0,52 +10,477 +5,445 +6,942 +35 +65 +3,1431 +5,42999 +0,5788 +0,579 +9.381 +5,43 +5,89 +40 +60 +3.4749 +5.412 +0.6421 +0.642 +8.429 +5.412 +4,983 +45 +55 +X +4,199 +50 +50 +3,514 +55 +45 +MaTeMaTWyHa Mogeb y Bwrnaai noniHOMa cCTBopeHa Ta 36epeeHa +S= a1*x+ a2*y +a3*x^2+ a4*y^2+ a5xy+ a6+ a7*x^3+ a8*y^3+ +2,917 +60 +40 +a9*x^4+ a10*y^4 +3,157 +KoebiuicHTMMoAeni +65 +35 +a1=0,0000 +a2=0,0000 +a3=0,5890 +a4=0,9559 +3,754 +a5=0,0000 +a6=1,5522 +a7=5,5498 +a8=0,0000 +70 +30 +0000°0=6e +a10=17,4830 +4,306 +75 +25 +4,824 +80 +20 +OK +5,31 +85 +15 +7.8434 +5.1768 +1.5151 +1.515 +3,417 +5,177 +5,775 +90 +10 +8,5644 +5,138 +1,6669 +1,667 +3,082 +5,138 +6,223 +95 +5 +9,3588 +5,0953 +1.8368 +1,837 +2,774 +5.095 +6,658 ++ +Po3paxyHoKIapaMeTpisMaTeMaTMyHoiMoeJli +Po3paxyHoKHaikpamoro crliBBinHomeHHn649 +шуку. Результати подано на рис.10, при цьому змінні дорівнюють +l = 0,579062, m = 0,420938, а мінімум функції дорівнює F = 2,8949. Ці +результати добре корелюють з експериментальними даними з табл.6, +де мінімум, який знаходиться шляхом вибору найкращого експери- +менту, знаходиться у точці l = 0,55, m = 0,45 зі значенням функції F += 2,9172. Аналіз показує, що оптимізація співвідношення оливкової +та соняшникової олій у суміші з використанням математичної моделі +дає краще, більш точне значення інтегральної функції, що дозволяє +використовувати розроблені модель і програму при реальному роз- +рахунку параметрів кисломолочної суміші. + +Рис. 10. Результати розрахунку найкращого співвідношення олій у суміші + +CheeseProductModeller +X +Po3paxyHok +CriHkicTb +Bincrin +CyMini +O.ri +cyMii +eMy.lbcii +ba3H +MojeJIoBaHHa cyMii +OJMBKOBOi +Ta +COHALHMKOBOi +OJIi +HKK/ +MHKK/ +HKK/ +CyMapHe +COHHIIHMKOBOi +OJIMBKOBOi +HKK +MHKK +IIHKK +MHKK +IIHKK +IIHKK +BXMJIeHHH +5 +95 +1.523 +5,.517 +0.276 +0.276 +19.989 +5.518 +16.731 +10 +90 +1,756 +5,505 +0,319 +0,319 +17,257 +5,505 +13,943 +15 +85 +2 +5,491 +0,365 +0,364 +15,044 +5,479 +11,659 +20 +80 +2,263 +5,426 +0,413 +0,417 +13,138 +5,479 +9,7 +25 +75 +2,539 +5,477 +0,465 +0,464 +11,778 +5,46 +8,274 +30 +70 +2,831 +5,447 +0,5199 +0,52 +10,477 +5,445 +6,942 +35 +65 +3,1431 +9,381 +5,43 +5,89 +40 +60 +3,4749 +X +8,429 +5,412 +4,983 +45 +55 +3.8291 +7,596 +5,393 +4,199 +Haikpawe cniBBigHoweHR: +50 +50 +4,2081 +58 Ha 42 +6,859 +5,372 +3,514 +55 +45 +4,6146 +CyMapHe BiAXMneHH9 2.895 +6,204 +5,351 +2,917 +60 +40 +5,0516 +5,618 +5,327 +3,157 +35 +OK +65 +5,5227 +5,09 +5,302 +3,754 +70 +30 +6,0322 +5,2743 +1,1437 +1,144 +4,612 +5,274 +4,306 +75 +25 +6,5848 +5.2446 +1,2555 +1.256 +4,177 +5,245 +4,824 +80 +20 +7,1863 +5.2122 +1,3787 +1,379 +3,781 +5,212 +5,31 +85 +15 +7,8434 +5,1768 +1,5151 +1,515 +3,417 +5,177 +5,775 +90 +10 +8,5644 +5,138 +1,6669 +1,667 +3,082 +5,138 +6,223 +95 +5 +9.3588 +5,0953 +1.8368 +1,837 +2,774 +5,095 +6,658 ++ +Po3paxyHoK IapaMeTpiB MaTeMaTMHHoi MojeJi +Po3paxyHoK Haikpamoro clliBBinHomeHHn650 +Цю ж програму можна використати для розрахунку оптималь- +них параметрів гомогенізації різного хімічного складу емульсій. +Розглянемо спочатку модель залежності стійкості емульсії від тем- +ператури та тиску. Експериментальні дані наведено в табл. 7, від- +повідне вікно програми у вкладці «стійкість емульсії» наведено на +рис. 11. + +Рис. 11. Введення експериментальних даних у вкладці «стійкість емульсії» +Вкладка «стійкість емульсії» відповідає за перегляд, додавання, +видалення та редагування записів експериментальних даних й роз- +рахунок на їх основі оптимального режиму гомогенізації для макси- + +CheeseProductModeller +一 +口 +X +Po3paxyHok +CriikicTb +Biucrii +CyMii +O.rii +cymimi +eMyIbci +a3m +MoJeJIFOBaHHA cTiiKOcTi eMyIbci +OMBKOBOI +COHALHWKOBOi +THCK, +Temrieparypa +Po3paxyHoK +MIla +% +BinXWIeHHA +C +Y +7 +55 +98,1 +10 +55 +98.3 +12 +55 +98 +15 +55 +98.8 +60 +98,4 +10 +60 +100 +12 +60 +100 +15 +60 +100 +65 +99 +10 +65 +100 +12 +65 +100 +15 +65 +100 +7 +70 +99,3 +10 +70 +100 +12 +70 +100 +15 +70 +100 +Po3paxyHoKIapaMeTpiBMaTeMaTvHoiMonei651 +мальної стійкості емульсії отриманої суміші. Для опису процесу го- +могонезації у вигляді залежності стійкості емульсії від температурі та +тиску будемо використовувати функцію (11) двох змінних S(x,y) як +поліном 4-го ступеня, де x — значення тиску, y — значення темпера- +тури, S — значення стійкості емульсії. Для знаходження коефіцієнтів +математичної моделі за методом найменших квадратів шукати буде- +мо мінімум функції (12) за допомогою викладеного раніше методу ви- +падкового пошуку:: +( +) +( +) +( +) +2 +1 + +, + +, +min. +n +i +i +i +i +i +S x +y +D x +y += +− +→ +∑ + +Результати розрахунків у вигляді коефіцієнтів наведено на рис.12 +та у формулі (13). + +Рис. 12. Результати розрахунку коефіцієнтів математичної моделі стійкості +емульсії суміші + +CheeseProductModeller +X +Po3paxyHok +CriikicTb +Biucrii +CyMii +O.ri +cymimi +ey.Ibcii +da3H +MoneJIFOBaHHa cTiKOcTieMVIbci +OMBKOBOi +-TaCOHAHMKOBOi +Ji +TMCK. +Temreparypa. +Po3paxyHoK +C +% +BinxWJIeHHA +MIIla +Y +7 +55 +98,1 +88,325 +9,775 +10 +55 +98.3 +98.358 +0.058 +12 +55 +98 +100,739 +2.,739 +15 +55 +98.8 +91,752 +7,048 +7 +60 +98.4 +89,19 +9,21 +10 +60 +100 +99.223 +0,777 +MaTeMaTWyHa Mogeb y Bwrnaai noniHoMa cTBopeHa Ta 36epeeHa +Y= a1*x+ a2*y +a3*x^2+ a4*y^2+ a5xy+ a6+ a7*x^3+ a8*y^3+ +12 +60 +100 +101,604 +1,604 +a9*x^4+ a10*yA4 +15 +60 +100 +92,617 +7,383 +KoeiuiEHTW MoAeni: +a1=-0,0047 +a2=-0,0265 +a3=0,5774 +a4=0.0764 +7 +65 +99 +88.04 +10,96 +a5=-0,0000 +a6=1,5507 +a7=-0,0219 +a8=-0,0012 +a9=-0,0007 +a10=0,0000 +10 +65 +100 +98.074 +1,926 +12 +65 +100 +100,454 +0,454 +OK +15 +65 +100 +91.467 +8,533 +7 +70 +99,3 +84.877 +14,423 +10 +70 +100 +94,91 +5,09 +12 +70 +100 +97,291 +2,709 +15 +70 +100 +88.304 +11,696 +Po3paxyHoK IapaMeTpi MaTeMaTMyHoiMoneli +Po3paxyHoKpeKoMeHoBaHoro pexKMa roMoreHisali652 +Таким чином, отримана математична модель у вигляді + +S(x, y) = -0,004666x-0,026530y+0,577439x2+0,076405y2– + –0,000010xy+1,550705–0,021941x3–0,001249y3–0,000656x4+0,000005y4. +Її можна використовувати при розрахунку режиму гомоненізації +емульсій різного хімічного складу при виробництві кисломолочного +сиру для знаходження значень стійкості в залежності від температури +та тиску. +Розглянемо математичну модель залежності відстою жирової фази +також від температури та тиску. Вхідні експериментальні дані наве- +дено у табл.9. та на рис.13. Вкладка «відстой фази» використовує ті +ж прийоми для заповнення даними, що і раніше описані процедури, +тому на рис.12 наведено лише результат розрахунків коефіцієнтів мо- +делі. Після знаходження коефіцієнтів шуканої функції (14) матема- +тична модель набуде вигляду + +G(x,y) = -0,004837x-0,027562y+0,005950x2+0,034753y2– + –0,000011xy+1,599765–0,008708x3–0,000901y3+0,000438x4+0,000006y4. +Цю модель можна використовувати при розрахунках та оптиміза- +ції залежності відстою жирової фази також від температури та тиску. +Однак у більшій мірі використовують дві отримані моделі разом, +для розрахунків режимів гомогенізації, оскільки на сьогоднішній +день в молочній промисловості гомогенізація є єдиним способом +утворення стійкої емульсії, в тому числі і з рослинними оліями. При +цьому стійкість емульсії повинна бути максимальною, відстій жиро- +вої фази — мінімальним. Якщо використовувати дві останні отримані +математичні моделі для оптимізації процесу гомогенізації, отримає- +мо рішення, яке представлене на рис. 12. Оптимальні параметри про- +цесу гомогенізації, моделі виглядають таким чином: тиск дорівнює +12 Мпа, температура 60°C, при цьому стійкість емульсії дорівнює +100 %, відстій жирової фази 3,167 %. Ці дані добре корелюють з да- +ними, отриманими іншим експериментальним шляхом в табл. 3, 4. +Висновки. У роботі представлений підхід до побудови математич- +них моделей отримання кисломолочних продуктів для покращення +розрахунків параметрів одержуваної суміші з рослинними оліями. +В ході виконання досліджень були вирішені такі завдання: про- +аналізовано результати натурного фізичного експерименту і ви- +брано клас математичної моделі; оброблено експериментальні дані + +653 + +Рис. 13. Результати розрахунку оптимальних параметрів і процесу гомогені- +зації +за допомогою методів регресійно-кореляційно аналізу в розробле- +ній програмі, знайдено числові коефіцієнти математичних моделей; +проаналізовані отримані коефіцієнти на предмет адекватності моделі +вхідним даним; проаналізовано переваги та недоліки застосовуваних +алгоритмічних мов та обрано для програмування мову C#; побудова- +но комп’ютерну програму для розрахунку співвідношення вихідних +інгредієнтів для отримання заданих властивостей кисломолочного +продукту; в якості алгоритму оптимізації запропонована модифіка- +ція методу випадкового пошуку Монте-Карло, який, хоча і вимагає + +CheeseProductMocleller +X +Po3paxyHoK +CTiHKicTb +Biucri +Cyminui +O.ri +cymimi +eMy.lbcii +ba3H +MoneIFOBHHBincTOrpBia +OMBKOBOI +Ta +COHAWHMKOBOI +TMCK +Tereparypa +V. +Po3paxyHoK +% +V +BinxMIeHHA +MIIla +C +12 +60 +3.4 +3.027 +0,373 +15 +60 +7.7 +2,241 +5,459 +7 +65 +5 +4,624 +0,376 +10 +65 +3,6 +2,518 +1,082 +12 +65 +1.5 +1,131 +0.369 +X +15 +65 +1 +0.346 +0.654 +7 +70 +3.5 +3.294 +0,206 +PekoMeHgoBaHwi peKWM roMoreHi3aLii +10 +70 +2.1 +1,188 +0,912 +12MNa npw 60C +BiAcoTOK BiACTOrO MpOBoi Φa3W: 3,167% +12 +70 +0.9 +-0.198 +1,098 +15 +70 +0.6 +-0.984 +1.584 +OK +7 +60 +7.7 +6,519 +1,181 +10 +60 +5.3 +4.413 +0.887 +7 +55 +9,2 +8.53 +0,67 +10 +55 +6,9 +6,424 +0,476 +12 +55 +5.2 +5.038 +0,162 +15 +55 +4.2 +4,253 +0.053 +Po3paxyHoKIapaMeTpin MaTeMaTvHoi Moneli654 + значних часових комп’ютерних ресурсів, проте є досить універсаль- +ним і стійким до вхідних даних; в якості керуючого параметра алго- +ритму використовується кількість невдалих спроб генерації чисел, +тому в процесі декількох експериментальних прогонів програми зна- +йдено оптимальне значення кількості невдалих спроб; розроблено +практичні рекомендації користувачеві для використання програми +при розробці рецептури нового типу кисломолочного продукту. +Практичні результати дослідження полягають у тому, що розро- +блена програма дає в руки користувача-технолога інструмент, яким +він може користуватися для розрахунку рецептури нових сортів кис- +ломолочних продуктів з додаванням рослинних олій, не проводя- +чи фізичних експериментів, досліджуючи властивості продукту на +комп’ютері на підставі розроблених математичних моделей. +СПИСОК ВИКОРИСТАНОЇ ЛІТЕРАТУРИ +1. 102 questions with answers in Design Expert [Електронний ресурс]. 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А., Чабанова О. Б. та ін. Кореляційно- +регресійний аналіз рецептурних складників низьколактозного морозива. +Вчені записки ТНУ імені В. І. Вернадського. Серія: Технічні науки. Том 30 +(69). Ч. 2, № 3. 2019. С. 127–136. +45. Что такое .NET и чем занимаются .NET-разработчики? [Електронний ре- +сурс]. Режим доступу: https://training.epam.ua/#!/News/301?lang=ru +46. Эрл М., Эрл Р. Примеры разработки пищевых продуктов. Анализ кейсов. +Москва: Профессия, 2010. 400 с. +47. Ясаков А. В. Компьютерное проектирование пищевых продуктов со +сложным сырьевым составом [Електронний ресурс]. Режим доступу: +http://conf.omgtu.ru/node/128 + +658 +Розділ V +КОМП’ЮТЕРНІ ТЕЛЕКОМУНІКАЦІЙНІ МЕРЕЖІ +ТА ТЕХНОЛОГІЇ +МЕТОДИКА РІВНОМІРНОГО РОЗПОДІЛУ ЗАВДАНЬ +МІЖ ОБЧИСЛЮВАЛЬНИМИ КОМПЛЕКСАМИ +Завертайло К. С. +В роботі розглядається проблема балансування навантаження і рівно- +мірний розподіл завдань між обчислювальними комплексами. Ця проблема +розглядається в загальному вигляді, щоб запропоновані методи могли бути +базовими для розробки програмних засобів для всіх сфер інформатики, де ви- +никає проблема нерівномірного навантаження і розподілу завдань. Описані +основні причини виникнення нерівномірного навантаження. Зроблені висно- +вки і запропоновано методи усунення вказаної проблеми. +The paper considers the problem of load balancing and uniform distribution of +tasks between computer systems. This problem is considered in general, the reason +is that the proposed methods could be the basis for the development of software for +all areas of computer science, where there is a problem of uneven workload and +distribution of tasks. The article will describe the main causes of uneven load. +Conclusions are made and methods of elimination of the specified problem are +offered. +Проблема нерівномірного розподілу завдань виникає там, де за- +стосовують обчислювальні комплекси. У випадках, коли в обчислю- +вальних елементів різна продуктивність роботи, ризик виникнення +нерівномірного навантаження між ними підвищується. Оскільки +при різних можливостях обчислювальних елементів значно склад- +ніше планувати розподіл завдань і навантаження між ними. Також +причиною неправильного балансу може бути висока завантаженість +системи в цілому, тому що в таких випадках потрібно розраховувати +не тільки теперішнє навантаження між компонентами, а й їх продук- +тивність. В такій складній ситуації, коли інтенсивність надходження +завдань на обробку до комплексу зростає, ризик виникнення дисба- +лансного навантаження також зростає. +Також до причин нерівномірного навантаження можна віднести +різний обсяг завдань, що надходять до обчислювальних комплексів. + +659 +Зрозуміло, що в такій ситуації простим кількісним шляхом розподілу +завдань між обчислювальними елементами досить складно рівномір- +но їх розподілити. +Основним негативним наслідком від некоректного балансування +навантаження в комплексних системах є те, що одні обчислювальні +елементи використовуються всією системою не на повні свої можли- +вості. Тому таким елементам, можна сказати, притаманно часткове +простоювання впусту. Також при нерівномірному балансуванні на- +вантаження практично завжди є елементи, які отримують занадто +багато завдань на відміну від інших. Це сильно впливає на продук- +тивність всієї системи, особливо це відчутно, коли інтенсивність над- +ходження задач значно зростає. +Також з попередньо описаного негативного наслідку від нерів- +номірного навантаження випливає ще один. Він полягає в тому, що +значне навантаження на певні елементи системи підвищує ризик +відмови в роботі обчислювального елемента. Ще можна додати, що +надмірне навантаження знижує зносостійкість апаратної частини об- +числювальних компонентів. +Звісно, що неправильне балансування навантаження негативно +впливає на пропускну спроможність в мережах і час відгуку. Коли за- +пити розподіляються між серверами не рівномірно, значна частина +запитів простоює, очікуючи своєї черги, а це знижує ефективність +роботи системи серверів в цілому. +З наведених вище негативних наслідків можна зробити висновок, +що балансування навантаження є дуже важливим елементом в тих ін- +формаційних галузях, де застосовуються комплекси обчислювальних +систем. Тим більше застосування ефективного балансувальника на- +вантаження важливо, якщо продуктивність обчислювальних елемен- +тів різна, що на практиці виникає досить часто. +Теоретичні відомості. Питання планування навантаження потріб- +но вирішувати на ранній стадії розвитку будь-якого проекта. Вихід з +ладу системи загрожує серйозними наслідками — як моральними, так +і матеріальними. Спочатку проблеми недостатньої продуктивності +системи у зв’язку зі зростанням навантажень можна вирішувати шля- +хом нарощування потужності або оптимізацією використовуваних +алгоритмів, програмних кодів і тому подібне. Але рано чи пізно на- +стає момент, коли ці заходи виявляються недостатніми [1; 7]. +Доводиться вдаватися до кластеризації, наприклад, кілька серве- +рів поєднуються в кластер; навантаження між ними розподіляєть- + +660 +ся за допомогою комплексу спеціальних методів, які називаються +балансуванням. Крім вирішення проблеми високих навантажень, +кластеризація допомагає також забезпечити взаємне резервування +серверів. Ефективність кластеризації безпосередньо залежить від +того, як розподіляється навантаження між елементами кластера. За- +гальна схема роботи балансувальника навантаження наведена на ри- +сунку 1. +Рис. 1. Узагальнена схема роботи балансувальника навантаження +В подальшому буде проведено короткий огляд теорії балансуван- +ня навантаження у двох важливих в сфері комп’ютерних наук на- +прямках: +– Балансування навантаження для багатопроцесорних комп’ю- +терів; +– Балансування навантаження мережі. +Балансування навантаження в багатопроцесорних системах. Кому- +нікаційний дисбаланс навантаження обумовлений різністю в продук- +тивності комунікаційних зв’язків між багатоядерними процесорами +або іншого кластера в групі багатоядерних процесорів. З іншого боку, +дисбаланс в обмінах може бути пов’язаний і з паралельним додатком +і визначатися алгоритмом розв’язання задачі. Важливим прикладом + +HaAXOAKeHH +3aNMTiB +O6yMcOBabHMM +KOMNOHeHT 1 +O6yMcoBabHMM +KoMNOHeHT 2 +6anaHcyBabHMK +HaBaHTaKeHHg +O6yMcIoBabHMi +KoMNOHeHT 3 +O6yMcoBabHMi +KoMNOHeHT 4661 +для балансування є гетерогенні обчислювальні системи з розділеною +пам’яттю. Тут необхідні ресурси можна визначити лише під час робо- +ти програми, і балансування має проводитися динамічно, можливо +між різними операційними системами [2; 12]. +Потрібно виділити кілька рівнів і дати характеристику алгоритмів, +що їх реалізують, для досягнення балансування навантаження про- +цесорів для окремого паралельного застосування. +Балансування лише на рівні операційної системи, механізми — +кластеризація, поділ навантаження та міграція процесів на етапі +виконання; балансування на рівні проміжного програмного забез- +печення, механізм — високорівневе балансування навантаження в +контексті сесії або запиту, розподіл команд у стадії трансляції; балан- +сування на рівні користувацького додатку, реалізовується механізм +балансування за допомогою прикладних паралельних програм.Іс- +нуючі операційні системи покладаються на однозначний статичний +розподіл завдань користувачем, який може призводити до значного +розбалансування процесорів. Кластеризація допоможе подолати +труднощі, що виникають. Технологія кластеризації має дві основні +переваги. Вона підвищує масштабованість та обчислювальну потуж- +ність. Більшість кластерних рішень забезпечують збалансованість на- +вантаження та автоматичне перемикання з одного вузла на інший у +разі перевантаження або відмови. Одним з таких кластерних рішень +для Linux є система MOSIX. +OpenMOSIX — системне програмне забезпечення для ядер, таких +як Linux, що складається з адаптивних алгоритмів розподілу ресурсів. +Алгоритми розділу ресурсів OpenMOSIX розроблені відповідно до +використання ресурсів вузлів у режимі реального часу. +Усі ці алгоритми реалізуються завдяки механізму міграції про- +цесів. З кожним процесом асоціюється ідентифікатор унікального +домашнього вузла, з якого він був запущений. Для міграції процес +розбивається на дві частини: контекст користувача і системний кон- +текст. Частина користувача складається з коду програми, даних, сте- +ка, карт пам’яті та регістрів процесу. Системна частина включає опис +ресурсів, що належать даному процесу, та визначає машиннозалежну +частину, яка завжди залишається на унікальному домашньому вузлі +процесу. Мігруючий процес використовує ресурси нового вузла, на- +скільки це можливо, але взаємодіє з ОС через домашній вузол. +Міграція базується на інформації, що забезпечується одним із ал- +горитмів поділу ресурсів. Стратегія призначення завдань, заснована + +662 +також на економічних засадах та конкурентному аналізі. Ця стратегія +дає можливість керувати гетерогенними ресурсами способом, близь- +ким до оптимального. +Прикладне програмне забезпечення, інтерфейс для передачі об- +міну повідомленнями забезпечують вихідне фіксоване розміщення +процесів по вузлах кластера, тоді як openMOSIX виконує це динаміч- +но залежно від конфігурації доступних ресурсів. Прикладне програм- +не забезпечення й інтерфейс для передачі повідомлень працюють +на рівні користувача, на якому діють звичайні програми. Рішення +openMOSIX функціонує як модуль ядра операційної системи і є пов- +ністю прозорим для додатків. Немає необхідності модифікувати про- +грами під openMOSIX або пов’язувати їх з бібліотеками. Операційна +система openMOSIX — це, з одного боку, альтернатива технології ін- +терфейсу передачі повідомлень, а з іншого боку, їхній розвиток. Тут +необхідно зазначити, що openMOSIX і інтерфейс передачі повідо- +млень можуть працювати одночасно на одному і тому ж кластері. +Користувачі та програми можуть безпосередньо взаємодіяти +з openMOSIX через API інтерфейс, який забезпечує інформацію +про стан локальних процесорів та процесів. Очевидним недоліком +openMOSIX є великі накладні витрати при виконанні системних ви- +кликів. Додаткові витрати виникають під час операцій мережного до- +ступу. Наприклад, всі сокети створюються в ідентифікаторі домаш- +нього вузла, це призводить до великих комунікаційних витрат, якщо +процес мігрує з ідентифікатора домашнього вузла. +Загальні недоліки такого балансування у гнучкості та адаптив- +ності. Перші виникають через неможливість у режимі виконання +приймати рішення про балансування навантаження у додатку; дру- +гі — через відсутність зворотного зв’язку з репліками, об’єктами, які +працюють на стороні сервера балансування, і під його керуванням +всі разом представляють процеси, що піддаються балансуванню. Ще +один недолік — стандартне проміжне програмне забезпечення обме- +жено використовує ці можливості операційної системи, вони реалі- +зовані по-різному в різних операційних системах. +Основне проміжне програмне забезпечення для розподілу про- +цесів у паралельних системах передбачає середовище виконання, що +потребує адаптованих додатків та поінформованості користувача про +це. Воно включає утиліти для ініціалізації прив’язки процесу до вуз- +ла, ігноруючи доступні ресурси, наприклад, вільна пам’ять і процеси +введення-виводу. Це прикладне програмне забезпечення запускаєть- + +663 +ся на рівні користувача, як звичайна програма, таким чином, стає не- +здатним реагувати на нестійке завантаження і адаптивно перерозпо- +діляти обчислювальне навантаження. +Балансування навантаження на проміжному рівні виявляється +кращим, ніж балансування на нижчих рівнях мережі або операційної +системи, які відрізняються відсутністю гнучкості та адаптованості. +Проміжне програмне забезпечення може забезпечити багатий набір +метрик для балансування, у тому числі користувацьких, залежних від +додатків (гнучкість); тоді як мережеві або операційної системи балан- +сувальники працюють лише з фіксованими описами навантаження. +Проміжне програмне забезпечення може бути використане спільно +як зі стандартними, так і зі спеціалізованими мережами, операцій- +ними системами, а також із системами балансування навантаження, +тоді як низькорівневі балансувальники тісно пов’язані з апаратно- +програмним середовищем, для якого вони призначені [3; 10]. +Механізми балансування навантаження можуть реалізуватися в +прикладному програмному забезпеченні, наприклад, MIST, Dynamite, +mpC. У системах обміну повідомленнями процеси, що містять код +усієї прикладної програми, запускаються на різних обчислювальних +вузлах відповідно до заданої конфігурації. При розбалансуваннях, що +виникають під час виконання, їх необхідно перервати, перемістити +між вузлами та знову запустити в колишньому контексті. У системах +обміну повідомленнями балансування навантаження формулюється +через ефективний перерозподіл між обчислювальним вузлами, при +цьому міграція процесів — це основний механізм балансування. +Також механізми балансування навантаження можуть реалізову- +ватися шляхом планування ресурсів. Розподілені системи спочат- +ку складаються з окремих модулів, які, взаємодіючи один з одним, +призводять до розбалансування системи. Тому необхідно ефек- +тивно пов’язувати модулі під час роботи розподіленої системи для +вирівнювання навантаження. У розподілених системах балансу- +вання може бути описано за допомогою структур даних (або об’єктно- +орієнтованих інтерфейсів), які дозволяють побудувати відповідність +між постачальниками та споживачами ресурсів. +Проміжне програмне забезпечення динамічного балансування +паралельних і розподілених багатопроцесорних обчислювальних +систем має забезпечувати оптимальне розподілення паралельних +додатків при динамічно змінних ресурсах, за рахунок міграції таких +процесів між обчислювальними вузлами багатопроцесорної системи. + +664 +До складу проміжного програмного забезпечення для динаміч- +ного балансування навантаження входять такі компоненти: монітор +навантаження, планування процесу виконання, міграції завдань та +ін. Менеджер балансування навантаження розраховує балансування +навантаження. Якщо система розбалансована, починає працювати +менеджер міграції, який визначає нові місця виконання процесорів +та міграції. Окремий сервіс створює копію процесу, включаючи в +нього інформацію про встановлені комунікаційні з’єднання і відкри- +ті файли. Для переміщення процесу в новий вузол або процесор дані +передаються мігратору завдань. Процес за допомогою системи пере- +запуску завдань відновлює вихідний стан процесу на новому вузлі, і +паралельна програма продовжує виконуватись. +Прикладне програмне забезпечення обміну повідомленнями +складається з сервісу та бібліотеки, яка включається до коду приклад- +ної програми. Шляхом розширення, тобто модифікації вихідного +коду можна реалізувати додаткову функцію міграції процесів. +Основна ідея полягає в такому: +– Мігруючий процес припиняється. Приймаючий сервіс визначає +відповідний цьому процесу виконуваний файл; +– Стан мігруючого процесу, завантажений у пам’ять код і дані, +стек, відкриті канали (файли, мережеві з’єднання тощо), передається +на сторону, що приймає; +– Усі накопичені за перші два кроки повідомлення, адресовані мі- +груючому процесу, також передаються на сторону, що приймає; +– Вихідний екземпляр мігруючого процесу повністю зупиняється, +новий — запускається з того місця (стану), на якому було призупине- +но вихідний. +Для реалізації міграції процесів потрібна наявність відповідних +можливостей (API — прикладний програмний інтерфейс) операцій- +них систем, на яких використовуватиметься розширене прикладне +програмне забезпечення. API має включати функції призупинення +процесів, визначення адресного простору процесів, запуск процесів +у контексті і т. д. Міграція процесів може бути реалізована в однорід- +ній обчислювальній мережі, оскільки у процедурі міграції задіяні такі +параметри як адресний простір процесу (переміщення процесу між +вузлами з різними розмірами оперативної пам’яті реалізувати важко). +Рішення, мігрувати завданню чи ні, залежить від низки параме- +трів, які мають бути оцінені керуючою програмою переміщення (де- +мон UNIX). У разі паралельного завдання, що виконується на клас- + +665 +тері, програма, що управляє, бере до уваги: навантаження кожного +вузла; середнє навантаження у МВС, продуктивність мережі; час, +необхідний для запровадження контрольних точок, переміщення і +перезапуску завдання; прогнозоване подальше навантаження про- +цесора. +Балансування навантаження мережі. Для будь-якої хмарної мікро- +сервісної архітектури однією з основних характеристик є масштабо- +ваність. У сучасному світі будь-який сервіс, призначений для надан- +ня послуг широкому числу споживачів, повинен відрізнятися гарною +масштабованістю і швидкістю відповіді. Потенційні користувачі ні +за що не захочуть терпіти постійні помилки, втрати запитів, відмову +в обслуговуванні та інші проблеми, пов’язані з нестачею продуктив- +ності сервісу. Вони просто звернуться до конкурентів, навіть якщо їх +пропозиція буде менш вигідною, але працюватиме стабільно. +Найочевиднішим вирішенням проблеми може бути збільшення +потужності. Чим потужнішим буде центральний сервер і чим більше у +нього буде ресурсів, тим менша ймовірність виходу з ладу сервісу або +недоступність послуг. Так, це буде працювати до певного часу. Доки +серверу не буде потрібне обслуговування [4; 11]. +Другим рішенням буде зробити кілька серверів, які зможуть під- +тримувати працездатність сервісу надання послуг. Але при цьому від- +разу виникає кілька проблем: +– Яким чином клієнтська програма зможе визначити сервер, який +обслуговуватиме клієнта в даний момент часу; +– Як саме визначити доступність сервера та доступність сервісу в +цілому; +– Якщо один із серверів вже перебуває під навантаженням чис- +ленних запитів і не має змоги дозволити собі прийняти додаткове на- +вантаження, то як визначити, до якого доступного сервера необхідно +звернутися, щоб не створити другий вкрай завантажений сервер. +Вирішенням цієї проблеми є балансування навантаження. Це су- +купність методів розподілу задач між пристроями в мережі, з метою +оптимізації використовуваних як апаратних та обчислювальних, так і +мережевих ресурсів, скорочення часу обслуговування запитів та збіль- +шення максимального обсягу завдань, які може виконати система. +Для вирішення цього завдання в комп’ютерній мережі необхідна +розробка додаткового програмного забезпечення, яке взяло б на себе +функцію балансувальника. Балансувальник може бути не обов’язково +програмним засобом, а й окремим мережевим пристроєм. + +666 +Введення ще одного елемента в систему допоможе уникнути +помилок на стороні клієнта в системі, і зробити його роботу більш +легкою і продуктивною. Клієнт може безпосередньо звертатися до +балансувальника через заздалегідь визначений механізм, згідно з ал- +горитмами та стратегією, закладеними в балансувальник. +Балансувальник зможе у фоновому режимі проводити моніторинг +доступності серверів і маршрутів до них, щоб у момент запиту від клі- +єнта маршрутизувати запити навколо перевантаженого елемента ме- +режі найкоротшим шляхом. +І найважливіша функція балансувальника — це усунення неодно- +рідності в мережі, тому що часто створити великий сервіс в одній зоні +або регіоні недостатньо, і тоді на плечі балансувальника лягає подо- +лання подібних дрібних системних нестиковок, які для стандартної +клієнт-серверної моделі суттєво ускладнили б завдання. +Процедура балансування здійснюється за допомогою комплексу +алгоритмів та методів, що відповідають рівням моделі OSI: мережево- +му, транспортному і прикладному. +Балансування навантаження на мережевому рівні передбачає ви- +рішення такого завдання: потрібно зробити так, щоб за одну кон- +кретну IP-адресу сервера відповідали різні фізичні машини. Таке +балансування може здійснюватися за допомогою багатьох різнома- +нітних способів: +– DNS-балансування. На одне доменне ім’я виділяється кілька +IP-адрес. Сервер, на який буде направлений запит клієнта, зазвичай +визначається за допомогою алгоритму Round Robin. +– Побудова класу NLB. При використанні цього способу сервери +поєднуються в кластер, що складається з вхідних та обчислювальних +вузлів. +– Розподіл навантаження здійснюється за допомогою спеціально- +го алгоритму. Використовується в рішеннях компанії Microsoft. +– Балансування IP за допомогою додаткового маршрутизатора. +– Балансування за територіальною ознакою здійснюється шляхом +розміщення однакових сервісів з однаковими адресами у територі- +ально різних регіонах Інтернету. +Балансування навантаження на транспортному рівні. Цей вид +балансування є найпростішим: клієнт звертається до балансуваль- +ника, той у свою чергу перенаправляє запит на один з серверів, +який його оброблятиме. Вибір сервера, на якому оброблятиметь- +ся запит, може здійснюватися відповідно до найрізноманітніших + +667 +алгоритмів: шляхом простого кругового перебору, шляхом вибо- +ру найменш завантаженого сервера з пулу. Іноді балансування на +транспортному рівні важко відрізнити від балансування на мереж- +ному рівні [5; 9]. +Відмінність між рівнями балансування можна пояснити так. До +мережного рівня відносяться рішення, які не термінують на собі сесії +користувача. Вони просто перенаправляють трафік і не працюють у +режимі проксі. +На мережному рівні балансувальник просто вирішує, на який сер- +вер передавати пакети. Сесію з клієнтом здійснює сервер. +На транспортному рівні спілкування з клієнтом замикається на +балансувальник, який працює як проксі-сервер. Він взаємодіє із сер- +верами від свого імені, передаючи інформацію про клієнта у додатко- +вих даних та заголовках. Таким чином працює, наприклад, популяр- +ний програмний балансувальник HAProxy +Балансування навантаження на прикладному рівні балансуваль- +ник працює в режимі «розумного проксі». Він аналізує клієнтські за- +пити і перенаправляє їх у різні сервери залежно від характеру запиту- +ваного контенту. +Так працює, наприклад, веб-сервер Nginx, розподіляючи запити +між фронтендом та бекендом. За балансування у Nginx відповідає мо- +дуль Upstream. +Як ще один приклад інструменту балансування на прикладному +рівні можна навести pgpool — проміжний шар між клієнтом та серве- +ром СУБД PostgreSQL. З його допомогою можна розподіляти запити +по серверах баз даних в залежності від їх змісту. Наприклад, запити на +читання будуть передаватися на один сервер, а запити на запис — на +інший. +Класифікація стратегій балансування навантаження. Для розробки +методу балансування навантаження необхідно розглянути існуючі +методи, алгоритми та стратегії, що застосовуються в цій галузі. Буде +розглянуто основні класи стратегій балансування навантаження. +Причиною того, чому будуть розглянуті саме класифікації підходів +балансування навантаження є те, що саме виокремлені класифікації +та їх ознаки наглядно демонструють теоретичну основу і розуміння +самих підходів рівномірного розподілу завдань [6]. +Перший клас балансування навантаження — коли принципи ба- +лансування навантаження розподіляються на статичні, напівдина- +мічні, динамічні. При використані статичної стратегії балансування + +668 +навантаження план розподілу задач між обчислювальними комплек- +сами відомий заздалегідь, оскільки розподіл навантаження викону- +ється заздалегідь. Статична стратегія більш проста в реалізації, але +менш ефективна, ніж динамічна чи напівдинамічна. +При використані напівдинаміної стратегії розподілу навантажен- +ня план визначається на етапі ініціалізації, до того як починаються +основні обчислення. Тобто попередньо оцінюються всі ресурси, що +є в наявності. На відміну від статистичної стратегії напівдинамічна +є більш ефективною в роботі, оскільки оцінка на початку ситуації в +системі дозволяє краще в подальшому балансувати навантаження +між обчислювальними елементами. Статистична стратегія балансу- +вання є більш простою в реалізації. +Найбільш ефективною в роботі є динамічна стратегія розподілу +навантаження. Вона змінюється протягом роботи всього обчислю- +вального комплексу. Ця стратегія змінюються під впливом певних +факторів і регулярно оцінює стан середовища, у якому працює. За- +звичай динамічна стратегія базується на тому, що проводить оцінку +стану середовища через певний встановлений інтервал часу. Хоча та- +кож можна не фіксувати цей інтервал чітко, а він буде визначатись +після кожної оцінки середовища, в залежності від того, в якому стані +буде це середовище. Також динамічна стратегія може змінюватися не +тільки між інтервалами. В складних системах, де є підвищений ризик +виходу з-під контролю нормального балансу навантаження, дина- +мічна система може в будь-який момент отримувати сигнали, коли +навантаження різко змінюється. Ці сигнали можуть свідчити про те, +що необхідно виконувати певні зміни до закінчення встановленого +інтервалу. Описана стратегія є найбільш складною в реалізації, проте +вона є найбільш ефективною на практиці. Слід зауважити, що вико- +ристання динамічної стратегії є доцільним лише в складних обчис- +лювальних системах. Тому що в незначних за складністю обчислю- +вальних комплексах з завданням балансування навантаження може +впоратись і напівдинамічна, і в навіть в зовсім простих статична. +Тому дуже важливо розуміти доцільність використання динамічної +стратегії балансування навантаження. +Наступним класом поділу стратегій балансування є принцип по- +ділу на залежний і незалежний розподіл. Залежним розподілом за- +вдань, між обчислювальними елементами можна вважати розподіл, +який змінює принцип розподілу завдань між вузлами в залежності +від певних подій, що виникають при роботі цілої комплексної систе- + +669 +ми. Конкретно умови, при яких відбуваються ці зміни в плануванні, +визначаються заздалегідь, і вони залежать конкретно від системи, +під яку працює планувальник. Зазвичай цими параметрами є під- +вищення чи зменшення навантаження, як і в усій системі, так і на +одному, конкретному обчислювальному елементі. Також до цих па- +раметрів можна віднести зменшення під час роботи продуктивності +одного з обчислювальних елементів. Враховуючи те, що в залежності +від певних факторів змінюється стратегія планування, то залежний +розподіл планування співвідноситься з динамічною стратегією пла- +нування. +При розгляді незалежного принципу балансування навантаження +мається на увазі те, що немає ніякого впливу якихось факторів на ро- +боту балансувальника навантаження чи ці впливи зведені до мініму- +му. Зазвичай незалежний можна порівняти і зі статичним чи напівди- +намічним підходом, оскільки робота балансувальника навантаження +планується заздалегідь, перед роботою самої системи. Тому зазвичай +незалежний розподіл задач між обчислювальними елементами засто- +совується до простих систем. +Також необхідно виокремити класифікацію, що поділяє спо- +соби балансування навантаження на спеціалізовані та універсаль- +ні. В принципі з самої назви можна визначити, що спеціалізована +стратегія має на увазі розробку алгоритму під конкретну тополо- +гію мережевого середовища чи конкретну архітектуру розподіленої +системи. Також зрозуміло, що ефективність від спеціалізованих +підходів розробки балансувальника навантаження вища від універ- +сальних. До недоліків можна віднести те, що ціна розробки таких +балансувальників вища і вузька направленість не дає змоги засто- +совувати до багатьох напрямів, де потрібне балансування наванта- +ження. +Про універсальні можна сказати, що, як видно з їх назви, вони є +багатонаправленими. І фактично це і є їх основною перевагою над +спеціалізованими. Зазвичай універсальними є методи, які є базою +для алгоритмів, а спеціалізовані підходи — це вже безпосередньо ал- +горитми, що розроблені для конкретних архітектур. +Наступна класифікація полягає у врахуванні і неврахуванні при- +чин зміни балансу навантаження в системі. Необхідно визначити при +розробці методу і алгоритму, чи потрібно враховувати причини зміни +балансу навантаження. Розглядаючи ті алгоритми, що не враховують +причини переміни балансу розподілу задач в системі, можна зазначи- + +670 +ти, що перевагою цього є те, що це спрощує розробку балансувальни- +ка навантаження. Недоліки цього підходу очевидні, вони полягають +в тому, що навіть ефективний алгоритм балансування навантаження, +який не враховує причини перепаду навантаження, будуть поступа- +тися алгоритмам, які враховують принципи зміни навантаження, та +як саме на майбутнє змінювати стратегію роботи відносно обчислю- +вального комплексу. +На відміну від вищеописаного ті методи, що враховують причину +зміни навантаження в майбутній роботі системи, визначають більш +точно, яким чином необхідно перерозподілити саме завдання між об- +числювальними елементами. З переваги оберненого до цього підходу +випливає і обернений недолік. Визначається він тим, що розробка +способів балансування навантаження між обчислювальним елемен- +тами є більш складною і затратною. Саме такі обернені один до одно- +го переваги і недоліки ставлять основні питання з приводу того, який +саме підхід необхідно застосувати. +Системи, де враховуються причини перепаду балансу між ком- +понентами системи, застосовують у складних системах, де просто +необхідна ефективність і точність виконання рівномірного розпо- +ділу між вузлами. Підходи, що не враховують виникнення причин +зміни балансу в системах, застосовують до простих у своїй структурі +системах. +Потрібно відмітити те, що клас балансувальників навантаження, +що враховують причини зміни балансу, можна поділити на два під- +класи. Першими є фактори, що впливають на баланс навантаження +на систему ззовні. Другими є ті, що впливають на баланс наванта- +ження всередині самої системи. До прикладу, збільшення запитів до +комплексу серверів у час пік — є зовнішніми факторами. А, напри- +клад, зменшення продуктивності з причини поганої зносостійкості, +одного з обчислювальних елементів є фактором, що впливає на сис- +тему зсередини. +Стратегії балансування навантаження також можна поділити +на прогностичні, тобто ті, що моделюють навантаження на обчис- +лювальні компоненти в системі в майбутньому, і на ті, що не здатні +прогнозувати поведінку навантаження в подальшій роботі обчис- +лювального комплексу. Зрозуміло, що прогностичні підходи є більш +ефективними. Оскільки завдяки коректному прогнозу і розподілу +навантаження в подальшій роботі системи продуктивність її роботи +значно підвищується. Завдяки прогностичним підходам підвищу- + +671 +ється робота не частини певних факторів, а всіх разом. Це дозволяє +підвищити як пропускну спроможність, так і швидкість обробки об- +числювальними елементами поставлених перед ними завдань. Недо- +ліком врахування прогностичності в підходах балансування наванта- +ження є значні витрати на розробку безпосередньо способу прогнозу +роботи системи в майбутньому. Саме з цієї причини такий спосіб за- +стосовують лише з урахуванням того, що розроблені алгоритми ба- +лансування будуть застосовуватися до тих систем, які є значними за +своїм обсягом, дуже чутливі до точності визначення розподілу задач +між вузлами і потребують значної ефективності у виконанні постав- +лених перед ними завдань. +При огляді тих систем балансування навантаження, що не здатні +прогнозувати подальшу поведінку навантаження в обчислювальному +комплексі, слід відразу відмітити, що такі системи значно поступа- +ються у своїй ефективності прогностичним. Проте все ж потрібно в +черговий раз зауважити, що існують обчислювальні комплекси, які, +хоч і можуть бути значними за своїм обсягом, але не є складними за +своєю суттю і не такі вибагливі щодо високої точності розподілу за- +вдань між обчислювальним елементами. Саме для таких систем дуже +часто застосування не прогностичних стратегій балансування є більш +доцільним, аніж прогностичних. +Однією з найбільш важливих класифікацій поділу способів балан- +сування є розподіл на централізовані і децентралізовані. Такий поділ +підходів до стратегій балансування навантаження є дуже важливим +при розробці методу балансування навантаження, тому його потріб- +но розглянути дуже детально. Для початку розглянемо централізо- +ваний підхід до розробки методу балансування навантаження. Цей +спосіб пропонує єдиний балансувальник навантаження для всіх об- +числювальних елементів у системі. Саме балансувальник повинен +оцінювати інтенсивність надходження завдань на обробку, оцінювати +можливості і ступінь завантаженості в конкретний момент часу об- +числювальних елементів, аналізувати ситуацію в системі в цілому і +проводити розподіл завдань. Перевага такого способу очевидна: єди- +ний балансувальник навантаження значно краще координує роботу +між обчислювальним елементами, швидше оцінює стан системи в ці- +лому і може вплинути на неї при її подальшій роботі чи подати сигнал +щодо її критичного стану при необхідності. Звісно такий підхід має +свої недоліки. Одним з таких недоліків є те, що при відмові в роботі +балансувальника навантаження чи початку його некоректної роботи + +672 +балансування навантаження у всій системі починає проводитися не- +коректно, що швидко призведе до значних негативних наслідків. Та- +кож потрібно відмітити, що централізовані балансувальники наван- +таження зазвичай більш негативно впливають на масштабованість, +ніж децентралізовані. +При розгляді децентралізованих слід відмітити, що в кожного об- +числювального компонента є свій балансувальник навантаження, +завданням якого є оцінка навантаження свого компонента, визна- +чення інтенсивності надходження завдань чи запитів до його ком- +понента і обчислення для визначення подальшої продуктивності +роботи обчислювального елемента, за який він відповідає. Всі ба- +лансувальники навантаження обмінюються між собою інформацією +з приводу навантаження на своєму обчислювальному вузлі. В під- +сумку, кожен балансувальник навантаження визначає ступінь наван- +таження його елемента і робить висновок з приводу того, чи його +обчислювальний елемент є занадто навантаженим, чи його обчис- +лювальний елемент використовується не на повну потужність. У всій +системі всі балансувальники навантаження підтримують між собою +зв’язок, обмінюються інформацією. Завдяки цьому обміну даними +всі балансувальники навантаження містять інформацію про заван- +таженість кожного балансувальника навантаження в системі. Тому, +коли є необхідність, менш завантажений балансувальник може при- +йняти частину запитів з черги більш завантаженого. Перевага децен- +тралізованого балансування навантаження перед централізованим +походить від недоліку централізованого підходу. Ця перевага поля- +гає в тому, що при відмові в роботі чи початку некоректного плану- +вання виходить з ладу лише один балансувальник навантаження зі +всієї системи, на відміну від того, що в централізованих алгоритмах +це відразу негативно впливає на баланс навантаження всієї систе- +ми, оскільки там балансувальник один. Недоліками децентралізо- +ваного підходу балансування навантаження є те, що, на відміну від +централізованого, така стратегія балансування не може загалом оці- +нювати ситуацію в усій системі, оскільки в кожного обчислюваль- +ного компонента свій балансувальник. Тому при критичній ситуації, +яка впливає на систему і потрібно приймати рішення, яке повинно +глобально впливати на весь обчислювальний комплекс, централізо- +ваний спосіб балансування явно переважає децентралізований. На +рисунку 2 зображено схему з п’яти обчислювальних компонентів, що +обмінюються даними. + +673 +Причиною того, чому саме на класифікацію поділу на централі- +зовані і децентралізовані стратегії балансування було звернено ува- +гу, полягає в тому, що вибір одного з цих підходів часто змінює весь +принцип підходу в моделюванні і створені методу розподілу завдань +між обчислювальним елементами. Звертаючи увагу на те, для чого +саме будуть застосовуватися розроблені методи, потрібно вибирати +на початковому етапі одну з цих стратегій: централізовану чи децен- +тралізовану. +Рис. 2. Децентралізоване балансування навантаження +Останнім поділом на класи стратегій балансування є розподіл +на адаптивні і неадаптивні способи балансування навантаження. +Адаптивна стратегія балансування навантаження передбачає при- +стосування до кардинальних змін в системі. Цими змінами можуть +бути, наприклад, додавання нових обчислювальних вузлів у систему +чи виключення з неї існуючих. Звісно, тим, що така стратегія може +пристосовуватися до кардинальних змін, вона має перевагу над не- +адаптивним підходом. Проте недоліком такого способу є те, що при +її розробці виникає додаткова робота і необхідно враховувати, чи + +O6yMcoBaIbHMi +eeMeHT 2 +O6yMcoBabHMM +eneMeHT1 +O6yMcnoBabHwM +eeMeHT3 +O6yMcioBabHw +eeMeHT5 +O6yMcoBabHwi +eneMeHT4674 +взагалі потрібно буде її реалізовувати. Адже, якщо в системі вза- +галі не передбачається ні включення, ні виключення нових обчис- +лювальних елементів, не буде змінюватися ресурсна конфігурація +розподіленої системи й інші значні зміни, то застосування такого +підходу просто не має сенсу. Адаптивна стратегія балансування на- +вантаження дуже сильно подібно до динамічної, її навіть можна +вважати динамічною, тільки в більш вузькому розумінні цього ви- +значення. На рисунку 3 зображено централізований адаптивний ба- +лансувальник навантаження, до якого додаються ще два обчислю- +вальних елемента, вони відмічені штрихом. На рисунку 4 зображено +децентралізований адаптивний балансувальник навантаження, до +трьох взаємодіючих між собою елементів додаються ще два, які та- +кож відмічені штрихом. + +Рис. 3. Централізований адаптивний балансувальник навантаження +Неадаптивна стратегія балансування навантаження не враховує +і не передбачає кардинальних змін у роботі. Це є її недоліком перед +адаптивною. Проте для систем, що не передбачають кардинальних +змін у роботі, цей спосіб розподілу завдань підходить ідеально. + +HaXOnKeHH +3anWTIB +O6yMcoBabHMM +KoMNOHeHT 2 +baaHcyBabHWK +HaBaHTaKeHHA +O6yncnoBabHMM +KoMNOHeHT 3 +HoBWMo6yWcnroBaIbHW +KOMnOHeHT +HoBwi o6yMcnoBanbHMi +KOMNOHeHT675 +Опис методу балансування навантаження. Було проведено огляд +того, за якими показниками можна класифікувати стратегії балан- +сування навантаження, щоб застосувати їх для методу балансування +навантаження, що пропонується в нашій роботі. Причиною того, +чому саме через класифікації буде описано теоретичну базу методу +є те, що саме така характеристика чітко показує можливості і його +властивості. + +Рис. 4. Децентралізований адаптивний балансувальник навантаження +При короткому огляді методу балансування навантаження, перш +за все, слід відзначити, що його роботу відразу потрібно поділити +на дві складові. Функції першої складової передбачають глобальну +оцінку всієї системи, відслідковування інтенсивності надходження +завдань на обчислення до системи, рівномірний розподіл між об- +числювальними елементами задач відносно можливостей продуктив- +ності обчислювальних елементів і завдяки визначенню інтенсивності +надходження запитів до обчислювального комплексу визначати спо- +сіб розподілу завдань між обчислювальними вузлами в майбутньому. +Перерозподіл надходження запитів до обчислювальних елементів +буде здійснюватися щоразу через встановлений проміжок часу. Який +саме проміжок часу буде встановлюватися, залежать від конкретної +системи. Також допускається, що під час роботи обчислювального +комплексу цей інтервал часу буде змінюватися в залежності від робо- +ти самої системи. + +O6yMcoBabHMi +O6ycoBabHMM +KoMNOHeHT 1 +KoMNOHeHT 2 +O6yWcIoBabHMM +KoMNOHeHT 3 +HoBWi +HoBWi +O6ycoBaIbHwi +O6yMcoBaIbHMi +KOMNOHeHT +KOMNOHeHT676 +Розподіляючи завдання між вузлами, оперувати балансувальник +навантаження буде обсягом надходжень завдань, зіставляючи його +з продуктивними можливостями кожного обчислювального компо- +нента в системі. Тому для роботи балансування навантаження по- +трібно оцінювати продуктивність кожного обчислювального вузла +за допомогою базових характеристик цього вузла. Передбачається, +що характеристики потужності роботи кожного елемента потрібні +балансувальнику навантаження лише на початку роботи системи. +В подальшому продуктивність буде визначатися за допомогою оцін- +ки ефективності роботи кожного обчислювального елемента, тобто +на практиці. +Оцінка інтенсивності надходження завдань до системи є ключо- +вою складовою першої частини балансувальника навантаження. За +допомогою однієї з основних і базових формул теорії вірогідності +і оцінки інтенсивності надходження запитів у попередніх ітераці- +ях буде визначатися прогноз на роботу в подальших ітераціях, що +будуть виникати через встановлені проміжки часу. Сенс цього про- +гнозу полягає в тому, щоб порівнювати при кожному перерозподі- +лі завдань між обчислювальним компонентами системи точність +прогнозу. Порівняння буде відбуватися за допомогою співставлен- +ня кількості задач, що надішли і спрогнозовані, також оцінка хиби. +Якщо прогноз дуже близький до реально отриманих завдань, то пе- +рерозподіл не відбувається, а все працює за способом, визначеним +в попередній ітерації. Перевага такого підходу полягає в тому, що +просте порівняння даних між собою займає дуже мало часу і обчис- +лювальних можливостей і фактично не впливає на роботу як систе- +ми, так і балансувальника навантаження. А ось якщо щоразу пере- +розподіляти, то це вимагає певних витрат. Тому навіть якщо прогноз +не буде співпадати з реальними даними, що надійшли значну кіль- +кість разів, це буде вимагати перерозподіляти стратегію поділу на- +вантаження, що і так потрібно б було виконувати. Коли прогноз +співпадає з даними, що надійшли, то перерозподіляти нічого не по- +трібно, і так буде зрозуміло, яким чином надалі проводити розподіл +навантаження. А це вже буде давати певну економію як часу, так і +обчислювальних можливостей, як балансувальника навантаження, +так і всієї системи. +Також у функції першої частини балансувальника навантажен- +ня буде входити слідкування за навантаженням і роботою системи в +цілому. Наприклад, при значному збільшенні навантаження на всю + +677 +систему такий балансувальник зможе швидко визначати це і опера- +тивно реагувати на таку проблему, чи визначати проблеми в роботі +одного з обчислювальних елементів. Це є основною перевагою цен- +тралізованої стратегії балансування навантаження. +Підбиваючи підсумки щодо першої складової балансувальника +навантаження, необхідно визначити основні її характеристики з при- +воду описаних класифікацій. Безумовно, такий підхід є централізова- +ним, що дає можливість краще контролювати розподіл навантаження +в системі. Також передбачається, що перша частина методу балансу- +вання навантаження буде адаптивною, тобто вона може пристосува- +тися до роботи системи в тій ситуації, коли, наприклад, якийсь об- +числювальний компонент вийде з ладу чи будуть додані нові. Звісно, +враховуючи перерозподіл навантаження через кожний встановлений +проміжок часу, першу складову методу розподілу завдань можна на- +звати динамічною стратегією. Характеризується залежний розподіл, +оскільки, спираючись на зміни в системі і інтенсивність надходжен- +ня запитів, балансування навантаження безумовно буде враховувати +вказані фактори. І, звичайно, ця стратегія є прогностичною, оскільки +прогноз того, яким саме чином буде розподілено навантаження в по- +дальшому, є її основною суттю. +В другій частині методу розподілу задач між обчислювальними +елементами передбачається, що балансувальник навантаження буде +працювати безпосередньо з елементами системи. Причому оцінюва- +ти можливість роботи кожного елемента індивідуально. Також робота +буде здійснюватися циклічно, через встановлені проміжки часу, і іте- +рації будуть проходити після того, як перша частина виконала свою +роботу. +Можна зробити висновки, що друга складова балансувальника +навантаження виглядає як децентралізована, оскільки, працюючи з +кожним обчислювальним компонентом, балансувальник оцінює його +спроможності з приводу того, яке конкретно навантаження він змо- +же витримати. При цьому потрібно врахувати, що навантаження не +зменшить продуктивність роботи компонента. Звісно, якщо наванта- +ження зростає у всій системі з більш інтенсивним надходженням но- +вих задач, то через збільшення обсягу роботи всьому обчислювально- +му комплексу потрібно буде більше часу для того, щоб обробити всю +інформацію, що надійшла. Проте навіть у ситуації, коли обсяг роботи +зростає в цілому, то все одно балансувальник зобов’язаний розділити +його між обчислювальними вузлами рівномірно. + +678 +Таким чином, передбачається, що коли розпочне свій перероз- +поділ навантаження друга частина балансувальника навантаження, +всі обчислювальні елементи будуть обмінюватися інформацією між +собою. Конкретна інформація про стан розрахункових вузлів перед- +бачає в собі швидкість обробки запитів за той інтервал часу, який об- +межується перерахунками навантаження в системі, що виконуються +другою складовою балансувальника навантаження. Оцінюється про- +дуктивність роботи кожного обчислювального елемента в системі +протягом всієї її роботи. Також, оцінюючи роботу кожного вузла, +буде зроблена опора на практичний підхід, тобто буде оцінюватися +швидкість, з якою обробляє запити кожен компонент протягом всієї +роботи системи, і під час росту інтенсивності надходження нових за- +вдань, і під час її зменшення. +Друга частина буде виконувати функцію порівняння продуктив- +ності роботи між обчислювальними елементами і ступінь заванта- +женості. Також буде створена схема, що буде динамічно змінюватися +після кожного перерахунку навантаження. В такій схемі буде оціню- +ватися вплив обчислювальних елементів один на одного. Під впливом +розуміється те, яку частину завдань якийсь конкретний елемент, що +сильно перевантажений, може перекласти на інший, навантаження +якого незначне. Така схема є основною для другої частини балан- +сувальника навантаження. Адже таким чином створюється цілий +алгоритм, що дозволяє динамічно обмінюватися обчислювальним +елементам запитам із власної черги. При динамічній оцінці ступеня +навантаження кожного елемента буде враховуватися зміна його на- +вантаження відносно останньої і передостанньої ітерації, динаміка +зміни навантаження під час зростання чи зменшення інтенсивності +надходження нових завдань до системи і продуктивність компонента +від самого початку роботи всієї системи. Таким чином, за обрахунок +цих трьох складових будуть оцінюватися продуктивність і наванта- +ження в конкретний момент часу кожного обчислювального компо- +нента системи. +Слід зауважити, що визначення ефективності роботи кожного об- +числювального вузла в комплексі є важливим, оскільки це надасть +достовірну оцінку при перерахунку навантаження. В тому випадку, +коли компонент системи, що виконує розрахункові функції, не має +занадто великого навантаження, але при цьому його продуктивність +протягом роботи всієї системи значно поступається іншим елемен- +там, то перенаправляти частину роботи від більш навантажених ком- + +679 +понентів системи потрібно в останню чергу. Мається на увазі, що +спочатку навантаження перерозподіляється на менш навантаженні +обчислювальні елементи, що показують гарну продуктивність в ці- +лому, а лише потім частку завдань потрібно розподіляти на менш на- +вантаженні елементи, що поступаються у своїй продуктивності по- +переднім обчислювальним елементам. +При розгляді другої складової балансувальника навантаження +видно, що вона відрізняється від першої складової тим, що є децен- +тралізованою. Незважаючи на те, що функції цих складових різні, +алгоритми, що будуть розробляти на базі цих методик будуть значно +відрізнятися за своєю суттю. Також причиною різниці складових є +те, що перша полягає в прогностичності подальшого навантаження +і його подальшого розподілу, а друга складова займається оцінкою +навантаження на кожному обчислювальному елементі його перероз- +поділом. +Потрібно звернути увагу на те, що від самого початку роботи об- +числювального комплексу необхідно оцінити продуктивні можли- +вості системи [8]. Враховуючи те, що практичних даних на самому +початку не буде, то потрібно оцінити обчислювальну продуктивність +компонентів, що будуть займатися обрахунком завдань, що надхо- +дять до них. Для цього потрібно розглянути спрощену модель обчис- +лювальної машини, що складається із набору інструкцій I та доступ- +ної пам’яті M. Відмітимо, що під інструкцією x ∈ I мається на увазі +ще і значення всіх її операндів, а не лише назва цієї інструкції. Таким +чином, при наявності двох інструкцій з одним ім’ям, але з різними +значеннями операндів, вони вважаються різними і обидві включа- +ються в набір I. +Позначимо завдання перед процесором символом А, як дея- +ку послідовність інструкцій x (P) = x 1, x 2,..., x i ∈ I. При цьо- +му, якщо задача А, наприклад, містить цикл, який повторюється +декілька разів, то послідовність x(А) міститиме в собі тіло цього +циклу, що повторюється вказану кількість разів. Очевидно, що не +всі послідовності інструкцій можуть бути допустимі. Наприклад, +можливе існування пари інструкцій, при послідовному виконанні +яких може статися помилка під час роботи процесора. Для цього +потрібно визначити послідовність лише тих інструкцій, що є до- +пустимими. +Припустимо, що час виконання інструкції x дорівнює τ(x). Для +простоти будемо вважати, що для всіх інструкцій час їх виконання є + +680 +цілим числом та найбільший загальний дільник всіх τ (x), x ∈ I дорів- +нює 1 (це уточнення правильне для більшості процесорів, тому що як +час виконання завжди можна розглядати кількість тактів процесора), +завжди існує найпростіша інструкція, час виконання якої дорівнює +одиниці, тобто τ (x) = 1). У цій роботі це припущення при описі об- +числювальної здатності дозволить використовувати lim замість lim +sup. Таким чином, час виконання τ (y) послідовності інструкцій y = x +1 x 2 x 3..., x t описується формулою: + +( ) +( +) +1 +t +i +i +y +x +<τ += +τ +=∑ +. +(1) +Виведена формула (1) є простою і базовою в обчисленнях, які оці- +нюють продуктивність процесорів і обчислювальних систем. Вона +виводить час, за який виконується задача, яка, в свою чергу, розби- +вається на окремі завдання. Оскільки для початку нас цікавить тільки +час виконання обчислювальними елементами поставлених задач, то +в простих випадках такої формули буде достатньо, щоб надати базу +для методу балансування в подальших розрахунках, опираючись на +те, з якою швидкістю обробляються запити, що надійшли. Якщо та- +ких простих формул не буде достатньо, то потрібно буде застосову- +вати більш складні формули та підходи, спираючись на роботи, що +присвячені продуктивності комп’ютерів. +Підводячи підсумки теоретичного огляду, потрібно зауважити, що +при такому поділі на два етапи роботи балансування навантаження +основною перевагою є так звана додаткова перевірка і перерозпо- +діл. Зрозуміло, що це виконується другою частиною балансуваль- +ника навантаження. Після виконання прогностичних обчислень на +наступний перерозподіл навантаження алгоритми першої частини +балансувальника навантаження розподіляють навантаження між об- +числювальними компонентами згідно з оцінкою навантаженості на +цих же компонентах і їх продуктивних можливостей. Після того, як +робота другої частини була виконана, знову через встановлений ін- +тервал викликається на роботу друга частина і, оцінюючи навантаже- +ність на обчислювальних компонентах, при потребі виконує новий +перерозподіл навантаження. Це підвищує точність роботи балансу- +вальника. А прогностичність першої частини може заощадити час +при точному прогнозі. +Також потрібно зауважити, що дві частини, які різними спосо- +бами будуть перераховувати навантаження між обчислювальними + +681 +компонентами, не будуть між собою конфліктувати, незважаючи +на те, що стратегії балансування в них відрізняються. Причиною +відсутності конфліктів є те, що обидві частини опираються на одні +і ті ж дані — показники швидкості розрахунку завдань обчислю- +вальними елементами та інтенсивність надходження запитів. За- +гальна схема роботи балансувальника навантаження зображена на +рисунку 5. +При більш детальному розгляді запропонованого методу спочатку +потрібно звернути увагу на першу частину балансувальника наван- +таження. Перш за все, будуть проводитися прогностичні обрахунки, +які спираються на базову формулу в теорії вірогідності, що має назву +формула повної ймовірності: + +( ) +( +) ( +) +1 +n +i +i +i +P A +P B P B +A += += +∨ +∑ +. +(2) +Формула (2) застосовується при розрахунку прогнозу того, яка +кількість завдань буде поставлена перед обчислювальним комплексом +в наступній ітерації. Для цього застосовують дані з попередньої ітера- +ції. Цими даними є кількість запитів, що було надіслано за попередній +проміжок часу. Дані, що відображають кількість запитів з попередньої +ітерації, вважаються подією, що відбулася, тобто P(B), оскільки вони +вже були розподілені по всіх обчислювальних вузлах і обчислюваль- +ний комплекс працював з тим навантаження, яке йому розподілили. +Дані, які відображають кількість запитів, що надійшли під час діючої +ітерації, вважаються подією P(A), що залежна від даних попередньої +ітерації. Такі параметри, як i та n, співвідносяться кількістю останніх +ітерацій, що будуть задіяні в цих обрахунках. За рахунок обчислень ін- +формації про кількість надісланих завдань за дві поспіль ітерації отри- +муються дані, які вважаються прогностичними та наближеними до тієї +ітерації, що буде наступною. +Звісно, можна сперечатись з приводу точності такого прогнозу. +Тому що інтенсивність надходження завдань до обчислювального +комплексу не є стабільною. Проте, як зазначалось, для ефектив- +ності роботи прогнозу інтенсивність підвищення навантаження чи +його зменшення повна бути рівномірною. При нерівномірній інтен- +сивності буде проходити щоразу перерахунок прогнозу на наступну +ітерацію. Але сенс застосування такого підходу полягає в простоті +описаної формули та її простій програмній реалізації. Оскільки вона +не є громіздкою, обчислення будуть проходити швидко і це ніяк не + +682 +вплине на ефективність роботи балансувальника навантаження. Тим +більше, якщо зростання або зменшення інтенсивності надходження +завдань відбувається поступово, то потрібно зауважити, що достатньо +простого порівняння і, якщо хиба незначна, скажімо, в 10–20 відсот- +ків, то немає потреби в тому, щоб виконувати перерахунки стану на- +вантаження на всіх елементах, а можна розподіляти навантаження +між ними згідно зі стратегією, що застосовувалась у попередній іте- +рації. Тим більше, слід зауважити, що, якщо хиба все-таки відчутно +вплине на продуктивність роботи і навантаження на окремих обчис- +лювальних компонентах, то друга частина балансувальника, оцінюю- +чи роботу кожного компонента, перерозподілить навантаження між +ними більш доцільно. + +Рис. 5. Загальна схема роботи балансувальника навантаження + +noyaTok po6oTM +nepWoiacTwHw +baaHcyBabHMKa +HaBaHTa>KeHHA +TepeBipKaToyHOcTi +nporHo3y +6anaHCyBaHH3riAHO +O6paxyBaHHAHOBoro +3IBCTaHOBeHMM +6aaHcy +nporHo3om +Po3paxyHoK HoBoro +nporHo3y Ha +HacTynHy iTepauiro +6aaHCyBaHH9 +HaBaHTaKeHHAApyrOIO +yacTWHoIo6aaHcyBabHWKa683 +Тому можна підвести підсумки відносно прогностичної частини +балансувальника навантаження: прогноз відбувається в тому випад- +ку, якщо інтенсивність надходження запитів до обчислювального +комплексу є рівномірною і поступовою. У випадках, коли між над- +ходженнями запитів різниця в їх обсягу є значною, то прогностична +частина не буде корисною для балансування навантаження. Врахо- +вуючи вже зауважену простоту в реалізації, застосування прогнос- +тичної частини ніяк не вплине на ефективність роботи всієї системи, +оскільки вона не буде вимагати багато часу та ресурсних витрат на +своє обчислення. +Безпосередньо саме балансування навантаження буде вираховува- +тися таким відношенням: + +( +) +( ) +1 +i n +i n +k +k +− +. +(3) +В наведеній формулі (3) значеннями є відношення кількості по- +ставлених запитів відносно діючої і попередньої ітерації. Символ і +позначає обчислювальний компонент, до якого застосовують це від- +ношення, k відображає кількість завдань, що надійшли за вказану +ітерацію, а n відображає порядковий номер ітерації. Спочатку запити +розділяються рівномірно, потім порівнюються між собою отримані +коефіцієнти, якщо знаходяться ті обчислювальні елементи, значен- +ня яких суттєво відрізняється, то частина запитів розподіляється від +більш навантаженого до менш навантаженого. Таким чином сортуєть- +ся до тих пір, поки відношення не стануть рівномірними в порівнян- +ні між собою. Далі проводяться обрахунки продуктивності кожного +обчислювального елемента, в такому випадку робиться відношення +швидкості роботи за попередній інтервал часу і той, що щойно завер- +шився. Таким чином оцінюється продуктивність. Потім проводяться +обрахунки у відношенні між рівномірно розподіленими запитами на +елементах відносно продуктивності елементів. Це потрібно для того, +щоб визначати більш продуктивні обчислювальні вузли і розподіляти +більше навантаження саме на них. Таким чином навантаження між +компонентами, що роблять обрахунки в системі, розподілиться рів- +номірно не тільки відносно обсягу надісланих запитів, а й відносно +продуктивності роботи кожного компонента. +Точно визначити інтервал між ітераціями неможливо, тому що це +залежить конкретно від системи, для якої буде застосовуватись ме- + +684 +тод рівномірного розподілу завдань. Адже при реалізації є різниця, +наприклад, між комплексом серверів, що обраховують запити, що +надійшли, і багатопроцесорним комп’ютером. Тому конкретні реа- +лізації можуть відрізнятись. Проте можна встановити, що проміжок +між ітераціями не може бути значним. Причиною цього є невелика +складність запропонованих формул для програмної реалізації. Так +само складно знайти точну похибку, яка дозволяється в прогнозуван- +ні, це залежить від системи, де балансувальник реалізується. Мож- +на відмітити, що вимагати точного прогнозу і відкидати можливість +похибки не є доцільним тому, що точно спрогнозувати інтенсивність +надходження запитів неможливо. Так само не потрібно завищувати +допустимість похибки, тому що це буде призводити до некоректної +роботи першої частини балансувальника навантаження. Як було вка- +зано, краще звертати увагу на похибку в діапазоні до 15 відсотків, +хоча все ж потрібно перш за все враховувати середовище, де саме цей +метод балансування навантаження застосовується. +Друга частина балансувальника навантаження працює, оціню- +ючи і порівнюючи навантаження і продуктивність обчислювальних +елементів один з одним. Це виконується відразу після роботи першої +частини балансувальника навантаження. Друга частина оцінює, на- +скільки дисбалансним є розподіл, встановлений першою частиною, +і робить перерозподіл. Тільки це робиться, не оцінюючи ситуацію в +цілому, а сортуючи дані навантаження всіх обчислювальних елемен- +тів, порівнюючи між собою. Спираються розрахунки на формулу (3), +тільки для двох елементів. Таким чином друга частина роботи балан- +сувальника навантаження є так званою корекцією першої. Вона ви- +рівнює навантаження між обчислювальними вузлами, яке встанови- +ла перша частина. +Інтервал часу, який необхідно вказувати між закінченням роботи +першої частини і початком роботи другої, також встановити складно, +це залежить конкретно від середовища, де описаний метод балансу- +вання навантаження буде застосовуватись. Необхідно зауважити, що +інтервал часу між закінченням ітерації першої частини балансуваль- +ника і початком роботи ітерації другої повинен бути не більшим, ніж +інтервал часу між закінченням роботи ітерації другої частини балан- +сувальника і початком роботи наступної ітерації першої частини ба- +лансувальника навантаження. У випадку, коли друга частина почне +свою роботу пізно, втрачається сенс того, щоб вирівняти баланс на- +вантаження, встановлений першою частиною. + +685 +Незважаючи на те, що визначення похибки в прогнозі буде більш +ефективним для конкретної системи, рекомендується використову- +вати формулу: + +1 +1 +n +n +i +n +i +i +k +n +− += += ∑ +. +(4) +Формула (4) передбачає визначення середньої арифметичної +похибки за весь час роботи системи. Параметри i та n відобража- +ють числове значення запитів і номер ітерації відповідно. Реко- +мендується ввести константні значення, що зменшують чи збіль- +шують інтервал між ітераціями. Наприклад, можна визначити, +що константні числа інтервалу і середньої похибки можуть бути +пропорційним один до одного. Наприклад, при похибці в 50 % +випадків інтервал між ітераціями зменшується вдвічі. Все ж при +застосуванні наведеної вище формули і визначені констант, при +яких будуть проводитися зміни, рекомендується враховувати, для +яких саме сфер комп’ютерних наук буде розроблятися алгоритм, +що буде базуватися на запропонованому методі. Таким чином +можна вираховувати динаміку зміни інтервалу, базуючись на двох +складових — похибки в прогнозуванні й у відношенні кількості +перерахованого навантаження, мається на увазі кількості запитів +діючої ітерації до попередньої. Важливо, щоб взаємозв’язок пере- +рахованого відношення було визначено, спираючись на дані дру- +гої частина роботи балансувальника навантаження. Тому що саме +друга частина корегує навантаження після роботи першої. Так +само можна застосувати формулу до двох вищевказаних факторів +і вираховувати середнє значення і порівнювати його зі встановле- +ними константами. Саме це вкаже на ефективність роботи методу +планування розподілу навантаження. Якщо значення похибки і +коректності навантаження будуть значними, це є сигналом того, +що інтенсивність не є рівномірною. Зрозуміло, що при зменшенні +часового інтервалу між ітераціями зменшиться кількість відчут- +них перепадів інтенсивності надходження завдань в самому інтер- +валі. Інтервали між ітераціями можна робити відносно коротки- +ми, оскільки, як зазначалося, програмна реалізація та виконання +цього методу нескладні. +Підсумовуючи роботу балансувальника навантаження, пропонує- +мо ввести схему всіх обчислювальних елементів в системі. За весь час + +686 +роботи в системі динамічно визначається швидкість роботи кожного +обчислювального компонента, що вказує на продуктивність кожно- +го. Суть схеми полягає в тому, щоб відзначити, які компоненти за час +роботи в системі працюють більш ефективно, а які менш. Такі дані +нададуть можливість визначати заздалегідь, з яких саме елементів +переносити частину задач на інші, менш продуктивні. На рисунку 6 +зображено схему, на якій найменш продуктивний обчислювальний +елемент перенаправляє частину завдань на інші обчислювальні еле- +менти. Рисунок 7 відображає схему, на якій частина завдань перена- +правляється від двох найменш продуктивних елементів до найбільш +продуктивного в системі. + +Рис. 6. Перенаправлення завдань до найбільш продуктивних обчислюваль- +них компонентів + +O6yMcoBabHMM +eJeMeHT2 +O6yMcoBabHMi +eeMeHT1 +O6McnIoBaIbHMi +eNeMeHT3 +O6yMcoBabHWM +eeMeHT5 +O6yMcloBabHMM +eneMeHT4 +baaHCyBabHMK HaBaHTaKeHHA687 + +Рис. 7. Перенаправлення завдань від найменш продуктивного компонента +Висновки. Спираючись на описані стратегії балансування ми за- +пропонували нову теорію балансування навантаження. Враховува- +лось, що запропонований метод буде універсальним і буде основою +для розробки алгоритмів для різних інформаційних систем, які по- +требують балансування навантаження. Також описаний метод про- +гнозує розподіл навантаження на подальшу роботу системи при +рівномірній інтенсивності надходження завдань. Описаний метод +балансування навантаження є динамічним, він змінює розподіл на- +вантаження між обчислювальними компонентами системи через +встановлені інтервали часу. Метод спирається не лише на оцінку ін- +тенсивності надходження завдань, а і продуктивність роботи обчис- + +O6yMcloBabHMi +KOMNOHeHT1 +O6yMcoBabHMM +KoMOHeHT 2 +O6yMcloBabHwi +KoMNOHeHT 3 +O6yMcnoBabHM +KOMNOHeHT4 +O6McnoBanbHMM +KoMnOHeHT 5 +baaHCyBanbHMKHaBaHTaXKeHHA688 +лювальних компонентів. Продуктивність визначається через оцінку +швидкості роботи кожного компонента за весь час роботи всієї сис- +теми. +СПИСОК ВИКОРИСТАНОЇ ЛІТЕРАТУРИ +1. Классен Р. К., Хисамиев Л. Р. Моделирование процессов балансировки +нагрузки в глобальных информационных системах // XXI Туполевские +чтения (школа молодых ученых): международная молодежная научная +конференция, Казань, 19–21 ноября 2013 г.: материалы конференции. — +Казань, 2013. — Т. 1. — С. 323–324. +2. Балансировка нагрузки: основные алгоритмы и методы [Електронний +ресурс] / Блог компании Селектел. — URL: http://habrahabr.ru/company/ +selectel/blog/250201/ (дата звернення: 24.12.2015). +3. Бершадский А. М., Курилов Л. С. Исследование стратегий балансировки +нагрузки в системах распределенной обработки данных // Известия ву- +зов. Поволжский регион. Технические науки. — 2009. — № 4. — С. 38–48. +4. Райхлин В. А., Классен Р. К. Моделирование процессов балансировки на- +грузки в распределенных СУБД, использующих ресурсы сети RUNNet // +Научный вестник НГТУ. — 2015. — Т. 61, № 4. — С. 90–100. +5. Корнилина М. А., Якобовский М. В. Динамическая балансировка загруз- +ки процессоров при моделировании задач горения // Высокопроизводи- +тельные вычисления и их приложения: материалы Всероссийской науч- +ной конференции. Черноголовка-2000. — Москва: МГУ, 2000. — С. 34–38. +6. Балансировка сетевой нагрузки [Електронний ресурс] / АСПЕКТ СПб: +web-сайт. — URL: http://www.aspectspb.ru/solutions/it/highavailability/nlb. +html (дата звернення: 24.12.2015). +7. Чжоу Т. Системы балансировки нагрузки Web-серверов [Електронний +ресурс] / Windows IT Pro/RE. — 2000. — № 3. — URL: http://www.osp.ru/ +win2000/2000/03/174228/ (дата звернення: 24.12.2015). +8. Ракитский А. А., Рябко Б. Я., Фионов А. Н. Аналитический метод срав- +нения и оценки производительности компьютеров и вычислительных +систем // Вычислительные технологии. — 2014. — Т. 19, № 4. — С. 84–98. +9. Punetha S., G., Gnanambigai N., Dinadayalan P. Survey on fault tolerant — +Load balancing algorithmsin cloud computing // 2nd International Conference +on Electronics and Communication Systems (ICECS). — 2015. — P. 1715– +1720. +10. Asghar S. A., Bremner E. D. A Dynamic Moldable Job Scheduling Based Parallel +SAT Solver // 2013 42nd International Conference on Parallel Processing. — +2013. — P. 110–119. +11. Bolch G. et al. Queueing Networks and Markov Chains: Modeling and +Performance Evaluation with Computer Science Applications. — Wiley, 1998. — +P. 126. + +689 +12. Chang K. C. et al. The Research Queuing Package Modeling Environ- +ment (RESQME) [Text] // Evans G. W., Mollaghasemi M., Russell E. C., +Biles W. E., editors. Winter Simulation Conference. — ACM Press, 1993. — +P. 294–302. +АКТУАЛЬНІСТЬ РОЗВИТКУ МЕРЕЖІ NGN +Кунуп Т. В. +Сучасний етап розвитку людства характеризується перебудовую +технічного та економічного базису суспільства, де основою стають ін- +форматика, зв’язок, енергетика і транспорт. Оптимальна побудова ін- +фокомунікаційних систем та мереж, що забезпечують рух інформації, +матеріальних цінностей, суттєво зменшує витрати суспільства на нор- +мальне функціонуваннях. Розглянуто етапи розвитку телекомунікаційних +мереж, актуальність розвитку сучасних мереж та зростання попиту на +використання таких систем зв’язку та мереж NGN. Одним із основних +аспектів NGN є забезпечення відповідності якості сервісу, що надається, +це пов’язано з ефективністю функціонування системи та надання сервісів +у мережах. +The current stage of human development is characterized by a restructuring of +the technical and economic basis of society, where computer science, communica- +tions, energy, and transport become the basis. Optimal construction of infocommuni- +cation systems and networks that ensure the movement of information and material +values significantly reduces the costs of society for its normal functioning. The article +considers the stages of development of telecommunications networks, the relevance +of the development of modern networks and the growing demand for the use of such +communication systems and NGN networks. One of the main aspects of NGN is en- +suring compliance with the quality of the service provided.this is related to the effi- +ciency of the system and the provision of services in networks. +В історичному розвитку мереж та послуг зв’язку можна виді- +лити такі етапи: PSTN (Public Switched Telephone Network), IDN +(Integrated Digital Network), ISDN (Integrated Service Digital Network), +IN (Intelligent Network), NGN, FN (Future Network). +Перший етап — побудова телефонної мережі загального користу- +вання (PSTN). Телефонний зв’язок ототожнювався з єдиною послу- +гою — передачею мовних повідомлень. Надалі телефонними мережа- +ми за допомогою модемів стала здійснюватися передача даних. + +690 +Другий етап — цифровизація телефонної мережі: були створені +інтегральні цифрові мережі IDN, які також надавали в основному по- +слуги телефонного зв’язку на базі цифрових систем комутації та пе- +редачі. +Третій етап — інтеграція послуг: з’явилася концепція цифрової +мережі з інтеграцією служб ISDN. У процесі розвитку мереж зв’язку +особлива увага стала приділятися інтелектуальним послугам. Саме +тому інтеграція служб починає замінюватися концепцією IN. +Четвертий етап — інтелектуальна мережа (IN). Інтелектуальна +мережа — це архітектура, для якої характерні такі принципи [14; 15]: +– широке використання сучасних засобів обслуговування інфор- +мації; +– ефективне використання мережних ресурсів; +– модульність мережних функцій з можливістю багаторазового їх +використання; +– одночасне створення і впровадження сервісів завдяки модуль- +ним, повторно використовуваним мережним функціям; +– інваріантність засобів розміщення мережних функцій у різних +фізичних об’єктах; +– взаємодія мережних функцій через незалежні від сервісів стан- +дартизовані інтерфейси; +– можливість керування деякими атрибутами сервісів з боку або- +нентів і користувачів; +– стандартизоване керування логікою сервісів. +Функціональну архітектуру IN можна представити у вигляді фор- +мули: інтелектуальна мережа = комутатор + комп’ютер [22]. +Ця мережа призначена для швидкого, ефективного та еконо- +мічного надання інтелектуальних сервісів масовому користувачеві. +Принципова відмінність IN від попередніх мереж — у гнучкості та +економічності надання сервісів [14]. +Інтелектуальна мережа = комутатор + комп’ютер [22], до цієї фор- +мули протягом багатьох років прагнули як виробники комутаційного +обладнання, так і виробники засобів обчислювальної техніки. При +цьому перші отримували можливість гнучкого й оперативного ство- +рення і впровадження нових послуг зв’язку без істотних змін в кому- +таційному обладнанні, а другі — вихід на один з найбільших сегментів +ринку нових інформаційних технологій. +Сучасні мережі зв’язку отримали масу нових можливостей за- +вдяки розвитку концепції «інтелектуальних мереж» (IN, Intelligent + +691 +Networks). Основна ідея IN полягає в тому, щоб комутатор (MSC) за- +ймався виключно комутацією. А різні послуги організовувались за +допомогою сторонніх платформ, які по мережі сигналізації «спілку- +ються» з комутатором, вказуючи, що йому робити з викликом. При +такому підході вся логіка реалізується на окремому керуючому вузлі +(SCP, Service Control Point), а на комутаторі описуються тільки умови, +при яких необхідно перенаправити запит на потрібний SCP. Оскіль- +ки всі зміни логіки відбуваються поза комутатором — теоретично на +одному вузлі, — то це дозволяє скоротити час на розгортання послуг +і зробити їх дуже гнучкими. IN-архітектура спочатку розроблялася +для PSTN. Потім протоколи INAP (IN Application Part) поширилися +і в мобільному зв’язку. Однак у INAP був істотний недолік — закри- +тість архітектури і, як наслідок, несумісність рішень різних виробни- +ків одне з одним. У підсумку, INAP-сервіси можуть бути надані тіль- +ки всередині домашньої мережі. У роумінгу абонент їх втрачає. Для +вирішення цієї проблеми був розроблений протокол CAP (CAMEL +Application Part). CAP — це протокол для роботи додатків (послуг) +з комутаційним обладнанням. Представляє собою розширений про- +токол INAP з додаванням інформації про місцезнаходження абонен- +та. Розроблений ETSI (TS GSM 02.78 від липня 1996 року) [25]. Клю- +човою його відмінністю, крім функціональної відмінності з INAP, +можна вважати великий ступінь відповідності стандартам і уніфікації +його реалізацій у різних виробників базового комутаційного облад- +нання. Точково протокол впроваджується в Україні та інших країнах +з кінця 2002 року, повсюдно з середини 2003 року. +CAMEL, або CAP дозволяє забезпечити повний пакет інтелек- +туальних додаткових послуг (перш за все роумінг) своїм абонентам +(включаючи абонентів препейд) не тільки в домашній мережі, але в +роумінгу, в мережах, що підтримують стандарт CAMEL за рахунок +можливості контролю рахунку і тарифікації в домашній мережі в ре- +жимі реального часу. На відміну від, наприклад, USSD, забезпечує +мінімальний час з’єднання. Завдяки його відкритості обладнання +різних виробників може працювати між собою без проблем. Тобто, +навіть в роумінгу, в мережі іншого оператора є можливість користува- +тися своїми «розумними» сервісами. +Система надання інтелектуальних послуг — це платформа, що пра- +цює на основі протоколу CAMEL і дозволяє вирішувати найрізнома- +нітніший спектр завдань у сфері надання додаткових послуг зв’язку +[25]. Особливістю організації роумінгу за протоколом CAMEL, на + +692 +відміну від USSD, є те, що вона може бути надана тільки в мережі +того оператора, який також підтримує CAMEL. Розрізняють реалі- +зації в’їзного роумінгу, внутрішньомережевого роумінгу та виїзного +роумінгу. Існують версії протоколу: CAP2, CAP3 (CAMEL Application +Protocol phase 2 / phase 3) [25]. +Приклади послуг на базі системи: +1. Система надання передплачених послуг. Будь-які послуги +зв’язку (вихідні дзвінки, SMS, інтернет-трафік, надання контенту) +можуть тарифікуватися в реальному часі — перед початком або в про- +цесі надання послуги. +2. Віртуальний телефонний номер. Єдина точка доступу для кор- +поративного абонента. Будь-які правила маршрутизації вхідних +дзвінків, інтеграція з голосовою поштою або службою автоінформа- +тора і багато іншого. +3. Мелодії замість гудків (RBT). Той, хто подзвонить вам, почує +замість гудків виклику вашу улюблену мелодію. Або корпоративний +гімн, а може рекламу — і це вже не просто розважальна послуга. +4. Call Back («Передзвоніть мені!»). Якщо раптом у вас немає мож- +ливості виконати вихідний дзвінок (не дозволяє баланс особового +рахунку або умови роумінгу) — ця послуга допоможе передати вашо- +му адресату SMS або USSD повідомлення з проханням передзвонити +вам. +5. Чорний / білий список. Хочете позбутися небажаних дзвінків +або SMS? Або хочете мати номер, на який додзвоняться тільки по- +трібні люди? Ця послуга блокує небажані дзвінки на рівні комута- +тора, і ці дзвінки більше не турбують вас і не займають вашу лінію +зв’язку. +Інтелектуальні послуги зв’язку та можливості комп’ютерної те- +лефонії (Computer — Telephony Integration, CTI), що об’єднує два +різнорідних інформаційних простора, цій темі присвячено немало +публікацій. Набагато менше уваги приділяється її засобам — систе- +мам інтелектуальної комутації і маршрутизації в звичайній телефон- +ній мережі, які забезпечують формування мовного і факсимільного +трафіку та створюють технічні можливості для надання нетрадицій- +них (інтелектуальних) послуг зв’язку. Телекомунікаційні послуги, +пов’язані з нетрадиційною процедурою обробки дзвінків, встанов- +лення з’єднання або нарахування оплати набувають все більшої по- +пулярності. До подібних сервісів належать Freephone (дзвінки за +рахунок сторони, що викликається), Premium Rate Service (дзвінки + +693 +з нарахуванням додаткової оплати, наприклад, за доступ до інфор- +маційних ресурсів або за участь у телефонних лотереях, голосуваннях +і т. п.), Prepaid Calling (дзвінки за передоплатою з доступом абонентів +по паролях), Least Cost Routing (маршрутизація за найбільш вигідним +маршрутом) і ряд інших. +Розглянемо, як реалізуються такі послуги. Наприклад, якийсь +оператор має намір організувати для певної категорії абонентів один з +доданих додаткових сервісів. Для цього необхідно забезпечити спеці- +альну процедуру обробки виклику і встановлення з’єднання (напри- +клад, для послуги Prepaid Calling потрібна можливість динамічного +списування грошей з рахунку абонента в ході розмови). Однак базова +АТС телефонної мережі оператора не підтримує подібну процедуру. +Вийти з цієї ситуації можна «традиційними» способами, вклавши «ну +дуже великі гроші» в модернізацію обладнання мережі або зовсім від- +мовившись від ідеї надання абонентам інтелектуальних послуг. +Ще один спосіб (настільки ж безрадісний для оператора) — вдати- +ся до допомоги «телефонних панянок». Невже становище безнадій- +не? Зовсім ні, якщо скористатися системою комп’ютерної телефонії +Call Routing, заснованої на технології CTI. +Ідея застосування спеціалізованого ПЗ і апаратного забезпечення +досить очевидна, хоча і незвична для зв’язківців. Якщо АТС не дозво- +ляє реалізувати інтелектуальні послуги, то нехай вона вирішує тради- +ційні завдання, а відсутній інтелект додасть система Call Routing. Така +система підключається до АТС аналоговими або цифровими канала- +ми (двопровідними абонентськими, T1/E1/ISDN) і «спілкується» +останньою зрозумілою їй мовою (тобто підтримує практично будь- +які протоколи сигналізації — loop start, CAS, CCS і навіть ОКС 7). +Єдине, що повинна робити АТС, — обслуговувати стандартні дзвінки +звичайним чином і направляти дзвінки, що вимагають спеціальної +процедури встановлення з’єднання, в систему Call Routing. +Як кажуть, відчуйте різницю: заміна базового обладнання мере- +жі або установка Call Routing без будь-якої модернізації. Операто- +ру зв’язку потрібно лише запрограмувати свою АТС для комутації +певного типу викликів в систему комп’ютерної телефонії і виділити +необхідну кількість портів для її підключення. Своєю чергою, Call +Routing комплектується і програмується для забезпечення конкрет- +ного набору послуг. Тепер про економічний аспект проблеми. +Рішення на базі Call Routing коштують значно дешевше, ніж уста- +новка спеціалізованих АТС, що включають в себе ПЗ і апаратні мо- + +694 +дулі для організації інтелектуальних послуг. Справа в тому, що всі +процедури, пов’язані з інтелектуальними послугами (такі як голосове +спілкування з абонентом декількома мовами «за вибором», перевірка +паролів, встановлення з’єднання на замовлення абонента, динамічне +списування грошей з рахунку абонента), є для CTI «рідними» і за- +звичай підтримуються програмними засобами навіть найпростіших +систем Call Routing. Більш витончене ПЗ забезпечує індивідуальні +тарифікацію і маршрутизацію, елементи IP-телефонії, функцію зво- +ротного виклику (Call Back) і безліч інших можливостей [24]. +Перелік основних переваг систем Call Routing виглядає солідно: +1. Підтримка декількох типів ліній зв’язку. Системи підключають- +ся до АТС по каналах будь-якого типу (аналогових, цифрових — T1 / +E1 / ISDN); +2. Гнучкість. Підтримуються будь-які протоколи взаємодії з базо- +вим комутаційним вузлом мережі (loop start, CAS, CCS); +3. Масштабованість. Можна нарощувати потужність системи як +збільшуючи кількість обслуговуваних каналів (від декількох десятків +абонентських ліній дрібних операторів до десятків цифрових потоків, +що обслуговуються великими провайдерами), так і розширюючи на- +бір можливостей; +4. Простота розгортання. Не потрібно модернізації вже існуючої +мережі, досить виділити на АТС оператора зв’язку необхідну кіль- +кість аналогових або цифрових портів для підключення системи; +5. Економічна ефективність. Нерідко для впровадження нових +послуг зв’язку або підвищення ефективності використання застарі- +лої мережі зв’язку потрібні величезні капіталовкладення (наприклад, +при організації нових каналів зв’язку, заміні комутаційного облад- +нання і т. ін.). +Call Routing дозволяє організувати інтелектуальні послуги, влас- +тиві сучасним цифровим мережам, навіть на застарілих аналогових +каналах і декадно-крокових АТС. +До середини 80-х років основним завданням під час проектуван- +ня систем зв’язку було забезпечення високої пропускної спромож- +ності за прийнятною ціною. Оскільки ця мета була частково досяг- +нута з розгортанням волоконно-оптичних систем і впровадженням +технологій SDH, B-ISDN, ATM, на телекомунікаційному ринку на- +буває значущості інший фактор — можливість швидкого розвитку +комплексних телекомунікаційних послуг, що задовольняють зроста- +ючі потреби абонентів. Загалом в історичному розвитку телекомуні- + +695 +каційних мереж і послуг можна умовно виділити такі основні етапи +(рисунок 1): +1. Побудова телефонної мережі загального користування ТМЗК +(Public Switched Telephone Network, PSTN). На цьому етапі створю- +валася національна аналогова телефонна мережа загального користу- +вання, орієнтована на передачу мовних повідомлень. Надалі в ТМЗК +за допомогою модемів стала здійснюватися передача даних. +2. Цифровізація телефонної мережі. Для підвищення якості по- +слуг зв’язку, підвищення автоматизації управління та технологічнос- +ті обладнання на цьому етапі починають створюватися інтегральні +цифрові мережі (Integrated Digital Network, IDN), які надають також +в основному послуги телефонного зв’язку на базі цифрових систем +комутації та передачі інформації. +3. Інтеграція послуг. На цьому етапі розширюється спектр послуг, +що надаються абонентам мережі, і з’являється концепція цифрової +мережі з інтеграцією служб (Integrated Service Digital Network, ISDN). +Однак ця концепція не мала значного поширення через високу вар- +тість обладнання. +4. Створення інтелектуальної мережі (Intelligent Network, IN). +Концепція IN була розроблена для більш швидкого впровадження +нових послуг при максимально ефективному використанні існуючої +інфраструктури телекомунікаційної мережі [20; 22]. +IN +PSTN +IDN +ISDN +Етап 1 +Етап 4 +Етап 3 +Етап 2 + +Рис. 1. Етапи розвитку телекомунікаційних послуг і мереж +Подальшим розвитком стала поява мереж зв’язку наступного по- +коління. +До 50-х років ХХ століття телекомунікаційні мережі обмежувалися +тільки передачею аналогової телефонії. Основне завдання, яке в цей +період ставили розробники мереж, полягало в якісній передачі мови +на великі відстані з високою надійністю та мінімальною вартістю. +До середини XX століття в розвинених країнах оператори опини- +лися перед фактом значного зниження темпів зростання доходів від +надання традиційних послуг. Попит на такі послуги був повністю за- + +696 +доволений і в міру розвитку всіх галузей людської діяльності на ринку +зв’язку стали з’являтися користувачі, які вимагали нових типів по- +слуг окрім традиційного двоточкового мовного з’єднання. Звичайні +мовні з’єднання між двома абонентами більше не могли задоволь- +нити потреби клієнтів ділового сектора, і вже з другої половини 60-х +років оператори мереж зв’язку почали пропонувати ряд послуг, щоб +залучити нових користувачів: послуги, зроблені на замовлення для +простих абонентів, і послуги Centrex для ділових абонентів. +Перелік послуг, зроблених на замовлення, визначався можливос- +тями комутаційних станцій, наприклад, абонент міг попросити роз- +будити його дзвінком у певний час тощо. +Під Centrex спочатку розумівся спосіб надання послуг зв’язку +абонентам декількох компаній на основі спільно використовува- +ної відомчої комутаційної станції. З появою комутаційних станцій +із програмним управлінням термін «Centrex» став означати спосіб +надання додаткових послуг діловим абонентам мережі загально- +го користування, аналогічних послугам відомчої АТС. Для цього +АТС доустатковувалися спеціальним блоком, а багато компаній- +користувачів заощаджували засоби на закупівлю, монтаж і екс- +плуатацію власних відомчих АТС, оскільки могли за допомогою +Centrex створювати свої корпоративні мережі, використовуючи +ресурси телефонної мережі загального користування. Centrex до- +зволяв користуватися скороченим набором номера, тристорон- +нім конференц-зв’язком, переадресацією виклику, переведенням +з’єднання на інший номер, постановкою виклику на очікування, +встановленням з’єднання із зайнятим у цей момент абонентом піс- +ля його звільнення тощо. +Centrex — це складене слово з двох слів: Central Exchange, і від- +носиться до виду телефонного зв’язку. Centrex — це назва центра- +лізованих послуг АТС / УАТС, які забезпечує провайдер телефонії і +які зазвичай забезпечуються офісними АТС (Private Branch Exchange +PBX). Пакет послуги Centrex дозволяє організації або компанії від- +мовитися від придбання та обслуговування офісної PBX власними +силами, тому що всі необхідні кошти забезпечує централізований +телефонний вузол оператора фіксованого зв’язку. Схожий пакет по- +слуг може надаватися й оператором мобільного зв’язку. У мобільних +мережах це зазвичай називається FMC (Fixed Mobile Convergence). +Мінімально необхідний набір послуг Centrex: використання вну- +трішніх 2- або 3-значних номерів для дзвінків всередині офісу; пе- + +697 +реведення вхідного з міста дзвінка; переведення вихідного в місто +дзвінка (класичний приклад «Наталія Петрівна! Наберіть мені Ми- +колая!»); перехоплення дзвінка [4]. +У випадку Centrex надання нових послуг вимагало узгодження +оператором із замовником ряду специфічних вимог, виконувати які +повинен був працівник АТС. Внаслідок цього стандартизація для +Centrex практично відсутня, а його послугами користується досить +незначна кількість абонентів з тих, кому ці послуги доступні. +З початком чергового бурхливого етапу інформаційної револю- +ції з’явилася потреба передачі даних у величезних обсягах з високою +швидкістю, у тому числі й комутованими каналами. При цьому швид- +кість комутації аналогової телефонії перестала бути задовільною. По- +дальший розвиток розвинених аналогових мереж із досить високою +якістю передачі мови в країнах Заходу до кінця 60-х років став не- +доцільним. У 70-х роках з’явилася концепція цифрової телефонії на +базі можливості здійснення з’єднання зі швидкістю 64 кбіт/с, а також +розвитку цифрових сполучних ліній (наприклад, ІКМ). З середини +80-х років основна мета забезпечення високої пропускної спромож- +ності за прийнятною ціною була почасти досягнута з розгортанням +волоконно-оптичних систем і впровадженням таких технологій як +SDH і ATM. +Цифровізація мереж не тільки дозволила підвищити якість послуг, +але й сприяла зростанню їх кількості. Внаслідок цього були сфор- +мульовані основні принципи створення цифрової мережі з інтегра- +цією послуг, або ISDN. Абонент ISDN одержує два інформаційних +канали по 64 кбіт/с і один канал сигналізації 16 кбіт/с для управління +з’єднанням (2b+d). Загальна пропускна спроможність каналу стано- +вить 144 кбіт/с, що дозволяє передавати навіть один відеоканал у ре- +альному часі. +Ці нові мережі складаються з ISDN-станцій, які комутують циф- +рові потоки, що містять будь-яку інформацію: мова, дані, стисле ві- +део тощо. Перетворення в аналоговий сигнал відбувається безпосе- +редньо в абонентському терміналі. Крім того, всі комутаційні станції +мережі ISDN на відміну від аналогових можуть працювати як одна +велика станція, дозволяючи здійснювати автоматичну маршрути- +зацію виклику, рівномірний розподіл навантаження, мати єдиний +план номерів, створювати віртуальну мережу та надають ряд інших +додаткових послуг. За час свого розвитку концепція ISDN пережила +зльоти й падіння, пов’язані з коливанням потреб ринку та наявністю + +698 +в абонентів комп’ютерів. Нині практично всі комутаційні станції на +мережах розвинених країн мають функції ISDN. +Однак ISDN та інші методи надання абонентам додаткових послуг +мають свої проблеми, що виражаються також у недостатній стандар- +тизації, внаслідок чого у світі діє кілька несумісних стандартів. Крім +того, для введення нових послуг необхідно замінити програмне забез- +печення кожної ISDN-станції, що вимагає значних капіталовкладень +і колосальної інтуїції від оператора мережі, оскільки в цьому випадку +крок «не в ту сторону» коштує ще дорожче. Час життя комутаційно- +го обладнання триває кілька десятків років, тому заміняти його що- +разу для надання нової послуги недоцільно (і не заміняти не можна, +оскільки існує різке зростання вимог до збільшення кількості функ- +цій, які мають бути підтримані мережею). Крім того, при введенні в +такий спосіб нових послуг ускладнюються структура мереж, а також +процеси управління та експлуатації. +Необхідність модернізації обладнання та програмного забезпе- +чення на всіх АТС мережі є слабким місцем усіх перерахованих техно- +логій при розширенні набору послуг, які надає мережа. Для вирішен- +ня питання про послуги, які оператор мережі хотів би запропонувати +своїм клієнтам, необхідно було погоджувати з виробником обладнан- +ня характеристики майбутніх послуг і можливості їхньої реалізації. +Розгортання кожної нової послуги вимагало модифікації апаратних +засобів у всіх комутаційних станціях. Цей процес ускладнювався ще +й тим, що мережа оператора, як правило, складалася з обладнання +декількох різних виробників, і іноді траплялося, що послуги в зоні +обслуговування цього оператора виявлялися не повністю ідентични- +ми. Крім того, після введення послуги в експлуатацію модифікувати +її з урахуванням вимог нових груп клієнтів також було дуже непросто. +Найчастіше для цього доводилося погоджувати з постачальником об- +ладнання додаткові зміни апаратних засобів. Як наслідок, операто- +ру були потрібні роки, щоб спланувати та реалізувати у своїй мережі +нову послугу. Створення комутаційних станцій із програмним управ- +лінням було суттєвим кроком уперед, який дозволив зробити логіку +надання послуг програмованою, що значно полегшило реалізацію +процесу надання послуг. Однак концепція надання послуг не була +модульною. В міру зростання складності окремих послуг і залежності +між ними додати нову послугу до вже існуючих ставало все складні- +ше. Оператор не міг сам використати логіку, що підтримує одну по- +слугу, для підтримки іншої. + +699 +Велика кількість, складність і частота введення нових функцій у +мережі зв’язку вимагали нового підходу, який міг кардинально змі- +нити всі аспекти створення та надання послуг, а також експлуата- +ційного управління ними. Виникла необхідність заміни консерва- +тивного підходу, який використовувався протягом тривалих років і +передбачав надання невеликого переліку послуг, до створення нової +платформи, що дозволяє вводити широкий спектр нетрадиційних +послуг і надає можливість «налаштовувати» їх під індивідуальні ви- +моги клієнта. Таким новим підходом стала концепція інтелектуаль- +ної мережі. +Подальшим розвитком стала поява мереж зв’язку наступного по- +коління. Основу мережі NGN складає мультипротокольна мережа — +транспортна мережа зв’язку, яка входить до складу мультисервісної +мережі, що забезпечує перенос різних типів інформації з використан- +ням різних протоколів передачі. NGN являє собою єдину транспорт- +ну платформу, на базі якої об’єднуються різні види сервісів. +Ключовими особливостями мережі NGN є: +– використання режиму комутації пакетів для передачі даних; +– поділ функцій управління на функції, пов’язані з управлінням +транспортом, управлінням викликами/сесіями і додатками/сервісами; +– відділення процесу надання сервісів від процесу транспорту, ви- +користання відкритих інтерфейсів; +– підтримка великого набору сервісів, додатків і механізмів, за- +снованих на конструктивних блоках, включаючи потокові сервіси, +сервіси в режимі реального та нереального часу, мультимедійні сер- +віси; +– підтримка широкосмугових технологій з наскрізним («з кінця в +кінець», end-to-end) забезпеченням якості обслуговування; +– взаємодія з існуючими мережами через відкриті інтерфейси; +– мобільність в загальному сенсі (generalized mobility); +– необмежений доступ користувачів до різних постачальників +сервісів; +– безліч схем ідентифікації абонента; +– одні й ті ж характеристики для однакових з погляду користувача +сервісів; +– конвергенція сервісів мобільних і фіксованих мереж; +– незалежність сервіс-орієнтованих функцій від транспортних +технологій; +– підтримка різних технологій для реалізації мережі доступу та ін. + +700 +На сьогоднішній день можна говорити про пост-NGN, а точніше, +про використання підходів IMS. +Розглянемо більш детально основні етапи розвитку мультисервіс- +них мереж. +Сьогодні існує концепція мереж наступного покоління, в яких +ключове місце відведено поняттю «послуга» — NGS (New Generation +Services). +Інтелектуальна мережа була першим кроком на шляху переходу до +модульної архітектури мережі і дозволила відокремити шар комута- +ції від шару надання сервісів. Завдяки успіху IN, розвитку пакетних +технологій на сучасному етапі виявилося можливим створити NGN +(Next Generation Network — мережа наступного покоління). Перехід +до NGN можна вважати радикальною модернізацією телекомуніка- +ційної системи. Міняються не тільки технологічні принципи переда- +чі і комутації. Вельми істотні зміни відбудуться на ринку інфокомуні- +каційних сервісів, в системі технічної експлуатації і не тільки. +Огляду архітектури NGN присвячені роботи багатьох сучасних +вчених. У працях Б. Гольдштейна і О. Гольдштейна та інших розкри- +ваються питання переходу до мереж наступного покоління, аналі- +зуються дві конкуруючі концепції NGN — IPCC і TISPAN, а також +доповнюючі технології NGN — MPLS, Softswitch, Call-центри, про- +токол SIP. Основні положення зазначеного напрямку можна знайти +в [10]. +Для мережі NGN характерні істотні особливості, що виділяють її в +новий клас телекомунікаційних систем [9]: +• передача з пакетною комутацією; +• розділення функцій управління між пропускною спроможністю +каналу-носія викликом/сеансом, а також додатком/сервісами; +• розмежування між наданням сервісів і транспортуванням і на- +дання відкритих інтерфейсів; +• підтримка широкого спектру сервісів, додатків і механізмів на +основі уніфікованих блоків обслуговування (включаючи сервіси в ре- +альному масштабі часу, в потоковому режимі, в автономному режимі +і мультимедійні сервіси); +• можливості широкосмугової передачі наскрізною функцією +QоS (якості обслуговування); +• взаємодія з існуючими мережами за допомогою відкритих інтер- +фейсів; +• універсальна мобільність; + +701 +• необмежений доступ користувачів до різних постачальників +сервісів; +• різноманітність схем ідентифікації; +• єдині характеристики обслуговування для одного і того ж серві- +су з точки зору користувача; +• зближення сервісів між фіксованим і рухомим зв’язком; +• незалежність пов’язаних з обслуговуванням функцій від вико- +ристовуваних технологій транспортування; +• підтримка різних технологій «останньої милі»; +• виконання всіх регламентарних вимог, наприклад, для аварій- +ного зв’язку, захисту інформації, конфіденційності, законного пере- +хоплення і так далі. +З’ясувавши особливості мережі наступного покоління, слід дати +визначення цього терміна. +Мережа зв’язку наступного покоління (NGN) — концепція по- +будови мереж зв’язку, що забезпечують надання необмеженого набо- +ру сервісів з гнучкими можливостями з управління, персоналізації і +створення нових сервісів за рахунок уніфікації мережних рішень, що +припускає реалізацію універсальної транспортної мережі з розподі- +леною комутацією, винесення функцій надання сервісів в крайові +мережеві вузли й інтеграцію з традиційними мережами зв’язку [14]. +В роботі [13] Б. С. Гольдштейн запропонував дещо інший варіант +трактування терміна NGN, в якому за основу була взята можливість +мережею надавати потрійний сервіс (Triple — play services — мова, +відео, дані): NGN — це мережа, здатна забезпечити обслуговування +виду Triple-play services за рахунок використання устаткування пере- +дачі і комутації, заснованого на пакетних технологіях. +Говорячи про NGN, маємо на увазі мультисервісну мережу на +основі пакетів з відокремленням функцій надання сервісів від функ- +цій комутації. +Архітектура мережі NGN представлена на рисунку 2 [13]. +NGN запозичила в ІN принцип відділення функції комутації від +функції надання сервісів. Функції ІN були розподілені між Softswitch +та серверами. Відповідність ІN та NGN представлена на рисунку 3. +В такому випадку Softswitch виконує функцію комутації інтелек- +туальних сервісів, а функцію управління сервісом здійснює сервер +додатків. +Вводиться новий елемент мережі: програмний комутатор Soft- +switch, що виконує функцію управління викликами і сесіями + +702 +CSCF (Call Session Control Function), який, з одного боку, управляє +з’єднанням, а з іншого — взаємодіє з серверами надання сервісів за +SIP протоколом (Session Initiation Protocol) [11]. + +Рис. 2. Архітектура мережі NGN +У термінах NGN платформа надання інтелектуальних сервісів на- +зивається SDP (Service Delivery Platform). Основа ідеології NGN — це +відкриті стандарти консорціуму 3GPP (3’rd Generation Partnership +Project). +Ідеологія побудови NGN забезпечує можливість надання абонен- +там сервісів Triple-Play (передача мови, даних і відео) на базі мульти- +сервісних мереж. +На сьогоднішній день мова йде про об’єднання стільникового та +стаціонарного зв’язку — у відповідності з концепцією IMS. +Для IMS розроблена багаторівнева архітектура з поділом транспор- +ту для перенесення трафіку і сигнальної мережі IMS для управління +сеансами (рисунок 4) [11]. Таким чином, 3GPP при розробці IMS +фактично переніс на мобільні мережі основну ідеологію Softswitch. +Хоча деякі функції не завжди легко віднести до того чи іншого рів- + +国 +CepBep +Menma +MGCP, +cepBep +API +H.248.SIP +(3-9 CTOPOHB) +SIP/SIP-T,H.323,Q.BICC +Sigtran +(M3UA/SCTP) +Softswitch +(H.323,SIP,MGCP +Softswitch +Megaco) +Wnio3 +SG +Sigtran +YnpaBneHMe +(M3UA, +IUA +Cpena +V5UA +MGCP +Megaco +YnpaBneHMe +IP.TeneoH +RTP/RTCP +(H.323,SIP, +QKC7/BICC +ISUP +MGMP +Megaco) +AG +MGCP +INAP +Cpena +Megaco +INSCP +OKC7/BICC +Wnio3 +RTP/RTCP +Aocryna +Tpon +CeTbAocTyna +IP-ceTb +(TDM/ATM +SeonpoBoaHan +O3MG703 +ня, але такий підхід забезпечує мінімальну залежність між рівнями. +У IMS можна виділити [11]: +– User Plane — рівень користувачів, або рівень передачі даних; +– Control Plane — рівень управління; +– Application Plane — рівень додатків. + +Рис. 3. Відповідність інтелектуальної мережі та NGN + +Рис. 4. Архітектура IMS + +·Po3IIMpeHi HocJIyTH +CepBepW AoAaTkiB, +SCP +Meniacepsepy +MapIIpyTH3ai BHKJIMkiB +· IIepeTBopeHH HoMepy +TCAP/IN +SIP +MappyTM3ai curHari3auii +pokci-cepBepM, +STP +CepBep nepeanpecaui +3'EIHaHH +e31leKa +TCAP/IN +SIP +YpaBJiHHA o6cJIyrOByBaHHAM BHKJIMKiB +AreHT KopWcTyBaya, +SSP +WNO3W +.YpaBJiHH pWIaaMM +YμpaBJiHH pecypcaMMDh +Ut +Sh, Si +AS +AS +AS +ISC +Cx +Dx +CeTb IP-AocTyna +LTE +I-CSCF +MynbTuMeAwiHble +Mm +IP-ceTM +Gm +Mw +UE +Mr +P-CSCF +S-CSCF +MRFC +Mw +MynbTWMeAwiHble +IP-ceTW +Gg +Mg +Go +PDF +MGCF +Mj +Mk +CGSN +BGCF +Mp +Mb +SGW +SGSN +Mn +Mb +AoMeH +IM-MGW +KOMMyTaLMM +KaHanOB CS +RAN +Mb +MRFP704 +3GPP, за прикладом ІN, а потім Softswitch в IPCC, специфікує не +вузли мережі, а функції. Це означає, що IMS-архітектура, як і ІN або +Softswitch, теж являє собою набір функцій, з’єднаних стандартними +інтерфейсами. +Розробники мають право комбінувати кілька функцій в одному +фізичному об’єкті або, навпаки, реалізувати одну функцію розпо- +ділено, однак найчастіше фізичну архітектуру ставлять у відповід- +ність до функціональної і реалізують кожну функцію в окремому +вузлі. +Таким чином, в IMS інтелектуальна надбудова практично транс- +формувалася в рівень додатків, що включає в себе три типи серверів +додатків: +– SIP AS (SIP Application Server — сервер додатків); +– OSA-SCS (Open Service Access-Service Capability Server — сервер +сервісів, який забезпечує інтерфейс до сервісів, які базуються на від- +критому доступі до сервісів); +– IM-SSF (IP Multimedia Service Switching Function — платформа +для надання сервісів IN мережі). +В IMS поняття інтелектуальний сервіс замінене поняттям новий +сервіс. +Наступницею NGN вважається мережа майбутнього (Future +Network — FN). +Згідно з рекомендацією МСЕ-T Y. 3001, мережа майбутнього — це +мережа, здатна надавати сервіси, можливості і засоби, які важко на- +дати з використанням існуючих мережевих технологій [9]. +Мережею майбутнього є: +– або нова компонентна мережа чи вдосконалений варіант існую- +чої компонентної мережі; +– або різнорідна група нових компонентних мереж чи група, що +складається з нових та існуючих компонентних мереж, які працюють +як єдина мережа. +Рекомендується, щоб FN надавали сервіси, функції яких спроек- +товані так, щоб відповідати потребам додатків і користувачів. Очі- +кується, що в майбутньому кількість і вибір сервісів будуть стрімко +зростати. Рекомендується, щоб FN забезпечувала можливість впро- +вадження цих сервісів, не вимагаючи, наприклад, істотного додатко- +вого розгортання і збільшення експлуатаційних витрат. +На рисунку 5 зображені взаємозв’язки між чотирма цільовими +установками та дванадцятьма цілями проектування FN [9]. + +705 + +Рис. 5. Чотири цільові установки та 12 задач проектування мереж майбутнього +Безпосередньо стосуються задач проектування: +– різноманітність послуг — у майбутніх мережах мають підтри- +муватись різноманітні послуги, пристосовані для передачі трафіку з +широким вибором характеристик і властивостей; +– функціональна гнучкість — майбутні мережі мають бути функ- +ціонально гнучкими для підтримки та забезпечення стійкості нових +послуг, які стануть відповіддю на потреби користувачів; +– управління мережею — у майбутніх мережах необхідно ефек- +тивно експлуатувати, обслуговувати та надавати все більше послуг і +додатків; +– оптимізація — майбутні мережі забезпечуватимуть достатню +якість роботи шляхом оптимізації можливостей мережевого облад- +нання, виходячи з вимоги до послуги і потреб користувача; +– надійність і безпека — проектування, експлуатацію та розвиток +майбутніх мереж необхідно здійснювати таким чином, щоб забезпе- +чити надійність і здатність до відновлення, з урахуванням складних +умов. +Прогнозували, що до 2020 року повинні були з’явитися мережі +майбутнього — FN. + +Ig@OpMOBaHicTE +IPO IOCIVTH +Pi3HOMaHiTTR HOCIVT +IxpopMosaxicTE +npo Jani +PHKnioHaJIEHa rHyHKicTE +Biprya,xisanix pecypcis +Aocry o JaHX +YMDaBniHHR MeDKe +IgenTHbikaniR +MobinbHicTE +HaniHnicTb Ta besneka +EHeprOcHOKHBaHHR +Ysieepcanisanis mocmT +OnTMisanis +EKOHOMiYHi HOCTyTH +Ooi3HaHicTb B mHTaHHRX +ObisxaxicTb B +HaBKOJIHIIHbOTO +cOiaJIbHO -eKOHOMiyHH +cepeOBHII/a +IHTaHHRX +Y.3001(11)_F01706 +Архітектура NGN, розроблена IPCC, розподілена на такі рівні [15; +16]. +На нижньому рівні архітектури знаходиться транспортний рівень +(Transport Layer), що відповідає за перенесення по мережі сигнальних +повідомлень і мультимедійної інформації. Крім того, він забезпечує +взаємодію і обмін сигнальною і медіаінформацією з PSTN та іншими +пакетними мережами. +Транспортний рівень, своєю чергою, підрозділяється на три під- +рівні: IP-транспорту, міжмережної взаємодії і відмінного від IP +(NON-IP) доступу. +Підрівень IP-транспорту надає магістральну мережу передачі і +структуру комутації/маршрутизації для транспортування пакетів по +VoIP-мережі. До цього рівня належать маршрутизатори і комутатори, +а також пристрої, що відповідають за забезпечення якості обслугову- +вання (Quality of Service, QoS) і політики передачі даних. +Підрівень міжмережної взаємодії відповідає за перетворення +сигнальної і мультимедійної інформації, що отримується із зовніш- +ніх мереж, у форму, придатну для передачі усередині VoIP-мережі, +і навпаки. Тут функціонують такі пристрої, як шлюзи сигналіза- +ції (Signaling Gateways), медіашлюзи (Media Gateways) і міжмережні +шлюзи (Interworking Gateways). +Підрівень NON-IP доступу об’єднує несумісні термінали і безпро- +водові радіомережі, що мають доступ до VoIP-мережі. До цього під- +рівня відносяться шлюзи доступу або резидентні шлюзи для несуміс- +них терміналів або телефонів, ISDN-термінали, кабельні модеми або +MTA (Multimedia Terminal Adaptors) для HFC-мереж (Hybrid/Fiber +Coaxial), медіашлюзи мереж GSM/3G і мереж радіодоступу. +Наступний рівень — управління викликами і сигналізації (Call +Control & Signaling). Управляє основними елементами VoIP-мережі, +що знаходяться на транспортному рівні. Пристрої і функції цього +рівня управляють викликом, ґрунтуючись на сигнальній інформації, +отриманій від транспортного рівня, зокрема здійснюють встановлен- +ня і розрив медіазв’язку в VoIP-мережі, передаючи команди мереже- +вим компонентам. Рівень управління викликами і сигналізації міс- +тить такі пристрої, як контролери медіашлюзів (MGC, Call Agent, Call +Controller), LDAP-сервери. +Третій рівень — сервісів і додатків (Service & Application) — забез- +печує управління, логіку і виконання деякого числа сервісів або до- +датків. Пристрої, що належать до цього рівня, управляють потоком + +707 +викликів, ґрунтуючись на запрограмованій логіці виконання серві- +сів, за допомогою взаємодії з пристроями рівня управління викли- +ками і сигналізації. До самого рівня сервісів і додатків належать такі +пристрої, як сервери додатків і сервери сервісів. +Останній рівень — управління (Management) виконує функції +призначеного для користувача забезпечення, підтримку операцій і +надання сервісів, а також вирішує завдання білінга й інші завдання +мережевого управління. Рівень управління може взаємодіяти з будь- +яким з трьох перерахованих, використовуючи стандартні або вну- +трішньофірмові протоколи і програмні інтерфейси API. +Тепер звернемося до концепції ETSI TISPAN. В цьому проекті, на +відміну від концепції IPCC, архітектура мереж описана не сукупністю +вузлів, а як набір функціональних модулів, які можуть бути реалізова- +ні в різних фізичних елементах. Взаємодія між модулями здійснюєть- +ся за стандартизованим інтерфейсом. Найчастіше взаємодія відбува- +ється за сигнальним протоколом SIP-I, інколи H.248 та ін. +Мережна архітектура, запропонована ETSI TISPAN, зображена на +рисунку 6 [15; 16]. + +Рис. 6. Підсистеми TISPAN + +Applications +Other +subsystems +Customer +Network +IMS +Attachment +PSTN/ISDN +PSTN/ISDN +Subsystem +Emulation +Premises Equipment +subsystem +Resourceand +AdmissionControl +Service Layer +Subsystem +Transport Layer +TransportFunctions708 +Однією з найважливіших підсистем TISPAN вважається система +управління викликами і сервісами IMS. +Серед важливих принципів IMS слід зазначити, що вона базуєть- +ся на відкритих Інтернет-стандартах і тому без додаткової адаптації +може використовувати всі сервіси і додатки мережі Інтернет, проте +усередині самої IMS передбачено застосування протоколу IPv6. +Другою особливістю архітектури IMS є інноваційний підхід до на- +дання сервісів, що дозволяє операторові створювати різні сервіси й +інтегрувати їх один з одним, що забезпечує широкі можливості для +персоналізації і збільшення кількості сервісів. +Підхід IMS припускає горизонтальну архітектуру (рисунок 6) [15; +16], що дозволяє операторові просто й економічно упроваджува- +ти нові сервіси, які персоналізуються, причому користувачі можуть +стримати доступ до різних сервісів в рамках однієї сесії зв’язку. +Нова архітектура надання сервісів дозволила змінити традиційний +погляд на їх створення і стандартизацію. Можливості, які привносить +впровадження IMS, безумовно, додають плюсів до рішення TISPAN. +В МСЕ був створений форум з мереж майбутнього, який зараз +продовжує активно функціонувати. Мережа наступного покоління +спроможна надати найширший спектр сервісів. Дамо визначення +терміна «сервіс» та спробуємо класифікувати існуючі сервіси. У реко- +мендації МСЕ I.112 термін сервіс визначається як: «те, що пропону- +ється споживачам для задоволення певної комунікаційної потреби». +У цій же рекомендації сервіс надання зв’язку визначений як «вид об- +слуговування, що повністю реалізує можливості (включаючи функції +термінального устаткування) зв’язку між користувачами відповідно +до протоколів, встановлених для відповідного виду зв’язку». Під сер- +вісами користувача розуміється те, що пропонується користувачеві, +здається йому в оренду або оплачується ним. +На сьогоднішній день оператори часто класифікують сервіси за +одним з критеріїв. Це у свою чергу приводить до певних труднощів, +наприклад, при розрахунку тарифів. Тому інколи доцільно класифі- +кувати сервіси, використовуючи систему класифікаторів. +Найбільш розповсюджені види класифікацій такі: +1. Класифікація сервісів за типом інформації, котра передається +(контенту). +2. Класифікація сервісів за способом забезпечення доступу клієн- +та до сервісу. +3. Класифікація сервісів за типом клієнта. + +709 +4. Класифікація сервісів за типом обміну інформацією. +Для кожного типу сервісів можливий їх підрозділ за наступними +ознаками: +1. За пріоритетом впровадження та важливості — базові (основні) +сервіси та додаткові. +2. За маркетинговою функцією — сервіси, орієнтовані в основному +на отримання доходу, та сервіси, направлені на залучення нових клієнтів. +Особливий інтерес викликає розподіл сервісів на основні (basic +services) і додаткові (supplementary services). +Основний сервіс визначається функціональним призначенням +пристрою. Передача мови при з’єднанні двох користувачів телефон- +ної служби є прикладом надання основного сервісу. +Додаткові сервіси (сервіси з додатковою вартістю) можуть бути +постійними і разовими. Постійний додатковий сервіс надає на пев- +ний період часу власникові пристрою додаткові можливості, які для +пристрою даного типу не є обов’язковими. Разовий додатковий сер- +віс надається клієнтові за його запитом. +Найбільш поширеними в даний час додатковими сервісами є: +1. Безумовне перенаправлення виклику (CFU) — можливість направ- +ляти всі вхідні виклики на інший номер. +2. Перенаправлення виклику при зайнятості абонента (CFB) — мож- +ливість направляти на інший номер всі вхідні виклики, що надходять +під час зайнятості крайового пристрою користувача. +3. Перенаправлення виклику при невідповіді абонента (CFNR) –мож- +ливість всі вхідні виклики, на які немає відповіді впродовж певного +проміжку часу, направляти на інший номер. +4. Конференц-зв’язок (CONF) — надає можливість брати участь і +управляти одночасним зв’язком декількох користувачів. +5. Утримання виклику (HOLD) — дозволяє користувачеві перерива- +ти і відновлювати зв’язок на існуючому з’єднанні. +6. Інші. +Відповідно до Рекомендацій МСЕ-Т Y.1540 якість послуг оціню- +ється за трьома показниками [9]: +– швидкість — це один з найважливіших показників, який ха- +рактеризує якість надання більшості ІС. Показник швидкості визна- +чається контрольними термінами. Контрольні терміни — це макси- +мальний час, протягом якого повинен бути наданий сервіс; +– точність і достовірність — це характеристики споживчих влас- +тивостей сервісу, тобто наскільки він придатний для використання. + +710 +– надійність — це властивість засобів зв’язку надавати якісні сер- +віси. +В останніх працях з цього напряму зазначається, що надання сер- +вісу залежить від таких мережних показників: IPTD (затримки пе- +редачі пакету IP з інформацією управління), IPDV (зміни затримки +пакета IP), IPLR (відсотка втрачених пакетів IP) і IPER (відсотка по- +милкових пакетів IP). +Згідно з рекомендаціями МСЕ-ТI.380/Y.1540, 2007 [9] визначен- +ня якості функціонування NGN має спиратися на формування таких +показників: +• затримка перенесення пакетів; +• варіація затримки пакетів (джиттер); +• коефіцієнт втрати пакетів; +• коефіцієнт помилок по пакетах. +Згідно з рекомендацією МСЕ-Т [7–9] якість обслуговування (QoS) +визначено як сукупність характеристик послуги електрозв’язку, які +стосуються її можливості задовольняти встановлені і передбачувані +потреби користувача сервісу. +Паралельно існує поняття якості сприйняття (QoSЕ) — рівня +якості, який, за заявою абонентів / користувачів, вони відчували. +Показники роботи мережі (NP), зокрема показники якості роботи +інтелектуальної надбудови, характеризують здатність останньої або її +частини забезпечувати функції, пов’язані з наданням ІС користува- +чам та управлінням цим сервісом. +У зв’язку з ускладненням сервісів з’являється нове устаткування, +яке окрім стандартних функцій комутації виконує функції управлін- +ня сервісами. В такому випадку використовується так званий мереж- +ний інтелект. +Мережний інтелект — це програмне забезпечення, призначене +для управління процесами з’єднання крайового устаткування і на- +дання користувачам інфокомунікаційних сервісів [19]. Використан- +ня мережного інтелекту та розподіл сервісної логіки і логіки комута- +ції передбачає створення так званої інтелектуальної надбудови. +Додаткові сервіси, що надаються за допомогою інтелектуальної +надбудови, називають інтелектуальними сервісами. Інтелектуальні +сервіси включають і персоніфіковані сервіси, що базуються на по- +стійно оновлюваній інформації про місцеположення користувача, +про його записи в органайзері, особистих перевагах і тому подібне, +підказують цьому користувачеві найбільш доцільний напрям пере- + +711 +сування, нагадують йому про покупку подарунка до дня народжен- +ня, організують поїздки, бронювання квитків, отримання інформації +про погоду у вказаному пункті, надають банківську інформацію, про- +водять фінансові операції і багато іншого. +У Рекомендаціях МСЕ з інтелектуальних сервісів специфіковано +чотири набори ІС: CS-1, CS-2, CS-3, CS-4 [5–9]. Набір сервісів CS-1 +(Capability Set 1) включає 25 сервісів і 38 властивостей (основополож- +них і допоміжних), які мають дві загальні характеристики, що стан- +дартизовані МСЕ: +– сервіс замовлюється єдиним користувачем (single ended); +– виконання сервісу контролюється єдиною точкою контролю +сервісу (single control). +Сьогодні перелік інтелектуальних сервісів значно збільшився. До +найбільш популярних сервісів можна віднести Freephone (дзвінки за +рахунок сторони, що викликається), Premium Rate Service (дзвінки +з додатковою платою, наприклад, за участь в лотереях, голосуваннях +тощо), VAS (Value Added Services, послуги з доданою вартістю) та інші. +Сервіси CS-1 відносяться до сервісів типу А (однокінцеві) з цен- +тралізованою логікою управління. CS-1 включає 25 видів сервісів, +підтримується мережами PSTN, ISDN. +Останніми роками телекомунікаційні оператори не тільки пра- +цюють над поліпшенням якості і поширенням традиційних послуг +зв’язку, а й активно пропонують нові сервіси, які стають найважливі- +шою точкою зростання обороту компаній в умовах гострої конкурент- +ної боротьби на ринку. При цьому для реалізації різних сервісів по- +трібен відповідний розвиток мереж зв’язку і зокрема їх транспортної +інфраструктури. Світове телекомунікаційне співтовариство прийшло +до висновку про необхідність створення мереж наступного покоління, +так званих (Next Generation Networks). Велика частина особливостей +NGN схожі з характеристиками сучасного Інтернету. Однак NGN по- +винна підтримувати набагато більшу кількість протоколів виробників +різного устаткування — як «старого», так і перспективного. +Поставлене запитання «NGN: мода чи необхідність?» сьогодні ви- +глядає абсолютно недоречним — про жодну моду тепер годі й казати, +провідні телекомунікаційні оператори не тільки успішно впроваджу- +ють фрагменти мереж наступного покоління, а й повністю формують +свою інфраструктуру за принципами NGN. Багато компаній тепер +повідомляють, що їхні міжміські та міжнародні мережі зв’язку побу- +довані на основі NGN. + +712 +За минулі роки була остаточно осмислена концепція NGN і став- +ся помітний прогрес у випуску обладнання для IP-мереж. Визначи- +лися можливості і вигоди створення інфраструктури мереж NGN, +з’явилася комерційна складова проектів. Відбувся перехід від за- +хопленого уявлення про нові технології до їх комерційного впрова- +дження. При цьому NGN стає передовою основою для впровадження +послуг Triple Play (голос, передача даних і відеосервіси по одній або- +нентської лінії). +У рекомендаціях Міжнародного союзу електрозв’язку (МСЕ/ITU) +дано таке визначення Next Generation Network: NGN це мережа з +комутацією пакетів, здатна надавати телекомунікаційні послуги за +допомогою широкосмугових транспортних технологій, що підтриму- +ють якість обслуговування (QoS), в якій функції послуг не залежать +від використовуваних транспортних технологій [1; 7]. +Відмінною рисою моделі NGN, пропонованої сектором МСЕ-T, +є її функціональний розподіл на рівень послуг і транспортний рівень +[1]. Останній забезпечує виконання функції обміну дискретною ін- +формацією будь-якого типу між будь-якими двома географічно роз- +несеними точками [8]. +Перший рівень реалізує прикладні функції, пов’язані з затребу- +ваними послугами, наприклад, з організацією передачі мови і відео- +зображень окремо або в комбінації. Відповідно до рекомендацій +МСЕ-T, NGN повинна здійснювати конвергенцію послуг передачі +даних, мови, відео-, аудіо- та візуальних даних в індивідуальному, гру- +повому і широкомовному режимах [1]. +Мережі NGN повинні забезпечувати надання необмеженого на- +бору послуг з гнучкими можливостями щодо їх управління, персо- +налізації і створення нових послуг за рахунок уніфікації мережевих +рішень. +Властивості NGN: +1. Мультисервісність — незалежність технологій надання послуг +від транспортних технологій; +2. Широкополосність — можливість гнучкої і динамічної зміни +швидкості передачі інформації в широкому діапазоні в залежності від +поточних потреб користувача; +3. Мультимедійність — здатність мережі передавати багатокомпо- +нентну інформацію (мова, дані, відео, аудіо) з необхідною синхроні- +зацією цих компонентів в реальному часі і використанням складних +конфігурацій з’єднань; + +713 +4. Інтелектуальність — можливість управління послугою, викли- +ком і з’єднанням з боку користувача або постачальника послуг; +5. Інваріантність доступу (або можливість) організації доступу до +послуг незалежно від використовуваної технології; +6. Багатооператорність — участь декількох операторів у процесі +надання послуги і поділ їх відповідальності в залежності від області +їх діяльності [2]. +На основі аналізу існуючих сьогодні концептуальних документів та +експертних оцінок можна зробити висновок про те, що NGN являє +собою універсальну багатоцільову мережу, призначену для передачі +мови, зображень і даних з використанням технології комутації пакетів. +Її фундаментом є мультипротокольна-мультисервісна транспорт- +на мережа зв’язку, що забезпечує перенесення різнорідного трафіку +по різних протоколах передачі. +Концепція NGN передбачає підтримку необмеженого набору +послуг з гнучкими можливостями управління ними, реалізацію уні- +версальної транспортної мультипротокольної мережі з розподіленою +комутацією, інтеграцію з традиційними мережами зв’язку. Базовим +принципом NGN є поділ функцій перенесення і комутації, управлін- +ня викликом і управління послугами. +Замість прийнятої в традиційних мережах канальної парадигми, +в рамках якої з’єднання між абонентами будуються за принципом +«точка — точка», в NGN реалізується перехід до ідеології віртуальних +приватних мереж (VPN), які організовують доставку сервісів кінцево- +му користувачеві поверх протоколу IP. +Технологія NGN відкриває масу можливостей побудови накладе- +них сервісів поверх універсального транспортного середовища — від +пакетної телефонії (VoIP) до інтерактивного телебачення і Web-служб. +Вона характеризується доступністю сервісів незалежно від місця роз- +ташування клієнта і використовуваних ним інтерфейсів (Ethernet, +xDSL, Wi-Fi і т. д.). Таким чином, будь-який сервіс, створений в будь- +якій точці NGN, стає доступним кожному споживачеві [3]. +Гетерогенність інфраструктури, зростаюча конкуренція і знижен- +ня продажів базових сервісів, вважають західні експерти, сьогодні +можуть розглядатися як головна загроза телекомунікаційній інду- +стрії. Мережеві оператори прагнуть переосмислити свої бізнес-моде- +лі і перетворити їх інфраструктуру в платформу, повністю засновану +на IР. Головна мета і основна мотивація переходу до NGN — знизити +витрати і створити нові джерела доходів. + +714 +Останніми роками на ринку склалася ситуація, яка підготувала +ґрунт для просування NGN. На ринку зв’язку сформувалися такі умови: +– відкрита конкуренція між операторами, що стала наслідком +приватизації підприємств зв’язку і ослаблення державного регулю- +вання ринку; +– конвергенція мереж електрозв’язку та інформаційно-обчислю- +вальних мереж, розвиток інформаційно-комунікаційних мереж; +– бурхливе зростання цифрового трафіку, в основному за рахунок +розширення використання Інтернету; +– високий рівень попиту на рухомий зв’язок і нові мультимедійні +служби; +— конвергенція операторів, мереж, терміналів, служб/послуг +електрозв’язку. +Зазначені фактори створюють передумови до впровадження опе- +раторами широкого спектру нових послуг. За статистикою операто- +рів, дохід від одного користувача нових телекомунікаційних послуг в +кілька разів вищий, ніж від абонента традиційної телефонії. +Зазначимо також, що оператори фіксованих мереж, впроваджую- +чи NGN, мають на меті — скорочення капітальних витрат і опера- +ційних витрат за рахунок створення єдиного мультисервісного транс- +портного середовища для пропуску різнорідного трафіку. +Підходи до побудови транспортних мереж NGN представляють +однаковий інтерес як для операторів мереж зв’язку загального корис- +тування (стаціонарних і мобільних), так і для операторів технологіч- +них мереж зв’язку — відомчих і корпоративних. Незважаючи на те, +що технологічні мережі зв’язку, як правило, мають певну професійну +орієнтацію і спеціалізацію, при їх розвитку також враховується ідео- +логія NGN. +Розвиток мереж NGN та корпоративних відеокомунікацій є вза- +ємовигідними і взаємопосилюючими процесами. Мережа NGN може +з високою якістю передавати відеотрафік, дозволяє споживачеві са- +мому керувати пропускною здатністю й іншими параметрами мережі, +домагаючись найефективнішого використання доступної смуги про- +пускаючими. +Якщо подивитися на динаміку розвитку відеозв’язку, то мере- +жі NGN з’явилися вчасно. З одного боку, в сучасному відеооблад- +нанні реалізовані новітні технології для управління сеансами (SIP), +стиснення даних (H.264), динамічного керування смугою пропуску, +проходження міжмережевих екранів і ін. Все це «піднімає» якість, + +715 +підвищує керованість, що особливо важливо у зв’язку з поступовим +переходом на телебачення високої чіткості HD. +Останнім часом у всьому світі, особливо у період пандемії +CОVID-19 швидко виросла потреба в відеокомунікаціях. А у зв’язку +з розвитком та удосконаленням корпоративного управління, а саме +скороченням витрат на відрядження, зниженням навантаження на +навколишнє середовище, розвитком телемедицини, оперативнішим +реагуванням на надзвичайні ситуації, відеоконференцзв’язок став +дуже привабливим для корпоративних і інших користувачів. +Будь-яку сучасну послугу, доступ до якої надається операто- +ром, можна представити як сукупність трафіків даних, мови та ві- +део. Дослідження останніх років показують, що динаміка розвитку +мовного трафіку в загальносвітовому масштабі залишається ста- +більною. В протилежність йому трафік даних зростає від року в рік +експоненціально. Сьогодні більшість інформаційних потоків, що +проходять мережами зв’язку, належать саме до трафіку даних. Існую- +чі телекомунікаційні мережі, концепції яких розроблювалися більше +десяти років і були орієнтовні, в першу чергу, на передачу мовного +трафіку, скоро не в змозі будуть задовольнити всі потреби користува- +чів, що продовжують збільшуватися. +Концепція NGN – це технічні рішення, що з’явилися на етапі +розвитку цифрового зв’язку, коли трафік даних став важливішим за +мовний. Мережа NGN представляє собою мультисервісну систему +зв’язку, ядром якої є транспортна IP-мережа, що підтримує інтегра- +цію послуг передачі даних, мови і відео та реалізує принцип конвер- +генції технології. +В мережі NGN нам може знадобитися захист таких ресурсів: +– послуги в галузі зв’язку та комп’ютерних операцій; +– інформація та дані, включаючи програмне забезпечення, і дані, +пов’язані з послугою забезпечення безпеки; +– обладнання та засоби. +В мережі NGN необхідно гарантувати захист інформації від таких +загроз. +DoS (Denial of service – відмова сервісу) — напад на комп’ютерну +систему з наміром зробити комп’ютерні ресурси недоступними для +користувачів, для яких комп’ютерна система була призначена. +Одним з поширених методів нападу є насичення атакованого +комп’ютера або мережевого устаткування великою кількістю зовніш- +ніх запитів (часто безглуздих або невірно сформованих) так, що ата- + +716 +коване устаткування не може відповісти користувачам або відповідає +так повільно, що стає фактично недоступним. Взагалі відмова сервісу +здійснюється: +1) примушенням атакованого устаткування зупинити роботу про- +грамного забезпечення або устаткування або витратити наявні ресур- +си так, що устаткування не може продовжувати роботу; +2) заняттям комунікаційних каналів між користувачами і атакова- +ним устаткуванням так, що якість сполучення перестає відповідати +вимогам. +Підслуховування — загроза конфіденційності, що виникає завдя- +ки перехвату повідомлень між відправником та отримувачем інфор- +мації каналом зв’язку. +Неавторизований доступ — доступ до мережних об’єктів повинен +бути обмеженим та відповідати політиці безпеки. У випадку якщо +зловмисники його отримають, система буде не захищена від інших +несанкціонованих дій, таких як DoS атаки, підслуховування, маску- +вання та інше [3]. +Зміна інформації — зловмисники пошкоджують дані, запобігаючи +тим самим доступу до ресурсів з боку авторизованих користувачів. +Відмова — зловмисники запобігають доступу до ресурсів з боку +активних учасників телекомунікаційного з’єднання. Можливі мето- +ди атаки включають відмову в передачі, отримані, модифікації даних +під час розмови. +Оскільки всі шлюзи NGN будуть приєднані до Інтернету, то для +цих мереж будуть актуальними всі загрози, які є в інших IP-мережах. +Наприклад, шахрай може виконати атаку підміни IP-адреси. +У традиційних телекомунікаційних мережах використовуються, +як правило, пропріетарні алгоритми та протоколи. Це ускладнює по- +рушнику досягнення його цілей, вимагаючи наявності певної інсай- +дерської інформації. На відміну від цієї ситуації протоколи IP-мереж +добре відомі і задокументовані. +Телефонна мережа загального користування має централізовану +архітектуру, «інтелект» мережі зосереджений в АТС, а телефони не во- +лодіють великою функціональністю. На противагу цьому IP-мережі +децентралізовані за своєю природою, абонентськими терміналами є, +по суті, комп’ютери, використовуючи які, шахраї можуть створювати +численні загрози +Користувацькі термінали знаходяться в тому ж просторі IP-адрес, +що й елементи. Порушники можуть одночасно використовувати для + +717 +організації атак кілька різних способів доступу: мідний кабель, опто- +волокно, радіоканал. Для виявлення шахрайства необхідний постій- +ний обмін інформацією між всіма елементами NGN, що досить про- +блематично. +Білінгові моделі мереж NGN відрізнятимуться від нині при- +йнятих і в них будуть враховуватися не тільки обсяг трафіку або час +з’єднання, але і тип трафіку, вибрана якість обслуговування і т. п. Від- +повідно можна очікувати появи нових типів шахрайства. +Вважається, що розвиток NGN дасть поштовх поширенню мо- +більної торгівлі. Тому й увага шахраїв буде звернена в основному в +цьому напрямку: вартість контенту буде істотно перевищувати вар- +тість самих сполук. Так що зловмисники перейдуть від махінацій з не- +законними дзвінками ТфЗК / GSM до махінацій з контентом: +1) споживання неоплаченого трафіку; +2) незаконний перепродаж сервісів; +3) завищення плати за послуги [2; 3]. +Головна тенденція, яка простежується при аналізі сучасних стан- +дартів в області інформаційної безпеки, полягає у відмові від жор- +сткої універсальної шкали класів безпеки і гнучкому підході до оцін- +ки безпеки. +Висноки. Мережа NGN представляє собою мультисервісну сис- +тему зв’язку, ядром якої є транспортна IP-мережа, що підтримує +інтеграцію послуг передачі даних, мови і відео та реалізує принцип +конвергенції технології. Останнім часом, а особливо в період панде- +мії CОVID-19 в усьому світі, швидко виросла потреба в відеокому- +нікаціях. Відеоз’єднання стало чи не єдиним засобом, спроможним +вести справи в епоху, коли особисті контакти не бажані. А у зв’язку +з розвитком та удосконаленням корпоративного управління, а саме +скорочення витрат на відрядження, зниження навантаження на на- +вколишнє середовище, розвивиток телемедицини, оперативне реагу- +вання на надзвичайні ситуації, саме відеоконференцзв’язок став дуже +привабливим для корпоративних і інших користувачів. +СПИСОК ВИКОРИСТАНОЇ ЛІТЕРАТУРИ +1. Международный союз электросвязи (ITU) офіційне інтернет-представ- +ництво. — Режим доступу: https://www.itu.int/en/ITU-T/publications/ +Pages/default.aspx (Дата звернення 15.10.2021). +2. Бакланов И. Г. NGN. Принципы построения и организация. — М.: Эко- +Трендо, 2008. — 40 с. + +718 +3. https://www.itweek.ru ’ infrastructure ’ article ’ detai (Дата звернення +15.10.2021). +4. https://ru.wikipedia.org/wiki/Centrex (Дата звернення 13.12.2021р). +5. ITU-R Recommendation E. 800 — Quality of telecommunication services: +concepts, models, objectives and dependability planning — Terms and +definitions, related to Quality of Services and network performance including +dependability. — Approoved in 2008. — 30 p. +6. ITU-T Recommendation Q. 1215. — Physical plane for intelligent network +CS-1. — Helsinki, 1993. +7. ITU-T Recommendation Q. 1220. — Series intelligent network capability +Set-2. — Helsinki, 1993. +8. ITU-T Recommendation Q. 1230. — Series intelligent network capability +Set-3. — Helsinki, 1993. +9. ITU-T Recommendation Y. 1540 — Internet protocol data communication +service — IP packet transfer and availability performance parameters. — +Approoved in 2007. — 46 p. +10. http://www.rusnauka.com/36_PWMN_2010/Informatica/75853.doc.htm. +11. Глобальная информационная инфраструктура, аспекты протокола Ин- +тернет и сети последующих поколений. — Recommendation МСЕ–T +Y. 3001 (05/2011), ITU–T Study Group. Серия Y., утв. 2011. — 26 с. +12. Гольдштейн А. Б., Гольдштейн Б. С. SOFTSWITCH. — СПб.: БХВ, 2006. — +368 с. +13. Гольдштейн Б. С., Кучерявый А. Е. Сети связи пост-NGN. — СПб.: БХВ: +Петербург, 2014. — 160 с. +14. Гольдштейн Б. С. и др. Интеллектуальные сети. — М.: Радио и связь, +2000. — 504 с. +15. Гольдштейн А. Б. Подводная часть айсберга по имени NGN. [Ч. 2] +16. Гольдштейн А. Б., Соколов Н. А. // Технологии и средства связи. — +2006. — № 3. — С. 22–29. +17. Гольдштейн А. Б., Атцик А. Построение NGN: IPCC vs. TISPAN // Мир +связи. — 2006. — № 4. — С. 90–95. +18. Додонов А. Г., Ландэ Д. В. Живучесть информационных систем. — К.: +Наук. думка, 2011. — 256 с. +19. Князева Н. А., Кальченко А. С. Оценка качества услуг связи с пози- +ций удовлетворенности потребителей // Science and Education a New +Dimension: Natural and Technical Science. — Budapest, 2013. — Vol. 8. — +P. 156–161. +20. Стеклов В. К., Беркман Л. Н. Особенности проектирования системы +управления интеллектуальной сетью // Вісн. держ. ун-ту «Львівська +політехніка». — 2000. — № 387. — С. 19–22. +21. Проектування телекомунікаційних мереж: підруч. для студ. вищ. навч. +закл. за напрямком «Телекомунікації» / Стеклов В. К., Беркман Л. Н.; за +ред. В. К. Стеклова. — К.: Техніка, 2002. — 792 с. + +719 +22. Стекольников Ю. И. Живучесть систем. — СПб.: Политехника, 2002. — +155 с. +23. Сети последующих поколений — Структура и функциональные модели +архитектуры: МСЭ-Т. — Y. 2001. — [Действителен от 2004–17–12]. — Же- +нева, 2005. — 12 с. — [Международный стандарт электросвязи]. +24. http//kunegin.com 08.12.2021 (вільной доступ). +25. http://pro-gprs.info/tag/camel 13.12.2021 (вільной доступ). + +720 +Список авторів +Величко Віталій Юрійович (Vitalii Velychko), д. т. н., доцент, с. н. с., Ін- +ститут кібернетики ім. В. М. Глушкова Національної академії наук +України (Київ) +Воінова Світлана Олександрівна (Svitlana Voinova), к. т. н., доцент, +Одеський національний технологічний університет (Одеса) +Граняк Валерій Федорович (Valery Granyak), к. т. н., доцент, Вінниць- +кий національний аграрний університет (Вінниця) +Гурський Олександр Олександрович (Alexander Gurskiy), к. т. н., доцент, +Одеський національний технологічний університет (Одеса) +Завертайло Костянтин Сергійович (Kostiantyn Zavertailo), аспірант, Ін- +ститут проблем математичних машин і систем (Київ) +Іванова Лілія Вікторівна (Liliia Ivanova), к. т. н., директор, Відокремле- +ний структурний підрозділ «Одеський технічний фаховий коледж +ОНТУ» (Одеса) +Котлик Діана Олександрівна (Diana Kotlyk), викладач, Відокремле- +ний структурний підрозділ «Одеський технічний фаховий коледж +ОНТУ» (Одеса) +Котлик Сергій Валентинович (Sergii Kotlyk), к. т. н., доцент, Одеський +національний технологічний університет (Одеса) +Кудряшова Альона Вадимівна (Alona Kudriashova), к. т. н., старший ви- +кладач, Українська академія друкарства (Львів) +Кунуп Тетяна Василівна (Tetiana Kunup), к. т. н., викладач, Відокремле- +ний структурний підрозділ «Одеській технічний фаховий коледж +ОНТУ», (Одеса) +Малахов Кирило Сергійович (Kyrylo Malakhov), магістр (Інформаційні +технології), н. с., Інститут кібернетики ім. В. М. Глушкова Націо- +нальної академії наук України (Київ) +Піх Ірина Всеволодівна (Iryna Pikh), д. т. н., професор, Українська ака- +демія друкарства (Львів) +Пунченко Наталія Олегівна (Nataliia Punchenko), к. т. н., доцент, Одесь- +кий державний екологічний університет (Одеса) +Сеньківський Всеволод Миколайович (Vsevolod Senkivskyy), д. т. н., +професор, Українська академія друкарства (Львів) +Сергєєва Олександра Євгенівна (Olexandra Sergeeva), д. ф.-м. н., про- +фесор, Одеський національний технологічний університет (Одеса) + +721 +Соколова Оксана Петрівна (Oksana Sokolova), старший викладач, +Одеський національний технологічний університет (Одеса) +Федосов Сергій Никифорович (Sergiy Fedosov), д. ф.-м. н., професор, +Одеський національний технологічний університет (Одеса) +Хошаба Олександр Мирославович (Oleksandr Khoshaba), к. т. н., до- +цент, Вінницький національний технічний університет (Вінниця) +Цира Олександра Василівна (Olexandra Tsyra), к. ф. н., доцент, Дер- +жавний університет інтелектуальних технологій і зв’язку (Одеса) +Чаплінський Юрій Петрович (Yuri Chaplinskyy), к. т. н., с. н. с., Інститут +кібернетіки імені В. М. Глушкова НАН України (Київ) + + + + + + + + + + + + + + + + + + + +Наукове видання + + +ВЕЛИЧКО Віталій Юрійович + +ВОІНОВА Світлана Олександрівна + +ГРАНЯК Валерій Федорович +та інші +НОВІ ІНФОРМАЦІЙНІ + +ТЕХНОЛОГІЇ, МОДЕЛЮВАННЯ + +ТА АВТОМАТИЗАЦІЯ + + +Монографія +Надруковано в авторській редакції +Завідувачка редакції + +Т. М. Забанова + +Технічний редактор + +М. М. Бушин + +Дизайнер обкладинки + +В. І. Костецький + +Коректор + +І. В. Шепельська + + + + +Scientific publication (issue) +Published in the author’s edition + +Editor-in-Chief +Sergii Kotlyk + +Vitalii Velychko +https://orcid.org/0000-0002-7155-9202 +Svitlana Voinova +https://orcid.org/0000-0003-0203-0599 +Valery Granyak +https://orcid.org/0000-0001-6604-6157 +Liliia Ivanova +https://orcid.org/0000-0003-1738-7697 +Sergii Kotlyk +https://orcid.org/0000-0001-5365-1200 +Alona Kudriashova +https://orcid.org/0000-0002-0496-1381 +Tetiana Kunup +https://orcid.org/0000-0003-0246-0951 +Kyrylo Malakhov +https://orcid.org/0000-0003-3223-9844 +Iryna Pikh +https://orcid.org/0000-0002-9909-8444 +Nataliia Punchenko +https://orcid.org/0000-0003-1382-4490 +Vsevolod Senkivskyy +https://orcid.org/0000-0002-4510-540X +Olexandra Sergeeva +https://orcid.org/0000-0002-5534-9563 +Oksana Sokolova +https://orcid.org/0000-0001-9224-6734 +Sergiy Fedosov +https://orcid.org/0000-0002-5775-1468 +Oleksandr Khoshaba +https://orcid.org/0000-0001-5375-6280 +Olexandra Tsyra +https://orcid.org/0000-0003-3552-2039 +Yuri Chaplinskyy +https://orcid.org/0000-0001-7697-3958 +Olexander Gurskiy + +Kostiantyn Zavertailo + +Diana Kotlyk + + + +NEW INFORMATION TECHNOLOGIES, +SIMULATION AND AUTOMATION + + +MONOGRAPH + + + +IOWA STATE UNIVERSITY DIGITAL PRESS +2022 + diff --git a/CdAzT4oBgHgl3EQfGftE/content/tmp_files/load_file.txt b/CdAzT4oBgHgl3EQfGftE/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..c480eafd7817864379ec724def076c348e608d1b --- /dev/null +++ b/CdAzT4oBgHgl3EQfGftE/content/tmp_files/load_file.txt @@ -0,0 +1,20469 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf,len=20468 +page_content='NEW INFORMATION TECHNOLOGIES, SIMULATION AND AUTOMATION MONOGRAPH Scientific publication (issue) Editor-in-Chief Sergii Kotlyk Velychko V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} 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Sergeeva O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Sokolova O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Fedosov S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Khoshaba O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=',Tsyra O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Chaplinskyy Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' IOWA STATE UNIVERSITY DIGITAL PRESS 2022 MINISTRY OF EDUCATION AND SCIENCE OF UKRAINE ODESA NATIONAL UNIVERSITY OF TECHNOLOGY NEW INFORMATION TECHNOLOGIES, SIMULATION AND AUTOMATION MONOGRAPH Scientific publication (issue) Editor-in-Chief Sergii Kotlyk IOWA STATE UNIVERSITY DIGITAL PRESS 2022 UDC 004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='01/08 H73 Recommended by the Academic Council of The Odesa National University of Technology (Protocol № 11 dated 05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2022) Reviewers: Оlexandr Romanyuk, DSc, Prof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Vinnytsia National Technical University Valery Plotnikov, DSc, Prof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Odesa National Academy of Food Technologies Оlexandr Shpinkovski, PhD, Docent, Odesа Polytechnic State University Editor-in-Chief Sergii Kotlyk PhD, Docent, Odesa National University of Technology Team of Authors: Velychko V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Voinova S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Granyak V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Gurskiy O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Zavertailo K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Ivanova L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Kotlyk D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Kotlyk S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Kudriashova A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Kunup T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Malakhov K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Pikh I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Punchenko N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Senkivskyy V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Sergeeva O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Sokolova O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Fedosov S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Khoshaba O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Tsyra O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Chaplinskyy Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' H73 New information technologies, simulation and automation: Monograph / Velychko V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Voinova S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Granyak V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', et al;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Editor-in-Chief Kotlyk S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Iowa State University Digital Press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The monograph summarizes and analyzes the current state of development of computer and mathematical simulation/modeling, the automation of management processes, the use of information technologies in education, the design of information systems and software complexes, the development of computer telecommunication networks and technologies — most areas that are united by the term Industry 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The monograph will be useful both for experts and employees of companies engaged in the field of IT and automation, as well as for educators, masters, students and postgraduates of higher educational institutions, and everyone interested in issues related to Industry 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' DOI https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='31274/isudp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='121 ISBN 978-617-7867-37-0 (Print) ISBN 978-1-958291-01-6 (e-book) © 2022 Velychko V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Voinova S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Granyak V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', et al Preface The fourth industrial revolution (Industry 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0) envisages a new approach to production based on the mass introduction of information technologies into the industry, large-scale automation of business processes, and the spread of artificial intelligence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The benefits of the Fourth Industrial Revolution are obvious: increased productivity, more significant safety for employees due to the reduction of jobs in hazardous working conditions, increased competitiveness, fundamentally new products, and much more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=" However, it also has shortcomings that can negatively affect society's development, thus, studying the evolution of Industry 4." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0 directions is a necessary condition for the practical application of modern science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The monograph summarizes and analyzes the current state of development of computer and mathematical simulation/modeling, the automation of management processes, the use of information technologies in education, the design of information systems and software complexes, the development of computer telecommunication networks and technologies — most areas that are united by the term Industry 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The monograph was compiled based on the results of the XIV International Scientific and Practical Conference "Information Technologies and Automation - 2021", which took place in October 2021 at The Odesa National University of Technology (the former Odesa National Academy of Food Technologies).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The range of problems presented in the monograph is extremely wide — the application of information technologies for the design of post-printing processes and new food products,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' the development of decision-making theory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' mathematical simulation/modeling in ferroelectric polymers and polarized films,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' the development of logic control algorithms,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' the automation of maintenance of powerful electric machines and shipping mooring systems,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' applications of information technologies in education,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' digital health and distribution between computing complexes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The presented monograph is a significant help to experts, educators, students, graduate students who are trying to learn about the current state of science in the field of Industry 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This information can be used to solve a wide range of problems in the specified sections that arise both in the educational process and in research and scientific plans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Одеса «Екологія» 2022 МІНІСТЕРСТВО ОСВІТИ І НАУКИ УКРАЇНИ Одеський національний технологічний університет НОВІ ІНФОРМАЦІЙНІ ТЕХНОЛОГІЇ, МОДЕЛЮВАННЯ ТА АВТОМАТИЗАЦІЯ Монографія За загальною редакцією С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Котлика УДК 004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='01/08 Н73 Колектив авторів: В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Величко, С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Воінова, В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ф.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Граняк, О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Гурський, К.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Завертайло, Л.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Іванова, Д.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Котлик, С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Котлик, А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кудряшова, Т.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кунуп, К.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Малахов, І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Піх, Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Пунченко, В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сеньківський, О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Є.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сергєєва, О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' П.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Соколова, С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Федосов, О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Хошаба, О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Цира, Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' П.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Чаплінський Рецензенти: О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Романюк, д.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' т.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', професор, зав.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' кафедри програмного забезпечення Вінницького національного технічного університету;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Плотніков, д.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' т.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', професор, зав.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' кафедри інформаційних технологій та кібербезпеки Одеської національної академії харчових технологій;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Шпинковський, к.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' т.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', доцент кафедри інформаційних систем Дер- жавного університету «Одеська політехніка» Рекомендовано до друкування рішенням вченої ради Одеської націо- нальної академії харчових технологій (протокол № 11 від 5 квітня 2022 р.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=') © Величко В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Воінова С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Граняк В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ф.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', 2022 Н73 ISBN 978-617-7867-37-0 (Print) Нові інформаційні технології, моделювання та автомати- зація : монографія / кол.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' авт.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' : В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Величко, С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Воінова, В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ф.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Граняк [та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='] ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' за заг.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ред.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Котлика.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' — Одеса : Еко- логія, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' — 724 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ISBN 978-617-7867-37-0 (Print) У монографії узагальнено і проаналізовано рівень сучасного стану розвитку комп’ютерного та математичного моделювання, автоматизації процесів управління, застосування інформаційних технологій в освіті, проектування інформаційних систем і програмних комплексів, розвитку комп’ютерних телекомунікаційних мереж та технологій — більшості на- прямків, які об’єднуються терміном Індустрія 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Монографія буде корисною як для фахівців і працівників фірм, зайня- тих в галузі ІТ і автоматизації, так і для викладачів, магістрів, студентів і аспірантів вищих навчальних закладів, і всіх, хто цікавиться питаннями, пов’язаними з Індустрією 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' УДК 004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='01/08 3 Зміст Передмова .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5 Розділ I МАТЕМАТИЧНЕ І КОМП’ЮТЕРНЕ МОДЕЛЮВАННЯ СКЛАДНИХ ПРОЦЕСІВ Контекстно-онтологічна системна оптимізація проблемно- орієнтованої підтримки прийняття рішень (Чаплінський Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' П.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=') .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6 Теоретичні основи інформаційної технології прогностичного оцінювання якості проєктування післядрукарських процесів (Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Піх І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Кудряшова А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=') .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 44 Thermally stimulated processes and pyroelectricity in ferroelectric polymers (Sergeeva A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=') .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 139 Distribution of ferroelectric polarization in poled PVDF and P(VDF-TFE) films (Fedosov S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=') .' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 179 Розділ ІІ АВТОМАТИЗАЦІЯ ТА УПРАВЛІННЯ ТЕХНОЛОГІЧНИМИ ПРОЦЕСАМИ Технологічний розвиток судноплавства, систем швартування судноплавства майбутнього (Пунченко Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Цира О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=') .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 291 Система автоматизованого контролю технічного стану та діагностування потужних обертових електричних машин (Граняк В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ф.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=') .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=') .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 385 Системний підхід при організації навчального процесу у закладах вищої освіти з застосуванням нових інформаційних технологій (Воінова С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=') .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 453 4 Розділ IV ПРОЕКТУВАННЯ ІНФОРМАЦІЙНИХ СИСТЕМ І ПРОГРАМНИХ КОМПЛЕКСІВ Ukrvectōrēs та vHealth: інтелектуальні сервіси підтримки дистанційної медичної реабілітаційної допомоги (Величко В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Малахов К.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 596 Розділ V КОМП’ЮТЕРНІ ТЕЛЕКОМУНІКАЦІЙНІ МЕРЕЖІ ТА ТЕХНОЛОГІЇ Методика рівномірного розподілу завдань між обчислювальними комплексами (Завертайло К.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=') .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 658 Актуальність розвитку мережі NGN (Кунуп Т.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=') .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 689 Список авторів .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 720 5 Передмова Четверта промислова революція (Індустрія 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0) передбачає новий підхід до виробництва, що базується на масовому впровадженні інфор- маційних технологій у промисловість, масштабній автоматизації біз- нес-процесів та поширенні штучного інтелекту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Переваги Четвертої промислової революції очевидні: підвищення продуктивності, велика безпека працівників за рахунок скорочення робочих місць у небезпечних умовах праці, підвищення конкуренто- спроможності, принципово нові продукти та багато іншого.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Однак вона має й недоліки, які можуть негативно впливати на розвиток сус- пільства, тому вивчення розвитку напрямів Індустрії 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0 — необхідна умова практичного застосування сучасної науки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У колективній монографії представлені результати практичних і тео- ретичних досліджень в області комп’ютерного та математичного моделю- вання, автоматизації процесів управління, застосування інформаційних технологій в освіті, проектування інформаційних систем і програмних комплексів, розвитку комп’ютерних телекомунікаційних мереж та тех- нологій — більшості напрямків, які об’єднуються терміном Індустрія 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Монографія складена за підсумками проведення XIV Міжнародної науково-практичної конференції «Інформаційні технології та автома- тизація — 2021», яка відбулася в жовтні 2021 року в Одеському націо- нальному технологічному університеті (колишня Одеська національна академія харчових технологій).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Спектр представлених у монографії проблем надзвичайно широ- кий — застосування інформаційних технологій для проектування піс- лядрукарських процесів і нових харчових продуктів,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' розвиток теорії прийняття рішень,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' математичне моделювання в сегнетоелектричних полімерах і поляризованих плівках,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' розробка алгоритмів логічного управління,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' автоматизація обслуговування потужних електричних ма- шин і систем швартування судноплавства,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' застосування інформаційних технологій в освіті та розподіл між обчислювальними комплексами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Представлена монографія являє собою істотну підмогу фахівцям, викладачам, студентам, аспірантам, які намагаються дізнатися про сучасний стан науки в галузі Індустрія 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ця інформація може бути використана для вирішення широкого кола проблем в зазначених роз- ділах, що виникають як в навчальному процесі, так і в дослідницькому і науковому планах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6 Розділ I МАТЕМАТИЧНЕ І КОМП’ЮТЕРНЕ МОДЕЛЮВАННЯ СКЛАДНИХ ПРОЦЕСІВ КОНТЕКСТНО-ОНТОЛОГІЧНА СИСТЕМНА ОПТИМІЗАЦІЯ ПРОБЛЕМНО-ОРІЄНТОВАНОЇ ПІДТРИМКИ ПРИЙНЯТТЯ РІШЕНЬ Чаплінський Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' П.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Показана актуальність використання знання-орієнтованих підходів до прийняття рішень, що базується на використанні системної оптимізації, онтологій та контексту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Описана технологія підтримки прийняття рішень для розв’язання управлінських задач, яка ґрунтується на методології сис- темної оптимізації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Досліджуються різні ситуації при прийнятті рішень в рамках запропонованої технології.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Процес прийняття рішень на основі сис- темної оптимізації розглядається через модель певного контексту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визна- чені контекстна онтологія та її складові, які дозволяють розпізнати, зро- зуміти, представити та підтримати розв’язання задачі прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Представлені онтологія шарів та онтологія аспектів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The actuality of the usage of knowledge-oriented decision-making approach based on the use of system optimization, ontologies and context is shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The de- cision — making technology for solving management problems, which is based on the methodology of system optimization, is described.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Various situations of decision making within proposed technology are researched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The decision-making process based on system optimization through the model of some context is considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Con- textual ontology and its components, which allow to recognize, understand, present and support the solution of the decision-making problem are identified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The ontology of layers and the aspects ontology are presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сьогодні комплексна та системна підтримка прийняття рішень є домінуючим динамічним діловим середовищем.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це визначається ха- рактерними рисами сучасного прийняття рішень: інтеграція наукових знань, зростання кількості міждисциплінарних проблем, комплекс- ність проблем та необхідність їх вивчення у єдності технічних, еконо- мічних, соціальних, психологічних, управлінських та інших аспектів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ускладнення аналізованих проблем та об’єктів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' динамічність ситуацій прийняття рішень;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' дефіцитність ресурсів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' підвищення рівня стандар- 7 тизації та автоматизації елементів виробничих та управлінських про- цесів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' глобалізація конкуренції, виробництва, кооперації, стандарти- зації тощо;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' підвищення ролі людського фактора в управлінні та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому прийняття рішень відбується як через горизонталь- ні перехресні вузли, так і через вертикальні перехресні ієрархічні зв’язки, при цьому можливо отримання раніше недоступної інфор- мації, що в подальшому дає змогу розвивати нові знання та розумін- ня.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому неможливо із загального процесу прийняття рішен- ня виділити будь-які окремі задачі, оскільки вони об’єднані в одну загальну задачу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це означає, що діяльність як окремих людей, так і підприємств все більшою мірою залежить від наявних у них знань як одного з найцінніших ресурсів і можливості їхнього ефективного ви- користання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Управління знаннями сьогодні розглядається як потужна конку- рентна перевага на підприємстві, орієнтованому на постійні зміни ділових процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Під представленням знань розуміється їх структу- ризація з метою формалізації процесів рішення задач у певній про- блемній області.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такий розгляд прийняття рішень визначає перехід від вузькодис- циплінарного прийняття рішень до взаємодіючої множини предмет- них областей, що об’єднує різні аспекти розгляду: представлення, зміст, інтерпретацію та використання;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' постійної зміни середовища прийняття рішень, постійного накопичення нових знань, викорис- тання активних знань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Слід також зазначити, що знання в таких складних предметних об- ластях дуже швидко змінюються або застарівають, з’являються нові задачі та нові методи розв’язання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому необхідно розглядати мультидисциплінарні сфери, що пов’язані з відповідною прикладною проблемою, їх взаємодію та інтеграцію.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Результати розв’язання задач прийняття рішень є результатом по- єднання та інтеграції знань, розуміння та ідей розв’язання множин взаємопов’язаних задач з різних предметних областей, кожна з яких має свої специфічні передумови.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вони характеризуються різноманіт- ністю, багатовимірністю, багаторівневістю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Реалізацію ефективного прийняття рішень будемо розглядати на основі методології систем підтримки прийняття рішень, основою якої є між-/мульти-/транс- дисциплінарність, контекст та онтологія, як засоби розуміння та представлення предметних областей і процесів прийняття рішень та інтеграції методів системного, процесного та ситуаційного аналізу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 8 В рамках такого прийняття рішень людині, що приймає рішення (ЛПРу), необхідно врахувати множину властивостей, що визнача- ються та використовуються одночасно.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це вимагає розгляду проце- сів, структур, ресурсів, навколишнього середовища, а також взаємодії між акторами процесу прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для цього необхідно ви- користовувати тільки ті особливості дійсності, які є найважливіши- ми для ситуації чи проблеми.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому необхідно сконцентрувати увагу на деяких конкретних характеристиках, які визначаються через точки зору (аспекти розгляду).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це надає можливість використовувати аспекти або точки зору для того, щоб формулювати, розв’язувати та керувати складними та взаємозв’язними ситуаціями, які можуть ба- зуватися не тільки на знаннях окремої предметної області, а на деякій сукупності проблемних областей.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому необхідно розуміти від- ношення між елементами середовища прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тому є актуальною є задача розв’язання проблемних ситуацій з ви- користанням відповідних інтелектуальних засобів, що розроблені на принципах інженерії знань для сукупності певних проблемних облас- тей.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому необхідно використовувати та враховувати когнітив- ні знання («знаю, що»);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' прикладні знання застосування («знаю, як»);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' системне розуміння («знаю, чому»);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' особисту мотивацію («хочу знати, чому»).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для цього всі знання, що використовуються, розглядаються в розрізі знань, що описують контент, та знань, що описують контекст.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З іншого боку, прийняття рішень у системах управління описуєть- ся взаємозалежними задачами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При чому, як правило, такі задачі ви- являються несумісними через їхню структуру, що склалася, та обме- жуючі фактори, так званими «вузькими місцями», до яких відносять вимоги до функціонування системи, обсяги фінансування;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' наявність достатніх людських ресурсів, виробничі можливості підприємств, нормативні чи фактичні годинні етапи життєвого циклу виробництва продукції тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При чому прийняття рішень в таких задачах вима- гає врахування таких особливостей, системності, альтернативності, неспільності (суперечності), багатокритеріальності, врахування ду- мок аналітиків та експертів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Застосування традиційних методів для розв’язання таких задач у класичній постановці, тобто знаходження розв’язання в незмінній протягом рішення моделі, вимагає внесення всіх варіацій параметрів (нових технологій, додаткових ресурсів) до початкової постановки, а це веде до надмірної розмірності задачі, і, отже, складнощів розв’язання задачі і неможливості отримання рі- шення за прийнятний час і прийнятної точності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 9 Таким особливостям задач прийняття рішень задовольняє техно- логія системної оптимізації, яка була запропонована В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Глушко- вим [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Суть якої полягає в цілеспрямованій зміні моделей прийняття рішень для досягнення спільності й у виборі найбільш прийнятного рішення поставленої задачі, що формулюються як задачі багатокри- теріального лінійного програмування та для різних видів припусти- мих варіацій параметрів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Створення різних засобів підтримки прийняття рішень — це без- перервний процес формування, уточнення вимог та розв’язання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому необхідно враховувати, що функціонування систем від- бувається в умовах інформаційної та реалізаційної неоднорідності, розподіленості та автономності інформаційних ресурсів системи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інформаційна неоднорідність ресурсів полягає в різноманітності їх- ніх прикладних контекстів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Реалізаційна неоднорідність джерел про- являється у використанні різноманітних комп’ютерних платформ, засобів управління базами даних, моделей даних і знань і таке інше.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, потрібна підтримка розвитку систем та підсистем до складніших, інтегрованих систем, що базуються на інтероперабель- ній взаємодії компонентів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Реалізація такої підтримки прийняття рішень базується на підтримці повного циклу прийняття рішень для того, щоб пройти від формулювання проблеми, визначення відповід- них моделй та алгоритмів розв’язання до використання розв’язувача, вимагає застосування знань для прийняття рішень для конкретної за- дачі з врахуванням навичок та досвіду користувача.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Метою роботи є представлення онтологокерованої підтримки прийняття управлінських рішень на основі методів та алгоритмів системної оптимізації й онтологічних методів представлення та об- робки знань з урахуванням контекстів розв’язання задач прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для врахування цих особливостей і властивостей прикладних систем управління та багатьох інших вимог, що виникають в процесі функціонування різних систем управління, потрібна побудова єдиної технології прийняття рішень, що дозволяє виробляти найбільш при- йнятні рішення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому вибір того або іншого рішення не пови- нен порушувати системність розгляду і цілісність процесу прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Слід зазначити, що сучасне розв’язання задач вимагає вико- ристання інформації різного походження.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це визначає необхідність зрозуміти складність проблеми, взяти до уваги різноманіття оточуючого світу та науковий розгляд про- 10 блеми, поєднати абстрактне і конкретне знання, розвивати знання та діяльність в напрямку досягнення результатів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому необ- хідно враховувати, що використання інформації та знань у проце- сі прийняття рішень, як правило, відбувається в контексті складної структури процесу прийняття рішень, який часто формується за до- помогою ряду чинників.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такі системи з точки зору прийняття рішень включають: наявність складного змістовного об’єкта (системи), з яким пов’язана загальна проблема (задача) прийняття рішення;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' розбиття даної системи на взаємозв’язані підсистеми, з відповід- ною декомпозицією загального завдання на підзадачі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' наявність спільної мети при розподілі функцій по підсистемах;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' фізична або віртуальна відособленість кожної з підсистем;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' мож- ливість відносно самостійного вибору своїх станів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' наявність засобів обміну станами між підсистемами, а також засобів узгодження, подолання протиріч і синхронізації процедур розв’язання підзадач.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В роботі [2] пропонується розглядати прийняття рішень в рамках трьох етапів: аналіз, розробка та вибір.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Аналіз (опис системи, розу- міння поведінки системи, оцінка поточної ситуації, формулювання цілей) включає в себе пошук середовища для умов виклику прийнят- тя рішення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розробка (формулювання моделі, генерація альтернатив) належить до створення, розробки та аналізу можливих варіантів дій, в той час як вибір (оцінка впливу альтернатив, оцінка та прийняття рі- шення, пояснення: візуалізація та спілкування) включає в себе вибір напрямку дій з наявних.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основною частиною підтримки прийняття рішень є збір, оцінка, організація та перетворення цієї інформації в форми, що придатні для аналізу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для успішної розробки та впровадження систем підтримки при- йняття рішень (СППР) необхідно [3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4]: участь кінцевих користувачів в розробці СППР;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' проектування СППР для потреб кінцевих користу- вачів, а не потреб, як їх розуміє розробник;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' гнучкість, адаптивність та оновлюваність системи;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' простий інтерфейс, який вимагає обмежено- го часу для навчання користування системою;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' візуальне відображен- ня результатів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' врахування факторів, що стосуються якості системи, якості інформації та представлення інформації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Область прийняття рішень будемо розглядати як багаторівневу структуру, що включає область проблем, область моделей, область ме- тоду та область реалізацій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Область прийняття рішень можна деком- 11 позувати на елементарні об’єкти, кожен з яких описується сукупніс- тю атрибутів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В рамках такого розгляду необхідно визначити поняття та конструкції, за якими можуть бути визначені природа, структура та представлення процесу формування та прийняття рішень та відповід- них складових областей, що описують такий процес.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В роботі під прийняттям рішень будемо розуміти інтерактив- ний процес нагромадження, обробки, використання та поширення знань, що дає можливість обміну інформацією, знаннями і досвідом та підвищення рівня інформованості, можливість отримання та ви- роблення усвідомленого вибору між альтернативними рішеннями, можливість підвищення фахового рівня.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Метою такого процесу є розв’язання проблем: надання знанням доступності та корисності, так, що відповідні достовірна інформація та знання, що впливають на прийняття рішень та розуміння проблеми, будуть донесені відпо- відному користувачу в відповідному форматі в відповідний час.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Та- ким чином, підтримка прийняття рішень, що реалізована як певна система прийняття рішень, повинна відповідати SMART-критеріям, тобто рішення мають бути конкретними, вимірними, погодженими, реалістичними, чітко прив’язаними до часу та простору.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Будемо розуміти під підтримкою прийняття рішень інтелектуаль- ну комп’ютерну технологію посилення можливостей ЛПР у процесі спостереження за станом предметної області, діагностики проблем- них ситуацій і цілей дій, планування дій і генерацію способів їх реа- лізації, формування раціональних варіантів рішень з використанням експертних знань і методів моделювання та оптимізації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому прийняття рішень реалізується на основі інформаційних моделей да- них;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' на основі логічних моделей;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' на основі формальних моделей;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' на основі типових рішень або прецедентів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Під основними етапами при- йняття рішень будемо розглядати: моніторинг і збір достовірних даних про процеси функціону- вання системи;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' розпізнавання, прогнозування розвитку й оцінка штатних і кри- тичних ситуацій, що мають місце у діяльності системи;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' постановку цілей і пошук альтернативних дій з їх досягнення в умовах ситуацій, що складаються в підсистемах підприємства і в сис- темі в цілому;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' адекватну оцінку можливих способів дій, аналіз наслідків і вибір найбільш ефективних з них з комплексним аналізом всього спектру характеристик альтернативних рішень;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12 організацію виконання рішень, що включає оцінку і вибір на- прямів робіт з реалізації рішень, конкретних заходів і термінів, роз- поділ ресурсів для реалізації рішень;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' контроль виконання рішень на основі оцінки і порівняння ста- нів і результатів (проміжних у зіставленні з бажаними кінцевими) ді- яльності, оцінку якості рішень, що приймалися, і правильності орга- нізації їх вироблення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Прийняття рішень можна представити у вигляді багаторівневої системи, що складається з сукупності завдань, що знаходяться на різних рівнях ієрархії та відповідають за певну функцію чи діяльність та пов’язані з відповідною логічною структурою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Прийняття рішень в такій системі будемо розглядати як через горизонтальні перехрес- ні вузли (перетину кордону), так і через вертикальні перехресні іє- рархічні зв’язки (перетин ієрархічних рівнів), при цьому можливо отримання раніше недоступної інформації, що в подальшому дає змогу розвивати нові знання та розуміння.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кожна задача, що від- повідає конкретному напрямку(ам) діяльності, може мати підзадачі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Задача та підзадачі описуються відповідними формалізованими за- вданнями, які описуються комплексами взаємопов’язаних моделей.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формалізовані моделі реалізуються певними методами, алгорит- мами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сам процес будемо розглядати як систему, яка складається з деякого набору підсистем (етапів) та їх елементів (процедур, дій, операцій), які взаємодіють між собою, кількість та склад яких мо- жуть змінюватись у залежності від умов та розв’язуваних завдань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому інтеграція рішень, що приймаються, в рамках підсистем досягається за рахунок прийняття узгоджених рішень у завданнях, а інтеграція управління усією системою в цілому буде отримана шля- хом узгодження дій між пов’язаними підсистемами, що належать одному або різним рівням.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визначимо, що між різними підсистемами, функціональними за- дачами (підзадачами), моделями можливі різні види взаємодії.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Така взаємодія може реалізовуватися через відношення прямого підпо- рядкування, інформаційного обміну, функціонального підпоряд- кування, функціонального узгодження і координації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відношення прямого підпорядкування і функціонального підпорядкування є базою для опису побудови системи управління за організаційною та функціональною ознаками.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ці відношення можуть бути задані при визначенні ієрархії функціональних задач, що розв’язуються окре- мими підсистемами, та пріоритетів їхньої взаємодії.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відношення ін- 13 формаційного обміну визначається при описі взаємодій окремої під- системи (задачі) з іншими підсистемами (задачами) у рамках цілісної системи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це може бути задано при визначенні для даної підсистеми деякої нормативно-довідкової інформації, яку використовує у про- цесі реалізації своїх функцій дана підсистема або задача.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відношення функціонального узгодження і координації визначається при описі функціональних задач підсистеми.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це відношення задається вхід- ними і вихідними параметрами функціональних задач підсистеми, а також ресурсами підсистеми.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відношення функціонального узго- дження і координації реалізується в процесі розв’язання конкретних взаємозв’язаних задач, що виникають всередині системи управлін- ня.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тип зв’язків між окремими підсистемами визначається в процесі опису організаційно-функціональної структури системи управління.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При реалізації прийняття рішень будемо розрізняти три стратегії прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це — створення, інтеграція та адаптація.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Створен- ня означає «абсолютно нову проблему», або «на порожньому місці» концепцію розв’язання проблеми в ситуації, коли не існує відповід- ної моделі, методу та/або алгоритму розв’язання, що могло би ви- користовувався як основа для прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це важливо, якщо деяка частина з процесу прийняття рішень має бути спроектована без підтримки існуючого.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інтеграція означає концепцію розв’язання проблеми, згідно з якою побудовано процес розв’язання проблеми, збираючи компоненти з існуючого.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Чим більше компонентів багато- кратного використання, з яких складений процес прийняття рішень, тим легше процес інтеграції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Адаптація означає концепцію процесу прийняття рішень, згідно з якою побудовано розв’язання проблеми, знижуючись або змінюючи деяку частину(и) існуючого, або розши- рюючи існуюче деякою новою частиною(ами).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розв’язання задач на основі системної оптимізації можна предста- вити в вигляді послідовності людино-машинних процедур, що вклю- чають формування моделі початкової задачі в термінах предметної області, переведення сформованої моделі в область задач, наприклад, математичного програмування, та розв’язання задачі математичного програмування в багатокритеріальній постановці.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому рішення задачі складається з перевірки здійснимос- ті вимог за якістю функціонування системи (директивні вимоги) в області власних можливостей системи, і в разі їх нездійсненності — знаходження «вузьких місць», вироблення заходів, спрямованих на усунення нездійсненності директивних вимог, і в виборі найбільш 14 прийнятного рішення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, видно, що системна оптиміза- ція дає можливість представлення рішення досить складних задач у вигляді послідовності рішення простіших задач.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При реалізації системної оптимізації враховується те, що обмін інформацією про рішення, які приймаються, здійснюються між за- дачами (етапами) з чітко вираженими зв’язками та існує пріоритет в прийнятті рішень між задачами (етапами) як з точки зору правил їх взаємодії, так і часу їх виконання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1) Аналіз виконання управлінських рішень, отримані з зада- чі (етапу), що має більший пріоритет за взаємодією чи за часом розв’язання, або заданих власними цілями з функціонування даної задачі (етапу), в рамках існуючих можливостей задачі (етапу), що розв’язується.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У разі неможливості реалізації цих рішень задачею (етапом) по- трібно виконати такі кроки: підготувати пропозиції щодо бажаної та можливої зміни отри- маних рішень;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ініціювати процес взаємодії з відповідними задачами (етапами).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2) Пошук управлінських рішень з урахуванням власних можли- востей завдання (етапу) й існуючих взаємних зв’язків з іншими за- дачами (етапами).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3) Визначення завдань наступного завдання (етапу) для реалізації отриманих рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В ході процесу взаємодії при пошуки узгоджених рішень структура взаємодії, тобто множина взаємопов’язаних задач (етапів) і відповід- них осіб, які приймають рішення, не може бути задана заздалегідь.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ця структура генерується безпосередньо під час пошуку рішення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У відповідності з цим інструментарій повинен забезпечити: передачу і прийом управлінських рішень або генерацію власно- го напрямку(ів) рішення поставленого завдання (такі рішення буде- мо називати директивними);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' модельне представлення власних можливостей і інтересів дано- го завдання (етапу), директивних рішень і взаємних зв’язків з іншими задачами (етапами);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ініціювання процесу взаємодії з відповідними особами, які при- ймають рішення;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' формування модельного представлення задач пошуку узгодже- них рішень з урахуванням можливостей даного завдання (етапу);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' методи і алгоритми визначення розв’язку сформованих задач.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 15 Такий розгляд дозволяє запропонувати підхід до реалізації вза- ємодії між підсистемами і відповідно певними задачами (та нада- лі його використати при розгляді певних моделей, формалізованих задач тощо), що базується на понятті відношення пріоритету вза- ємодії.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це відношення на множині взаємопов’язаних локальних за- дач визначає характер впливу відповідних підсистем і задач один на одного.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таке відношення може бути розглянуте як відношення не- строгого порядку R , визначене таким чином: якщо K — множина взаємопов’язаних задач, то iRj ( ,i j K ∈ ) означає, що задача i має пріоритет у прийнятті рішення по відношенню до задачі j , тобто її рішення є обов’язковими (директивними) для задачі j і входять в її модель як деякі параметри.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це відношення визначає відношення прі- оритету взаємодії.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оскільки R є відношенням нестрогого порядку, то воно розбиває множину взаємопов’язаних задач на класи еквівалент- ності, які розглянемо в подальшому.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Опишемо реалізацію відношень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для цієї мети ми введемо такі позначення (без врахування структури системи): I — множина підсистем системи, lI — множина задач для l -ї структурної одиниці (підсистеми);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Припустимо, що задачі прийняття рішень в структурній одиниці структуровані, а задача вибору рішення у всій системі в цілому має бути сформульована через інтеграцію розподілених підсистем і відпо- відно через інтеграцію задач, що реалізуються в підсистемах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для формалізації специфічних проблем інтеграції функціональ- них задач введемо позначення: xp — вектор, що визначає вибір дії в p -й функціональній задачі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' { , } p p j p s s j J = ∈ — вектор, що визна- чає вплив (відношення функціонального узгодження і координа- ції) інших функціональних задач, які описують множину , p p J J I ∈ , на p -ту функціональну задачу;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' { , } p p j p z z j Z = ∈ — вектор, що ви- значає відношення інформаційного обміну інших функціональних задач, які описують множину , p p Z Z I ∈ , з p -ю функціональною задачею;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' { , , } p p p ji l u u j J i I = ∈ ∈ — вектор директивного впливу (під- порядкування) через пріоритет взаємодії на p -ту функціональну за- дачу, який може визначати дію як інших функціональних задач l -ї підсистеми, так і інших функціональних задач підсистем, що мають директивні взаємозв’язки з цією задачею, що визначають множину , p p J J I ∈ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому визначимо вектори: { , } j v p p p s s j J = ∈ , { , } j z p p p z z j Z = ∈ , { , , } j p p pi u l u u j J i I = ∈ ∈ , які описують відповідні вектори та множини, 16 що визначають вплив, інформаційний обмін та директивний вплив даної задачі на інші задачі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В рамках СППР взаємодія між множиною підсистем багаторівне- вої системи та множинами супутніх задач в цих підсистемах, які від- повідають за різні напрямки діяльності системи, реалізується через принцип системності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Принцип незалежності в функціонуванні СППР підсистем базу- ється на тому, що кожна підсистема за своєю функціональною зада- чею може робити свій вибір власної дії, яка описується вектором xp, у відповідності зі своєю власною моделлю вибору.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Така дія дасть змогу розв’язання задачі самоуправління з виконання підсистемою своєї функціональної діяльності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Проте принцип цілісності вимагає побу- дови такої моделі задачі вибору рішень, область припустимих рішень якої враховувала б вплив підсистем та функціональних задач.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З цією метою введемо такі типи припустимих областей задач при- йняття рішень в СППР: 0( ) p D z — область, що визначає область ви- бору припустимих рішень (дій) на підставі власних можливостей від- повідної підсистеми в p -й функціональній задачі при виборі власних рішень p x з урахуванням вектора p z ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0( ) p D s — область припустимих рішень p x p -ї функціональної задачі, що визначається вектором ps ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0( ) p D u — область припустимих рішень p x , що описує директивну об- ласть, утворену вектором p u .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Як відомо, більшість задач прийняття рішення розв’язується при врахуванні деякої множини 1, J M = характеристик оцінки рішення p x , яке може визначитися в кількісній або якісній шкалі за допо- могою множини критеріальних функцій { ( ), } p i f f x i J = ∈ , при цьому критерії можуть носити як кількісний, так і якісний характер.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перш за все припустимо, що 0 0 0 ( ) ( ) ( ) p p p D z D s D u ≠ ∅ \uf049 \uf049 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В дано- му випадку ми зможемо розв’язати задачу та знайти p x у врахуван- ням множини критеріальних функцій f та припустимих областей.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо 0 0 0 ( ) ( ) ( ) p p p D z D s D u = ∅ \uf049 \uf049 та 0 0 ( ) ( ) p p D z D u = ∅ \uf049 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' то об- ласть 0( ) p D u не має припустимих рішень з областю 0( ) p D z з вра- хуванням впливу інших задач,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' і нам необхідно змінювати область 0( ) p D z за рахунок можливостей задачі з метою одержання сумісності з областю 0( ) p D u або у разі неможливості досягнення сумісності фор- мувати обмеження на вектор p u з метою інформування більш пріо- ритетної задачі про неможливість розв’язання задачі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 17 Якщо 0 0 0 ( ) ( ) ( ) p p p D z D s D u = ∅ \uf049 \uf049 і 0 0 ( ) ( ) p p D z D u ≠ ∅ \uf049 , то область 0( ) p D s не має припустимих рішень з областю 0( ) p D z з урахуванням директивного впливу, і нам необхідно формувати вектор ps для мно- жини , p p J J I ∈ з метою реалізації процедури узгодження рішень взаємопов’язаних задач.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зазначимо, що модель задачі, метод та алгоритм розв’язання за- дач можуть не тільки бути з області математичного програмування, а і описуватися в області інформаційних та логічних моделей.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У випадку реалізації стратегії створення формалізований опис де якої локальної задачі, що формулюється як задача математично- го програмування та розв’язується в системі підтримки прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оскільки будь-яка математична модель задачі прийняття рішення включає декілька критеріїв оптимальності і системи об- межень, що описує множину припустимих альтернатив, то всі види впливу на цю модель можуть бути зведені до впливу на критерій і впливу на обмеження.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розглянемо останній з них.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В цьому випад- ку множина обмежень локальної задачі включатиме обмеження, що описують зв’язки з іншими задачами, і обмеження, що описують ло- кальну область припустимих рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розглянемо модель локальної задачі прийняття рішення у багато- рівневій організаційній системі, яка має загальний вигляд: { xi i M C = , 0 X , 1 ( ) i X u − , ( ) i X u , ( ) U x , 1 ( ) i U x + }, де i — індекс зада- чі, що розглядається ( 1, i I M ∈ = ), { ( ) , 1, } xi xi i j C C x extr j J N = → ∈ = — множина оцінок вибору рішення задачі i M ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0 i X — область можливих рішень, що визначається локальними об- меженнями задачі i M (область 0( ) p D z ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 ( ) i X u − — область бажаних рішень, яка визначається обмеження- ми, які називають директивними (область 0( ) p D u );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) i X u — область рішень, яка визначається з урахуванням ком- промісних зв’язків із завданнями, які володіють однаковими з даним завданням пріоритетами взаємодії (область 0( ) p D s );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) U x — область змінних u , яка залежить від рішення x даної за- дачі (вектор ps );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 ( ) i U x + — область змінних, що характеризують вплив даної задачі на пов’язані з нею завдання з меншим пріоритетом взаємодії (вектор p u ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наявність у завданнях прийняття рішення локальних цілей та прі- оритетів взаємодії призводить до різних ситуацій взаємодії між від- 18 повідними завданнями.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ці ситуації визначаються взаємним розташу- ванням областей відносно одна одної.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, процес прийняття рішень може складатися з послі- довності етапів, кожен з яких включає такі елементи: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' визначення рішень локальних задач з урахуванням результатів, отриманих на попередніх етапах;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' узгодження рішень пов’язаних локальних задач.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перший етап полягає в аналізі моделей локальних задач.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо припустимих рішень в локальній задачі не існує, то виникає необхід- ність у цілеспрямованій зміні області 0 i X для виконання директив- них вимог, що визначаються областю 1 ( ) i X u − , де 1 iu − отримано при розв’язанні більш пріоритетних задач.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Така задача корекції 0 i X інтер- претується як задача системної оптимізації [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином рішення локальної задачі 1 ( , , ) i i y x u u − = (локальне припустиме рішення) буде знайдено безпосередньо або буде отри- мано в результаті розв’язання задачі системної оптимізації, тобто 1 0 ( ) i X X u − ≠ ∅ \uf049 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оскільки рішення y визначено без врахування області зв’язків ( ) i X u , то значення параметра u визначені незалежно в кожній із пов’язаних задач і можуть не збігатися.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тоді узгодження рішень по- лягає у знаходженні таких локально допустимих (оптимальних, компромісних) рішень, для яких значення параметрів зв’язку рівні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Можливі підходи до реалізації алгоритмів узгодження рішень по па- раметрах зв’язку наведено в [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У разі відсутності таких узгоджених рішень необхідне корегування моделей пов’язаних задач для досягнення сумісності в просторі па- раметрів u , яка може бути зведена до задачі системної оптимізації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основною проблемою при цьому є вибір напрямку і величини коре- гування областей 0 i X , 1 ( ) i X u − .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Отримане рішення y визначить зна- чення параметра 1 iu + , що характеризує вплив даної задачі на пов’язані з нею задачі з меншим пріоритетом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розглянемо формулювання локальної задачі як задачу лінійного математичного програмування, що розв’язується в системі підтрим- ки прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В цьому випадку множина xi C задається через деяку множина критеріальних функцій 1 , n i ij j j f c x extr i I = = → ∈ ∑ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' об- ласть директивних вимог g D щодо функціонування системи управ- ління визначається множиною ( ) 0 { : , 1, }, g g j j D x x x j n = = = або областю 19 { : , 1, }, g b u j j j P x x x x j n = ≤ ≤ = або областю 0 2 1 { : , };' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' n g g ij j i j D x a x u i Q = = ≤ ∈ ∑ область припустимих рішень описується множиною 0 0 0 1 { : , , 0, 1, } n ij j i j j D x b x b i Q x j n = = ≤ ∈ ≥ = ∑ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Згідно з методологією системної оптимізації, необхідність у розв’занні задачі системної оптимізації виникає у разі неспільності області директивних вимог g D та області припустимих рішень 0 D .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основна мета алгоритмів системної оптимізації полягає в побудові нової області припустимих рішень відповідно до первинної області 0 D і додаткової обмеженої області варіацій ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ij i b b i Q j n Δ Δ ∈ = па- раметрів ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ij i b b ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' що будується в процесі рішення з урахуванням того,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' узгоджуються директивні вимоги й інтереси даної системи управ- ління g D чи ні,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' в якій існуватимуть рішення із значеннями по всіх критеріальних функціях більшими або рівними значеннями крите- ріїв,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' що задаються вимогами людини,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' що приймає рішення (ЛПР),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' в області директивних вимог g D .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ці алгоритми носять ітераційний характер.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Збіжність процедур в рамках системної оптимізації реалізується через ітераційне відсікання неприпустимих варіантів рішення, при цьому гарантується, що припустимі варіанти не будуть відсікатися.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Що в підсумку дає нам можливість або отримати рішення поставле- ної задачі, або зробити висновок про неможливість розв’язання по- ставленої задачі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перевірка виконання вимог g D в області 0 D проводиться або прямою підстановкою ( ) g x x = в систему обмежень області 0 D при 0 g g D D = або на основі якого-небудь методу лінійного програмуван- ня для областей та у разі порожнього перетину g D і 0 D можливі різ- ні випадки взаєморозташування області g D та області 0 D щодо кри- теріальних функцій, які в загальному випадку можуть бути такими: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Всі точки директивної області g D мають кращі значення за всі- ма критеріями в порівнянні зі значеннями, що досягаються у відпо- відних їм за перевагою точках області 0 D , тобто повне узгодження.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для будь-якої точки з директивної області g D в області припус- тимих рішень 0 D існує точка з кращими значеннями за всіма крите- ріями одночасно, тобто директивні вимоги не узгоджуються з цілями даної системи, що задані набором критеріальних функцій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тільки частину точок директивної області g D дає поліпшення значень за всіма критеріями одночасно, тобто вимоги лише частково узгоджуються з цілями даної системи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У разі виконання другого варіанту ЛПРу потрібно перевизначити область директивних вимог g D , оскільки в області g D не будуть ви- конуватися вимоги до значень критеріальних функцій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З урахуванням інших варіантів розташування, а також з урахуван- ням вигляду директивних областей можна виділити обмеження об- ласті, які перешкоджають спільності й узгодженості рішень з g D і області припустимих рішень 0 D і які називають суттєвими обмежен- нями.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Множину індексів суттєвих обмежень позначимо як 0 Q .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У разі директивної області вигляду 0 g D суттєвими обмеженнями будуть співвідношення, що порушуються при підстановці g x x = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При виділенні суттєвих обмежень можна розглянути випадки з урахуванням заданої множини критеріїв і без урахування цільових функцій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При врахуванні критеріїв після з’ясування реалізованого варі- анту узгодження виділяється множина точок, яку будемо називати областю захоплення і яка апроксимує область g D при реалізації першого варіанту або будується область захоплення g g X D ⊆ (яка містить точки, що мають кращі значення за всіма критеріями одно- часно в порівнянні з розв’язками області 0 D ) при реалізації третьо- го варіанту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=" Якщо ж вирішується задача системної оптимізації без ураху- вання множини критеріальних функцій, то визначення суттєвих обмежень залежить від вибраної ЛПРом області захоплення g X , g g X D ⊆ , яка може описуватися паралелепіпедом або деякою об- ластю або точкою ' ' , g x x D ∈ ." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому задачу системної опти- мізації будемо розв’язувати відносно деякої точки , g g g x x X ∈ , яка є вершиною відповідного багатокутника.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Отримана область захо- плення g X визначить відповідні множину точок і множину індек- сів суттєвих обмежень, щодо яких будемо розв’язувати задачу сис- темної оптимізації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для приналежності заданої області захоплення g X змінній моделі будується система обмежень, що описує область P .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для визначення можливості зміни параметрів моделі задачі для досягнення вимог з 0 D і отже можливості рішення самої задачі сис- 21 темної оптимізації, так і сформованої локальної задачі, вихідної по- будуємо перетин області P варіації параметрів обмежень множини 0 Q і області 0P припустимих варіацій цих параметрів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо 0 P P ≠ ∅ \uf049 , то область зміни параметрів моделі буде обме- жена і це дозволить вирішити задачу побудови нової моделі 1 D , в якій виконуються вимоги з області 0 D .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В цьому випадку необхідно або змінювати чи перевизначити ЛПРом свої вимоги або обмеження 0P .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для корекції області припустимих варіацій 0P можна зокрема по- будувати параллелепіпед, який вписано в область P , на основі якого ЛПР зможе задати або відкорегувати обмеження області 0P , так що 0 P P ≠ ∅ \uf049 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Задача вибору варіацій параметрів , , , 1, ij i b b i Q j n Δ Δ ∈ = при непо- рожньому перетині областей P і 0P зводиться до задачі оптимізації, в якій як критерії вибрані витрати, що пов’язані зі змінами параметрів моделі ( ) , ) C B b Δ Δ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо функцію витрат побудувати неможливо, то задача вибору формується як багатокритеріальна задача, в якій кожен параметр ви- ступає як окремий критерій і залежно від фізичної суті може макси- мізуватися або мінімізуватися.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, нова область допустимих рішень згідно з умовами побудови в новій області 1 D , забезпечується здійснимість вимог за- дачі і існують розв’язки зі значеннями критеріїв не гірше бажаних.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Умови розв’язання задачі системної оптимізації дозволяють алго- ритму сходитися до відповідного ефективного рішення задачі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Цей процес ітераційний.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Збіжність процедур у рамках системної оптимі- зації реалізується через ітераційне відсікання недопустимих варіантів рішення, при цьому гарантується, що допустимі варіанти не будуть відсікатися.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це в підсумку дає нам можливість отримання рішення поставленого завдання або дає можливість зробити висновок про не- можливість вибору варіанту інвестиційного проекту або неможли- вість реалізувати даний проект.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У разі реалізації стратегії адаптація та інтеграції можна викорис- тати апарат прецедентів, який допомагає визначити рішення для по- точної ситуації на основі прецедентів, які вже мали місце у минуло- му при розв’язанні подібних задач.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В загальному випадку прецедент може включати такі компоненти: опис задачі (проблемної ситуації);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' рішення задачі (діагноз із проблемної ситуації і рекомендації ЛПР), 22 результат (або прогноз) застосування рішення, результат використан- ня знайденого рішення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До основних переваг технології прецедентів можна віднести мож- ливість безпосередньо використовувати досвід, накопичений систе- мою, без інтенсивного залучення експертів в тій чи іншій предметній області, а також можливість виключення отримання помилкового рі- шення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Істотними недоліками цього підходу є зниження продуктив- ності системи при великій кількості прецедентів у базі прецедентів і неможливість отримання рішення задач, для яких немає прецедентів у бібліотеці прецедентів (БП) системи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В цьому випадку процес підтримки прийняття рішень формаль- но представляється як: { , }, , ( ), СППР KB Rule Case M S M Dec =< > , де { , } KB Rule Case — база знань, що містить множину правил Rule та мно- жину Case прецедентів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 1 2 , ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', , n Case x x x Sol = , де 1 2 , ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', n x x x — пара- метри ситуації, яка описує даний прецедент, N — кількість параметрів для опису прецедента, а 1 2 , ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', n X X X — області допустимих значень відповідних параметрів, Sol — рішення (діагноз, рекомендації ЛПР).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' { } i Rule R = , де iR — i-те правило, 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', i I = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=" Правила iR Rule ∈ визна- чаються в такій формі: ' 1 1 1 , , ,." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', , ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' , , , n n m b A a U a U P P b U S S < > , де ia A ∈ є передумови проблемної ситуації (ПС);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' i U U ∈ — необхідні оцінки міри упевненості в передумовах;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' V P P ∈ є предикати, 1, 0 V m ≥ ≥ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' b B ∈ — укладення c оцінкою міри упевненості b U ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' S — початкова проблемна ситуація (ПС);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=" 'S — проблемна ситуація, що виникає в результаті прийнятого рішення." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 { ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', } N M M M = — множина моде- лей, що реалізують функції процесу прийняття рішень;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) S M — мо- дуль, що реалізує функцію вибору необхідної моделі (моделей) для даної задачі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Dec — модуль формування рішень на основі бази знань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це дозволяє реалізувати званий цикл прецедентів або цикл навчання за прецедентами, що включає такі етапи: витягання найбільш відповідного (подібного) прецедента (пре- цедентів) для проблемної ситуації, що склалася, з бібліотеки преце- дентів (БП);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' повторне використання витягнутого прецедента для спроби розв’язання поточної проблеми;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' перегляд та адаптація в разі потреби отриманого рішення відпо- відно до поточної проблеми;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' збереження знову прийнятого рішення як частини нового пре- цеденту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 23 Пошук рішення на основі прецедентів полягає в визначенні міри схожості поточної ситуації з ситуаціями прецедентів з БП.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому враховуються ваги параметрів для ситуацій з БП, задані експертом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Міра схожості залежить від близькості поточної ситуації до ситуації прецедента і визначається за допомогою алгоритму пошуку найближ- чого сусіда за допомогою простого зіставлення поточної ситуації з си- туацією прецедента (кожен параметр для опису ситуацій з БП розгля- дається як одна з координат).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В результаті визначається відстань D між поточною ситуацією і ситуацією прецедента і максимальна від- стань max D на основі меж діапазонів параметрів для ситуацій преце- дентів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Потім обчислюється значення міри схожості max 1 / sim D D = − .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для цього можна використати метод найближчого сусіда (найближ- чих сусідів) (К найближчих сусідів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Необхідно враховувати, що міркування на основі прецедентів може не привести до необхідного рішення проблемної ситуації, що виникла, наприклад, у разі відсутності подібної (аналогічної) ситу- ації у БП.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ця проблема може бути розв’язана через можливість по- повнення БП безпосередньо в процесі міркування (висновку).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це може включати: визначення існуючої практики, яка є прийнятою та реалізованою;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' використання часткової стратегії автоматизації узго- дження розрізненої інформації з декількох джерел інформації на основі математичних моделей та експертних систем;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' використання стратегічної мети усунення невизначеності, неповноти інформації та врахування суб’єктивної експертної інформації від декількох джерел інформації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Як показує вищепредставлене, процес прийняття рішень склада- ється з декількох етапів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На кожному етапі розв’язуються свої зада- чі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Задача приймає вхідні дані і виробляє певний результат.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вхідни- ми для задач є ситуації, кожна з яких представляє собою множину пов’язаних відношеннями об’єктів предметної області.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виділяється клас проблемних ситуацій, тобто ситуацій, в яких значення атрибутів деяких об’єктів виходять за область нормальних значень або критич- но близько підходять до її кордонів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Результатом рішення задачі може бути повідомлення, ситуація або задача.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Повідомлення — це оста- точний результат рішення задачі, який користувач приймає до відо- ма.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ситуація — це результат, який може бути підданий подальшому аналізу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ситуація може являти собою наслідки прийнятих рішень або ж початкові рішення, які повинні привести до бажаних результатів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо в якості розв’язання отримано кілька ситуацій — альтернатив, 24 то може бути згенерована нова задача, яка буде оцінювати отримані альтернативи і вибирати з них найбільш прийнятні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для розв’язання задач використовуються різні методи підтримки прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Деякі з них можуть мати комп’ютерну реалізацію, тобто можуть бути реалізовані в деякому програмному модулі, який, у свою чергу, інтер- претується тим чи іншим розв’язувачем.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інші методи можуть не мати програмної підтримки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В цьому випадку використовується текстовий (можливо, формалізований) опис методу, а в якості розв’язувача, ін- терпретуючого такий модуль, виступає людина — учасник процесу прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Учасниками можуть бути ЛПРи, власники про- блеми, різні активні групи, експерти та фахівці з прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, представлення знань про розв’язання задачі за до- помогою технології системної оптимізації необхідно описати: моделі, що описують вихідне завдання та виникають у процесі реалізації технології системної оптимізації;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' методи та алгоритми розв’язання сформованих моделей;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' процес розв’язання задачі за допомогою технології системної оптимізації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Цей процес реалізується через певні етапи [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, для реалізації системної оптимізації необхідно опи- сати та використовувати підходи та засоби для: формування рішень з урахуванням даних.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тут розглядається об- ласть деталізованих даних,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' тобто пошук інформації з використанням засобів СУБД як в окремих базах даних,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' так у загальному сховищі даних,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' область агрегованих показників,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' тобто збір у сховище даних відповідної інформації,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' її узагальнення та агрегація,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' гіперкубічне по- дання та багатовимірний аналіз (оперативна аналітична обробка да- них (OLAP)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' сфера закономірностей,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' тобто пошук функціональних та логічних закономірностей у накопиченій інформації,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' побудова моделей та правил,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' які пояснюють знайдені аномалії та/або прогно- зують розвиток деяких процесів (інтелектуальна обробка даних (Data Mining));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' формування рішень на основі логічних моделей та правил (при- йняття рішень на основі продукційних моделей, семантичних мереж тощо);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' формування рішень на основі математичних моделей (оптимі- зація через використання аналітичних формул, оптимізація через ал- горитми, оптимізація вибору з багатьох альтернатив тощо);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' формування рішень на основі типових рішень або прецедентів (типові рішення та моделі, прецеденти проблемних ситуацій).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 25 При цьому необхідно розглядати різні аспекти прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такими можуть бути,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' наприклад,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' поведінковий аспект (описує ситуа- ції прийняття рішень та порядок,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' в якому розглядаються завдання та в якому виконуються відповідні дії),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' організаційний аспект (описує структуру середовища прийняття рішень,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ресурси та засоби та визначає організаційну структуру,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' в якій розв’язання задачі виконується або буде виконуватися,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' і відносини між елементами структури),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' інформаційний аспект (описує інформацію,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' яка використовується при прийнятті рі- шень,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' як вона представляється та як вона може застосовуватись).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В рамках такого представлення прийняття рішень необхідно іден- тифікувати модель предметної області;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' визначити взаємодії між за- дачами та відповідними моделями на підставі відносин пріоритетів взаємодії;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' визначити усі види впливу даної задачі (моделі) на інші задачі (моделі);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' визначити всі можливі випадки активізації даної за- дачі (моделі) як для локальних ситуацій прийняття рішення, так і для розподіленого прийняття рішень;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' визначити можливі схеми реаліза- ції даної задачі (моделі) в відповідній предметній області;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' визначити множини даних, на яких реалізується дана задача (модель) і які опи- сують результат розв’язання задачі на вибраній моделі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому прийняття рішень будемо описувати через три вимі- ри (світи) розуміння процесу прийняття рішень: світ 1: реальний світ (прикладний світ), світ 2: формальний світ (формальні моделі, мето- ди, алгоритми тощо) та світ 3: світ програмного забезпечення (про- грамні засоби, платформи тощо).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При реалізації прийняття рішень в розрізі моделей реалізується ефект тріади: за допомогою сприйняття та концептуалізації побуду- вати модель прикладної області (модель представляється з точки зору опису (об’єкти,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' процеси,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' відношення,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' властивості та характеристики) та з точки зору діяльності (визначення процесів,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' побудова концепту- альної моделі) і за допомогою знаків або мови,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' зробити формалізацію відносин (вплив,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' регулювання,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' управління) та створити формалізо- вану модель,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' наприклад,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' символьну модель (модель представляється з точки зору опису,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' як математична модель,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' та з точки зору діяльнос- ті через визначення структури моделі,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' оцінку параметрів,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' достовірні властивості та характеристики).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зв’язок між формальною моделлю та моделлю програмного забезпечення (модель обчислювань, програмні модулі та визначення програмної концепції, узгодження програмних модулів) визначає методи та алгоритми, які необхідні для розв’язання формальної системи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 26 Основою для використання знань та реалізації процесу прийняття рішень за допомогою системної оптимізації, представлення відпо- відного інтегрованого середовища прийняття рішень, взаємодії між складовими частинами середовища, опису предметних областей та розв’язання задач в такому середовищі є онтологія, як засіб явного розуміння та представлення областей та процесів прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Під онтологією [7] будемо розуміти систему, що описує структу- ру певної проблемної області або множини проблемних областей та складається з множини класів понять, пов’язаних відношеннями, їх визначень та аксіом, що задають обмеження на інтерпретацію цих понять в рамках даної проблемної області або їх множини.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Така онтологія [8] базується на взаємопов’язаній множині онто- логій,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' що представляє собою багаторівневу асоціативну структуру,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' що включає метаонтологію або онтологію верхнього рівня,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' базову онтологію,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' контекстну онтологію,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' множина онтологій представ- лення процесу прийняття рішень,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' що включає представлення задач та їх розв’язання на рівні проблемної області,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' онтологій предмет- но-формального та формального представлення та реалізацій цього процесу,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' онтологію реалізацій,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' що включає опис програмного забез- печення для підтримки прийняття рішень,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' онтологію представлен- ня користувача та взаємодії з ним,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' модель машини виведення,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' що асоціюється з побудованою онтологічною моделлю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Мета онтоло- гії полягає у забезпеченні інтегрованої концептуальної основи для того, щоб вона була визначена, зрозуміла, структурована та пред- ставляла явища при прийнятті рішень за допомогою систем під- тримки прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Метаонтологія розглядається як засіб інтеграції різних складових реалізації процесу підтримки прийняття рішень та найбільш загального його опису.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сутностями метаонто- логії є такі поняття, як об’єкт, атрибут, значення, відношення і т.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' п.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', наприклад, описувати метаінформацію на основі моделі Захмана.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Мета базової онтології полягає у забезпеченні ключових понять та конструкцій для того, щоб визначити, зрозуміти, структурувати та представити основні принципи області прийняття рішень, в рамках якої функціонує СППР.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекстна онтологія реалізує контекстну систему, що допомагає розпізнати, зрозуміти та представити при- йняття рішень через контексти та в межах контекстів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Множина он- тологій представлення процесу прийняття рішень розглядається як компонента бази знань при роботі з конкретною проблемною об- ластю та є, у свою чергу, шаблоном для побудови динамічної ком- 27 поненти бази знань, що змінюється при переході від дослідження однієї конкретної задачі до іншої.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Онтологія реалізацій, що включає опис програмного забезпечення для підтримки прийняття рішень: функціональний, поведінковий, організаційний та інформаційний.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому опис ґрунтується на функціональних (що робить про- грамне забезпечення) та нефункціональних вимогах (обмеження використання).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Онтологія представлення користувача та взаємодії з ним реалізує формування моделі сценарію та компонентів діалогу (автоматично або автоматизовано).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Реалізація онтологічного представлення перш за все базується на визначенні та взаємодії понять та термінів для опису предметних областей та розв’язання певних задач у відповідних предметних об- ластях.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Будемо розглядати проблемну область прийняття рішень як множину предметних областей та задач, що розв’язуються в них.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таке онтологічне представлення складається з консолідованого пред- ставлення певних проблемних областей, через які прийняття рішень може бути представлене та визначене на основі вибраної точки зору (стан проблеми або проблемної області, поведінка проблеми або про- блемної області та розв’язання проблеми).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поняття та терміни, що стосується проблемної області, включа- ють такі поняття: об’єкт, задача (проблема), модель (формулювання проблеми), методологія (сценарій, метод, алгоритм), система харак- теристик (властивостей), що їх описують, значення, відношення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Об’єкт — термін або поняття (сутність), що визначається семантич- ним представленням та з яким пов’язані відповідні властивості, ре- алізується певний зв’язок з іншим терміном(ами), з задачами та мо- делями, що ініціювали присутність цього терміна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Задача — кожен екземпляр цього класу визначає задачу для конкретного об’єкта, має ідентифікатор, вказує на об’єкт та термін або властивість та значення властивості, що ініціюють цю задачу тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Модель — кожен екземп- ляр цього класу визначає опис об’єкта на певній мові, зокрема фор- малізованій, що складений з метою вивчення його властивостей.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До такого опису вносяться, наприклад, чинники, що впливають на вибір моделі, такі як період часу, змінні рішення, критерії оцінки, числові параметри та відношення, включаючи математичні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Моделі інтегру- ються в класи моделей.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Є кілька класів моделей для прийняття рішень, які, у свою чергу, можуть бути розв’язані декількома альтернативни- ми методами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кожен клас моделі краще підходить для представлення певних видів процесів прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Властивість — певна ознака, 28 що характеризує термін, має властивості, аналогічні класу термінів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Окрім цього він вказує на екземпляри класу значень, які визначають його в задачах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Значення — визначають дані, що використовуються при пошуку в семантичному представленні, вказують на задачу та на властивість, рішенням якої воно є.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відношення — визначає зв’язок між двома термінами та вказує на терміни або властивості та об’єкти знань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інші терміни визначають ті поняття,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' що пов’язані з системою характеристик (структура,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' обмеження,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' середовище,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' контекст,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' рівень узагальнення тощо),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' проблемою (предмет проблеми,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' проблема верх- нього рівня,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' проблема нижнього рівня,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' методи (сценарії) рішення,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' складність проблеми,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' атомна проблема,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' складена проблема,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' опис проблеми,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' проблемна тема,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' контекст проблеми,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' власність проблеми,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' відповідальність за проблему,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' оцінка проблеми,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' проблемна область,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' вплив на проблеми,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' вплив з проблем,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ініціювання,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' час,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' взаємодія,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ак- тор тощо),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' моделлю (мета,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' обмеження,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' контекст,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' проблемна область,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' проблема,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' методологія,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' об’єкти,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' вхідні параметри,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' вихідні параметри,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' інші параметри,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' умови,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' тригери (який випадок запускає),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' передумови (що на початку),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' післяумови (що в кінці) та пов’язані знанням про- блемної області (область знання,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' функціональні знання,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' структурне знання,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' знання обробки тощо).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поняття з прийняття рішень, вклю- чаючи системну оптимізацію, пов’язані між собою відношеннями класифікації, узагальнення, агрегації та групування, асоціативними відношеннями, визначення яких здійснюється через представлення проблемної та предметних областей.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В рамках такого підходу прийняття рішень базується на представ- ленні багаторівневої системи управління та розглядається через один або декілька взаємопов’язаних контекстів (модель певного контек- сту), в яких хтось (актор) щось робить (дія) з деяких причин (цілі) для когось (об’єкт) за допомоги деякого (об’єкта), десь (місце знахо- дження) та іноді (час).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Представлення контексту складається зі зміс- ту, що базується на онтологіях, які охоплюють певну частину моделі контексту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для опису контексту необхідно знайти поняття та конструкції, які визначають природу, структуру та представлення процесу формуван- ня та прийняття рішень і відповідних складових областей, які опису- ють такий процес.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекст повинен бути описаний стандартизова- ним способом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Представлення знань процесу прийняття рішень має підтримувати операції, що необхідні для представлення контексту та управління ним.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 29 Контекст будемо розглядати як концептуальну або інтелектуальну конструкцію, яка складається з понять в межах відповідних контекст- них областей та допомагає нам зрозуміти, проаналізувати та викорис- товувати природу, значення та ефекти через елементарні сутності у відповідному середовищі або обставинах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Також контекст представ- ляє ціле, що визначається через певні сутності, які є важливими для даного розгляду.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це дозволяє розглядати контекст як будь-яку інформацію, яка може бути використана для опису ситуації, в якій щось існує чи від- бувається та яка може допомогти пояснити ситуацію та визначити напрямок її розв’язання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ця ситуація залежить від знань, світогля- ду, практики та обставин, які можуть бути використані для побудови «нескінченної і частково відомої сукупності припущень» [8], які ви- значають інтегральне розв’язання проблем та які забезпечують умови для створення, підтримки та застосування знань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому, по-перше, контекст є невід’ємною властивістю випад- ків взаємодії, а не є стабільним об’єктивним набором функцій, які зовнішньо характеризують діяльність.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекст залишається кри- тично важливим для розуміння, контекстуалізації та нерозуміння форм діяльності та інформації, але саме в контексті природи необхід- но постійно домовлятися та переглядати його.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' По-друге, ці контекст- ні властивості беруть на себе їх значення або релевантність через їх зв’язок з формами практики, тобто займаються діями навколо арте- фактів та інформації, яка робить ці артефакти значущими та актуаль- ними для людей.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тоді сенс технології не може бути відірваний від спо- собів, яким люди мають його використовувати.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такі моделі контексту мають давати змогу розв’язувати проблеми, що характеризуються контекстно-залежними властивостями: неоднорідність та мобільність;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' відносини та залежності;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' своєчасність;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' недосконалість;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' міркування;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' відповідність формалізму прийняття рішень;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ефективне контекстне забезпечення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розгляд використання контексту в проблемних областях допо- магає виявити всі семантичні відношення, надати всю необхідну ін- формацію та правильні інтерпретації для прийняття рішень, оскільки використання інформації в процесі прийняття рішень, як правило, 30 відбувається в контексті складної структури процесу прийняття рі- шень, який часто формується за допомогою ряду чинників.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Як показано в [10], контекстна система допомагає розпізнати, зрозуміти та подати відповідні елементи прийняття рішень як кон- тексти та в рамках контекстів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекстом є будь-яка інформація, яка може бути використана або характеризує відповідну проблемну область.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекст є важливим фактором у процесі прийняття рішень, до- помагає визначити, яка інформація необхідна для підтримки при- йняття рішень та представляється множиною взаємопов’язаних ком- понентів [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В [12] визначено, що контекст можна розглялати як представлен- ня проблеми, беручи до уваги такі властивості контексту [12;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13]: контекст — це форма інформації, тобто контекст розглядається як те, що може бути відомо, представлено та закодовано;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' контекст є вичерпним, тобто вважається можливим сказати, що заздалегідь визначається як контекст для конкретного використання;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' контекст є стабільним, тобто, коли контекст може відрізнятися від застосування до програми, він не відрізняється від екземпляра до примірника взаємодії з додатком;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' контекст та діяльність є розділеними, тобто контекст викорис- товується для опису особливостей середовища, в межах якого здій- снюється діяльність, але елементи діяльності не належать до самого контексту та не розглядаються як контексти.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основним недоліком багатьох існуючих систем, що базуються на контексті, є неможливість реалізації динамічного опису контексту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Існуючі контекстні моделі є «статичними» або обмеженими.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для того, щоб додати до властивостей контексту динамізму, буде- мо розглядати контекст, який можна охарактеризувати як: виникає через простір і час;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' причинно-наслідковий процес прийняття рішень;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' визначений, але не обов’язково передбачуваний;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' семантична інтер- претація відносин між актором, завданням або діяльністю та сере- довищем, в яких вони знаходяться;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' обмежувальні критерії, за допо- могою яких можна моделювати цілеспрямовану діяльність.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Обмеження контексту також зменшує складність часу обчислення потенційних рішень для діяльності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ми використовуємо такі обме- жувальні критерії: наявність даних або відсутність;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' повнота;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' набори включення / виключення;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' часові межі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' просторові межі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' область ді- яльності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 31 Контекст розглядається як динамічні відношення між актором, цілеспрямованим завданням та оточенням, в яких вони знаходяться.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такий розгляд дозволяє контекстним зв’язкам виникати, змінювати- ся або зникати через час і простір та охоплювати складність просторо- во-часової динаміки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ми застосовуємо таке представлення контексту, оскільки воно дозволяє нам моделювати контекстну динаміку таким чином, що виникає в процесі розв’язання задачі, а не тільки вибира- ється на етапі формулювання проблеми та процесу розв’язання зада- чі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Модель контексту передбачає суб’єктивний погляд на проблемні рішення ситуації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, ми моделюємо контекст з практич- ної точки зору та представляємо структуру контексту, яка успадкову- ється від традиційних моделей контексту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такий погляд використовує позицію щодо властивостей контек- сту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' По-перше, замість того, щоб розглядати контекст як інформа- цію, він стверджує, що контекстуальність є реляційною властивіс- тю, яка визначається між об’єктами, діями, задачами, середовищем і т.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' д.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тобто щось є або не є контекстом;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Навпаки, вона може або не може бути контекстуально актуальною для розв’язання певної зада- чі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' По-друге, можна стверджувати, що множина контекстних функ- цій визначається динамічно.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' По-третє, можна стверджувати, що контекст є особливим для кожного випадку проблеми, задачі, діяль- ності, дії тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекст — це властивість, що пов’язана з певними налаштуваннями, окремими випадками проблем, задач, середовищ, дій та особами, що беруть участь у процесі прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' По- четверте, замість того, щоб розглядати контекст та контент як два відокремленими об’єкта, можна стверджувати, що контекст вини- кає в результаті діяльності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Іншими словами, контекст необхідно розглядати не тільки як проблему представлення, а й як проблему взаємодії.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оскільки контекст розглядається як множина динамічних відно- шень між актором, цілеспрямованою діяльністю, ресурсами, мож- ливостями, часом, розташуванням та середовищем, в яких вони зна- ходяться або використовуються.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це дозволяє контекстним зв’язкам виникати, змінюватися або зникати через час і простір та охоплюва- ти складність просторово-часової динаміки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ми застосовуємо таке представлення контексту, оскільки воно дозволяє нам моделювати контекстну динаміку таким чином, що виникає в процесі розв’язання задачі, а не тільки вибирається на етапі формулювання проблеми та процесу розв’язання задачі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 32 Для опису контексту необхідно з’ясувати поняття та конструкції, які визначають природу, структуру та представлення процесу форму- вання та прийняття рішень і відповідних складових областей, які опи- сують такий процес.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекст має бути описаний стандартизованим способом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Представлення знань процесу прийняття рішень повинне підтримувати операції, що необхідні для представлення контексту та управління ним.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для нагромадження, інтерпретації, подання та управління кон- текстом пропонується загальна модель управління контекстом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекст на онтологія складається з трьох основних компонентів: контексту семантики (онтологія), даних екземплярів контексту та контексту, що пов’язаний з правилами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Онтологія представляє се- мантики, концепти і відношення в рамках контексту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Така онтоло- гія утворюється в результаті злиття онтології, що описує абстрактні, конкретні контексти та контексти реалізації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Правила є аксіомами виведення, які використовують контекстно-орієнтовані системи для отримання рішення та міркування щодо дій, які необхідно виконати.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ці правила мають два джерела;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' правила, які явно визначені, та прави- ла, які неявно отримані самою системою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Складність в реалізації прийняття рішень полягає в необхідності синтезу різних точок зору зацікавлених сторін на проблему, управлін- ня великою кількістю інформації, що стосується завдання, та розу- міння рішень, які визначили такий розгляд задачі прийняття рішень та самого процесу прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Крім того, знання, пов’язані з проблемою, розподіляються серед різних зацікавлених сторонім як власників проблеми та ЛПРами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це визначає необхідність розгляду процесів прийняття рішень на основі представлення багаторівневої системи управління та прийнят- тя рішення в ній через модель певного контексту [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекстна онтологія cntxt O з урахуванням результатів [10] вклю- чає компонентні онтології: онтологія контексту, онтологія шарів і онтологія точок зору допомагають розпізнати, зрозуміти та пред- ставити відповідні явища як контексти та в межах контекстів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За- гальна мета контекстної онтології полягає в тому, щоб визначити поняття та конструкції, які допомагають нам зрозуміти природу, цілі та значення окремих сутностей.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, замість того, щоб розглядати проблемну область як базову структуру сутностей, он- тологія контексту визначає розгляд сутності в контексті від спеці- альних ролей або значень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Така онтологія представляється у вигляді 33 взаємопов’язаної множини онтологій, що є асоціативною структу- рою такого вигляду (рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1): , , cntxt ctx layer aspect O O O O = , де ctx O — онтологія контексту;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' layer O — онтологія шарів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' aspect O — онто- логія аспектів (точок зору).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Онтологія Онтологія аспектів (точок зору) Онтологія контексту Контекстна область Контекст Система аспектів Аспект Контекстні Області Вимір Онтологія шарів Шар Система шарів Аспекти Онтологія Контекстні Області Аспекти Онтологія Контекстні Області Аспекти області області області Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Складові контекстної онтології у взаємозв’язках Онтологія ctx O визначає такі контекстні області: область мети/ результату, область актора, область процесу/дії, область об’єкта, об- ласть середовища, область можливостей, область засобів, область представлення, область розташування та область часу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекст ви- значається як конструкція, яка складається з понять в межах десяти контекстних областей.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кожна контекстна область визначається від- повідними поняттями та конструкціями.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Онтологія контексту ctx O 34 містить деталізовані поняття та конструкції контекстних областей та міжобласних відношень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Онтологія шарів layer O підтримує структуру прийняття рішень та описує відношення на загальному рівні складових прийняття рішень та їх реалізацію на відповідних рівнях: проблема, модель, метод та ре- алізація в рамках системи результатів, системи об’єктів, системи ви- користання та системи управління.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Онтологія шарів layer O забезпечує поняття та конструкції для розуміння та структуризації прийняття рішень, особливо через поняття СППР, системи об’єктів та системи використання та також служить концептуальною основою для того, щоб структурувати прийняття рішень за чотирма шарами (реалізація, метод, модель та проблема).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Онтологія аспектів (точок зору) aspect O отримується з онтології ша- рів та онтології контексту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Онтологія aspect O підтримує множину ви- значених аспектів розгляду для конкретного представлення процесу прийняття рішень в СППР та структурування сприйняття складових прийняття рішень, зокрема з системної, концептуальної, функціо- нальної, інформаційної та реалізаційної точок зору.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ієрархічна організація, формальний характер, стандартизова- ність, підтримка ефективної аргументації, підтримка різних рівнів абстракції та взаємодій є одними з головних особливостей контекст- ної онтології.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому контекст розглядається на абстрактному, конкретному та реалізаційному рівнях [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Абстрактний контекст є онтологічною моделлю багаторівневої системи, побудованої на підставі інтегра- ції знань прикладних проблемних областей, що розглядаються при функціонуванні системи та релевантні конкретній задачі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Конкрет- ний контекст є представленням певного абстрактного контексту для конкретної задачі в відповідності з існуючими даними та визначе- ними вимогами до процесу прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекст реалізації є представленням кожного конкретного контексту в рамках існуючих реалізацій, зокрема програмного забезпечення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На підставі виявлених властивостей контексту та задач, що ви- никають при використанні контексту, сформульовані вимоги до управління контекстом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекст повинен бути описаний стан- дартизованими способами, що забезпечують незалежність способу представлення від платформи, модель представлення знань повин- на підтримувати операції, необхідні для представлення контексту та управління ним.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекст має надавати релевантну, реальну та 35 доступну інформацію для розв’язання конкретної задачі або для ро- зуміння поточної ситуації, що включається в контекст, інформація повинна містити безпосередньо одержувані дані, історію отриман- ня цих даних і знання, які на даний момент відомі взаємодіючим об’єктам.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Будемо розглядати контекст як конструкцію, що складається з понять в межах відповідних контекстних областей та описується онтологією контексту через таку структуру контекстних областей [14]: , , , , , , , , , AR A PA O E ctx ctx ctx ctx ctx ctx F Fclt R Plc T ctx ctx ctx ctx ctx O O O O O O O O O O O = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На загальному рівні ctx O описується контекстними областями: AR ctx O — мета/результат, A ctx O — актор, PA ctx O — процес/дія, O ctx O — об’єкт, E ctx O — середовище, F ctx O — можливості, Fclt ctx O — засоби, R ctx O — представлення, Plc ctx O — розташування, T ctx O — час.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для показу контекстних областей будемо використовувати класи об’єктів, відношень та атрибутів, що дає можливість представляти їх як семантичні аспекти, де семантика умов та відношень між ними визначені явним чином (роблячи кожен аспект формальною онтоло- гією).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Використання таких категорій дозволяє зробити формалізацію таких аспектів в логіці опису (дескрипційна логіка) (DL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекстні поняття взаємозв’язані через контекстні відношен- ня, включаючи внутрішньобласні, міжобласні та міжконтекстні відношення, тобто такі відношення включають не тільки відно- шення між компонентами однієї області, а й відношення між ін- шими контекстами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такі поняття та конструкції необхідні для того, щоб визначити, зрозуміти, структурувати та представити сутності як контексти та/або в межах контекстів, щоб зрозуміти природу, цілі та значення відповідних сутностей задач та процесу прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для розв’язання будь-якої задачі необхідно описати процес при- йняття рішень, який ґрунтується на онтології контекстів за спеціалі- зацією.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це будемо реалізовувати через онтологію шарів w layer O .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Онтологія шарів допомагає розпізнати, зрозуміти та представити структуру прийняття рішень на основі контекстів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Онтологія шарів описує відношення складових прийняття рішень на загальному рів- ні та їх реалізацію на відповідних рівнях: проблема, модель, метод та 36 реалізація в рамках системи реалізації, системи об’єктів, системи ви- користання та системи управління.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ми визначаємо онтологію шарів, яка забезпечує поняття та кон- струкції, щоб визначити, зрозуміти, структурувати та представити статичні та динамічні особливості представлення процесу прийняття рішень в розрізі чотирьох шарів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' , w s layer layer layer O O O = — онтологія шарів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' w layer O містить поняття та конструкції, які пов’язані з процесом прийняття рішень в ціло- му.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' s layer O представляє процес прийняття рішень структуровано та пов’язано з визначеною системою шарів w layer O .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ми будемо розрізняти , , , w w w w w layer layer layer layer layer O Prblm Mdl Mth Rlztn = як систему з чотирьох шарів: проблема, модель, метод та реалізація.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Роз- глянемо деякі з них.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В будь-якому контексті, що охоплює розв’язання задач, людина використовує конструкції, які можуть допомогти ви- значити, проаналізувати, розробити та реалізувати розв’язання про- блеми.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поняття та конструкції w layer O отримуються з базової онтології [15], онтології контексту [14], онтології шару s layer O та онтології точок зору та взаємодіють з онтологіями предметно-формального та формаль- ного представлення, онтологією реалізацій, що включає опис про- грамного забезпечення для підтримки прийняття рішень, онтологією представлення користувача та взаємодії з ним.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Шар , Pr, w prb layer Prblm Level View Rel = забезпечує поняття та кон- струкції для того, щоб визначити, зрозуміти, структурувати і пред- ставити сутності з точки зору проблеми в межах множини проблем СППР, що можуть бути розв’язані в рамках системи прийняття рі- шень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекст проблеми (задачі) пов’язаний з контекстами моде- лі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поняття та конструкції w layer Prblm отримуються з базової онтології [15], онтології контексту [14], онтології шару s layer O та онтології точок зору та взаємодіють з онтологіями предметно-формального та фор- мального представлення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекст проблеми пов’язаний з контек- стами моделі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Іншим шаром є моделі, що описує онтологія w layer Mdl : , , w mdl layer Mdl Level ViewP Rel = , яка забезпечує поняття та конструк- ції для того, щоб визначити, зрозуміти, структурувати і представити сутності з точки зору моделей в межах моделі системи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Будемо виді- ляти такі основні точки зору до поняття моделі: w layer Mdl розглядається з системної, концептуальної та реалізаційної точок зору.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визначен- 37 ня моделі має завжди висувати на перший план аспекти з цих трьох точок зору.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Модель будемо розглядати як сутність, що використову- ється, щоб допомогти або дозволити розуміння, комунікацію, аналіз, розробку та/або виконання деякої іншої сутності, до якої звертається модель.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Модель будемо представляти в одній з трьох форм, а саме як концептуальна конструкція (опис), як вираз на певній мові або як ре- алізація.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекст моделі пов’язаний з контекстами методу та кон- текстами проблеми.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наступним шаром є методи, які описуються через онтологію w layer Mth .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Знання методів w layer Mth складається з чотирьох компонентів: знання процесу виконання методу, знання проблемної області, зна- ння технологій реалізації та знання поведінки користувача.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Знан ня процесу виконання означає знання, які стосуються виконання мето- ду.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Знання проблемної області означає знання, яке стосується реаліза- ції прийняття рішень, її системи використання та її системи об’єктів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В кожній проблемній області є власні специфіки, які необхідні, щоб знати та виконати метод.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Знання технології означає знання, яке сто- сується пошуку, використання та налаштування апаратного та про- грамного забезпечення для прийняття рішень у визначеній задачі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Знання поведінки користувача означає знання, що визначають осо- бливості проблем людини та її поведінки, а також соціальні та органі- заційні аспекти, які мають бути взяті до уваги в розробці та в організа- ції роботи методу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Метод забезпечує явне знання в формі принципів, процедур і т.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' д.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Методи можна розділити на технології, сценарії, меха- нізми та алгоритми.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Технологія включає мову представлення та про- цедуру.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекст методу пов’язаний з контекстами моделі та контек- стами реалізації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Цільові контексти методу влючають контексти, для яких було визначено модель.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Механізми та алгоритми використовуються процедурою при- йняття рішень, що описуються через шар реалізації w layer Rlztn : , , w rlztn layer Rlztn Level ViewP Rel = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вони можуть або бути загальними, тобто застосованими до усіх мов, що можуть бути використаними при прийнятті рішень, визначеними, тобто застосованими тільки до особливих мов, або гібридними, тобто з певними частинами, що є за- гальними та визначеними частинами, що є визначеними або присто- совуваними.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекст реалізації пов’язаний з контекстами методу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Щоб включити інформацію і знання та їх використати в різних формах та на різних шарах, будемо розрізняти чотири види систем, які тісно пов’язані з прийняттям рішень: 38 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ті, які описують інформацію та знання, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ті, які пов’язані зі накопиченням, зберіганням, обробкою та за- стосуванням інформації, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ті, які використовують інформацію, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ті, які управляють та можливо змінюються на основі результатів прийняття рішень та використання інформації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином будемо розглядати систему s layer O , що інтегрує сис- тему об’єктів layer So , систему реалізацій layer Sr , систему використання layer Su та систему управління layer Sm : , , , s layer layer layer layer layer O Sr So Su Sm = — контекстні знання, що пов’язані з прийняттям рішень: система реалізацій layer Sr , система об’єктів layer So , система використання layer Su , система управління layer Sm .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' layer Sr можна визначити як систему, що описує акторів, інформа- цію та дані, засоби та розташування і яка збирає, зберігає, оброб- лює та поширює інформацію про результати, що представляється системою об’єктів, для того, щоб реалізувати та/або поліпшити дії системи використання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Структурно layer Sr складається з акторів, дій, інформації та даних, засобів (включаючи програмне забезпечення) та розташування, визначає відповідні результати на рівнях прийнят- тя рішень, які реалізують розв’язання задачі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' layer Sr існує для надан- ня інформації, що відповідає критеріям релевантності, своєчасності тощо, для того, щоб задовольнити потреби користувачів у результа- тах процесу прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' layer Sr — функціональна одиниця, яка збирає, зберігає, оброблює та поширює інформацію про результати прийняття рішень, що представляються системою об’єктів layer So , та для того, щоб реалізувати та/або покращити дії системи викорис- тання layer Su .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Користувачі системи реалізацій layer Sr є акторами, що бажають підвищити рівень знань про систему об’єктів layer So за до- помогою системи реалізацій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це також вносить зміни в здатність користувачів виконувати завдання, які стосуються системи управ- ління layer Sm .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' layer So представляє систему, що збирає, зберігає, обробляє та по- ширює інформацію для та внаслідок інтересів системи використання layer Su .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Межа layer So повністю визначається інтересами системи вико- ристання layer Su .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' layer So є частиною дійсності, яку розглядають як про- блемну область для прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 39 layer Su можна представити як систему, яка використовує послуги, забезпечені системою реалізації layer Sr , в процесі прийняття рішень для того, щоб планувати та виконати зміни (тобто зміни стану (пе- реходи) за допомогою системи управління layer Sm .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Актори в системі використання layer Su — користувачі, програмні компоненти системи реалізацій layer Sr .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В рамках layer Su ми можемо розрізнити два види ко- ристувачів: кінцеві користувачі, які збільшують своє знання, взаємо- діючи безпосередньо з СППР;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' непрямі користувачі, які збільшують своє знання, отримуючи результати СППР через користувачів СППР.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' layer Su можна класифікувати за різними критеріями, наприклад, роз- глядати на стратегічному, тактичному або оперативному рівнях.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ре- зультати layer Su можуть стосуватися людини-актора, програми-акто- ра.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' layer Su можна визначити як систему, яка використовує послуги, що реалізуються системою реалізації layer Sr , для прийняття рішень або ін- ших дій, щоб планувати та виконати зміни (тобто зміни стану) в сис- темі управління layer Sm .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' layer Sm — система, яка використовує систему використання layer Su .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Між системою реалізацій layer Sr , системою об’єктів layer So , сис- темою використання layer Su та системою управління layer Sm існують певні відношення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інформаційні об’єкти системи реалізацій пред- ставляють сутності системи об’єктів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Також інформаційні об’єкти системи використання представляють сутності системи об’єктів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відношення між системи об’єктів і іншими системами залежить від того, чи ці системи перетинаються чи не перетинаються.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ми може- мо визначити чотири різних випадки щодо того, в якій частина сис- тема об’єктів є частиною інших систем.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В першому випадку система об’єктів повністю не перетинається з іншими системами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це означає, наприклад, що інформація збирається з абсолютно різних сутностей у порівнянні з тими, які знаходяться під впливом системи викорис- тання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це, звичайно, дуже рідкісна ситуація.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В другому випадку сис- тема об’єктів збігається з системою управління.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В третьому випадку система об’єктів перетинається з системою використання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В цьому випадку система реалізацій використовується, наприклад, для пла- нування, контролю або виконання роботи в системі використання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нарешті система об’єктів може перетинатися з системою реалізацій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Як показано вище, третьою складовою контекстної онтології ctx O є онтологія аспектів (точок зору) aspect O .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 40 Поняття аспекту або точки зору не має чіткого визначення, тому будемо використовувати аспект (точку зору) як певний спосіб розгля- ду або оцінювання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Використання аспекту призводить до обмеженої або визначеної концепції певних сутностей та їх властивостей в ре- альності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Щоб отримати та пов’язати ці представлення, визначається певна структура.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Онтологія аспектів (точок зору) , , , , , , Sys Cncpt Man Inf aspect aspect aspect aspect aspect Rlz aspect aspect aspect VofP VofP VofP VofP O VofP Dim Rel = , де Sys aspect VofP — системна точка зору, що відбиває склад взаємодіючих у процесах об’єктів проблемної області та відбиває взаємодію у про- цесах прийняття рішень;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Cncpt aspect VofP — концептуальна точка зору, що відбиває зміст об’єктів проблемної області та їх взаємодію в процесах прийняття рішень;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Man aspect VofP — точка зору управління, що відбиває події та правила, які виникають, використовуються та впливають на виконання процесів прийняття рішень;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Inf aspect VofP — інформаційна точка зору, що відбиває взаємозв’язок функцій (дій) щодо перетворення об’єктів у процесах прийняття рі- шень;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Rlz aspect VofP — реалізаційна точка зору, яка описує засоби реалізації елементів СППР та прийняття рішень;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' aspect Dim — виміри розгляду точок зору;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' aspect Rel — відношення точок зору.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В цьому випадку контекст є як результатом інтеграції релевантних сформованих вимог до розв’язання задачі частин декількох онтоло- гій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Під інтеграцією розуміється інтеграція декількох частин вихідних онтологій, результатом якої є уніфікована онтологія або контекст, в якому однаково представлені знання з інтегрованих частин, і по- вністю підтримується логічний висновок, що заданий в цих частинах, та які можуть бути отримані з множини однорідних або різнорідних джерел.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Системна точка зору базується на системі об’єктів та системі ви- користання, яка складається з пов’язаних точок зору розгляду кож- ного з шарів та пов’язаних контекстних областей.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тут визначають, наприклад, для проблеми, за яких умов може виникнути, які можуть 41 існувати впливи на проблему щодо започаткування або використан- ня, як може бути використана, які існують або були реалізовані кон- тексти моделі, методу та реалізації тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для шару метод визначає, які контексти моделі мають бути враховані стосовно методу, які є цілі, можливі актори та обмеження використання методу з урахуванням як контекстів проблеми та моделі, так і контексту реалізації тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Концептуальна точка зору розглядає прийняття рішень через се- мантичний зміст інформаційних об’єктів, який означає, що точка зору адресується контексту системи об’єктів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ця точка зору зосере- джується на концептуальному змісті відповідних об’єктів у врахуван- ням структурної та динамічної складових.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З управлінської точки зору система розглядається як система управління з відповідними подіями та правилами функціонування такої системи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для цього визначають акторів (людина, програмна система), як вони можуть взаємодіяти, де вони знаходяться, як мо- жуть бути сфомульовані відповідні процедури та алгоритми в рамках відповідних шарів тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З інформаційної точки зору розглядається система, що базується на системі об’єктів, яка вважається функціональною структурою ін- формаційної обробки мети, дій та об’єктів, незалежно від будь-яких особливостей представлення, реалізації та використання, тобто ви- значається, яка інформація обробляється і чому, які дії та правила об- міну та обробки тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З реалізаційної точки зору розглядається система,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' що базується на системі реалізації,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' яка пов’язана з конкретним організаційним,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' управ- лінським та технологічним контекстами,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' тобто визначаються актори,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' що виконують дії в процесі реалізації прийняття рішень,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' як вони вза- ємодіють і де вони розташовані,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' де та як зберігаються необхідні дані,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' які засоби використовуються та коли,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' яке апаратне та програмне за- безпечення використовуються,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' і як вони пов’язані між собою тощо Відношення між точками зору можуть бути побудовані на декіль- кох критеріях.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оскільки неможливо знайти щось, що покривало би всі необхідні особливості прийняття рішень та забезпечувало необ- хідні поняття та конструкції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому вибір критеріїв визначає, що точки зору повинні підтримати структурований розгляд багатогран- них особливостей процесу прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Критерії мають дозво- ляти розглянути кожну точку зору з урахування процесу прийняття рішень, що дозволяє визначити, що відповідає точці зору та що має бути проігноровано.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 42 Представлена система аспектів (точок зору) розглядається з трьох вимірів: вимір розкладання, концептуальний вимір, незалежність ре- алізації — вимір залежності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Використання точок зору, таких як системна, інформаційна, управлінська, надає можливість руху вздовж вимірювання розкла- дання, тобто від «чорного ящика» до системи, яка складена з цілей, дій та об’єктів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У цьому процесі переважно застосовані принципи розкладання та спеціалізації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Системна, управлінська та реалізаційна точки зору дають змогу проаналізувати зміни вздовж виміру розкладання, з одного боку, та вздовж незалежності реалізації — вимірювання залежності, з іншого боку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, може бути отримано певне ієрархічне представлен- ня системи точок зору, що будується на критерії залежності реаліза- ції, оскільки кожний шар визначає більш конкретні поняття, і відно- шення, що розгорнуті на нижчих рівнях абстракції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Отже об’єкти, що реалізуються через певні інформаційні об’єкти, дії, що розділені на дії людини та дії програмної системи, і тимчасові конкретні специфі- кації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У цьому процесі визначаються ієрархія мети, засобів, структури розкладання дії, структура розкладання об’єкта.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такий розгляд контексту в рамках задач прийняття рішень до- зволяє, не впливаючи безпосередньо на процес прийняття рішень, обмежити його лише значущими для даного контексту правилами / процедурами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це дозволяє: 1) логічно виводити новий контекст з на- явних;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2) повторно використовувати контекст за допомогою засто- сування контекстів вищих рівнів абстракції, їх інтеграції та конкре- тизації для відповідних умов і завдань;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3) отримувати контекст більш високого рівня абстракції з відповідного розглянутого контексту;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4) розбивати контекст на складові відповідні логічно пов’язані вну- трішньо узгоджені контексти.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Реалізація інтегрованого погляду на прийняття рішень через сис- тему аспектів (точок зору) надає можливість використання інформа- ції, яка міститься в декількох контекстах та визначає контекст, який може бути використаний, наприклад, прикладною програмою для розв’язання певних завдань, підвищити достовірність контекстної інформації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Аспекти або точки зору дозволяють використовувати тільки ту частину даних, інформації або знань, яка є релевантною для задачі, що розв’язується.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Також вони дозволяють копіювати фраг- менти контексту, повторно використовувати їх для інших цілей тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 43 Використання системної оптимізації,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' яке базується на викорис- танні знань у вигляді онтології та контексту,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' дає можливість внести до організації процесу прийняття рішень ряд важливих властивостей,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' перш за все дає можливість перейти до безперервного аналізу ситуацій та планування дій,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' забезпечує проведення корекції процесу прийнят- тя рішень без порушення технологічної цілісності та взаємозв’язків,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' допускає багатоваріантність рішень та можливість їх отримання за різними критеріями і моделями,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' будує взаємопов’язану систему під- готовки та вибору рішень,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' як для даної проблеми,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' так і для взаємодії з іншими комплексами проблем і завдань,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' дозволяє приймати рішен- ня з урахуванням наслідків їх реалізації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому в рамках таких технологій вдасться врахувати взаємозалежність рішень, негативні наслідки реалізації, обмеження поведінки, інформаційні обмеження, час та середовище, що постійно змінюється, визначеність, ризик, не- визначеність тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Результати роботи використано в рамках науково-дослідної робо- ти «Розробити типові онтологокеровані процедури системної опти- мізації для розв’язання прикладних задач».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' СПИСОК ВИКОРИСТАНОЇ ЛІТЕРАТУРИ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Глушков В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' О системной оптимизации.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кибернетика.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1980.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 89– 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Westmacott S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Developing decision support systems for integrated coastal man- agement in the tropics: Is the ICM decision-making environment too complex for the development of a useable and useful DSS?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Journal of Environmental Management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' No 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 55–74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Bharati P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Chaudhury A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' An empirical investigation of decision-making satis- faction in web-based decision support systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Decision Support Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' No 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 187–197.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Чаплінський Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' П.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Алгоритми системної оптимізації для різних припус- тимих варіацій параметрів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Проблеми інформатизації та управління.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 163–168.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Волкович В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Л.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Коленов Г.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Метод раздельного решения взаимосвязан- ных оптимизационных задач.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Изв.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' АН СССР.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сер.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Техн.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' киберн.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 28–43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Чаплінський Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' П.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Онтологічне представлення процесів прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Проблеми інформатизації та управління.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 146– 151.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 44 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Чаплінський Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' П.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Онтологічні складові підтримки прийняття управлін- ських рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наукові праці НУХТ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 48.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' No 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 19–30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Bettini C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Brdiczka O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Henricksen K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A survey of context modelling and reasoning techniquesю Pervasive and Mobile Computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' No 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 161– 180.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Чаплінський Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' П.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Субботіна О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Онтологія та контекст при розв’язанні прикладних задач прийняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Штучний інтелект.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 147—155.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Чаплінський Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' П.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Надточій В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Базова онтологія в прийнятті рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Проблеми інформатизації та управління.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 45–51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ТЕОРЕТИЧНІ ОСНОВИ ІНФОРМАЦІЙНОЇ ТЕХНОЛОГІЇ ПРОГНОСТИЧНОГО ОЦІНЮВАННЯ ЯКОСТІ ПРОЄКТУВАННЯ ПІСЛЯДРУКАРСЬКИХ ПРОЦЕСІВ Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Піх І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Кудряшова А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розроблення інформаційної технології прогностичного оцінювання якос- ті проєктування післядрукарського опрацювання книжкових видань на первинному етапі передбачає опис предметної області, зокрема означення особливостей реалізації, послідовності післядрукарських процесів та пере- бігу їх проєктування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На основі теоретичного обґрунтування та експертних висловлювань виокремлено ключові фактори впливу та здійснено функціо- нальне моделювання визначених процедур.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наведено контекстні діаграми, де основними функціями систем є реалізація та проєктування післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Описано процес декомпозиції кожної з них.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для формалізації наведе- них знань та отримання можливості встановлення оптимального розв’язку основної та побічних задач застосовано розроблені онтології проєктування післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Внаслідок аналізу предметної області відбувається синтезування моделі пріоритетного впливу факторів на якість проєктування після- 45 друкарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зокрема описано особливості побудови семантич- ної мережі та опису зв’язків між факторами за допомогою логіки пре- дикатів, встановлено пріоритетності впливу факторів на досліджувані процеси методами математичного моделювання ієрархій та ранжування факторів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наступним етапом є оптимізація моделі пріоритетного впливу фак- торів на якість проєктування післядрукарських процесів, що полягає у по- кращенні вхідних даних, та здійснюється за методом аналізу ієрархій, який передбачає розв’язання ряду задач: побудову матриці попарних порівнянь;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' обчислення компонент та нормалізацію значень головного власного векто- ра матриці;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' перевірку результатів оптимізації за критерієм максимального значення головного власного вектора, нормативних значень індексу узгодже- ності та відношення узгодженості;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' синтез оптимізованої моделі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для встановлення оптимальної альтернативи реалізації проєктування післядрукарських процесів обрано два методи: багатофакторний вибір аль- тернатив на основі лінійного згортання критеріїв та на основі нечіткого від- ношення переваги.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Отримання конкретного кількісного показника якості реалізації дослі- джуваного процесу реалізовано методами та засобами нечіткої логіки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На основі виокремлених етапів побудовано структурно-функціональну модель та IDEF0-моделі інформаційної технології.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The development of the information technology for prognostic assessment of the design quality of post-press processing of book editions at the initial stage involves the description of the subject area, including the characteristics of implementation, se- quence of post-press processes and the course of their design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Key factors of influence have been identified and functional modelling of certain procedures has been carried out on the basis of theoretical substantiation and expert statements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Contextual dia- grams are presented, where the main functions of the systems are the implementation and design of post-press processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The process of decomposition of each of them is described.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' To formalize the knowledge and get the opportunity to establish the optimal solution of the main and secondary problems, it is suggested to develop an ontology of design of post-press processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' As a result of the analysis of the subject area, a model of the priority influence of factors on the design quality of post-press processes is synthesized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In particular, the paper describes the features of constructing a semantic network and describing the relationships between factors using predicate logic, prioritizing factors by mathemat- ical modelling of hierarchies and factors ranking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The next step is to optimize the model of priority influence of factors on the de- sign quality of post-press processes, which consists in improving the input data and is carried out by the method of hierarchy analysis, which involves solving a number of problems: the construction of a matrix of pairwise comparisons;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' the calculation of components and the normalization of the values of the main eigenvector;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' checking the results of optimization by the criterion of the maximum value of the main eigen- 46 vector, the normative values of the consistency index and the consistency ratio;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' the synthesis of an optimized model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' To establish the optimal alternative for the implementation of design of post- press processes, two methods have been chosen: a multifactor selection of alterna- tives based on linear convergence of criteria and on the basis of fuzzy benefit ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Obtaining a specific quantitative indicator of the quality of implementation of the studied process is presented by methods and means of fuzzy logic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The structural-functional model and IDEF0-models are constructed on the ba- sis of the selected stages of the information technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Постановка проблеми.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Завершальний етап технології виготовлення книжкової продукції, до якого відносяться брошурувально-палітурні процеси, часто помилково ототожнюють із набором механічних, ци- клічно повторюваних дій, позбавляючи їх високоінтелектуальної ін- формаційної складової.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такий підхід призводить до підвищення ймо- вірності часткового чи повного відбракування тиражу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Типовою хибою є також невідповідність виготовленої продукції її функціональним та експлуатаційним характеристикам.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Так, для прикладу, стосовно видан- ня, яке повинно служити десятиліття, застосовують клейове скріплен- ня органічного походження, непридатне для забезпечення прийнятих вимог, та обирають невідповідний оздоблювальний матеріал [79].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Останніми роками використовується моделювання вказаних про- цесів за допомогою комп’ютерної техніки та спеціального програмно- го забезпечення [5;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Важливо враховувати той факт, що обладнання для виконання окремих операцій брошурувально-палітурних проце- сів та матеріали, що використовуються для різних видів продукції, є індивідуальними [7;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 9;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 17;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 19;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 24;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Активно застосовується прин- цип вертикального проєктування, при якому розрізняють процедури аналізу і синтезу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У результаті синтезу створюються описи об’єктів, які відображають їхню структуру і параметри [11;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вибір технології та післядрукарського устаткування залежить від виду друкованої продук- ції, її призначення, обсягів виробництва, економічних та фінансових показників діяльності друкарень [1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 23;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 31;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 37;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 74;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Суттєвою про- блемою є дотримання стандартів на виготовлення видань, метрологіч- ні характеристики, що стосуються якості у поліграфії, моделювання бізнес-процесів [40;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 45;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 77], що є важливими чинниками планування та ефективного функціонування поліграфічних підприємств [79].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Слід зазначити, що автоматизація з використанням комп’ютери- зованих технологій не приносить очікуваних результатів, адже засто- совані процедури не пов’язуються при цьому в єдину, нероздільну 47 систему.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За таких умов доцільним та необхідним є поопераційний інформаційний супровід, наслідком якого стане прогностичне оці- нювання якості майбутньої продукції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Подібний підхід при наявності умов невизначеності вимагає виокремлення ключових факторів впли- ву на якість проєктування післядрукарських процесів, встановлення міри важливості кожного з них та пріоритетності впливу на досліджу- ваний процес;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' формування, розрахунку та багатокритеріального оці- нювання альтернативних варіантів реалізації післядрукарських про- цесів на основі лінійного згортання критеріїв та нечітких відношень переваги і визначення оптимального з них;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' обчислення інтегрально- го показника рівня якості проєктування післядрукарських процесів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' розроблення інформаційної технології прогностичного оцінювання вказаних процедур, що слугуватиме методологічною основою для отримання продукції належної якості [79].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основним завданням дослідження є розроблення інформаційної технології прогностичного оцінювання якості проєктування після- друкарських процесів, що передбачає виконання таких підпорядко- ваних завдань: – проаналізувати етапи проєктування та реалізації післядрукар- ських процесів, дослідити основні операції та функції, розробити он- тологію;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – виокремити фактори впливу на якість проєктування післядру- карських процесів та сформувати семантичні мережі зв’язків між ними;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – синтезувати та оптимізувати моделі пріоритетного впливу фак- торів на якість проєктування післядрукарських процесів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – визначити оптимальні альтернативні варіанти реалізації за ме- тодами багатофакторного вибору альтернатив на основі лінійного згортання критеріїв та нечіткого відношення переваги;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – побудувати функції належності лінгвістичних змінних і розраху- вати їх значення із використанням нечітких логічних рівнянь;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – визначити інтегральний показник якості проєктування після- друкарських процесів шляхом дефазифікації нечітких множин за принципом центра ваги;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – розробити структурно-функціональну модель інформаційної технології прогностичного оцінювання якості проєктування після- друкарських процесів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – розробити IDEF0-моделі інформаційної технології прогностич- ного оцінювання якості проєктування післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 48 Виклад суті дослідження.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Незважаючи на багатовікову історію зу- силь вчених та практиків, скерованих на формування узагальнюючих методів, способів та засобів апріорного оцінювання якості процесів, пов’язаних з виробництвом різнорідної продукції, проблема на сьо- годні до кінця не вирішена.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Спробуємо пояснити причини такого стану.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Найчастіше поняття «якість» співвідносять з виробом, що на перший погляд є логічним, оскільки споживача цікавить насам- перед добротність саме готової продукції [12;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' І тут постає ди- лема — що вважати якістю і як її трактувати.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Адже користувачі у переважній більшості не знайомі зі стандартами, тому кожний по- своєму оцінює товар, не кажучи вже про те, що його не цікавлять деталі технології виготовлення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У цьому випадку якість стає кате- горією суб’єктивною.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З іншого боку, наявність і строге дотримання нормативів і стандартів якості, згідно з якими оцінюється продукція і розробляються вимоги до технології, машин та режимів реалізації процесів та окремих процедур, стають об’єктивною передумовою отримання якісних результатів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Загальною парадигмою як підсумок до сказаного слугує той факт, що якість виступає в ролі апостеріорної категорії, отриманої для ха- рактеристики виходу виробничого процесу у статичному режимі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У цьому випадку якість — це сукупність властивостей продукції, які обумовлюють задоволення потреб користувача у відповідності з її призначенням [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основна увага пропонованого дослідження буде звернена на дина- міку формування якості книжкових видань, тобто механізм апріорно- го встановлення прогнозованого показника критерію ефективності, як оцінки якості видавничо-поліграфічних етапів засобами сучасних інформаційних технологій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Враховуючи сказане, можна стверджува- ти факт існування упорядкованих взаємозв’язків між рівнями техно- логічного процесу випуску книжкових видань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Структурування ходу дослідження встановить послідовність дій, а також підтвердить ефек- тивність та більш строго обґрунтує логіку застосування інформаційної концепції до прогнозування якості поліграфічної продукції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З огляду на сказане, на початку ери становлення електронних ін- формаційних засобів могло здатися, що друковану продукцію чекає повний занепад, про що в останні роки йшли серйозні дискусії.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Од- нак дані про темпи та обсяги випуску друкованих видань (особливо книжкових) в Україні свідчать про те, що скептики традиційної (па- 49 перової) поліграфії не врахували багатьох суттєвих чинників.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Так, у публікації [4] вказано на фактори, що свідчать про відродження укра- їнського книгарства.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На початок третього тисячоліття в Україні склався добрий гурт професійно підготовлених і рішуче налаштованих на працю видавців і друкарів різних форм власності, які вміло продовжують кращі тра- диції своїх попередників на книговидавничому полі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Незважаючи на економічні негаразди, в українському суспільстві існує стабільно високий попит на добротну українську книгу: худож- ню, навчальну, наукову, пізнавальну, довідкову тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За прикладом країн Західної Європи Україна все більше починає відчувати вплив щорічного ярмаркового буму в книжковій справі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Створено групи приватних видавництв в обласних центрах, які за короткий час своєї діяльності змогли серйозно заявити про себе на загальнодержавному рівні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Технологія виготовлення друкованої продукції є складовою час- тиною інформаційних технологій, адже від оперативності та доско- налості друкарських процесів та охоплення ними усіх сфер суспільної діяльності залежать обсяги та швидкість розповсюдження інформа- ції — основи існування та поступу людства.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інформаційні видавничо- поліграфічні технології належать до одного з видів сучасних техно- логій, пов’язаних з виготовленням як паперових, так і електронних носіїв даних і знань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Як різновид соціальних інформаційних техноло- гій, вони породжені суспільною необхідністю удосконалення проце- су виготовлення твердих та електронних носіїв інформації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ця техно- логія виникла не через появу комп’ютерної техніки як такої, а через суспільне усвідомлення можливості організувати видавничий процес більш ефективно, оперативно включитися в загальнолюдську інфор- маційну систему, стати її активним джерелом і споживачем у реальній інформаційній ситуації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' І ця технологія активно впроваджується у ви- давничий процес, є ефективною, найбільш автоматизованою техно- логією виготовлення книги, журналу, газети чи іншої друкованої та «електронної» продукції [3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 36;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 48;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 65;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Останніми роками поліграфічні корпорації створили та успішно використовують концептуально нову інформаційну технологію ор- ганізації та функціонування видавничо-поліграфічного комплексу, названу терміном «робочий потік» (Workflow) [8;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 14;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 39;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 49;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 71].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Він забезпечує послідовність реалізації конкретних операцій, пов’язаних з даними, відображеними форматами файлів PDF, СІР3, СІР4, про- 50 грамним та апаратним забезпеченням, а також взаємодію апаратно- го і програмного забезпечення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Мета полягала в тому, щоб об’єднати технічно й організаційно потоки даних Workflow і перекинути міст між клієнтами, друкарнями і брошурувальними підрозділами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ці по- токи використовуються для обробки цифрової інформації на всіх ета- пах поліграфічного виробництва;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' вони забезпечують інтеграцію сис- тем CtP (Computer to Plate) з цифровим Workflow, а також з системами кольоропроби.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сюди входять процеси прийому даних, виробництво, коректура, управління кольорами, поділ на кольори, спуск полос і їх виведення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На сучасному етапі спостерігається тенденція зменшення тиражів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це привело до появи друку на вимогу PoD (Print on Demand).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кож- на система PoD має своє призначення і свої можливості.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Спільним є те, що друкарські комунікації здійснюються за допомогою цифрових способів друку, а також післядрукарських технологій, орієнтованих на нього.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Аналіз теперішнього стану технологій друкарства та системних і програмних засобів їх реалізації свідчить про відсутність на даний час універсального механізму апріорного оцінювання ефективності реалізації етапів, стадій чи окремих операцій видавничо-поліграфіч- ного циклу саме на інформаційному рівні, що унеможливлює апрі- орне досягнення очікуваної якості за допомогою автоматизованих систем, орієнтованих на експертно-прогностичне вирішення вказа- ної проб леми.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Підставою для формування структурно-функціональної моделі інформаційної технології прогностичного оцінювання якості проєк- тування післядрукарських процесів є виокремлення та систематиза- ція основних етапів інформаційної технології [10;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 32;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 46;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 67].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Етап 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Аналіз предметної області 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Узагальнений опис операцій та технологій післядрукарського опрацювання книжкової продукції Післядрукарські процеси — це сукупність послідовних дій, на- правлених на перетворення віддрукованих аркушів та інших кон- струкційних елементів у готову книгу [35;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Післядрукарське опрацювання книжкових видань можна розді- лити на два великі блоки: брошурувальні та палітурні процеси.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До брошурувальних процесів належать: виготовлення зошитів, комп- лектування та скріплення блоків.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Можливе також з’єднання блоків 51 з обкладинками та обрізування з трьох сторін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До палітурних процесів належать: опрацювання книжкових блоків, виготовлення та оздоб- лення палітурок, з’єднання книжкових блоків з палітурками, кінцеве опрацювання книг [6;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розглянемо згадані операції детальніше.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виготовлення зошитів полягає в зіштовхуванні, розрізуванні арку- шів на частини, фальцюванні, пресуванні та приклеюванні додатко- вих елементів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зіштовхування виконується для покращення точності підрізання та розрізання аркушів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ця операція полягає у вирівнюван- ні країв аркушів за горизонтальним та вертикальним краями пачки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розрізування — це поділ друкарських чи палітурних аркушів на части- ни.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Фальцювання полягає у згинанні аркушів у визначеному поряд- ку з фіксацією згинів з метою одержання зошитів бажаного формату та конструкції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Фальцювання класифікується за такими ознаками: число згинів (однозгинне, двозгинне, трьохзгинне, чотирьохзгинне, багатозгинне), взаємне розміщення згинів (паралельне, перпенди- кулярне, комбіноване), розміщення згинів на аркуші (симетричне, зміщене), число полос (одинарне, двійником, четверником), число аркушів (один, два і більше, більше чотирьох згинів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Пресування і упаковування зошитів здійснюється для зручності транспортування та зберігання перед наступними операціями.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В якості додаткових еле- ментів можуть бути приєднані форзаци, ілюстрації, частини аркушів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Комплектування блока — це операція, спрямована на розміщен- ня аркушів або сфальцьованих зошитів у правильній послідовності в межах книжкового блоку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Є два основні способи комплектування: вкладанням (для видань обсягом до 64–80 сторінок;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' аркуші встав- ляються один в один) та підбиранням (для видань обсягом понад 80 сторінок;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' сфальцьовані аркуші накладають один на одного).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Скріп- лення зошитів скомплектованого блоку може здійснюватися шит- тям дротом, шиттям нитками або за допомогою незшивних спосо- бів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо покривним матеріалом є обкладинка, то здійснюється з’єднання книжкового блоку з обкладинкою та обрізування з трьох сторін [6;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 9;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо покривним матеріалом є палітурка, то подальше опрацю- вання книжкових блоків може полягати у пресуванні, заклеюванні корінця, сушінні блоку, обтискуванні корінця, обрізуванні блоку з трьох сторін, зафарбовуванні обрізів, зміні форми корінця, каширу- ванні, приклеюванні лясе, наклеюванні капталу, наклеюванні смужки паперу, гільзи тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виготовлення палітурки загально може склада- тися з трьох основних операцій: розкрій покривного матеріалу, збір та 52 з’єднання деталей, круглення корінця.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При потребі покривний мате- ріал оздоблюється.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вставлення блоку в палітурку виконується одним з чотирьох способів: звичайне вставлення, на гільзу, «глухе», в кишені.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Після вставлення блоків у палітурки здійснюється пресування книг, штрихування, обгортання книг суперобкладинкою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Завершальною операцією є пакування книжкової продукції [6;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 9;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 35;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, виготовлення книжкових видань в обкладинці пе- редбачає виконання лише брошурувальних процесів, а в палітурці — брошурувальних і палітурних.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Загалом брошурувально-палітурне ви- робництво характеризується неабиякою варіативністю операцій, що пов’язано зі значною кількістю елементів виробів, різновидами на- півфабрикатів, тривалим технологічним ланцюжком, різноманітніс- тю матеріалів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Разом з використанням класичних методів опрацюван- ня спостерігається постійне вдосконалення напрямків автоматизації післядрукарських процесів та бажання прогностичного оцінювання результатів діяльності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Проєктування досліджуваних процесів є клю- човим етапом для досягнення успішної реалізації необхідних опера- цій і забезпечення якості книжкового видання [35;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Функціональне моделювання післядрукарського опрацювання книжкової продукції З огляду на системний характер проєктування післядрукарських процесів, його доцільно розглядати та досліджувати як певну сис- тему.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При вивченні системи використовуються системний підхід та системний аналіз.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Системний підхід полягає у дослідженні об’єкта як системи, виявленні та дослідженні сукупності відношень і зв’язків у ньому.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основними принципами системного підходу є принцип взаємозв’язку, принцип багатоплановості, принцип багатомірнос- ті, принцип ієрархічності, принцип різнопорядковості, принцип динамічності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Системний аналіз являє собою сукупність методів та алгоритмів, спрямованих на вирішення проблеми.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основною ідеєю системного аналізу є перетворення складної проблеми у чітку по- слідовність знань, розв’язок яких є уже відомим або до яких можна застосувати відомі методи вирішення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Процедура системного аналізу складається з двох частин: аналізу та синтезу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Аналіз полягає у роз- кладанні основної проблеми на підпроблеми та застосуванні опти- мальних методів їх вирішення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Об’єднання окремих розв’язків під- проблем в один загальний розв’язок проблеми називається синтезом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Фактично аналіз та синтез є дзеркальними процедурами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перш ніж 53 застосовувати системний аналіз, необхідно чітко сформулювати про- блему, яка потребує вирішення, та визначити межі системи в яких буде вирішуватися дана проблема.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розрізняють два підходи системного аналізу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перший полягає у застосуванні математичних прийомів, зокрема теорії оптимізації та дослідження операцій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому ставиться математична задача, ме- тою якої є знайдення оптимального проєкту системи чи/та найкра- щого режиму її функціонування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основою другого підходу є логіка системного аналізу, яка використовується у тих випадках, коли засто- сування математичного підходу є неефективним.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Логіка системного аналізу випливає зі специфіки задач, для вирі- шення яких він застосовується, та реалізованого підходу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Системний аналіз застосовують для погано структурованих задач.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При наявності невизначеностей у системному аналізі, метою якого є вплив на ви- бір способу дії, присутні такі елементи, як проблема та проблемати- ка, цілі, засоби для досягнення цілей, альтернативи, ресурси, які по- трібні для кожної альтернативи, моделі, критерії вибору оптимальної альтернативи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Етап формулювання проблеми полягає у її розширенні до про- блематики, тобто виявленні системи пов’язаних із нею проблем, без врахування яких ключова проблема не може бути розв’язана.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наступ- ним за важливістю є етап виявлення цілей, на якому визначається, що потрібно зробити для розв’язання проблеми.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Цілі є антиподом проблеми.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На наступних етапах визначається, яким чином потрібно розв’язати проблему [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Підвищенню ефективності та удосконаленню післядрукарсько- го опрацювання книжкових видань сприяє використання сучас- них методів системного аналізу, які реалізовуються за допомогою комп’ютерної техніки та спеціальних програмних продуктів — CASE- технологій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' CASE-засоби підтримують процеси аналізу і формулю- вання вимог до різноманітних складних систем, процеси створення і супроводження інформаційних систем тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Одним з напрямів CASE-технологій є SADT-технології, спрямовані на створення, ана- ліз та подальше використання моделей складних систем [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На базі SADT-методології розроблена методологія IDEF0-моделі, що перед- бачає побудову контекстних діаграм деревовидної структури, ство- рених за принципом декомпозиції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекстну діаграму познача- ють як А-0, а діаграму декомпозиції першого рівня — А0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Стрілками типу вхід (те, що опрацьовується) є множина значень { } 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', n I I I = , 54 стрілками типу керування (процедури та стратегії управління) — множина { } 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', n C C C = , стрілками типу вихід (результат) — множи- на { } 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', n O O O = , а стрілками типу механізми (необхідні ресурси) — множина { } 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', n M M M = [40;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 77].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основною функцією є реалізація післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зв’язок системи із навколишнім середовищем ілюструється такими граничними стрілками: I1 — віддруковані аркуші, I2 — покривний матеріал, I2 — інші матеріали, C1 — нормативно-технічна та техно- логічна документація, C2 — проєкт, C3 — альтернативи реалізації, O1 — рівень якості післядрукарських процесів, O2 — готові видання, M1 — брошурувально-палітурне устаткування, інші знаряддя праці, M2 — особовий склад працівників, експерти з предметної області, за- цікавлені особи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Проаналізуємо інформаційне навантаження компонент множин граничних стрілок IDEF0 моделі реалізації післядрукарських процесів: Граничні стрілки типу «Вхід» (Input): – 1I (віддруковані аркуші).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Результатом додрукарського опрацю- вання авторських оригіналів та друкування накладу є віддруковані паперові аркуші, які надходять на дільницю післядрукарського опра- цювання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – 2I (покривний матеріал).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Аркуші покривного матеріалу, які слу- гують для виготовлення обкладинок чи палітурок (залежно від харак- теристик).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – 3I (інші матеріали).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Матеріали для скріплення, оздоблення тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Граничні стрілки типу «Контроль» (Control): – 1 C (нормативно-технічна та технологічна документація).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До нормативно-технічної документації належать технічні вимоги та за- конодавчі положення, зокрема: закони, стандарти, технічні умови, кодекси усталеної практики та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – 2 C (проєкт).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визначає перебіг усіх технологічних дій, направле- них на реалізацію післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – 3 C (альтернативи реалізації).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Парето-оптимальні альтернативи, визначені оцінюванням нечітких відношень на заданій множині аль- тернатив.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Граничні стрілки типу «Вихід» (Output): – 1 O (рівень якості післядрукарських процесів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Результат, отри- маний внаслідок реалізації післядрукарського опрацювання книжко- вих видань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 55 Реалізація післядрукарських процесів Віддруковані аркуші Рівень якості післядрукарських процесів Брошурувально- палітурне устаткування, інші знаряддя праці Особовий склад працівників, експерти з предметної області, зацікавлені особи Альтернативи реалізації Проєкт Нормативно-технічна та технологічна документація Готові видання Покривний матеріал Інші матеріали Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекстна діаграма А-0 моделі IDEF0 реалізації післядрукарських процесів – 2 O (готові видання).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Книжкові видання в обкладинках чи палі- турках, готові до розповсюдження.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Граничні стрілки типу «Механізми» (Mechanism): – 1 M (брошурувально-палітурне устаткування, інші знаряддя праці).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Устаткування, необхідне для реалізації післядрукарських про- цесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Можливе також використання спеціалізованих знарядь праці при виконанні деяких операцій вручну.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – 2 M (особовий склад працівників, експерти з предметної облас- ті, зацікавлені особи).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Реалізація післядрукарських процесів передба- чає участь працівників брошурувально-палітурної дільниці, кількість та кваліфікація яких залежать від обсягу та рівня автоматизації вироб- ництва.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Можливе залучення профільних експертів, зокрема науков- ців та інших зацікавлених осіб.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Процес функціональної декомпозиції контекстної діаграми, на- веденої на рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1, полягає у її розділенні на функції нижчого порядку та встановленні напрямів граничних стрілок, що сприяє деталізації діяльності в межах досліджуваного процесу [77].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Діаграма першого рівня декомпозиції А0 моделі IDEF0 реалізації післядрукарських процесів містить такі функціональні блоки: – РБП (реалізація брошурувальних процесів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0212101CC5M1M256 – РПП (реалізація палітурних процесів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Діаграма другого рівня декомпозиції А1 моделі IDEF0: – ВЗ (виготовлення зошитів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – КБ (комплектування блоків).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – СБ (скріплення блоків).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВО (виготовлення обкладинок).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ПБО (покриття блоків обкладинками).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – КОВО (кінцеве опрацювання видань в обкладинках).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Діаграма другого рівня декомпозиції А2 моделі IDEF0: – ОБ (опрацювання блоків).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВОП (виготовлення та оздоблення палітурок).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ЗБП (з’єднання блоків з палітурками).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – КОК (кінцеве опрацювання книг).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для відображення ієрархічної залежності функцій доцільно вико- ристовувати діаграму дерева вузлів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Аналіз факторів впливу на якість проєктування післядрукар- ських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розроблення онтології Проєктування післядрукарських процесів є ключовим етапом для досягнення успішної реалізації необхідних операцій і забезпечення якості книжкового видання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Важливим моментом при дослідженні післядрукарських процесів вважатимемо наявність технологічних характеристик чи параметрів, від яких залежить результативність проходження видання у загально- му циклі його виготовлення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Узагальнюючи подібні чинники, вво- димо поняття факторів, що стають основними елементами моделей визначення пріоритетності впливу факторів на хід реалізації та про- гностичного оцінювання якості післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Встанов- лення пріоритетності компонент сформованої множини слугуватиме раціоналізації післядрукарських процесів та сприятиме отриманню готової продукції очікуваної якості.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Проєктування післядрукарських процесів слугує усвідомлено- му та впорядкованому виконанню запланованих технологічних дій, направлених на перетворення віддрукованих аркушів та інших кон- струкційних елементів у завершене книжкове видання високої якос- ті.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відсутність етапу проєктування унеможливлює отримання про- гнозованого результату.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нехай { } 1 2 3 4 5 6 7 8 , , , , , , , R R R R R R R R R = — множина факторів про- єктування післядрукарських процесів, де 1 R — показники видання;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 57 2 R — конструкційні особливості;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3 R — умови експлуатації;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4 R — тип виробництва;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5 R — матеріали;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6 R — тип обладнання;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 7 R — техноло- гічні та економічні розрахунки;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 8 R — схема технологічного процесу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розглянемо детальніше кожен фактор досліджуваного процесу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Показники видання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До основних показників книжкового видання відносяться: вид і тип видання, формат видання та його обсяг.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вид видання — це сукупність видань, що об’єднані за однією чи кількома типологічними ознаками.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До таких типологічних ознак належать: знакова природа інформації, спосіб виготовлення, пері- одичність, матеріальна конструкція, склад основного тексту, мовна ознака, ступінь аналітико-синтетичного перероблення інформації, цільове призначення, характер інформації, структура, повторюва- ність випуску, обсяг, формат.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За знаковою природою інформації ви- дання поділяються на текстові, нотні, картографічні (атлас, мапа, карта), образотворчі (альбоми, образотворчі картки, образотворчі плакати, художні репродукції, естампи, наочні посібники), видан- ня брайлівським шрифтом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За способом виготовлення розрізняють друковані та електронні видання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За періодичністю: неперіодичні, серіальні, періодичні, продовжувані.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За матеріальною конструкцією: блочне видання (кодексне видання), книжкове видання (книга-пе- рекрутка, алігат), журнальне видання (журнал-перекрутка, алігат), аркушеве видання (плакат, буклет, газетне видання, карткове ви- дання), комплектне видання, комбіноване видання, книжка-іграш- ка.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За складом основного тексту бувають такі види: моновидання, полівидання (збірник, альманах, антологія), вибрані твори, зі- брання творів (академічне видання).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Види видань за мовною озна- кою: оригінальне, перекладне, одномовне, багатомовне (видання з паралельним текстом), паралельне видання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За ступенем аналіти- ко-синтетичного перероблення інформації: інформаційне видання (бібліографічне, реферативне (експрес-інформація, інформаційний листок), оглядове), дайджест.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За цільовим призначенням: офіційне, суспільно-політичне, наукове, науково-популярне, популярне, ви- робничо-практичне, навчальне, літературно-художнє, релігійне, до- відкове, рекламне, видання для дозвілля.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За характером інформації: офіційне (нормативно-правове видання,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' нормативне видання (стан- дарт,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' технічні умови),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' нормативно-інструктивне (інструкція),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' науко- ве (монографія,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' автореферат дисертації,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' препринт,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' тези доповідей,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' тези повідомлень,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' матеріали конференції,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' матеріали з’їзду,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' матеріали симпозіуму,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' збірник наукових праць),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' виробничо-практичне (прак- 58 тичний порадник,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' практичний посібник,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' методичні рекомендації,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' методичні настанови,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' методичний посібник,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' пам’ятка,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' паспорт (на вибір),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' навчальні (навчальна програма,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' підручник,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' навчальний по- сібник (навчально-методичний посібник,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' навчальний наочний по- сібник,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' хрестоматія,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' практикум,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' робочий зошит),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' довідкові і реклам- ні (енциклопедія (енциклопедичний словник),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' мовний словник,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' лінгвістичний словник,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' довідник,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' каталог,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' путівник,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' прейскурант,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' проспект,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' афіша).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За структурою: однотомне видання, багатотомне видання, серія (підсерія), серійне видання, додаток.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За повторюва- ністю випуску: перше, повторне (перевидання (видання без змін, доповнене видання, перероблене видання, виправлене видання), передрук (репринтове видання, факсимільне видання), нове.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За об- сягом видання поділяються на такі види: книга, брошура, листівка (аркушівка).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За форматом видання бувають: мініатюрне, малофор- матне, портативне, фоліант.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Окремо виділяють види періодичних та продовжуваних видань [1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Також книжкові видання бувають звичайного, покращеного та су- венірно-подарункового (рекламного) типу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До звичайного типу нале- жать видання, що видаються великими накладами, без або з невели- кою кількістю ілюстрацій в одну чи дві фарби: вибрані твори, зібрання творів, окремі видання, масові серії, масові рекламно-інформаційні видання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Видання покращеного типу призначені для довготривалого використання, містять середню кількість ілюстрацій в три або чоти- ри фарби: вибрані твори, зібрання творів, збірники, окремі видання, навчальні видання, покращені серії.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для видань сувенірно-подарун- кового типу характерні невеликі наклади, високоякісні матеріали, велика кількість багатоколірних ілюстрацій, нестандартні формати, великі поля, додаткове оздоблення та пакування, підвищена ціна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До них належать: видання виготовлені за індивідуальним замовленням, сувенірні, подарункові, ювілейні, факсимільні видання [35;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формат видання вказує на розмір готового книжкового блоку в міліметрах або друкарського аркуша в сантиметрах і частку аркуша.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Обирається видавництвом, за погодженням з друкарнею.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Залежить здебільшого від виду та типу видання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При поліграфічному відтво- ренні книжкових видань формат умовно позначають розміром арку- ша паперу в сантиметрах та часткою аркуша (долею) та вказують у випускних даних [2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 51;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формат у міліметрах для видання в обкладинці визначають за роз- мірами книги після обрізки з трьох боків.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формат у міліметрах для 59 видання в палітурці визначають за розмірами книжкового блока, об- різаного з трьох сторін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому максимальні відхилення у форма- тах не можуть перевищувати 1 мм по ширині та 1 мм по висоті.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формати аркушів та відповідні формати книжкових видань регла- ментуються ДСТУ 4489:2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основні формати книжкових видань наведені у таблицях 1–3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому на довжину аркуша для рулонних машин вказує машинний напрям паперу [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Також за форматом і часткою аркуші бувають великі, середні, ма- ленькі та мініатюрні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Загалом використовують 22 формати книжко- вих видань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Окремо виділяють формат друкування, який не завжди співпадає з форматом видання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Подальший вибір технологічного процесу виготовлення видання та необхідного устаткування за ідеальних умов залежить від обраного формату [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В тих випадках, коли про альтернативний вибір дру- карні не йдеться, а можливості обраної є обмеженими, залежність є оберненою, адже формат обирається з огляду не лише на тематичні та експлуатаційні вимоги видання, а й варіативність наявного устат- кування та економічна доцільність того чи іншого варіанту виготов- лення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Також виділяють формат сторінки складання (формат набору), тобто ширину і довжину сторінки без полів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вимірюється в друкар- ських одиницях.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Бувають текстові, ілюстраційні і змішані сторінки складання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таблиця 1 Формати книжкових видань для 1/8 частки аркуша Формат арку- ша паперу,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' мм ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Позначка ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='формату ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='аркуша* ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Формат книжкових видань ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Сфальцьова- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='ного аркуша ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='видання ' 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='600 M×840 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='A1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='210×300 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='205×290 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='202×288 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='500 M×700 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='B2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='175×250 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='169×239 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='165×235 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='460 М×640 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='SRA2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='160×225 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='148×210 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='145×208 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Згідно з ISO 216 та ISO 217.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М — розмір вздовж машинного напряму паперу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 60 Таблиця 2 Формати книжкових видань для 1/16 частки аркуша Формат арку- ша паперу,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' мм Позначка формату аркуша* Формат книжкових видань Сфальцьова- ного аркуша видання оптимальний мінімальний 890×1240 M 222×310 210×297 208×295 860×1220 M RA0 215×305 210×297 208×295 840×1080 M 210×270 205×260 192×255 750×900 M 185×225 182×216 179×213 700×1000 M B1 175×250 169×239 165×235 700×900 M 175×225 170×215 167×213 600×900 M 150×225 145×215 142×213 600×840 M A1 150×210 145×200 142×198 Згідно з ISO 216 та ISO 217.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М — розмір вздовж машинного напряму паперу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таблиця 3 Формати книжкових видань для 1/32 частки аркуша Формат арку- ша паперу,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' мм ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Позначка ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='формату ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='аркуша* ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Формат книжкових видань ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Сфальцьова- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='ного аркуша ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='видання ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='оптимальний ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='мінімальний ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1000 M×1400 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='B0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='175×250 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='169×239 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='165×235 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='890 M×1240 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='155×222 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='148×210 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='145×208 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='880 M×1120 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='140×220 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='136×210 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='133×208 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='860 M×1220 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='RA0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='152×215 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='148×210 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='145×208 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='840 M×1080 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='135×210 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='130×200 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='127×188 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='750 M×900 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='112×187 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='107×177 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='104×175 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='700 M×1080 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='135×175 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='130×165 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='127×163 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='700 M×1000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='B1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='125×175 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='120×165 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='117×163 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='700 M×900 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='112×175 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='107×165 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='104×163 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='600 M×900 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='112×150 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='107×140 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='104×138 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='600 M×840 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='105×150 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='100×140 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='97×138 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Згідно з ISO 216 та ISO 217.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М — розмір вздовж машинного напряму паперу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поля сторінки — це незаповнені ділянки навколо сторінки складан- ня, розміри яких визначаються різницею формату сторінки та формату сторінки складання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кожна сторінка має чотири поля: верхнє (голов- кове), нижнє (хвостове), зовнішнє (переднє) і внутрішнє (корінцеве).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оптимальні розміри полів завжди є пропорційними одне до одного.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 61 Рекомендовані розміри сторінки складання та полів для певних форматів залежать від варіантів оформлення видань (перший — най- більш економний, з невеликими полями;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' другий — звичайний, з се- редніми полями;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' третій — покращений, з великими полями) [2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таблиця 4 Рекомендовані розміри полів Формат паперу, см та частка аркуша Формат сторінки складання, кв.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розміри полів до обрізування (корінцеве,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' верхнє,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' зовнішнє,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' нижнє),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' мм Перший варіант оформлення 60×84/32 9,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 15,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20 60×90/32 9,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 18,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20 70×90/32 9,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 18,' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 23,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 29 Другий варіант оформлення 60×84/32 1 1 4 6 4 4 × 11,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 18,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 22 62 Продовження табл.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4 Формат паперу, см та частка аркуша Формат сторінки складання, кв.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 33 60×90/8 1 10 14 4 × 16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 24,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 28 70×100/8 3 3 11 16 4 4 × 16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 23,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 29 70×108/8 3 3 12 16 4 4 × 16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 25,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 29 84×108/8 3 1 12 20 4 2 × 16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 25,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 31 Третій варіант оформлення 60×84/32 4 6 × 13,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 18,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 24 60×90/32 1 4 6 4 × 13,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 18,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 23,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 24 70×90/32 1 1 4 7 4 4 × 13,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 18,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 27 75×90/32 1 4 8 4 × 13,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 18,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 25 63 Закінчення табл.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4 Формат паперу, см та частка аркуша Формат сторінки складання, кв.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розміри полів до обрізування (корінцеве,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' верхнє,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' зовнішнє,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' нижнє),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' мм 70×100/32 3 1 4 7 4 4 × 13,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 18,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 26,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 27 70×108/32 1 1 5 7 2 4 × 13,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 18,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 23,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 27 84×108/32 1 1 5 9 2 4 × 13,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 18,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 23,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 26 60×84/16 1 1 6 9 4 4 × 16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 22,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 24 60×90/16 1 6 10 4 × 16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 22,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 25 70×90/16 1 3 7 9 2 4 × 16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 24,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 29 75×90/16 1 3 8 9 4 4 × 16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 23,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 30 70×100/16 1 7 11 2 × 16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 24,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 32 70×108/16 1 7 12 2 × 16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 24,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 24 84×108/16 1 9 12 4 × 16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 27,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 24 60×84/8 1 1 9 13 4 2 × 18,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 22,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 26,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 35 60×90/8 1 3 10 13 4 4 × 18,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 22,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 27,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 31 70×100/8 1 1 11 16 2 2 × 18,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 22,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 25,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 31 70×108/8 1 1 12 16 2 2 × 18,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 22,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 27,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 31 84×108/8 1 1 12 20 2 4 × 18,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 22,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 27,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 34 Обсяг — це кількість сторінок або аркушів в одному примірнику видання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розрізняють такі види аркушів: паперовий, фізичний, умов- ний, авторський, обліково-видавничий.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Паперовий аркуш — облікова одиниця виміру кількості паперу, необхідного для друкування видан- ня.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Один паперовий аркуш дорівнює двом фізичним аркушам.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Фізич- ний друкарський аркуш — це фізичний обсяг видання, що дорівнює площі аркушу визначеного формату (84×108 см, 84×90 см, 70×100 см та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ), задрукованого з однієї сторони.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кількість фізичних аркушів у два рази більша за кількість паперових аркушів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Умовний друкарський аркуш — облікова одиниця обсягу видання, площею 60×90 см, при- 64 значена для порівняння обсягу видань різних форматів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вираження фізичних друкарських аркушів в умовних друкарських аркушах і на- впаки здійснюється за допомогою коефіцієнта переведення: , фа пр уа S K S = (1) де фа S — площа фізичного аркуша, уа S — площа умовного аркуша.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тоді обсяг видання в умовних друкарських аркушах визначається за формулою: , уа фа пр O O K = ⋅ (2) де фа O — обсяг в фізичних аркушах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Авторський аркуш — облікова одиниця обсягу твору.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Один ав- торський аркуш містить 40000 знаків прозового тексту (в тому числі пробіли, розділові знаки, цифри тощо) або 700 рядків віршованого тексту, або 3000 см2 ілюстрацій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Обліково-видавничий аркуш призначений для вимірювання об- сягу авторського твору з урахуванням матеріалів, доданих видавни- цтвом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визначається так само, як і авторський аркуш, але враховує об’єкти, що не є наслідком авторської праці (видавничу анотацію, зміст, титульні елементи, вихідні та випускні дані, передмову, дані на обкладинці, палітурці, суперобкладинці, колонцифру тощо).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Обсяг видання в аркушах слугує для обліку робіт, уніфікації ви- дань, підрахунку витрат та здійснення технологічних розрахунків.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кількість умовних та обліково-видавничих аркушів зазначається у випускних відомостях книги.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ще однією обліковою одиницею об- сягу видання є кількість сторінок, що зазначається в бібліографіч- ному описі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Від обсягу видання залежать вид та тип покрівельного матеріалу, спосіб фальцювання та комплектування, технологія скрі- плення книжкового блоку та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' [35;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 51;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Конструкційні особливості.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Враховується спосіб комплектування, спосіб скріплення книжкового блоку, вид і тип покрівельного матері- алу, наявність та вид додаткових елементів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Комплектування книжкових блоків відбувається двома способа- ми: вкладанням та підбиранням.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Комплектування вкладанням по- лягає у вкладанні сфальцьованих аркушів один в один, використову- ється для невеликих за обсягом видань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Накладання сфальцьованих зошитів або аркушів один на один називається комплектуванням ви- дань підбиранням (для видань обсягом понад 80 сторінок) [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 65 Способи скріплення поділяються на швейні, безшвейні і комбі- новані.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При швейному скріпленні використовують дріт або нитки, при безшвейному — клей чи механічні способи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Також виділяють позошитне та поблочне скріплення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При позошитному скріпленні блок повинен бути скомплектованим підбиранням.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тоді кожен зо- шит один за одним прошивається через фальц і скріплюється (швей- не скріплення).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При поблочному скріпленні блок комплектується вкладанням або підбиранням і скріплюється за один робочий цикл (швейне, незшивне клейове чи комбіноване скріплення).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поблочний спосіб скріплення є економічнішим, особливо для видань великого об’єму.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Скріплення дротом найчастіше використовується для видань із малим чи середнім терміном використання, зазвичай для брошур і книжок у м’якій обкладинці.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Забезпечує високу продуктивність, міц- ність та низьку собівартість.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Є чотири способи шиття дротом: ушив- кою, вшиттям, врознім, зустрічними скобами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При шитті ушивкою дротяні скоби проходять через згин корінця і загинаються всередину книги.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для запобігання корозії використо- вується дріт із покриттям або іноді латунний дріт.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Шиття ушивкою застосовується до блоків, скомплектованих вкладанням із накинутою зверху обкладинкою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Шиття вшиттям дроту використовується для видань, скомплекто- ваних підбиранням.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Прошивання здійснюється дротяними скобами на відстані 4–5 мм від краю корінця.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кінці скоби загинаються пара- лельно до спинки скоби на корінцевому полі останньої сторінки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для закриття спинки та ніжок скоби приклеюють обкладинку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Шиття дротом врознім використовується для видань у палітур- ках.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому скоби загинаються поверх блока на корінець.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Шит- тя врознім може бути як поблочним (для видань, скомплектованих вкладанням), так і позошитним.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Шиття дротом зустрічними скобами використовується для бло- ків товщиною більше 15 мм, скомплектованих підбиранням.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зазви- чай застосовується для виготовлення відкритих календарів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Міцність забезпечується невеликою відстанню між ніжками скоб (не менше 5 мм).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Шиття блоків нитками є одним з найбільш розповсюджених та надійних способів скріплення, дозволяє обробляти зошити на поопе- раційному обладнанні та потокових лініях.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Є чотири способи шиття нитками: впрострочку, вшиттям, позошитне, позошитне на марлі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 66 Шиття нитками впрострочку використовується для видань неве- ликого обсягу, скомплектованих вкладанням.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Прошивання здійсню- ється неперервним швом вздовж усього згину.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Шиття вшиттям ниток застосовується до блоків, скомплектова- них підбиранням.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Прошивання здійснюється вздовж усього корінця з відступом від краю 4–5 мм.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Позошитне шиття полягає у послідовному прошиванні корінце- вих згинів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відбувається не лише зшиття кожного аркуша, а й зоши- тів між собою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Допускається зшиття блоків на корінцевому матеріалі, наприклад, на марлі (для книг у палітурках), та без нього (для книг в обкладинках та палітурках).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Незшивне скріплення здійснюється за допомогою клейових плі- вок чи різних механічних пристроїв.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Незшивне клейове скріплення реалізується різними клеями та у різний спосіб і поділяється так: з повним зрізанням, частковим зрі- занням і без зрізання корінцевих фальців.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Незшивне клейове скріплення з повним зрізанням корінцевих фаль- ців при застосуванні полівінілацетатної дисперсії (холодне скріплення) здійснюється шляхом утворення клейової плівки внаслідок випарову- вання води з клею та його часткового вбирання папером.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Обладнання, що використовується для незшивного клейового скріплення з повним зрізанням корінцевих фальців при застосуванні термоклеїв (гаряче скріплення), повинно мати підігрівач бачка з клеєм, а при застосуванні полівінілацетатної дисперсії (холодне скріплення) — стіл з підігрівом чи сушильну секцію.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Загалом більшість операцій при холодному та гарячо- му скріпленнях є однаковими чи подібними, тож часто використовують універсальне обладнання, яке можна переналаштовувати.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Незшивне клейове скріплення з частковим руйнуванням корінце- вих фальців характеризується вищою міцністю порівняно з попере- днім способом, за рахунок збереження частини фальців.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому клей склеює зошити між собою та проникає у прорізи, склеюючи аркуші.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Блоки комплектуються підбиранням, а обсяг зошитів стано- вить 8 чи 16 сторінок.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Можливі такі способи: скріплення блоків за допомогою шнурів чи ниток у прорізах на корінці;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' скріплення блоків з прорізами, канавками поперек корінця;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' «флекстабіль», скріплен- ня блоків з вирубуванням окремих зон;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' скріплення блоків з зошитів, перфорованих за корінцем.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Незшивне клейове скріплення без руйнування корінцевих фаль- ців поділяється на такі способи: скріплення однозгинних зошитів, 67 скріплення дво- і тризгинних зошитів у корінцевих згинах вузькими смужками рідкого холодного клею, скріплення зошитів за корінцеви- ми фальцами з використанням термоклею, незшивне клейове скріп- лення з попереднім нанесенням на середину корінцевих полів сму- жок холодного поліамідного клею.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Механічні незшивні способи скріплення призначені для з’єднання блоків за допомогою механічних замків.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому блоки складають- ся з окремих аркушів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Застосовуються для виготовлення дитячих ви- дань, рекламних проспектів, каталогів, альбомів та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Швейно-клейове скріплення (комбіноване) здійснюється за до- помогою термониток.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому блоки повинні бути скомплектова- ні підбиранням.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Шиття відбувається при фальцюванні [9;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 35;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виділяють чотири типи обкладинок та п’ять типів палітурок.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Обкладинка — зовнішній покрівельний матеріал, що скріплюєть- ся з книжковим блоком без застосування форзаців.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розрізняють чо- тири типи обкладинок.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тип 1 — проста обкладинка для покриття блока наопашки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Засто- совується для видань обсягом до 64 сторінок.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Обкладинка складаєть- ся з одного аркушу, який накидається на зошит і скріплюється з ним дротяними скобами чи нитками.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Блок при цьому зазвичай комплек- тується вкладанням.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Найчастіше виготовляється з паперу, який, для збільшення довговічності, може бути покритий прозорим полімер- ним шаром з однієї або двох сторін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тип 2 — проста обкладинка для звичайного покриття блока.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Скріп- люється з книжковим блоком шляхом приклеювання по корінцю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Містить подвійне бігування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На відміну від обкладинки типу 1 може бути покрита прозорим полімерним шаром тільки з зовнішнього боку (щоб була змога приклеїти її по корінцю).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Блок комплектується під- биранням.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При відкриванні основне навантаження припадає на біги, тому може виникати відривання обкладинки від книжкового блока.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тип 3 — проста обкладинка для покриття блока врозпуск.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Скріп- люється з книжковим блоком шляхом приклеювання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому клей наноситься не лише на корінець, а й на бокові сторони блоку (на кілька міліметрів корінцевого поля першої та останньої сторінки).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Блок комплектується підбиранням.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такий тип обкладинки найбільш поширений, адже є довговічнішим за тип 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це пов’язано з наявністю чотирьох бігувань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тип 4 — складена обкладинка з обкантованим корінцем.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Матеріа- лом боковин може бути папір або палітурний картон, а як обкантовку 68 використовують палітурний матеріал.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Характеризується значно ви- щою міцністю та складністю виготовлення порівняно з обкладинками типів 1, 2 та 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зазвичай застосовується для видань великого обсягу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тобто, за конструкцією обкладинки типи 1, 2, 3 складаються з од- нієї деталі, а обкладинка типу 4 з боковин обкладинки та обкантовки [13;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Палітурка — цупкий, захисний зовнішній покрівельний елемент книги, який скріплюється з книжковим блоком за допомогою форза- ців.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розрізняють п’ять типів палітурок.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тип 5 — складена.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Складається з картонних боковин, корінця, від- ставу, вкритих різними покрівельними матеріалами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для видань тов- щиною до 10 мм можна виготовляти без розставів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Використовується для дитячої, художньої, наукової літератури, підручників для серед- ньої школи, невеликих за обсягом довідників.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Характеризується не- високою собівартістю, достатньою міцністю та великими можливос- тями оформлення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Може задруковуватися з подальшим лакуванням чи припресовуванням плівки, що підвищує довговічність та стійкість до стирання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тип 6 — палітурка з однієї деталі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Складається з одного суцільного матеріалу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зазвичай використовується для довідникових видань ма- лого формату та для паперово-білових виробів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тип 7 — суцільнокрита.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Складається з картонних боковин та від- ставу, вкритих суцільним покрівельним матеріалом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для видань тов- щиною до 10 мм можна виготовляти без розставів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Характеризується невеликою собівартістю та більшою міцністю, порівняно з палітурка- ми типів 5, 8 та 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Завдяки своїм характеристикам отримала широке застосування, зокрема для покриття підручників для закладів вищої та професійно-технічної освіти, передплатних, науково-популярних, наукових видань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тип 8 — палітурка з накладними боковинками і накладним ко- рінцем.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Складається з картонних боковинок, відставу, накладних боковинок, обкладених покрівельним матеріалом з усіх сторін, та накладного корінця.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Характеризується невисокою міцністю, серед- ньою собівартістю, привабливим виглядом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Використовуються при виготовленні наукових, науково-довідкових, науково-популярних видань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тип 9 — палітурка з накладними боковинками і обкантованим ко- рінцем.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Складається з картонних боковинок, накладних боковинок та обкантовувального матеріалу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зазвичай слугує для покриття під- 69 ручників для початкової та середньої школи, довідкових та науково- популярних видань [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Видання також може мати додаткові елементи: форзаци (для скріп лення книжкових блоків з палітурками та оформлення видань), ілюстрації (для оформлення видань).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Форзаци поділяються за та- кими характеристиками: характером оформлення (прості незадру- ковані, виготовлені з кольорового паперу та незадруковані, фонові, декоративно-орнаментні, тематичні), кількістю задрукованих сторін (односторонні, двосторонні), фарбовістю (однофарбові, двофарбові, багатофарбові), способом приєднання (приклейні, пришивні, про- шивні), конструкцією (суцільнопаперові, обкантовані, прикантова- ні, накидні, складені).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Додаткові ілюстративні елементи класифіку- ються залежно від місця розміщення в зошиті та способу приєднання до нього: приклейки (прості, складнофальцьовані, з окантуванням, в рамку, на стержень, на паспарту (на стержні, з плюром), з відігнутим фальцем, з бігуванням), вклейки (в роз’єм зошитів, з розрізуванням фальців зошитів, прості, складнофальцьовані), накидки, вкладки, окремий зошит.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Додатковими елементами також можуть бути части- ни аркушів — зошити з іншою кількістю сторінок, ніж основні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Обсяг додаткових зошитів повинен бути кратним чотирьом [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Умови експлуатації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Цей фактор містить дві основні складові: тер- мін та інтенсивність експлуатації книжкових видань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Термін служби — це календарний час експлуатації видання чи його довговічність, які залежать від конструкційних особливостей, інформаційної цінності, місця його використання та вікової категорії читачів [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За віковою категорією видання поділяються на ті, що призначені для дорослих читачів та для дітей.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Крім того дітей-читачів поділяють за швидкістю читання (досвідчені та читачі-початківці) та за віком (дошкільнята (до 6 років включно), читачі молодшого шкільного віку (від 7 до 10 років), читачі середнього шкільного віку (від 11 до 14 ро- ків) та читачі старшого шкільного віку (від 15 до 17 років).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Звісно, що зазвичай видання для дітей молодшого шкільного віку будуть менш довговічними, ніж для старшого [70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виділяють малий (до 2 років), середній (до 5–10 років) та великий (до 20 років і більше) термін служби видань [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За терміном використання також розрізняють видання для три- валого, разового та разового тривалого користування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Видання для тривалого користування можуть неодноразово перечитуватися од- 70 ним чи кількома читачами впродовж великого проміжку часу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На- приклад, мистецькі видання, літературна класика, вузькопрофільні видання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Видання для разового використання актуальні недовготри- валий період, зазвичай використовуються лише один раз та втрача- ють своє функціональне призначення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До таких видань належать програми святкових заходів, концертів, конференцій тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Видання для разового тривалого користування призначені для читання одним користувачем один раз протягом відносно тривалого часу, після чого можуть бути використані іншим читачем за тим самим принципом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сюди відносяться навчально-методичні матеріали, зокрема методич- ні вказівки, робочі програми тощо [70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інтенсивність експлуатації визначається числом подвійних пере- гинів елементів книги.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Чим більша кількість перегинів, тим вищою є інтенсивність експлуатації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розрізняють малу та велику інтенсив- ність.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При чому вона не залежить від терміну служби, адже, напри- клад, при малому терміні службі інтенсивність експлуатації може бути як малою, так і великою [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тип виробництва.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тип виробництва — багатоскладова характе- ристика організаційного та технічного рівнів виробництва, яка по- ширюється на обсяг виробництва, номенклатуру продукції, характер завантаження робочих місць, випуск однотипної продукції, собівар- тість продукції та кваліфікацію робітників.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Іншими словами, це рі- вень постійного завантаження робочих місць однотипною роботою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розрізняють такі типи організації виробничого процесу: одиничне, серійне, масове та змішане.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Одиничне виробництво характеризується високою собівартістю продукції, тривалим терміном виробництва, великою часткою руч- ної праці та відсутністю закріплених операцій за робочими місцями.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Впроваджується при наявності великої кількості номенклатур при невеликих тиражах, зазвичай для випуску книг на замовлення (Book on Demand).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При серійному виробництві виготовляється обмежений асор- тимент продукції, тобто робота проводиться з певними партіями.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Характеризується значною механізацією праці, паралельно-послі- довним переміщенням предметів праці, закріпленням періодично повторюваних операцій за визначеними робочими місцями, великою номенклатурою, однак меншою, ніж при одиничному виробництві.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Собівартість книжкової продукції також нижча, ніж при одиничному виробництві.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Буває дрібно-, середньо- та великосерійне виробництво.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 71 Масове виробництво характеризується виготовленням книжко- вої продукції великими накладами на вузькоспеціалізованих робочих місцях.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Характерною є висока механізація, автоматизація виробни- чого процесу та значно нижча собівартість продукції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Можливе ви- користання потокових ліній [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Матеріали.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основними матеріалами, характеристики яких врахо- вуються при проєктуванні післядрукарських процесів, є вид і параме- три паперу, на якому друкується наклад;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' палітурні матеріали;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' матері- али для скріплення книжкових блоків;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' оздоблювальні матеріали та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Загальними для всіх видів паперу є такі вимоги: – достатня механічна міцність;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – незасміченість;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – однорідність товщини, щільності та структури в межах однієї партії та всередині кожного аркуша;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – вологість 6–8 %;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – чітка прямокутна форма аркушів (допустимі відхилення косини не більше 2 мм).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Будову та структуру паперу характеризують такі параметри, як товщина, маса квадратного метра, щільність, пористість.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Товщина є основною характеристикою, що впливає на механічні та оптичні властивості паперу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Папір товщиною від 0,03 до 0,25 мм використовують для друкування (зазвичай 0,07–0,1 мм).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Матеріал із більшою товщиною, але до 3 мм називається картоном.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Товщина па- перу визначає масивність видання та його економічні показники.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для прикладу, від товщини корінця книги залежать витрати палітурних матеріалів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Чим тонший папір, тим компактніший книжковий блок.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ще одним важливим показником характеристики паперу є маса квадратного метра, яка пропорційна середній товщині паперу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для друкування використовують папір масою від 30 до 250 г/м2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Матеріал масою більше 250 г/м2 називають картоном.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сорти паперу однакової маси можуть мати різну товщину та щільність.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На щільність паперу впливає кількість наповнювача, ступінь розмелу волокон, каландрування паперу тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для друкування ви- користовують папір щільністю від 0,5 до 1,35 г/м2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Щільність паперу пов’язана з його пористістю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Пористість — це ступінь присутності порожнин у міжволокнис- тому просторі паперу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Чим більша пористість, тим вища вбирна здат- ність паперу та, відповідно, швидкість всотування фарби.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Однак при значній пористості зменшується контрастність друкарських відбитків.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 72 Неоднорідність структури пов’язана з технологічними особливос- тями виготовлення паперу і спостерігається між поперечними і по- здовжніми волокнами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поперечному напрямку притаманні менша цупкість, більше розширення структури при зволоженні (ніж видо- вження структури при зволоженні у поздовжньому напрямку).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ви- значення напрямку паперу здійснюється за допомогою дослідження на надрив, де при перпендикулярному розриві аркуша в поперечно- му напрямку виникає рваний надрив, а в поздовжньому — гладкий.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Також різниться лицевий та зворотній бік паперу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Лицевий бік глад- кіший, адже при виготовленні зворотній бік контактує з сіткою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ці особливості важливі не лише при друкуванні, а й при брошуруваль- но-палітурних процесах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наприклад, фальцювання краще відбува- ється вздовж напрямку відливу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для уникнення поперечних складок і хвилеподібності поверхні блоку напрям волокон для книжкового ви- дання повинен бути паралельним корінцю блоку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Важливим показником характеристики поверхні паперу є глад- кість.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Чим вища гладкість, тим краща якість віддрукованих зобра- жень, тому для друкування високоякісних ілюстраційних видань ви- користовують гладкий крейдяний папір.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До механічних властивостей паперу належать міцність та дефор- мація.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Міцність — це здатність паперу чинити опір руйнуванню під дією механічних сил.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Властивості міцності та деформації залежать від складу та структури: наявності наповнювача, поверхневої про- клейки, ступеня розробки рослинних волокнистих напівфабрикатів та каландрування, вологості паперу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При дослідженні міцності папе- ру послуговуються такими характеристиками: міцність на розрив і видовження, міцність на згин, міцність на надрив, міцність поверх- ні до стирання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Деформація паперу виникає під дією навантаження.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розрізняють зворотну (зникає при відсутності тиску) та незворотну (залишається після припинення навантаження) деформацію.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кожна з них використовується для певних цілей, наприклад, при тисненні на палітурці потрібно, аби рельєф залишався, а не зникав з часом, а при високому друку — навпаки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За характером деформація поділяється на пружну, еластичну та пластичну.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Пружність — це властивість, що до- зволяє паперу змінювати свою форму під час дії механічних сил, а піс- ля припинення цієї дії миттєво відновлювати початкову форму.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Елас- тичність дозволяє поступово відновлювати форму після припинення дії механічних сил.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Пластична деформація є незворотною, адже папір не може відновити свою початкову форму після усунення напруги.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 73 До оптичних властивостей паперу належать білизна, глянець, про- зорість, світлопроникність.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Білизна — здатність паперу рівномірно відбивати світло, характеризується коефіцієнтом відбивання (відно- шення кількості відбитого світла поверхнею паперу до кількості світ- ла, що падає на цю поверхню).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В цілому білизна паперу коливається від 60 до 98 %, а оптимальною для читання вважається від 70 до 80 %.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Глянець — частково дзеркальне відбивання світла від поверхні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За цим показником папір буває глянцевим (глянець може доходити до 75–80 %) і матовим (до 30 %).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Прозорість — один з випадків світло- проникності, який визначає здатність паперу пропускати крізь себе світло без розсіювання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зазвичай це негативне явище, яке призводить до видимості надрукованого на зворотному боці паперу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Друкарський папір поділяється на групи за певними ознаками: – призначенням: для офсетного, високого, глибокого способів друку;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – форматом: аркушевий, рулонний;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – видом друкарської продукції: книжково-журнальний, газетний, картографічний та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – волокнистим складом;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – масою метра квадратного тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Класифікація паперу у різних країнах відрізняється [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Картон у поліграфії використовується для виготовлення палітурок (палітурний картон), суцільнокартонних обкладинок (кольоровий пресшпан), упаковки різного виду (крейдяний хром-ерзац коробко- вий).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Також використовують гофрований картон.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поверхня палітур- ного картону повинна бути гладкою, рівною, нежолобленою, без плям і складок.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Є чотири марки палітурного картону: А (для ручного та ме- ханічного виготовлення палітурок, для виготовлення палітурок з при- клеєним ззовні покривним матеріалом), Б (для виготовлення футлярів книг, палітурок до малоформатних видань, палітурок з приклеєним ззовні покривним матеріалом), В (для виготовлення суцільнокартон- них палітурок типу 6 без поверхневої проклейки), Г (для виготовлення палітурок з приклеєним ззовні покривним матеріалом) [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Форзацний папір використовується для виготовлення форзаців.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Щільність форзацного паперу становить 900 кг/м3, а ступінь проклей- ки 1 мм.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо вказані показники вищі спостерігається ускладнення фальцювання, погіршення сприйняття клею та скручування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Неба- жаною також є підвищена пористість, що призводить до надмірного намокання при склеюванні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Неоднорідність щільності спричиняє жо- 74 лоблення, утворення пухирців та зморшок.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Недостатня міцність уне- можливлює задруковування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При намащуванні клеєм деформація і на- хил до скручування повинні бути мінімальними.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В цілому форзацний папір повинен бути достатньо міцним на згин та розрив, адже забезпе- чує довговічність видання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Форзацний папір поділяється на дві марки: А (для незадрукованих форзаців) та О (для багатофарбових форзаців).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для виготовлення обкладинок та обклейки палітурок використо- вують обкладинковий папір трьох марок: А (глазурований), Б (ма- товий), В (містить волокна деревної маси та поступається міцністю маркам А та Б).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такий папір не повинен змінювати розмір при зволо- женні і повинен мати високу міцність на розрив і згин.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Папір для відставу має масу 210 г/м2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Повинен бути пружним, щільним, цупким, не ламким.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для склеювання корінця книжкового блоку використовують міц- ний, непроклеєний та неглазурований папір, який добре сприймає клей.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Покривні матеріали повинні відповідати таким вимогам: – мати високу міцність на надрив, розрив та стирання;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – мати достатню щільність, аби глибоко не всмоктувати клеї та фарби;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – витримувати багаторазові згини впродовж тривалого часу;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – бути водо- та світлостійкими;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – сприймати друкарські фарби та тиснення фольгою;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – мати естетичний вигляд тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основними властивостями палітурного матеріалу є колір, яскра- вість, художньо-технічні елементи, що визначаються призначенням та змістом видання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За видом основа покривних палітурних матеріа- лів може бути ткана, паперова та неткана [19;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зазвичай як тканеву основу покривних палітурних матеріалів використовують міткаль — міцну тканину простого полотняно- го переплетення, що слугує основою для виготовлення палітурного коленкору й ледерину.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Також можуть використовувати дук (сильно апретована, товста бавовняна тканина, з рідким полотняним пере- плетенням;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' призначена для виготовлення суцільнотканинних оправ високохудожніх видань), рогожку (міцна, груба бавовняна тканина, з рідким полотняним переплетенням, зафарбована у природні кольо- ри волокон;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' призначена для виготовлення суцільнотканинних оправ високохудожніх видань) та шифон (міцна і тонка шовкова тканина;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' використовується для приклейки форзаца та як стержні для вкле- 75 йок).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Коленкор — це бавовняна тканина полотняного переплетення, що просочена розчином з крохмального клею, каоліну та барвника.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Коленкор не використовують для видань із тривалим терміном ко- ристування, адже швидко брудниться, а від надмірної вологості може пліснявіти та загнивати.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ледерин — це палітурний матеріал з нітро- целюлозним покриттям, який виготовляється на основі міткалі з просоченням крохмально-каоліновим розчином і нітроцелюлозним покриттям на лицевому боці.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Йому властива міцність, водостійкість, світло- і термостійкість, стійкість до згинання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ззовні нагадує шкіру.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Має підвищену жорсткість, тож вимагає використання дуже липкого клею.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З часом спостерігається старіння цього матеріалу, що призво- дить до підвищення жорсткості, крихкості та руйнування згинів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До покривних матеріалів на паперовій основі належать: ледерин на папері, папвініл, тевін та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ледерин на папері — це міцний ізо- ляційний папір, що виготовляється з волокон небіленої сульфатної хвойної целюлози, покритий шаром нітроцелюлозної сульфатної плівки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Значно дешевший, ніж ледерин на тканевій основі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зазвичай застосовується для виготовлення палітурок малоформатних видань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Папвініл — це матеріал з полівінілхлоридним покриттям, що має ви- соку водостійкість, міцність до стирання і згинання, однак з часом може розтріскуватися.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зовні подібний до шкіри.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тевін — покривний матеріал з вініловим покриттям, має широку колірну гаму та витри- мує понад 2000 подвійних згинів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До покривних матеріалів на нетканій основі належать: неткор, сін- тоніт, сканвініл, ламінар, маленіт.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Неткор покритий крохмально-као- ліновим покриттям, а його нетканева основа складається зі склеєних між собою лавсанових і віскозних волокон.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Використовується для ви- готовлення палітурок масових видань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сінтоніт покритий нітроцелю- лозою, зовні подібний до ледерину, використовується для виготовлен- ня палітурок об’ємних видань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сканвініл покритий полі хлорвінілом, за властивостями нагадує папвініл, використовується для оформлен- ня палітурок цінних видань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ламінар — дубльований палітурний мате- ріал, який складається з несклеєних нетканих та паперових полотен, використовується для виготовлення палітурок художніх та наукових видань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основа маленіту виготовляється з нетканого нітроцелюлозно- го полотна з відходів низькосортної бавовняної пряжі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виділяють також покривні матеріали без основи — пластмасова плівка товщиною від 0,2 до 0,45 мм, яку використовують для виготов- лення паперо-білових товарів, а не книжкових видань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 76 Для виготовлення оправ ювілейних та подарункових альбомів можуть застосовувати шкіру.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це ефектний, однак дорогий матеріал.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Найчастіше використовують гладку козячу шкіру товщиною від 0,4 до 1 мм — сап’ян.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Окрім звичайного, буває ще левантський сап’ян — зі шкіри гірського козла.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сап’ян з тисненням на лицевому боці нази- вають шагреневою шкірою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Також застосовують товсту, м’яку телячу шкіру (опойок) та шкіру жирового дублення, що отримують зі шкір лосів, оленів, овець та диких кіз (замшу) [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для скріплення книжкових блоків використовують дріт, нитки, термонитки, марлю, каптал, матеріал для обклейки корінців, клеї тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для скріплення ушивкою застосовують дріт поліграфічний або стальний низьковуглецевий загального призначення, іноді — латун- ний дріт.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для видань, скомплектованих вкладанням і масою папе- ру основного тексту до 80 г/м2 діаметр дроту варіюється в межах від 0,4 до 0,7 мм залежно від товщини блоку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо маса паперу більша 80 г/ м2, то діаметр дроту від 0,45 до 0,7 мм.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Маса 1000 м дроту зале- жить від діаметру дроту і обирається в межах від 5,9 до 39,45 кг.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При шитті дротом в рознім можуть використовуватися бавовняна полігра- фічна марля НШ та дротяні скоби кількістю від 2 до 4 шт, залежно від висоти видання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Під час шиття вшиттям дроту використовують від 2 до 3 скоб (залежно від висоти видання) з товщиною дроту від 0,4 до 0,85 мм (залежно від товщини корінця).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Шиття дротом зустрічними скобами передбачає розміщення скоб на відстані не менше ніж 5 мм одна від одної.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Стальний дріт, що використовується у поліграфії, повинен мати однакову товщину, гладку блискучу поверхню, бути м’яким та гнуч- ким.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для уникнення корозії дріт можуть покривати тонким шаром міді, олова, цинку або лаку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для зшивання зошитів також застосовують бавовняні нитки, син- тетичні та термонитки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Бавовняні нитки складаються з шести скру- чених між собою ниток, просочених крохмальними речовинами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вони мають стабільні властивості, практично не плутаються, не об- риваються, не розрізають папір під час зшивання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Синтетичні нитки удвічі міцніші за бавовняні, хоча й значно тонші та економічніші, од- нак дорожчі та можуть різати папір при зшиванні, плутатися та роз- тягуватися.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Майже не обриваються та не торочаться.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виготовлені з поліамідних полімерів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Бавовняні та синтетичні нитки іноді поєдну- ють.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Термонитки застосовують для скріплення блоків у корінцевих 77 фальцах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вони виготовлені з віскозного шовку, покритого поліпропі- леном.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Використання термониток уможливлює автоматизацію бро- шурувально-палітурних процесів [19;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поліграфічна марля — це бавовняна тканина з рідким полотняним переплетенням.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виробляється двох марок: НШ та БО.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Марля НШ за- стосовується для шиття ниткошвейними машинами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Є добре апре- тованою та просоченою клеєм, що забезпечує достатню жорсткість.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Марля БО характеризується меншою жорсткістю та використовуєть- ся для наклеювання корінця у блокообробних агрегатах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Попри неви- соку міцність вона значно зміцнює корінець.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Замінником марлі БО може бути мікрокрепірований папір [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для наклеювання видань на корінець у блокообробних агрегатах та для окантовки корінця при безшвейному клейовому скріпленні чи скріпленні термонитками можуть використовувати мікрокрепірова- ний папір.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В обклеювально-каптальних машинах і агрегатах для обклейки корінця використовують папір з сульфатної целюлози масою від 60 до 80 г/м2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для видань обсягом понад 10 аркушів використовують каптал, який являє собою стрічку шириною від 13 до 15 см з потовщеним кра- єм в 1,5–2 мм і виготовляється тканням різнокольорових шовкових, напівшовкових та бавовняних ниток [19;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При виготовленні поліграфічної продукції також застосовують клеї, які повинні легко і рівномірно розмащуватися, добре змочувати матеріал, мати високу швидкість скріплювання, бути світлими, щоб не залишати плям, не вступати в хімічні реакції з матеріалами, що скріплюються, не пліснявіти, не старіти та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Усі палітурні клеї поді- ляються на групи: водяної дисперсії (латексний, ПВАД та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ), водя- них клейових розчинів (кістковий, крохмальний, декстриновий), тер- мопластичних полімерів (термоклеї), у вигляді розчинів у органічних розчинниках, термореактивні клеї.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До клеїв рослинного походження належать крохмальний та декстриновий клеї.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Клеями тваринного по- ходження є кістковий, казеїновий.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Синтетичні клеї: полівінілацетат- ний, епоксидний, латексний на основі бутадієнстирольного каучуку, карбоксиметилцелюлозний, термоклей, клеї у вигляді розчинів у ор- ганічних розчинниках.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В цілому вибір клею залежить від характеру поліграфічного матеріалу та умов склеювання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для прикладу, при склеюванні пористого паперу доцільно застосовувати в’язкий клей, а для приклеювання пружного покривного матеріалу — більш липкий.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 78 Для заклеювання корінця можна використати палітурні клеї з хоро- шою еластичністю та високою міцністю клейової плівки [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У подарункових чи мистецьких виданнях часто використовують лясе — закладку у вигляді шовкової стрічки шириною від 3 до 8 мм, зазвичай червоного кольору.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Також лясе може бути виготовленою з товстого паперу чи пластмаси, мати орнамент чи медальйон.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для оздоблення палітурних матеріалів здійснюють тиснення палі- турною фольгою, лакування, припресовування плівки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Палітурна фольга використовується для нанесення кольорово- го чи металевого зображення шляхом тиснення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Фольга може бути на паперовій або лавсановій основі, є багатошаровим матеріалом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Буває кольорова, бронзова, «ювілейна» та голографічна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кольорова фольга буває різних кольорів та відтінків, що уможливлює втілення найрізноманітніших ідей оформлення поліграфічної продукції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Її по- верхня буває матовою та глянцевою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відбитки є стійкими до впливу зовнішніх факторів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тиснення бронзовою фольгою візуально нага- дує тиснення золотом, однак з часом тьмяніє, тож рідко використо- вується.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' «Ювілейній» фользі притаманний хороший блиск, який не тьмяніє з часом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вона міцно тримається на палітурному матеріалі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Завдяки розсіювання відбитого світла голографічна фольга створює ефект об’ємності зображення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За іншими властивостями нагадує «ювілейну».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При виборі фольги слід враховувати її сумісність з інши- ми.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Фольга, виготовлена на водяних розчинах, не буде друкуватися по фользі, що виготовлена на спиртових розчинах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На якість відбит- ків впливають: питомий тиск;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' температура штампа;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' швидкість та час тиснення;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' вид, характер та вологість покривних матеріалів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' характер та площа друкарських елементів штампа;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' відповідність адгезійного шару фольги поверхні друкарського матеріалу;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' вид і товщина матері- алу декеля [19;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 34;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Лакування служить для додаткового оздоблення поліграфічної продукції, захисту від стирання, підвищення міцності та довговічнос- ті.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За призначенням лаки поділяються на: ґрунтувальні (створюють адгезійний шар для подальшого нанесення іншого лаку чи фарби), матові, глянцеві, підвищеної стійкості до стирання, для термозва- рювання за допомогою ультразвуку, для термозварювання за допо- могою мікрохвильових пристроїв, для полегшення або ускладнення руху задруковуваного пакувального матеріалу, для каландрування, спеціального призначення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Лакове покриття може наноситися як на сухий, так і на мокрий відбиток на лакувальних машинах або в 79 лакувальних секціях.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для цього застосовують такі типи лаків: дру- карські (на масляній основі), дисперсійні, лаки ультрафіолетового закріплення, лаки на основі летких розчинників.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Друкарські лаки містять смоли, льняну оліфу, алкіди, сикативи та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' і закріплюються вибірковим всмоктуванням та окислювальною полімеризацією нена- сичених сполук.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Головними компонентами дисперсійних лаків є по- лімери на основі стирола-акрилата.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Закріплення відбувається через всмоктування і випаровування води, у зв’язку з цим окремі полімерні частинки зближуються і, внаслідок зростання капілярного тиску, мі- крочастинки з’єднуються в однорідну плівку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Лаки ультрафіолетового закріплення поділяються на такі види: радикального і катіонного за- кріплення (за вийнятком лаків, що накладаються офсетним спосо- бом зі зволоженням — засобами радикальної полімеризації).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Лаки на основі летючих розчинників закріплюються шляхом випаровування спирту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основними недоліками цих лаків є надмірна липкість та ви- сокий рівень забруднення навколишнього середовища.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Припресовування плівки підвищує вологостійкість матеріалу, міцність, довговічність, надає блиску та естетичного вигляду.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для оздоблення покривних матеріалів застосовують синтетичні полі- мерні плівки, які повинні бути міцними, безбарвними, прозорими, еластичними, не призводити до скручування та жолоблення відбит- ку, якнайменше деформуватися в процесі старіння, мати рівномірну товщину.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виокремлюють три способи припресовування плівки: кле- йовий, безклейовий, спосіб перенесення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Клейовий спосіб полягає у нанесенні на плівку тонкого клейового шару, який висихає під дією інфрачервоних променів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Потім плівка розігрівається разом з відбит- ком і припресовується до нього.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким способом оздоблюють видан- ня в обкладинках типів 1, 2, 3, 4 та у палітурках типів 6, 7, 8, 9, а також суперобкладинки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому використовують ацетилцелюлозні, по- ліпропіленові, поліетилентерефталатні плівки та клеї (розчин полі- мерів у летких органічних розчинниках), латекси (водяні дисперсії полімерів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вид і склад клею обирається залежно від плівки та паперу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Припресовуванням плівки безклейовим способом називається про- цес з’єднання поліграфічної продукції з термопластичними поліме- рами чи плівками (поліетилтерефталатними, поліамідними, цело- фановими та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=') із нанесеним заздалегідь клейовим шаром.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Плівка нагрівається, підплавляється і припресовується до поверхні матеріа- лу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такий спосіб використовується для оздоблення видань у палітур- ках типу 5, 7, 8, 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За способом перенесення на відбиток наноситься 80 прозора плівка (поліетилентерефталатна) на основі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Згодом основа відділяється та може бути використана повторно.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Цей спосіб вико- ристовують для оздоблення обкладинок та суперобкладинок [19;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тип обладнання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На основі ключових характеристик видання та схеми технологічного процесу здійснюється вибір обладнання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для кожної операції може бути обране специфічне обладнання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Також обладнання може бути універсальним, з можливістю зміни на- лаштувань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для розрізування і підрізування паперових аркушів чи палітурних матеріалів використовують одноножеві паперорізальні машини.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При відсутності спеціалізованого устаткування вони можуть також ви- користовуватися для обрізування книжкових блоків з трьох сторін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В цілому поділяються на три категорії: малі (ширина стопи до 70 см), середні (до 90 см), великі (більше 90 см).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Також існують два способи різання: марзанний (ніж у кінці руху врізається у пластмасову деталь, розташовану нижче стопи, — марзан) і безмарзанний (для розрізуван- ня використовується ніж та контрніж).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Одноножеві різальні машини характеризуються такими параметрами: довжина різу, мінімальна та максимальна відстань від площини подавача до лінії різу, шири- на переднього стола, зусилля тиску притискача, швидкість роботи, мінімальна та максимальна швидкість подавача, пружність голов- ного приводу, відстань від підлоги до поверхні стола, маса машини.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В якості допоміжних пристроїв паперорізальних машин можуть бути: «повітряна подушка» (пневматична система для полегшення ручного пересування або повороту стопи), гідравлічні стопопідйомники, при- стрій для заміни ножа, система вилучення обрізків тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Також ви- користовують велику кількість пристроїв для механізації допоміжних операцій з підготовки стопи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Фальцювання аркушів можливе вручну, однак найчастіше цю опе- рацію виконують механізовано.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Фальцювальні машини поділяються на чотири групи: ножові, касетні, комбіновані, спеціальні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У касет- них машинах фальцювання відбувається за допомогою касет з упо- ром і рухомих валиків.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ножове фальцювання складається з чотирьох етапів: попереднього рівняння, бічного рівняння, утворення петлі за допомогою ножа, обтискання валиками місця згину.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ножові фальц- апарати використовуються зазвичай в комбінованих фальцювальних машинах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Комбіновані машини мають ножеві та касетні фальцапара- ти: перший згин утворюється в касетній фальцсекції, а всі решта — в ножевих.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Спеціальні фальцмашини використовують для фальцюван- 81 ня стосу з 10–15 аркушів, при цьому весь папір згинається за один удар.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В цілому фальцмашини складаються з самонакладу, привода, контрольно-блокувальної системи, пневматичної системи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Пресування та пакування зошитів може здійснюватися за допомо- гою пакувально-обтискних пресів, які можна поділити на такі групи: пакувально-обтискні преси для обтискування та обв’язування сфаль- цьованих аркушів, блокообтискні преси для обтискування книжкових блоків та корінців, палітурно-обтискні преси для обтискування книг.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для автоматизації приклеювання форзаців, ілюстрацій, дробових частин зошита та інших додаткових елементів використовують при- клеювальні автомати.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для обкантування зошита з приклеєними фор- зацами — обкантовувальні автомати.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Також автомати можуть бути комбінованими: спочатку виконують приклеювання, а потім обкан- товування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для комплектування блоків вкладанням використовуються вкла- дально-швейні або вкладально-швейно-різальні автомати.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Комплек- тування блоків підбиранням здійснюється на аркушепідбиральних машинах, які повинні забезпечувати послідовність, комплектність зошитів і хороше зіштовхування [35;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для шиття блоків дротом використовують дротошвейні машини: операційні, вкладально-швейні, підбирально-швейні, а також дро- тошвейні секції вкладально-швейно-різальних агрегатів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для шиття блоків нитками застосовують ниткошвейні машини,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' які можуть бути автоматичними (усі операції виконуються без участі обслуговуючого персоналу) та напівавтоматичними (зазвичай меха- нізовані усі операції крім подачі та розкриття зошитів),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' універсальни- ми (можуть виконувати брошурне і палітурне шиття різними видами стібків на корінцевому матеріалі і без нього,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' призначені для видань різних форматів) та спеціалізованими (розраховані на шиття простим брошурним стібком без марлі видань обмеженого формату).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Залежно від технології,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' машини безшвейного скріплення можуть включати такі основні вузли та пристрої: пристрій введення блока в затискачі транспортера,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' вирівнювальний пристрій,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' фрезерна секція,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' торшонувальна секція,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' клейовий апарат для нанесення клею на ко- рінець книжкового блока,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' клейовий апарат для нанесення смужки клею на бокові зошити блока,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' сушильний пристрій,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' охолоджуваль- ний пристрій,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' секція подачі і приклеювання обкладинки,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' обканту- вальна секція,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' обтискуючий пристрій,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' пристрій виведення блока з машини,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' транспортувальний пристрій [75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 82 Фальцювання і шиття термонитками відбувається на фальцюваль- ному автоматі, який можна підключати до касетних і комбінованих фальцмашин.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Заклеювання корінця книжкового блоку може проводитися на різному обладнанні, наприклад, на блокозаклеювальному верстаті неперервної дії [35;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сушіння корінців рекомендовано проводи- ти в спеціалізованих сушильних пристроях, конвекційним способом (повітря кімнатної температури або нагріте, що подається вентилято- рами), радіаційно-конвекційним способом (теплоносієм є повітря та електромагнітні хвилі інфрачервоного і видимого діапазонів), опро- міненням.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Після сушіння здійснюється обтискування корінців у пре- сах з гідравлічним приводом пресувальної колодки [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Обрізування книжкових блоків з трьох сторін зазвичай відбува- ється на спеціальних різальних машинах, які можна поділити на такі види: одноножеві з поворотним столом, триножеві однопозиційні, для поштучного обрізування блоків.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оздоблення корінця здійснюється на потокових лініях зі спеці- альними секціями або на поопераційному обладнанні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Верстат для зафарбовування обрізів зазвичай складається з самонакладу, секції зволоження обрізів, секції зафарбовування обрізів, сушильного при- строю, приймального транспортеру.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Золочення обрізів проводиться тисненням спеціальної фольги на обладнанні, у якому обріз блока шліфують, полірують, при потребі ґрунтують і припресовують фольгу за допомогою нагрітого валика з термостійкої гуми.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Закруглювання корінця блока здійснюється на закруглювальних машинах, в секціях блокообробних агрегатів потокових ліній, на за- округлювально-відгинальних автоматах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Після закруглювання корін- ця блок передається на відгинання фальців [35;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Приклеювання лясе на великих підприємствах проводиться на спеціалізованих автоматах, які можна підключати до потокової лінії, призначеної для оброблення видань покращеного типу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Приклею- вання капталів, паперової смужки і корінцевого матеріалу може від- буватися вручну, на напівавтоматах, на блокообробних агрегатах і ав- томатах [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В цілому для заклеювання та сушіння, кругління корінців, відги- нання фальців, приклеювання до корінця зміцнювальних елементів можуть використовувати найрізноманітніше устаткування: опера- ційні машини, що призначені для виконання лише однієї операції (заклеювальний верстат, блокообтискний прес, закруглювальний 83 верстат тощо), машини для двох операцій (заклеювально-сушиль- ні, закруглювально-каширувальні тощо), агрегати для трьох і більше операцій, потокові лінії [76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для розрізування задрукованої та незадрукованої аркушевої та рулонної продукції, паперу, картону, палітурних та обкантувальних матеріалів, марлі, полімерної плівки застосовують заготівельно-роз- крійне устаткування: аркушерізальні, картонорізальні, картонороз- крійні, бобінорізальні, тканинорозкрійні машини.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Палітурки можуть виготовляти вручну, напівмеханізованим і ме- ханізованим способом на палітуркоробних машинах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сучасні палі- туркоробні машини є повністю автоматизованими і потребують втру- чання оператора лише для нагляду за процесом, переналагодження машини на новий тирах палітурок, подання заготовок або заміни бобін відставу, прийняття готової продукції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Більшість машин при- значені для виготовлення суцільнокритих палітурок.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Палітуркороб- ні машини класифікуються за напрямком технологічного процесу (з вертикальним, горизонтальним, комбінованим і карусельним ходом технологічного процесу), за характером руху напівфабрикату палі- турки (з періодичним і неперервним рухом), за швидкістю (середньо- швидкісні, швидкісні, високошвидкісні) [35;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Преси для тиснення на палітурках зазвичай будуються за тигель- ним принципом: тиск створюється двома пресувальними плитами, одна з яких нерухома, а інша має зворотно-поступальний рух.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Преси класифікуються за конструкцією (з горизонтальною і вертикальною площиною тиснення), призначенням (для опрацювання великих чи малих тиражів), ступенем механізації (автоматичні, напівавтома- тичні), принципом будови (тигельні, плоскодрукарські, ротаційні), технологічним призначенням (легкого і важкого типу).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Усі преси, як правило, складаються з механізму тиснення, станини, фольгопо- давального механізму, пристрою підігріву штампу, пристрою розмі- щення палітурки відносно штампу, пристрою регулювання глибини тиснення, приводу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вставляння блока в палітурку відбувається за принципом вер- тикального переміщення блока знизу вверх.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Книговставні машини складаються з таких механізмів та пристроїв: поштучної подачі бло- ків, розкриття блока посередині і базування за товщиною і форма- том, вертикального конвеєра з крилами для транспортування блоків, клейових апаратів, самонакладу з пристроєм кругління корінця, ба- зування палітурки перед вставлянням, суміщення блока з палітуркою 84 та їх обтиснення, знімання книги з крила і виведення на приймаль- ний пристрій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такі машини класифікують за швидкістю (тихохідні, напівавтоматичні і автоматичні, високошвидкісні), ступенем агрега- тування (операційні і агрегатовані), конструкцією (з одним і кількома крилами) [76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Після вставляння блоків у палітурки здійснюється пресування і сушіння книг, штрихування, обгортання суперобкладинкою, комп- лектування стосів з книг, упаковування книжкової продукції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Пре- сування книг здійснюється на палітурнообтискних пресах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Штриху- вальне устаткування поділяється на операційне (використовується невеликими і середніми підприємствами) і комбіноване.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зазначеного поширення набули комбіновані пресувально-штрихувальні машини неперервної і періодичної дії, які працюють разом з книговставни- ми машинами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Обгортання книг суперобкладинкою здійснюється вручну з використанням покривної машини або автоматизовано на спеціальних машинах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Пакування книг буває ручним, механізованим (із застосуванням комплектувальних, пакувальних і обв’язувальних машин) і автоматизованим.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У палітурному виробництві також застосовують потокові техноло- гічні лінії, які мають такі переваги: розташування устаткування по- слідовно виконанню операцій, синхронізація операцій, оперативна передача напівфабрикатів за допомогою транспортно-передавальних пристроїв, періодичність запуску напівфабрикатів на потік, виконан- ня операцій над ними і виведення з потоку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Потокові лінії класифіку- ються за однорідністю продукції (сталого та змінного потоку), про- дуктивністю (синхронного та несинхронного потоку), неперевністю руху напівфабрикатів (неперервного та перервного потоку), ступенем автоматизації та механізації (механізовані, комплексно-механізовані, автоматизовані потокові лінії).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для лакування можуть використовувати спеціалізовані машини для лакування всієї поверхні, системи зволоження офсетних ма- шин для лакування всієї поверхні або окремих ділянок, самостійні лакувальні секції друкарських машин.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Устаткування для припресо- вування плівки до аркушевих матеріалів називають ламінаторами [35;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Технологічні та економічні розрахунки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За відповідними формулами визначаються необхідна кількість матеріалів, розмір деталей, термін експлуатації та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідно до економічних розрахунків здійсню- ється вибір оптимального варіанту виготовлення видання [23, 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 85 Схема технологічного процесу відображає взаємопов’язану послі- довність виконання технологічних операцій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Технологічна схема бро- шурувально-палітурних процесів обирається залежно від технічних характеристик видання (обсягу, формату, особливостей конструкції, призначення видання), накладу, очікуваної собівартості та технічно- го оснащення поліграфічного підприємства.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розрізняють типові та індивідуальні технологічні схеми.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Можлива також адаптація типових схем, враховуючи конкретні умови проєктування та виготовлення поліграфічної продукції [35;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Основною метою розроблення будь- якої інформаційної технології є технологізація певного соціально значимого процесу, тобто цілеспрямований вплив на його перебіг із використанням комп’ютерно-обчислювальної техніки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вихідними даними при цьому є певна недостатньо систематизована інформація.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Високий рівень поділу процесів на етапи, системна повнота, регуляр- ність та однозначність сприяють його раціоналізації, завершеності, стандартизації й уніфікації, а, отже, плануванню й прогнозуванню.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для формалізації наведених знань доцільно розробити онтологію проєктування післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Структура онтології безпо- середньо впливає на здатність встановлювати оптимальний розв’язок основної чи побічних задач.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ітеративний підхід до створення полягає у поетапному навчанні (наповненні) онтології.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Можливе постійне додавання нових класів та зв’язків між ними.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У процесі збільшення моделі виникає необхідність оптимізації шляхом видалення застарі- лих класів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Існують декілька основних типів онтологій: – метаонтології: для опису загальних понять, що не належать до предметної області;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – онтологія предметної області: формальний опис та визначення термінологічної бази предметної області;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – онтологія конкретної задачі: визначення термінологічної бази поставленої задачі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – мережеві онтології: для опису результатів дії об’єктів предметної області чи задачі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основними принципами побудови онтологій є: – «формальна онтологія», запропонована Гуаріно, яка містить теорії частин, цілісності, рівності, залежності, узагальнень та перед- бачає такі принципи побудови: потреба у розумінні всієї предметної області, чіткість ідентифікації, класифікація структури, встановлен- ня ролей;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 86 – скелетна методологія побудови онтології вручну, запропонована Усолдом та Грунінґером, яка передбачає: встановлення мети та меж, побудову онтології, оцінювання, документування, визначення прин- ципів керування попередніми етапами;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Ontological Design Patterns (ODPs): для визначення структур, термінів, семантики.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В загальному побудова моделі складається з кількох етапів: – нагромадження знань про предметну область;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – декомпозиція: розділення досліджуваного процесу на окремі елементи, які стануть основою моделі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ідентифікація елементів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – класифікація: визначення класів та елементів, що до них нале- жать (ієрархія класів);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – опис властивостей;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – присвоєння значень властивостей;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – створення зв’язків;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – розширення та конкретизація онтології;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – перевірка;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – впровадження онтології [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Опис предметної області здійснюється за допомогою класів — основ них структурних одиниць онтологічної моделі, які можуть місти- ти інші класи та/або екземпляри.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Класи — це загальні поняття, колек- ції, набори об’єктів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Екземпляри виступають суб’єктами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зв’язок між екземпляром і класом, до якого він належить, задається предикатом rdf: type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Класи в онтології організовуються у таксономію (ієрархічну кла- сифікацію).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Так, для прикладу, Обкладинка та Палітурка є підкласами класу Вид_покрівельного_матеріалу, який є підкласом Конструкційні_ особливості: Вид_покрівельного_матеріалу SubClassOf Конструкцій- ні_особливості, Конструкційні_особливості SubClassOf Проєктуван- ня_післядрукарських_процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Властивості-відношення визначають існуючі зв’язки між екземплярами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наприклад: Значний_обсяг Ви- значає Комплектування_підбиранням.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Властивості-дані визначають конкретні характеристики екземплярів певних класів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наприклад, для екземпляра Малий_обсяг класу Обсяг — Кількість_сторінок 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Не менш важливими для опису є глосарій та тезаурус.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оформлені належним чином онтологічні словники сприяють полегшенню по- дальшого процесу створення онтології [73].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для запису завжди істинних тверджень використовують аксіоми.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Редактор Protégé 5 дозволяє використання таких аксіом: аксіоми 87 класів (SubClassOf, EquivalentClasses, DisjointClasses та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ), аксіоми властивостей об’єкта (SubObjectPropertyOf, EquivalentObjectProper- ties, InverseObjectProperties, FunctionalObjectProperty та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ), аксіоми властивостей даних (SubObjectPropertyOf, EquivalentDataProperties, DisjointDataProperties та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ), індивідуальні аксіоми (ClassAssertion, ObjectPropertyAssertion, DataPropertyAssertion, NegativeObjectPro- pertyAssertion та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ), аксіоми анотації (AnnotationAssertion, SubAn- notationPropertyOf, AnnotationPropertyDomain, AnnotationProper- tyRange) [78].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Функціональне моделювання проєктування післядрукарських процесів Проєктування післядрукарських процесів Показники видання Рівень якості проєктування післядрукарських процесів Апаратне та програмне забезпечення, інші знаряддя праці Особовий склад працівників, експерти з предметної області, зацікавлені особи Альтернативи реалізації Умови експлуа- таціїї Нормативно-технічна та технологічна документація Готовий проєкт Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекстна діаграма А-0 моделі IDEF0 проєктування післядрукарських процесів Використаємо методологію IDEF0 [40;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 77] для функціонального моделювання проєктування післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекстна діаграма зображена на рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому основною функцією сис- теми є проєктування післядрукарських процесів,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' а зв’язок системи із навколишнім середовищем зображується граничними стрілками: I1 — показники видання,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' C1 — нормативно-технічна та технологічна документація,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' C2 — умови експлуатації,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' C3 — альтернативи реалізації,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 01CCM1M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='88 O1 — рівень якості проєктування післядрукарських процесів,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' O2 — го- товий проєкт,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' M1 — апаратне та програмне забезпечення,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' інші зна- ряддя праці,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' M2 — особовий склад працівників,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' експерти з предмет- ної області,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' зацікавлені особи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Проаналізуємо інформаційне навантаження компонент множин граничних стрілок IDEF0 моделі: Граничні стрілки типу «Вхід» (Input): – 1I (показники видання).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ключовими показниками книжкових видань є вид, тип, формат та обсяг.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Граничні стрілки типу «Контроль» (Control): – 1 C (нормативно-технічна та технологічна документація).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До нормативно-технічної та технологічної документації належать: тех- нічні вимоги та законодавчі положення, зокрема: закони, стандарти, технічні умови, кодекси усталеної практики та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – 2 C (умови експлуатації).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Умови експлуатації включають термін та інтенсивність експлуатації готового видання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – 3 C (альтернативи реалізації).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Парето-оптимальні альтернативи, визначені оцінюванням нечітких відношень на множині альтернатив.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Граничні стрілки типу «Вихід» (Output): – 1 O (рівень якості проєктування післядрукарських процесів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ре- зультатом діяльності, спрямованої на створення проєкту, є відповід- ний рівень якості.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – 2 O (готовий проєкт).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визначає перебіг усіх технологічних дій, направлених на реалізацію післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Граничні стрілки типу «Механізми» (Mechanism): – 1 M (апаратне та програмне забезпечення, інші знаряддя праці).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Процес проєктування передбачає використання сучасних технічних та програмних засобів, в тому числі специфічного, вузькопрофільно- го програмного забезпечення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – 2 M (особовий склад працівників, експерти з предметної області, зацікавлені особи).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Проєктування післядрукарських процесів передба- чає участь висококваліфікованих працівників, обізнаних із тонкощами реалізації досліджуваних процесів, задля оцінювання вихідних даних та прогнозування результату.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Можливе залучення експертів, зокрема науковців та зацікавлених осіб (замовників, маркетологів та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Діаграма першого рівня декомпозиції А0 моделі IDEF0 містить такі блоки: – ВКВ (визначення конструкції видання);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 89 – ВВВ (визначення вимог до готового видання);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВПО (визначення послідовності технологічних операцій);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВРО (визначення режимів опрацювання).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Діаграма другого рівня декомпозиції А1 моделі IDEF0: – ВСК (вибір способу комплектування);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВСС (вибір способу скріплення);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВПМ (вибір покривного матеріалу);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ПДЕ (проєктування додаткових елементів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Діаграма третього рівня декомпозиції А2 моделі IDEF0: – ВВКБ (визначення вимог до книжкового блоку);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВВДЕ (визначення вимог до додаткових елементів);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВВПМ (визначення вимог до покривного матеріалу);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВВО (визначення вимог до оздоблення);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВВПБО (визначення вимог до покриття блоку обкладинкою);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВВВБП (визначення вимог до вставлення блоків у палітурку);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВВП (визначення вимог до пакування).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Діаграма третього рівня декомпозиції А3 моделі IDEF0: – ВПОБП (визначення послідовності операцій брошурувальних процесів);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВПОПП (визначення послідовності операцій палітурних про- цесів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Діаграма третього рівня декомпозиції А4 моделі IDEF0: – ВРОБП (визначення режимів опрацювання брошурувальних процесів);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВРОПП (визначення режимів опрацювання палітурних процесів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Етап 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Синтез моделей факторів проєктування післядрукарських процесів 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розроблення семантичної мережі взаємозв’язків між фактора- ми проєктування післядрукарських процесів На основі експертних суджень формується деяка множина фак- торів R={R1, R2, …, Rn}, що вміщає найбільш суттєві фактори.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для ви окремлення характерних чинників процесу залучаються представ- ники наукової спільноти та фахівці-практики.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Використання екс- пертного оцінювання дозволяє одержати кількісну оцінку ступеня важливості кожного з факторів, що формують множину значень чин- ників впливу на якість виконання процесу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зв’язки між визначеними факторами, необхідні для формування підґрунтя подальшого опису предметної області, кількісного оціню- 90 вання їх вагових значень та, відповідно, встановлення домінантності, визначаються та візуалізуються на основі теорії графів та семантич- них мереж.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вузли семантичної мережі відображатимуть семантику понять, тобто факторів, які згодом будуть представлені у вигляді аб- страктних лінгвістичних змінних.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Дуги відтворюють функціональні (семантичні) відносини чи зв’язки між ними.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поєднання мовознав- ства (семантика лінгвістичних змінних) та математики (мережі як ва- ріант графа) забезпечує, з одного боку, використання звичайної мови для опису бази знань досліджуваного процесу, з іншого — уможлив- лює застосування формальних методів та нечіткої логіки для дослі- дження, кінцевою метою якого є прогностичне оцінювання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вузлами семантичної мережі стають елементи множини R, а дугами — функці- ональні зв’язки з певними смисловими навантаженнями (Ri, Rj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Модель семантичної мережі створює базу для подальшого кон- структивного опису предметної області, є наочною та інтуїтивно зро- зумілою, адже є аналогом сучасних уявлень про фізіологічні механіз- ми пам’яті людини [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формалізація з’язків між факторами за допомогою предикат- них формул Логіка предикатів є частиною математичної логіки, її формаль- на мова представлена термами та взаємовідносинами між ними — преди катами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До термів, як словотвірних елементів, відносять такі конструкції мови предикатів: константи (конкретні реальні об’єкти), змінні (узагальнені можливі об’єкти, у нашому випадку фактори), функції (послідовність констант чи змінних, обмежених круглими дужками), функтори (оператори перед функцією, що повертають певне значення після впливу на об’єкт).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Предикатом називають ло- гічну функцію, яка приймає значення «істина», якщо відношення між її аргументами мають смисл, або «фальш» у противному випадку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином використання логіки предикатів полягає у виведенні усіх зв’язків між факторами, враховуючи структуру семантичної ме- режі [59;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 61;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Означимо впливи кожного фактора проєктування післядрукар- ських процесів: 1 2 – R R — визначає;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 3 – R R — визначає;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 4 – R R — ви- значає;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 5 – R R — обумовлює;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 6 – R R — обумовлює;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 7 – R R — фор- мує;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 8 – R R — обумовлює;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2 5 – R R — визначає;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2 6 – R R — впливає на вибір;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2 7 – R R — формує;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2 8 – R R — обумовлює;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3 5 – R R — впливає на вибір;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3 8 – R R — обумовлює;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4 6 – R R — визначає;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4 7 – R R — формує;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 91 5 6 – R R — впливає на вибір;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5 7 – R R — формує;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6 7 – R R — формує;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 8 5 – R R — обумовлює;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 8 6 – R R — визначає;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 8 7 – R R — формує.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для формалізації опису відносин між термами семантичних ме- реж використано предикатні формули, що включають такі конструк- ції: ∧ — логічне «і»;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ← — «якщо»;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ∀ — квантор спільності (для всіх);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ∃ — квантор існування (існує принаймні одне) [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ∀ iR ) [ ∃ ( 1 R , показники видання) ← визначає ( 1 2 , R R ) ∧ ви- значає ( 1 3 , R R ) ∧ визначає ( 1 4 , R R ) ∧ обумовлює ( 1 5 , R R ) ∧ обумовлює ( 1 6 , R R ) ∧ формує ( 1 7 , R R ) ∧ обумовлює ( 1 8 , R R )];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ∀ iR ) [ ∃ ( 2 R , конструкційні особливості) ← визначає ( 2 5 , R R ) ∧ впливає на вибір ( 2 6 , R R ) ∧ формує ( 2 7 , R R ) ∧ обумовлює ( 2 8 , R R ) ∧ визначається ( 2 1 , R R ) ∧ обирається залежно від ( 2 3 , R R )];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ∀ iR ) [ ∃ ( 3 R , умови експлуатації) ← впливає на вибір ( 3 2 , R R ) ∧ впливає на вибір ( 3 5 , R R ) ∧ обумовлює ( 3 8 , R R )];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ∀ iR ) [ ∃ ( 4 R , тип виробництва) ← визначає ( 4 6 , R R ) ∧ формує ( 4 7 , R R ) ∧ визначається ( 4 1 , R R )];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ∀ iR ) [ ∃ ( 5 R , матеріали) ← впливає на вибір ( 5 6 , R R ) ∧ формує ( 5 7 , R R ) ∧ обумовлюється ( 5 1 , R R ) ∧ визначається ( 5 2 , R R ) ∧ обира- ється залежно від ( 5 3 , R R ) ∧ обумовлюється ( 5 8 , R R )];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ∀ iR ) [ ∃ ( 6 R , тип обладнання) ← формує ( 6 7 , R R ) ∧ обумов- люється ( 6 1 , R R ) ∧ обирається залежно від ( 6 2 , R R ) ∧ визначається ( 6 4 , R R ) ∧ обирається залежно від ( 6 5 , R R ) ∧ визначається ( 6 8 , R R )];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ∀ iR ) [ ∃ ( 7 R , технологічні та економічні розрахунки) ← форму- ється ( 7 1 , R R ) ∧ формується ( 7 2 , R R ) ∧ формується ( 7 4 , R R ) ∧ форму- ється ( 7 5 , R R ) ∧ формується ( 7 6 , R R ) ∧ формується ( 7 8 , R R )];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ∀ iR ) [ ∃ ( 8 R , схема технологічного процесу) ← обумовлює ( 8, R 5 R ) ∧ визначає ( 8 6 , R R ) ∧ формує ( 8 7 , R R ) ∧ обумовлюється ( 8, R 1 R ) ∧ обумовлюється ( 8 2 , R R ) ∧ обумовлюється ( 8 3 , R R )] [61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Побудова моделі пріоритетного впливу факторів на якість про- єктування післядрукарських процесів за методом математичного мо- делювання ієрархій Окрім виокремлення необхідних лінгвістичних змінних сучасні умови виробництва вимагають чіткого розуміння їх пріоритетності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Саме завдяки ієрархічному впорядкуванню досліджуваних факторів можна сформувати цілісну картину необхідних технічних та інтелек- туальних компонент.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 92 Для встановлення рівнів пріоритетності факторів на основі семан- тичної мережі використовуємо метод математичного моделювання ієрархій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для початку будується матриця досяжності А, бінарні еле- менти якої визначаються за таким правилом: 1, 0, ij якщо з вершини і можна попасти у вершину j R в іншому випадку \uf8f1 = \uf8f2 \uf8f3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (3) Досяжність вершини Rj (j=1, 2, …, n) відносно вершини Ri (i=1, 2, …, n) обумовлюється наявністю зв’язку певного типу (прямого чи опосередкованого).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Позначимо підмножину досяжних вершин K(Ri).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому вершина Ri, для якої можлива зворотня досяжність з вер- шини Rj, буде її попередницею.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сукупність вершин попередниць формує підмножину P(Ri).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перетин вершин сформованих підмножин H(Ri)=K(Ri)∩P(Ri), за умови P(Ri)=H(Ri), визначає домінантність дії факторів, що ототожнюються з цими вершинами та встановлюється шляхом аналізу так званих ітераційних таблиць.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Внаслідок виконан- ня означених операцій над елементами семантичної мережі отриму- ємо багаторівневу модель, що відображає домінантність дії факторів на аналізований технологічний процес [58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На основі синтезованої семантичної мережі будується матриця досяжності за принципом (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для зручності відображення матрицю доцільно поміщати у таблицю, додавши позначення факторів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для подальшого встановлення пріоритетності факторів за ма- трицею досяжності будуються ітераційні таблиці, що міститимуть чотири колонки, де і — порядковий номер фактора у множині.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому для формування стовпця K(Ri) ітераційних таблиць ви- користовуємо дані, наведені у рядках матриці досяжності, а для формування стовпця P(Ri) — дані, наведені у стовпцях цієї матри- ці.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У стовпці K(Ri)∩P(Ri) подамо спільні для K(Ri) та P(Ri) фактори [58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На основі отриманих даних синтезується модель пріоритет- ного впливу факторів на якість проєктування післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, найвищий пріоритет належить фактору R1 (показ- ники видання), що є логічним з технологічної точки зору, адже вид і тип видання, формат видання та його обсяг справді є визначаль- ними при створенні проєкту реалізації післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На другому рівні знаходяться фактори R3 (умови експлуатації) та R4 (тип виробництва).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Третім за пріоритетністю є фактор R2 (конструк- ційні особливості), четвертим — R8 (схема технологічного процесу), 93 п’ятим — R5 (матеріали), шостим — R6 (тип обладнання).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Найнижчий рівень пріоритетності свідчить про підрядний характер фактора R7 (технологічні та економічні розрахунки).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Побудова моделі пріоритетного впливу факторів на якість про- єктування післядрукарських процесів за методом ранжування Уточнення чи підтвердження пріоритетності факторів проєкту- вання післядрукарських процесів здійснюється шляхом встановлен- ня їх рангів за методом ранжування, який полягає у синтезуванні деревовидних моделей на основі аналізу взаємозв’язків між виокрем- леними факторами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Слід зазначити, що згадані зв’язки поділяються на два типи: впливи та залежності, які передбачають прямі та опо- середковані дії.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Така методика дозволяє наблизити візуалізацію до реальних умов перебігу досліджуваного процесу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому кожному типу присвоюються відповідні числові показники, що уможливлює подальше математичне оцінювання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У дослідженні доцільно враховувати такі означення і твердження.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Означення 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Будь-який технологічний процес поліграфічного ви- робництва містить деяку множину факторів, які здійснюють визна- чальний вплив на якість його реалізації, відповідно й на якість дру- кованої продукції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З огляду на те, що кожен процес у поліграфії містить пев- ну множину факторів, що впливають на його якість, нехай { } 1 2 , ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', m D d d d = буде довільною множиною технологічних процесів, а { } 1 2 , ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', m m m n R r r r = — множиною факторів, що впливають на якість конкретного процесу, де m n — це кількість факторів m -го техноло- гічного процесу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому: ( ) ( ) ( ) 1 , 1,2,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', , n k jk j С S S k m = = ω = \uf055 (4) де ( ) k С S — значення функції якості m -го процесу;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) jk S ω — ваговий показник додаткової якості, принесеної j -м фактором у k -й техно- логічний процес.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тоді подамо означення таким чином: ( ) ( ) ( ) ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' k p r C r d D r R ∃ ∀ ∈ ∈ (5) Означення 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ранг та пріоритет фактора визначається ваговим ко- ефіцієнтом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Серед будь-якої множини факторів можна виокремити хоча б один пріоритетний.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 94 Тобто для множини ваг факторів { } 1 2 , ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', m m m n W w w w = , якщо ( ) { } 1 2 , ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', m m m n P w max w w w = , матимемо: ( )( ) ( );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' p w P w d D w W ∃ ∀ ∈ ∈ (6) Твердження 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Існування зв’язків між факторами є передумовою для їх формалізованого відображення у вигляді графа.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Твердження 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Облік та аналіз впливів та залежностей між факто- рами у вихідній графічній моделі, побудованій на основі експертних суджень, дозволяє визначити початкові ранги факторів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Твердження 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При порівнянні факторів у межах вихідного графа синтезована багаторівнева модель показує лише переваги між ними.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Твердження 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виявлення кінцевих вагових значень, які визнача- ють ранг та ступінь впливу факторів на m -й технологічний процес поліграфічного виробництва, можливе шляхом створення та обробки матриці попарних порівнянь і обчислення нормалізованих компо- нент головного власного вектора матриці.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Означення 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Множина факторів, упорядкованих за спаданням їх нормалізованих вагових значень, не містить абсолютно ідентичних за ступенем впливу на технологічний процес.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо ( ) 1 j j A w w w + > = для ( ) 1,2,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 j n = − , то вірним буде наступ- ний запис: ( ) ( );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' w A w w W ∀ ∈ (7) Згідно з твердженнями 1–4, синтез моделі пріоритетного впливу факторів на m -й технологічний процес поліграфічного виробництва здійснюється шляхом виокремлення характерних для аналізованого процесу факторів, створення, аналіз та обробку вихідної графічної моделі, у якій на основі експертних суджень встановлено зв’язки між факторами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За основу методу ранжування взято числові показники, які сто- суються кількостей впливів і залежностей між факторами та відпо- відних їм вагових коефіцієнтів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому розрізняємо прямі дії, назвавши їх впливами 1-го порядку, та непрямі — 2-го порядку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За- лежності також розрізнятимемо, встановивши для них аналогічно 1-й і 2-й порядки важливості.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для розрахунку сумарних вагових значень прямого та опосеред- кованого впливів факторів та їх інтегральної залежності від інших факторів введемо відповідні позначення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нехай ijk — кількість впли- 95 вів чи залежностей для j -го фактора 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', ) j n = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' iw — вага i -го типу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ідентифікуємо числові значення індексів наступним чином: 1 i = для впливів 1-го порядку, 2 i = для впливів 2-го порядку, 3 i = для залеж- ностей 1-го порядку, 4 i = для залежностей 2-го порядку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вважатиме- мо, що для впливів обох типів ваги будуть додатними, тобто 1 0 w > , 2 1 / 2 w w = , відповідно для залежностей — від’ємними, а саме: 3 0 w < , 4 3 / 2 w w = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нехай ij R — інтегральні вагові значення факторів за сума- ми ваг усіх типів зв’язків.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тоді формула для розрахунків матиме вид: 4 1 1 , n ij ij i i j R q w = = =∑∑ (8) де n — номер фактора досліджуваного процесу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідно до початкових умов 3 0 w < і 4 0 w < , отже 3 0 j R < і 4 0 j R < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Щоб привести вагові значення «до початку координат», тоб- то отримати додаткові величини, слід перемістити гістограму інте- грального графічного відображення усіх типів зв’язків вверх за таким співвідношенням: ( ) 3 4 , 1,2,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' j j j max R max R j n Δ = + = (9) На основі заданих умов отримаємо формулу підсумкових вагових значень факторів: ( ) 4 9 1 1 , Fj ij i j i j R k w = = = + Δ ∑∑ (10) де ( ) 3 4 , 1,2,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', j j j max R max R j n Δ = + = [30;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Величини Fj R служать підставою для ранжування ваг, тобто вста- новлення рівнів факторів якості реалізації технологічного процесу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За результатами ранжування здійснюється синтез графічної моделі за отриманими ваговими значеннями, що відображають пріоритетність впливу факторів на процес.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для реалізації методу стосовно кожного з факторів проєктування післядрукарських процесів на основі розробленої семантичної мере- жі будуються ієрархічні дерева зв’язків з іншими факторами, врахо- вуючи прямі та непрямі впливи і прямі та опосередковані залежності [30;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 58;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За допомогою методу ранжування встановлюються вагові значен- ня факторів та уточнюється їх пріоритетність.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином фактори R3 (умови експлуатації) та R4 (тип виробництва), що знаходилися на одному рівні, отримали відповідно другий та четвертий рівні пріори- 96 тетності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому фактор R2 (конструкційні особливості) змістився на третю позицію у моделі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Пріоритетність інших факторів лише під- твердилася.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Етап 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оптимізація моделі пріоритетного впливу факторів на якість проєктування післядрукарських процесів 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формування матриці попарних порівнянь факторів відповідно до шкали відносної важливості об’єктів за Сааті Оптимізація вагових значень факторів і синтез моделі здійсню- ються за методами багатокритеріальної оптимізації та попарних по- рівнянь.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Первинне визначення вагових значень факторів техноло- гічних процесів на основі методу ранжування передбачає отримання укрупнених результатів, що потребують подальшого експертного опрацювання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Метод аналізу ієрархій, реалізований на основі шкали відносної важливості об’єктів за Сааті, дозволяє встановити уточнені (оптимізовані) вагові значення та передбачає побудову матриці по- парних порівнянь, обчислення компонент її головного власного век- тора та їх нормалізацію, а також перевірку результатів за ключовими критеріями.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Унаслідок оптимізації здійснюється деталізація перебігу досліджуваного процесу, що позитивно впливає на його подальшу ре- алізацію.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З цією метою будуємо квадратну обернено-симетричну матри- цю попарних порівнянь (МПП), порядок якої визначається числом аналізованих факторів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Алгоритм її організації такий.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Порівнюються умовні міри впливу кожного із факторів першого стовпця матриці до- сяжності та кожний із факторів верхнього рядка матриці.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Додаткови- ми умовами при порівнянні служать отримані при ранжуванні вагові значення факторів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На перетині рядка і кожного зі стовпців МПП за- носимо числове значення переваги фактора, використовуючи шкалу відносної важливості об’єктів (табл.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Так, для двох факторів (напр.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', ri і rj), які порівнюються між собою, в залежності від їх важливості та міри впливу на проєктування післядрукарських процесів матимемо пропоновані у таблиці значення відповідного елемента матриці по- парних порівнянь у позиції (ri, rj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зрозуміло, що при такому алгорит- мі діагональні елементи МПП рівні одиниці.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нижня частина матриці попарних порівнянь заповнюється обер- неними значеннями.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Так, у позицію (ri, rj) заносимо відповідно 1, 1/3, 1/5, 1/7, 1/9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При незначних відмінностях між вагами критеріїв ви- користовують парні числа 2, 4, 6, 8 та їх обернені значення [58;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 59;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='97 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Таблиця 5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Шкала відносної важливості об’єктів ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Оцінка ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='важливості ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Критерії порівняння ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Пояснення щодо ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='вибору критерію ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Об’єкти рівноцінні ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Відсутність переваги ri над rj ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Один об’єкт дещо ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='переважає інший ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Існує підстава наявності ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='слабкої переваги ri над rj ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Один об’єкт переважає ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='інший ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Існує підстава наявності ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='cуттєвої переваги ri над rj ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='7 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Один об’єкт значно ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='переважає інший ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Існує підстава присутності ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='явної переваги ri над rj ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='9 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Один об’єкт абсолютно ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='переважає інший ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Абсолютна перевага ri над rj ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='не викликає сумніву ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 8 Компромісні проміжні значення Допоміжні порівняльні оцінки 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визначення компонент головного власного вектора матриці по- парних порівнянь Головний власний вектор ( ) 1 2 , ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', n R r r r МПП визначається як се- реднє геометричне компонент кожного рядка матриці: 1 2 1, , n i i i in R a a a i n = ⋅ ⋅ = (11) де n — кількість використаних факторів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для одержання головного власного вектора (тобто вектора пріори- тетів) матриці попарних порівнянь використаємо метод, запропоно- ваний Сааті [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розрахунки за вказаним методом з використанням ідей теорії імітаційного моделювання здійснюються за допомогою програми «Імітаційне моделювання в системному аналізі методом бінарних порівнянь» [57], розробленої на кафедрі комп’ютерних наук та інформаційних технологій Української академії друкарства.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Після завантаження програми отримуємо інтерфейс у вигляді діало- гового вікна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Опція «Введіть число критеріїв» обумовлює кількість факторів, далі — кнопка «задати».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' «Введіть назви критеріїв» — вво- димо цифрові номери факторів, кнопка «застосувати».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Заповнюємо таблицю вікна «Задання експертних оцінок переваг критеріїв» еле- ментами матриці попарних порівнянь, після кнопка «застосувати».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Результати опрацювання — у вікні «Вивід проміжних результатів», стовпець якого En відтворює компоненти нормалізованого вектора 98 R, що ідентифікують розраховані вагові значення факторів досліджу- ваного процесу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визначення компонент нормалізованого вектора матриці по- парних порівнянь Нормалізуємо значення компонент головного власного вектора n R МПП [58;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 59;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 68], встановивши попередній результат розв’язання задачі: 1 2 1 2 1 1, = ⋅ ⋅ = = ⋅ ⋅ ∑ n i i in in n n i i in i a a a i n R a a a .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (12) Для зручнішого подання вагових значень факторів множимо оптимізовані компоненти вектора n R на довільний коефіцієнт k .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нехай 500 k = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оцінка узгодженості вагових значень факторів обчислюється шляхом множення матриці попарних порівнянь справа на вектор n R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В результаті обчислення одержимо нормалізований вектор 1 n R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Компоненти власного вектора 2 n R матриці попарних порівнянь отримаємо, поділивши компоненти вектора 1 n R на відповідні компо- ненти вектора n R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Аналіз результатів оптимізації за максимальним значенням головного власного вектора матриці попарних порівнянь, індексом узго- дженості та відношенням узгодженості Максимальне власне значення max λ додатної обернено-симетрич- ної матриці A визначається як середнє арифметичне компонент век- тора 2 n R .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оцінка одержаного рішення визначається індексом узгодженості IU , який вираховується за формулою: max 1 n IU n λ − = − .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (13) Отримані значення порівнюють з еталонними значеннями по- казника узгодженості — випадковим індексом RI .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Результати можна вважати задовільними, якщо отримане шляхом обрахунків значення індекса узгодженості IU не перевищує 10 % еталонного значення випадкового індекса RI , обраного з урахуванням кількості аналізо- 99 ваних факторів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Отже для підтвердження адекватності розв’язку по- ставленої задачі повинна виконуватися нерівність 0,1 IU RI < × .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нижче наведена таблиця величин випадкового індекса для ма- триць різного порядку, в якій порядок матриці відповідає кількості аналізованих об’єктів (факторів) і вказується у першому рядку, а ета- лонне значення показника узгодженості для кожного порядку вказу- ється у другому рядку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таблиця 6 Значення випадкового індекса для матриць різного порядку Кількість об’єктів 3 4 5 6 7 8 9 10 11 12 13 14 Еталонне значення індекса 0,58 0,90 1,12 1,24 1,32 1,41 1,45 1,49 1,51 1,54 1,56 1,57 Додатково результати оцінюють відношенням узгодженості, вели- чину якого отримують із виразу: RU IU RI = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Результати попарних порівнянь можна вважати задовільними, якщо 0,1 RU ≤ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це свідчи- тиме про достатній рівень збіжності процесу та належну узгодженість експертних суджень стосовно попарних порівнянь факторів, відобра- жених у відповідній матриці.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При незадовільних значеннях індекса узгодженості та відношення узгодженості треба переглянути вихідний граф зв’язків між фактора- ми, уточнити значення величин відповідних їм попарних порівнянь, тобто розв’язати деяку обернену задачу, достовірність розв’язку якої перевіряється за наведеними вище критеріями.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Цікавими в цьому контексті можуть бути такі міркування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо максимальне значення власного вектора матриці попарних по- рівнянь і величина відношення узгодженості не виходять за межі допустимих значень, то їх можна вважати критеріями оптиміза- ції одержаної ієрархічної моделі впливу факторів на ефективність проєктування післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За цими значеннями встановлюється адекватність ієрархічної моделі реальній ситуації та її узгодженість з експертними оцінками важливості факторів [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідно max 8,483 λ = , 0,069 IU = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Еталонне значення індекса RI для матриці 8-го порядку становить 1,41, що не перевищує 10 % індекса узгодженості IU .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Отже нерівність 0,1 IU RI < × є вірною і 100 підтверджує адекватність розв’язку задачі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0,049 RU = , тож результа- ти попарних порівнянь можна вважати коректними.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Візуалізація співвідношень компонент вихідного та нормалізо- ваного векторів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Побудова оптимізованої моделі пріоритетного впливу факторів на якість проєктування післядрукарських процесів Для одержання вагових значень факторів на основі отриманих моделей їм присвоюється градація умовних числових позначень, від- повідно до рівня домінантності факторів, починаючи відлік з най- нижчого.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нехай вага найнижчого рівня буде рівною 20 умовним оди- ницям, а вага кожного наступного збільшуватиметься на 20 умовних одиниць відносно попереднього фактора.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Отримані числові значення факторів подаються у вигляді компонент вихідного вектора 0 R згідно з порядком їх розміщення у матриці.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На підставі отриманих вагових значень, представлених векторами n R та 0 R , будуються гістограма і порівняльний графік.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Порівняльне графічне відображення дає підставу стверджувати, що компоненти векторів, розрахованих за методом ранжування фак- торів та отриманих у результаті застосування методу попарних по- рівнянь, незважаючи на деяку різницю у вагових значеннях, по суті відтворюють останній порядок і суть слідування факторів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вказане уможливлює використання вагових компонент нормалізованого век- тора як основи для синтезування оптимізованої моделі пріоритетного впливу виокремлених факторів на якість проєктування післядрукар- ських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оптимізація дозволила уточнити значення ваг факторів досліджу- ваного процесу та деталізувати міру впливу кожного з них.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оптимі- заційні результати підтвердили достовірність проведених досліджень, не змінивши порядок пріоритетів факторів [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Після детального аналізу та порівняння вихідного та нормалізова- ного векторів синтезується оптимізована модель пріоритетного впли- ву факторів на процес.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вона служить підставою для проєктування альтернативних та розрахунку оптимальних варіантів реалізації тех- нологічного процесу, його етапів чи окремих операцій, фактори яких упорядковані за ваговими коефіцієнтами важливості.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 101 Етап 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визначення оптимальних альтернатив реалізації проєктуван- ня післядрукарських процесів 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Багатофакторний вибір альтернативи на основі лінійного згор- тання критеріїв Залежно від глибини пізнання проблеми розділяють на три класи: добре структуровані, неструктуровані та погано структуро- вані.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У добре структурованих проблемах існуючі залежності добре з’ясовані, тому можуть бути виражені у символах і числах та в під- сумку давати числеві оцінки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Неструктуровані проблеми містять лише описи ресурсів, характеристик та ознак, причому кількісні залежності між ними є невідомими.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Погано структуровані пробле- ми, у свою чергу, містять як якісні, так і кількісні елементи, а якіс- ні невизначені та маловідомі сторони проблеми мають домінуючу тенденцію.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визначення класу сформульованої проблеми дозволяє обрати ме- тодику її вирішення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Так, добре структуровані проблеми вирішуються шляхом використання методології дослідження операцій, неструкту- ровані — за допомогою евристичного методу, а погано структурова- ні — використовуючи системний аналіз.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З огляду на вищенаведені факти можна зробити висновок, що проблема встановлення оптимальної альтернативи проєктування післядрукарського опрацювання книжкових видань є погано струк- турованою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, визначення альтернативних варіантів ви- рішення проблеми реалізовується за допомогою системного аналізу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Генерування множини альтернатив уможливлює подальший вибір оптимальної альтернативи із цієї множини.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сформована множина альтернатив відображає можливі способи досягнення поставлених цілей.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вибір оптимальної альтернативи здійснюється із врахуванням обмежень та критерію оптимальності [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У ході дослідження були встановлені вагові значення факторів аналізованих технологічних процесів та побудовані моделі їх пріо- ритетного впливу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Отримана інформація є основою для планування стратегії реалізації проєктування післядрукарських процесів, яка по- лягає у виборі оптимального альтернативного варіанту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це дасть нам уявлення про необхідну затрату трудомісткості та міру важливості факторів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розв’язок поставленого завдання здійснюється за допомогою бага- токритеріальної (в нашому випадку в ролі критерію виступає фактор, отже багатофакторної) оптимізації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому є достатнім викорис- 102 тання лише домінуючих факторів, що обумовлено принципом Па- рето [22], суть якого полягає у використанні взаємно недомінованих факторів, які утворюють множину Парето ( ) P D , де n D R ⊂ — мно- жина допустимих розв’язків.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Фактори із помітно нижчими ваговими значеннями просто відкидаються.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Синтезована раніше семантична мережа є підставою для побудови матриці попарних порівнянь, опрацювання якої приводить до отри- мання умовних вагових значень, що визначають числові пріоритети факторів — міри важливості їх для технологічного процесу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Далі — розрахунок та визначення оптимального (серед альтернативних) ва- ріанту реалізації проєктування післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Багатокритеріальна оптимізація функцій ( ) ( ) ( ) ( ) 1 ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', n r x r x r x = на множині B полягає у виокремленні максимального значення функ- цій корисності ( ) max, i x B r x ∈ → 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' i n = Відповідно за методом лінійно- го згортання критеріїв об’єднання часткових цільових функціоналів 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' n r r здійснюється за формулою [25;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 59]: ( ) ( ) 1 , max;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' , n i i x D i R w x w r x w W ∈ = = → ∉ ∑ (14) ( ) 1 1 ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 , n T n j i i W w w w w w = \uf8f1 \uf8fc = = > = \uf8f2 \uf8fd \uf8f3 \uf8fe ∑ де iw — ваги факторів множини Парето.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для факторів незалежних за корисністю та перевагою існує така функція корисності [25]: ( ) ( ) 1 , n i i i i U x w u y = =∑ (15) де ( ) U x — багатокритеріальна функція корисності ( ) (0 1) U x ≤ ≤ певної альтернативи x ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' iw — встановлене вагове значення i -го кри- терію, причому 0 1, iw < < ( ) 1 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' n i i i i w u y = = ∑ — функція корисності i -го критерію ( ) (0 1) i i u y ≤ ≤ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' iy — значення альтернативи x за i-м крите- рієм [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для реалізації сформованої задачі виконуються такі дії: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формується множина Парето, взявши до уваги лише фактори з найвищою пріоритетністю: 1 R — показники видання (188 у.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' о.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3 R — умови експлуатації (105 у.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' о.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2 R — конструкційні особливості 103 (74 у.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' о.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4 R — тип виробництва (49,5 у.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' о.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Фактори з суттєво ниж- чою пріоритетністю відкидаються [25;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 54;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Задаються три альтернативні варіанти реалізації досліджувано- го процесу, які позначаються як 1 2 3 , , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A A A Формується таблиця оці- нювання альтернатив на основі міри важливості кожного виокрем- леного фактора.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Міра важливості кожного аналізованого фактора для заданих альтернативних варіантів виражається у відсотках.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Існує великий перелік можливих комбінацій (табл.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Реальні значення залежать від конкретного виробничого завдання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому загаль- на сума усіх альтернатив одного фактора не повинна перевищувати 100 %.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таблиця 7 Комбінації значень факторів Комбінації значень факторів у відсотках 10–10–80 20–10–70 30–10–60 40–10–50 10–20–70 20–20–60 30–20–50 40–20–40 10–30–60 20–30–50 30–30–40 40–30–30 10–40–50 20–40–40 30–40–30 40–40–20 10–50–40 20–50–30 30–50–20 40–50–10 10–60–30 20–60–20 30–60–10 50–10–40 10–70–20 20–70–10 60–10–30 50–20–30 10–80–10 70–10–20 60–20–20 50–30–20 80–10–10 70–20–10 60–30–10 50–40–10 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Створюється матриця попарних порівнянь вагових значень факторів, оцінених за шкалою відносної важливості об’єктів за Сааті.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Здійснюється нормалізація головного власного вектора матриці попарних порівнянь у програмі «Імітаційне моделювання в систем- ному аналізі методом бінарних порівнянь» [57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Унаслідок нормаліза- ції отримуються оптимізовані вагові значення факторів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Встановлю- ються критерії нормалізації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перевірка правильності розв’язку задачі здійснюється шляхом ви- конання нерівностей 0,1 IU RI < × та 0,1 RU ≤ , де RI — випадковий індекс для матриці 4-го порядку (табл.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6), 0,9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' RI = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визначаються функції корисності кожної запроєктованої аль- тернативи за факторами множини Парето.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визначаються багатокритеріальні оцінки корисності для трьох запроєктованих альтернатив.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 104 Підставивиши у формулу (15) значення R2: ( ) 4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' i i ij n u y u = = — ко- рисність j-ї альтернативи ( ) 1,2,3 j = за i-м фактором ( ) 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=',4 i = , отри- маємо наступне: 4 1 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1,2,3, j i ij i U w u j = = = ∑ (16) де j U — багатофакторна оцінка корисності j-ї альтернативи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На основі формули (16) формуються такі відношення: 1 1 11 2 21 3 31 4 41;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' U w u w u w u w u = × + × + × + × 2 1 12 2 22 3 32 4 42;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' U w u w u w u w u = × + × + × + × 3 1 13 2 23 3 33 4 43 [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' U w u w u w u w u = × + × + × + × (17) При цьому 1 0,264;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' U = 2 0,322;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' U = 3 0,414.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' U = Найкраща альтерна- тива реалізації проєктування післядрукарських процесів обирається за максимальним значенням Uj, ( 1,2,3) i = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідно альтернатива A3 є оптимальною для досліджуваного процесу, а визначальним є фак- тор «Показники видання» (R1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Багатофакторний вибір альтернативи на основі нечіткого від- ношення переваги Прийняття управлінських рішень щодо альтернативних варіантів реалізації технологічних процесів може ускладнюватися відсутністю інформації про їхню пріоритетність та неможливістю кількісного оцінювання переваг.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Натомість, можливо здійснити попарне порів- няння альтернатив на відрізку [0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1] та представити дані у числовому вигляді.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оцінювання здійснюється на основі багатокритеріальної оптимізації, де в ролі критеріїв виступають фактори технологічно- го процесу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За принципом Парето [22], як і в методі встановлення оптимальної альтернативи на основі лінійного згортання критеріїв, достатнім вважається вибір лише домінуючих факторів із найвищи- ми ваговими показниками, які формують множину Парето.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відпо- відно при нечіткому відношенні переваги на множині альтернатив прийняття рішень буде здійснюватися за Парето-оптимальними аль- тернативами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Введення чіткого відношення нестрогої переваги iR на множи- ні альтернатив { } 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', n X x x = дозволяє висловити одне з наведених тверджень для будь-якої пари альтернатив ( , ) x y : x не гірша y , тоб- 105 то ( ) , , x y x y R ≥ ∈ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' y не гірша x , що записується як ( ) , , y x y x R ≥ ∈ , x та y неможливо порівняти між собою, ( ) ( ) , , , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' x y R y x R ∉ ∉ Такий підхід уможливлює звуження класу раціонального вибору.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо існує строга перевага ( ) , z x y R ∈ , альтернатива x переважає y , тобто x y > .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За умови чітких функцій корисності jr множини X альтернатива x , що має вищу оцінку ( ) jr x за фактором ,j є кращою, ніж альтернатива y , оцінка якої ( ) jr y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Подане твердження описуєть- ся чітким відношенням переваги j R множини X : ( ) ( ) ( ) { } , : , , j j j R x y r x r y x y X = ≥ ∈ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (18) Визначимо якість проєктування післядрукарських процесів шля- хом оцінювання нечітких відношень переваги iR на множині аль- тернатив { } 1 2 3 , , X x x x = : 1 R (Показники видання) — 1 2 2 3 , x x x x = < ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2 R (Умови експлуатації) — 1 3, x x < 2 3 x x > ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3 R (Конструкційні осо- бливості) — 1 2 2 3 , x x x x > = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4 R (Тип виробництва) — 1 2 2 3 , x x x x > = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для виокремлення Парето-оптимальної альтернативи необхід- но обрати альтернативу 0x X ∈ із найвищою оцінкою корисності на множині усіх факторів: ( ) ( ) 0 , 1, ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' j j r x r y j m y X ≥ ∀ = ∀ ∈ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (19) Згортка усіх критеріїв сформованої множини Парето в єдиний скалярний здійснюється за способом перетину [22;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 59;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 79].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Позначимо 1 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' m j j Q R = =\uf049 Таким чином, множина альтернатив X = { } 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', n x x = із відношенням переваги 1 Q є відповідною до множини альтернатив з функціями корисності ( ) jr x .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визначення недоміно- ваних альтернатив за нечітким відношенням переваги 1 Q полягає у заміні кількох відношень ( ) 1, j R j m = на перетин між ними.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вважати- мемо, що ( ) , j x y µ є функцією належності чіткого відношення пере- ваги jr .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сформована умова матиме вид: ( ) ( ) ( ) ( ) ( ) 1, , , , 0, , j j j j якщо r x r y тобто x y R x y якщо x y R \uf8f1 ≥ ∈ \uf8f4 µ = \uf8f2 ∉ \uf8f4\uf8f3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (20) Відповідно функція належності згортки 1 Q запишеться таким чи- ном: ( ) ( ) ( ) ( ) { } 1 1 2 , min , , , ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', , Q n x y x y x y x y µ = µ µ µ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (21) 106 Згортка критеріїв із врахуванням вагових значень факторів техно- логічного процесу jv та відповідних функцій корисності матиме ви- гляд: ( ) ( ) min j j j Q x v r x = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (22) Згортка вихідних відношень 2 Q також формується ваговими зна- ченнями аналізованих факторів jv і відповідними функціями корис- ності: � � 2 1 1 , 1, 0 m m j j j j j j Q v r x äå v v � � � � � � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (23) Їй відповідає така функція належності [58]: ( ) ( ) 2 1 , , m Q j j j x y v x y = µ = µ ∑ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (24) У результаті обчислень отримаємо: ( ) [ ] 2 0,4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0,74;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1,26 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' нд Q ix µ = За перетином множин 1 нд Q та 2 нд Q максимальне значення функції належності ( ) нд Q ix µ належить 3x , тобто оптимальним вважається тре- тій варіант.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перевірка результатів Внаслідок проведення багатофакторного вибору оптимальної альтернативи на основі лінійного згортання критеріїв визначено ба- гатофакторні оцінки корисності: 1 0,264;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' U = 2 0,322;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' U = 3 0,414.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' U = Максимальною оцінкою корисності є 3 U , отже оптимальною є третя альтернатива.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У результаті багатофакторного вибору альтернативи на основі нечіткого відношення переваги одержано такі значення функції на- лежності: ( ) нд Q ix µ : 1 0,4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' x = 2 0,74;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' x = 3 1,26 x = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, можна стверджувати, що варіант 3x є оптимальною альтернативою проєкту- вання післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Результати, отримані внаслідок встановлення оптимальної аль- тернативи за методом лінійного згортання критеріїв та за методом на основі нечіткого відношення переваги, є тотожними, що свідчить про достовірність проведеного дослідження [79].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 107 Етап 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визначення інтегрального показника якості проєктування післядрукарських процесів Остаточно моделювання системи прогностичного оцінювання якості проєктування післядрукарських процесів на базі нечіткої логі- ки зводиться до розв’язання таких завдань [15;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 16;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 44;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 64]: – встановлення універсальної терм-множини значень та відповідних їй лінгвістичних термів виокремлених факторів (лінгвістичних змінних);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – побудова багаторівневої моделі логічного виведення, структура якої відтворює ієрархію факторів та лінгвістичних термів, що впли- вають на якість реалізації процесу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Компонента найвищого рівня визначає вихідний прогнозований показник якості досліджуваного процесу у вигляді нечіткої множини;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – побудова та опрацювання матриць попарних порівнянь для множини лінгвістичних термів відносно квантів поділу інтервалів значень універсальної множини та отримання для кожної з лінгвіс- тичних змінних функцій належності;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – нормування значень функцій належності та співвіднесення їх із квантами поділу універсальної множини;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – побудова суміщених графіків за нормованими значеннями функцій належності для лінгвістичних змінних і відповідних їм лінг- вістичних термів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – розроблення нечіткої бази знань (або матриці знань) з викорис- танням нечітких логічних висловлювань типу «якщо <умова>, тоді <висновок (або дія)>», що відтворює алгоритм формування якості проєктування післядрукарських процесів в залежності від рівня якос- ті лінгвістичних термів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – побудова нечітких логічних рівнянь на підставі матриці знань та функцій належності, які визначають зв’язок між функціями належ- ності вхідних та вихідних даних;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – побудова аналітичного виразу для формалізованої ідентифікації прогнозованого результату у вигляді нечіткої множини, отриманої на під- ставі багаторівневої моделі логічного виведення та нечіткої бази знань;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – дефазифікація нечіткої множини, суть якої полягає у розрахун- ку числового показника прогнозованої якості за методом центра мас або центра ваги плоскої фігури, обмеженої графіком функції належ- ності і віссю абсцис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При дефазифікації нечіткої множини використовуються значення функцій належності лінгвістичних змінних, область існування яких визначена універсальною множиною.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 108 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Фазифікація нечіткої множини Проєктування післядрукарських процесів — це необхідна складо- ва забезпечення якості готової книжкової продукції, яка включає ряд послідовних операцій, спрямованих на досягнення поставленої мети.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Однак фактори, які здійснюють неопосередкований вплив на реалі- зацію досліджуваного процесу, не завжди містять кількісну складову.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Натомість, значно інформативнішими стають певні лінгвістичні ха- рактеристики.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виникає необхідність заміни понять чіткої множини поняттями нечіткої множини.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Саме тому для забезпечення точності моделювання доцільно використовувати методи та засоби нечіткої логіки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Суттєвим елементом та перевагою нечіткої логіки є можливість фазифікації, тобто заміни компонент чіткої множини відповід- ними їм поняттями нечіткої множини.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відомо, що суть її полягає у зіставленні терм-множини значень аналізованих факторів від- повідника нечіткого формату змінних величин — функцій належ- ності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тобто змінні, які не можуть бути чітко вираженими за до- помогою кількісних значень та які зручно описувати словами чи словосполученнями, вважаються лінгвістичними змінними, таки- ми як: «Показники видання», «Конструкційні особливості» чи ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому значення кожної лінгвістичної змінної формуються у певну сукупність — терм-множину, компоненти якої називаються термами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Так, терм-множина лінгвістичної змінної «Показники видання» складається з термів «просте», «ускладнене», «складне».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Лінгвістичною вважається змінна, значення якої виражено засоба- ми звичайної мови — словами або словосполученнями.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому множину можливих значень лінгвістичної змінної прийнято нази- вати терм-множиною, а довільний її елемент — термом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Так, для лінгвістичної змінної «Тип обладнання» термами будуть лінгвіс- тичні оцінки «ручне», «механічне», «автоматизоване», що утворю- ватимуть терм-множину значень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Фазифікація забезпечує доволі високий рівень відповідності мо- делі реальному об’єкту і служить, як буде показано пізніше, основою для подальшого моделювання прогностичного оцінювання проєкту- вання післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У роботах основоположника нечіткої логіки Заде [20;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 21] вводить- ся поняття універсальної множини D , як такої, що стосується всієї проблемної області.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тоді нечітку підмножину M множини D визна- чають через шкалу D і функцію належності ( ) M d µ [20], тобто 109 ( ) ( ) { } , , M M d d d D = µ ∈ , (25) де ( ) ( ) 0 1 M d ≤ µ ≤ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Функція належності встановлює міру приналежності кожного елемента нечіткої множини універсальній множині, тобто M D ∈ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За умови дискретності і скінченності базової шкали (тобто поділеної на кванти чи проміжки) нечітка множина ( ) ( ) ( ) ( ) ( ) 1 1 2 2 1 / , / ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', / / n M M M n n M i i i M d d d d d d d d = = µ µ µ = µ ∑ , (26) або спрощено: 1 / n i i i M d = = µ ∑ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Запис означає «прикріплення» функції належності ( ) M id µ до елемента id .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Остаточно функції належності виступають ідентифікатором вхід- них значень лінгвістичних змінних у нечіткому форматі, тобто множині значень змінної d ставляться у відповідність функції належності ( ) d µ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вважатимемо, що реалізація визначеного технологічного процесу буде певною функцією G , у якості аргументів якої будуть виокремле- ні фактори m m 1 2 , ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', m n r r r , тоді: ( ) m m 1 2 , ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', m n G F r r r = , (27) де m n — кількість факторів m -го технологічного процесу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Отже досліджуваний процес є процедурою з множиною початко- вих змінних ( ) 1, ir i n = та кінцевою змінною G .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Існування кількісних значень змінних уможливлює задання про- міжку, що виражатиметься граничними значеннями цих змінних [13;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 14]: , , 1, ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' , i i r r i n G G = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зважаючи на те, що виокремлені фак- тори є якісними змінними, постає потреба формування множини та меж задання значень: ( ) ( ) ( ) { } 1 2 , ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', , j D d d d = де ( ), 1, k d k j = — мно- жина кількісних чи якісних умовних одиниць, потужність якої визначає індекс j .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тоді результуюча змінна G із граничними межами також може подаватися в умовних одиницях множиною ( ) ( ) ( ) { } 1 2 , ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' j G g g g = Такі універсальні множини забезпечують вико- нання залежності (27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В той же час доцільно оцінювати лінгвістичні змінні засобами природної мови (наприклад: «просте», «ускладне- не», «складне»), формуючи лінгвістичні терм-множини.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З огляду на наведені твердження побудова багаторівневої моделі нечіткого логічного виведення встановлення інтегрального показ- 110 ника якості досліджуваного технологічного процесу передбачає фор- мування часткових показників якості;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' виокремлення універсальної множини значень та терм-множини кожної лінгвістичної змінної;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' безпосередню візуалізацію ієрархічної залежності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вважатимемо процес проєктування післядрукарських процесів функцією ( ) 1 2 3 4 5 6 7 8 , , , , , , , , G F R R R R R R R R = з такими аргументами: 1 R — показники видання;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2 R — конструкційні особливості;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3 R — умо- ви експлуатації;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4 R — тип виробництва;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5 R — матеріали;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6 R — тип об- ладнання;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 7 R — технологічні та економічні розрахунки;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 8 R — схема технологічного процесу [27;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інтегральний показник якості про- єктування післядрукарських процесів визначатиметься за принципом ієрархізації структури процесу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідно залежність якості проєкту- вання видання може бути виражена через якість часткових показників: ( ) , , G G F M O P = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (28) Аргумент M визначає якість формування видання: ( ) 1 2 3 , , , M M F m m m = (29) де 1 m — лінгвістична змінна «показники видання», 2 m — лінгвістич- на змінна «конструкційні особливості», 3 m — лінгвістична змінна «умови експлуатації».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Аргумент O визначає якість організації виробництва: ( ) 1 2 3 , , , O O F o o o = (30) де 1o — лінгвістична змінна «тип виробництва»;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2o — лінгвістична змінна «матеріали»;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3o — лінгвістична змінна «тип обладнання».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Аргумент P визначає якість опрацювання видання: ( ) 1 2 , , P P F p p = (31) де 1p — лінгвістична змінна «редагування»;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2p — лінгвістична змінна «коректура».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сформуємо таблицю, вказавши лінгвістичну суть кожної змінної, універсальні множини значень та відповідні лінгвістичні терми.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Значення умов експлуатації сформовано на основі груп довговіч- ності користування книжковим виданням: 1-ша група — нетривалий термін служби (до двох років) з малою інтенсивністю користування;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' та 2-га група — нетривалий термін служби (до двох років) з великою ін- тенсивністю користування;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3-тя група — середній термін користування 111 (від 2 до 10 років) з малою інтенсивністю користування;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4-та група — середній термін користування (від 2 до 10 років) з великою інтенсив- ністю користування;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5-та та 6-та групи — тривалий термін (від 10 років і більше) з малою чи високою інтенсивністю користування [27;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 35;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таблиця 8 Терм-множини значень лінгвістичних змінних Змін- на Лінгвістична суть змінної Універсальна множина зна- чень (множина D) Лінгвістичні терми (множина L) m1 Показники видання (1–5) у.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' о.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Просте видання, ускладнене видання, складне видання m2 Конструкційні особли- вості (1–5) у.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' о.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Проста конструкція, ускладнена конструкція, складна конструкція m3 Умови експлуатації (гру- пи довговічності корис- тування) (1–5) кате- горія Нормальні умови, робочі умови, граничні умови o1 Тип виробництва (1–5) у.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' о.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Одиничне виробництво, серійне виробництво, масове виробництво o2 Матеріали (складність опрацюван- ня) (1–5) у.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' о.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Низька складність, середня складність, ви- сока складність o3 Тип обладнання (1–5) у.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' о.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ручне, механічне, авто- матизоване p1 Технологічні та економіч- ні розрахунки (ефективність виробни- цтва) (10–90) % Низька ефективність, середня ефективність, висока ефективність p2 Схема технологічного процесу (1–5) у.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' о.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Проста, ускладнена, складна Для візуалізації залежності якості проєктування післядрукарських процесів від значення лінгвістичних термів виокремлених факторів синтезується багаторівнева модель нечіткого логічного виведення [27;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Використання багаторівневої моделі нечіткого логічного ви- ведення сприяє послідовному встановленню прогнозу якості реалі- зації проєктування післядрукарських процесів шляхом накопичення знань від найнижчого до найвищого її рівнів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ця модель включає 112 підпорядковані моделі: модель якості формування видання, модель якості організації виробництва, модель якості планування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Рівень якості досліджуваного процесу позначено лінгвістичним термом G .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому універсальна множина D ділиться на части- ни (кванти).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У точках поділу задаються означені нами лінгвістичні змінні та ранги ( ) g i r d , що ідентифікують лінгвістичні терми.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Отже, вихідною базою даних буде множина { } 1 2 , ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' n D d d d = і ранги ( ) g i r d , що встановлюють пріоритетність лінгвістичних термів у діапазонах id ( ) 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' i n = З урахуванням сказаного лінгвістичний терм «рівень якості технологічного процесу» G подається у вигляді деякої нечіт- кої множини, елементи якої утворюють сукупності пар [15;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 28;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 41]: ( ) ( ) ( ) 1 2 1 2 , ,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', g g g n n d d d G d d d \uf8f1 \uf8fc µ µ µ \uf8f4 \uf8f4 = \uf8f2 \uf8fd \uf8f4 \uf8f4 \uf8f3 \uf8fe , (32) де G D ⊂ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) g id µ — міра належності елемента id D ∈ до множини G .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Міри або функції належності ( ) g id µ є базовими складовими ло- гічних рівнянь, розв’язання яких забезпечує числове значення функ- ції належності лінгвістичного терму G .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для функцій належності ви- конується умова нормування: 1 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' n µ + µ + + µ = При цьому розподіл мір (функцій) належності відповідає таким умовам: 1 2 1 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' n n r r r µ µ µ = = = , (33) де ( ) i g id µ = µ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) i g i r r d = для всіх 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', i n = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Числові значення функцій належності, що слугують для вста- новлення рангів факторів проєктування післядрукарських процесів, отримуються із співвідношень [28;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 41;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 43]: 1 2 3 1 1 1 1 1 1 3 2 2 2 2 1 1 2 3 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='. .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 n n n n n n r r r r r r r r r r r r r r r r r r − − − \uf8fc \uf8eb \uf8f6 \uf8f4 µ = + + + + \uf8ec \uf8f7 \uf8f4 \uf8ed \uf8f8 \uf8f4 \uf8eb \uf8f6 \uf8f4 µ = + + + + \uf8f4 \uf8ec \uf8f7 \uf8fd \uf8ed \uf8f8 \uf8f4 \uf8f4 \uf8f4 \uf8eb \uf8f6 \uf8f4 µ = + + + + \uf8ec \uf8f7 \uf8f4 \uf8ed \uf8f8 \uf8fe .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (34) 113 На основі наведеного теоретичного обґрунтування формуються ключові задачі: ( ) ( ) , , max, 1,3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1,3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1,2 0, 0, 0 max, , , 1,3 F a b c a b c g i i F G F m o p a b c m o p y y Y G Y i \uf8fc = → = = = \uf8f4\uf8f4 > > > \uf8fd \uf8f4 µ → ∈ ⊂ = \uf8f4\uf8fe .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (35) Для графічного відображення лінгвістичних термів діапазон зна- чень лінгвістичних змінних ділиться на чотири частини, у результаті чого виникає п’ять точок ( ) 1 2 3 4 5 , , , , d d d d d [52, 53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При відомих, або отриманих на основі матриць попарних порів- няннях, рангах для кожного з лінгвістичних термів розраховуються функції належності iµ у результаті опрацювання матриці 2 3 4 5 1 1 1 1 1 3 4 5 2 2 2 2 1 2 3 4 5 5 5 5 1 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 r r r r r r r r r r r r r r r r A r r r r r r r r \uf8ee \uf8f9 \uf8ef \uf8fa \uf8ef \uf8fa \uf8ef \uf8fa \uf8ef \uf8fa = \uf8ef \uf8fa \uf8ef \uf8fa \uf8ef \uf8fa \uf8ef \uf8fa \uf8ef \uf8fa \uf8f0 \uf8fb .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (36) Отримання підсумкового результату полягає у досягненні макси- мального значення функції, що характеризує рівень якості процесу при максимальних значеннях функцій належності термів оцінюван- ня факторів — лінгвістичних змінних.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Внаслідок побудови матриць попарних порівнянь для кожного терму аналізованих лінгвістичних змінних проєктування післядру- карських процесів формується певне кількісне уявлення про взаємо- відношення рангів у точках універсальної множини.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тобто викорис- тання шкали відносної важливості об’єктів за Сааті та методології створення квадратних обернено-симетричних матриць значно по- легшує сприйняття якісних ознак.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Однак порівняння відбувається в межах рангів одного терму, що не дає уявлення про взаємозв’язок термів лінгвістичної змінної.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Опрацювання функцій належності, на основі матриць попарних порівнянь, уможливлює перетворення екс- пертної думки у кількісні показники [28;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 29;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 114 Будуємо матриці попарних порівнянь для лінгвістичної змінної «показники видання» з терм-множиною значень ( ) 1 L m = = <про- сте, ускладнене, складне> та універсальною множиною значень ( ) [ ] 1 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 D m = у.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' о.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', що характеризують кількісні ознаки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 1 1 7 9 5 9 3 9 1 9 9 7 1 5 7 3 7 1 7 9 5 7 5 1 3 5 1 5 9 3 7 3 5 3 1 1 3 9 7 5 3 1 просте S m \uf8ee \uf8f9 \uf8ef \uf8fa \uf8ef \uf8fa \uf8ef \uf8fa = \uf8ef \uf8fa \uf8ef \uf8fa \uf8ef \uf8fa \uf8f0 \uf8fb ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 1 1 5 8 3 1 1 8 3 1 1 5 5 5 5 1 5 3 1 1 8 8 8 8 1 5 8 1 1 3 3 3 3 1 5 8 3 1 ускладнене S m \uf8ee \uf8f9 \uf8ef \uf8fa \uf8ef \uf8fa \uf8ef \uf8fa = \uf8ef \uf8fa \uf8ef \uf8fa \uf8ef \uf8fa \uf8ef \uf8fa \uf8ef \uf8fa \uf8f0 \uf8fb ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 1 1 5 7 8 9 1 5 1 7 5 8 5 9 5 1 7 5 7 1 8 7 9 7 1 8 5 8 7 8 1 9 8 1 9 5 9 7 9 8 9 1 складне S m \uf8ee \uf8f9 \uf8ef \uf8fa \uf8ef \uf8fa \uf8ef \uf8fa = \uf8ef \uf8fa \uf8ef \uf8fa \uf8ef \uf8fa \uf8f0 \uf8fb .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Внаслідок обчислення матриць значення функцій належності для термів «просте», «ускладнене» та «складне» лінгвістичної змінної 1 m «показники видання» будуть наступними: ( ) 1 0,36 просте y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 2 0,28 просте y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 3 0,2 просте y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 4 0,12 просте y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 5 0,04 просте y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 1 0,055 ускладнене y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 2 0,277 ускладнене y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 3 0,444 ускладнене y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 4 0,166 ускладнене y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 5 0,055 ускладнене y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 1 0,033 складне y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 2 0,166 складне y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 3 0,233 складне y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 4 0,266 складне y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 5 0,3 складне y µ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 115 Пронормовані відносно одиниці значення функцій належностей (коефіцієнт нормування ( ) ( ) 1 max , 1,2,3 е е i k y i = µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) nе i е y k µ = × ( ) е iy ×µ ) матимуть вид: ( ) 1 1 n просте y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 2 0,778 n просте y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 3 0,556 n просте y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 4 0,333 n просте y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 5 0,111 n просте y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 1 0,124 n ускладнене y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 2 0,624 n ускладнене y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 3 1 n ускладнене y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 4 0,374 n ускладнене y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 5 0,124 n ускладнене y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 1 0,11 n складне y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 2 0,553 n складне y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 3 0,777 n складне y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 4 0,887 n складне y µ = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) 5 1 n складне y µ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Утворимо нечіткі множини за формулою (32): 1 0,778 0,556 0,333 0,111 = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 2 3 4 5 просте видання \uf8f1 \uf8fc \uf8f2 \uf8fd \uf8f3 \uf8fe у.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' о.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0,124 0,624 1 0,374 0,124 = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 2 3 4 5 ускладнене видання \uf8f1 \uf8fc \uf8f2 \uf8fd \uf8f3 \uf8fe у.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' о.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0,11 0,553 0,777 0,887 1 = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 2 3 4 5 складне видання \uf8f1 \uf8fc \uf8f2 \uf8fd \uf8f3 \uf8fe у.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' о.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За нечіткими множинами побудуємо графік функцій належності термів «просте», «ускладнена», «складне».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому по осі абсцис відобразимо універсальну множину значень, а по осі ординат — нор- мовані значення функцій належності термів лінгвістичної змінної «показники видання» [29;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Опускаючи подібні викладки для решти лінгвістичних змінних, перейдемо до наступної компоненти нечіткої логіки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' База нечітких знань може бути представлена у вигляді матриці знань, яка пов’язує вхідні змінні (фактори m -го технологічного про- цесу) з вихідною змінною (результатом реалізації m -го технологічно- го процесу).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для побудови матриці знань використовується система висловлювань «якщо — і — тоді», «якщо — тоді — інакше», «якщо — або — тоді — інакше».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На основі матриці знань створюється система нечітких логічних рівнянь, яка дозволяє отримати числові значення функцій належності та інтегрального прогнозу якості m -го техноло- гічного процесу [26;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 116 0 0,5 1 1,5 1 2 3 4 5 Значення функцій належності Значення універсальної множини ПОКАЗНИКИ ВИДАННЯ Просте видання Ускладнене видання Складне видання Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Візуалізація функцій належності лінгвістичної змінної «показники видання» Наведемо комбінації отримання результату для двох значень функцій належності 1 µ та 2 µ : ( ) 1 1 2 1 2 1 2 2 1 2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' max ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' якщо якщо µ µ ≥ µ \uf8f1 µ ∨ µ = µ µ = \uf8f2µ µ < µ \uf8f3 (37) ( ) 1 1 2 1 2 1 2 2 1 2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' min ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' якщо якщо µ µ ≤ µ \uf8f1 µ ∧ µ = µ µ = \uf8f2µ µ > µ \uf8f3 (38) де операція ∨ у нечітких логічних рівняннях вказує на отримання максимального значення,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' а операція ∧ — мінімального значення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нехай для лінгвістичних змінних M (якість формування видан- ня), O (якість організації виробництва) та P (якість опрацювання видання) термами будуть «низька», «середня», «висока».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відпо- відно інтегральний показник G (якість проєктування післядру- карських процесів) описуватиметься такими ж термами [27;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 60;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тоді нечітка база знань для відношення ( ) , , G G F M O P = мати- ме вид: ЯКЩО (M = низька) І (M = середня) І (M = висока);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' І (O = низька) І (O = середня) І (O = висока);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' І (P = низька) І (P = середня) І (P = висока);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ТОДІ (G = низька) І (G = середня) І (G = висока).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сформовані умови відображаються у матриці знань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 117 Таблиця 9 Матриця знань для лінгвістичної змінної G Якість вихідних даних видання M Якість опрацювання видання O Якість оформлення видання P Якість проєктування післядрукарських процесів G низька низька низька низька низька середня низька середня низька середня середня висока середня середня висока висока висока висока висока середня висока Нечіткі логічні рівняння для термів «низька»,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' «середня»,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' «висока» інтегрального показника G матимуть вид: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' низька низька низька низька низька середня низька середня середня низька середня висока середня середня висока висока висока висока висока середня висока G M O P M O P G M O P M O P G M O P M O P µ = µ ∧ µ ∧ µ ∨ ∨µ ∧ µ ∧ µ µ = µ ∧ µ ∧ µ ∨ ∨µ ∧ µ ∧ µ µ = µ ∧ µ ∧ µ ∨ ∨µ ∧ µ ∧ µ Зважаючи на те,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' що залежності якості формування видання,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ор- ганізації виробництва та опрацювання видання також можуть бути виражені через якість часткових показників ( ) 1 2 3 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' M M F m m m = ( ) 1 2 3 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' O O F o o o = ( ) 1 2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' P P F p p = і на основі експертних суджень щодо множин 1 2 3 ( ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' L m m m 1 2 3 ( ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' L o o o 1 2 ( ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ) L p p формуються нечіткі бази знань,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' матриці знань і нечіткі логічні рівняння лінгвістичних змінних проєктування післядрукарських процесів [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Логічні висловлювання стосовно таких лінгвістичних змінних: – «якість формування видання»;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – «якість організації виробництва»;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – «якість опрацювання видання».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ЯКЩО (m1) = (просте, ускладнене, складне), І (m2) = (проста, ускладнена, складна);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' І (m3) = (нормальні, робочі, граничні);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ТОДІ (M) = (низька, середня, висока);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 118 ЯКЩО (o1) = (одиничне, серійне, масове), І (o2) = (низька, середня, висока);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' І (o3) = (ручне, механічне, автоматизоване);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ТОДІ (O) = (низька, середня, висока);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ЯКЩО (p1) = (низька, середня, висока), І (p2) = (проста, ускладнена, складна);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ТОДІ (P) = (низька, середня, висока).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Далі будуються матриці знань для аналізованих лінгвістичних змінних.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для зручності вони відображаються у табличній формі [50;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 60;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Таблиця 10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Матриця знань для лінгвістичної змінної M (якість формування видання) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Показники ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='видання m1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Конструкційні ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='особливості ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='(складність ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='конструкції) m2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Умови ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='експлуатації ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='m3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Якість вихідних ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='даних видання ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='M ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='складне ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='складна ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='граничні ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='низька ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='складне ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='складна ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='робочі ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='складне ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='ускладнена ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='робочі ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='середня ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='ускладнене ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='ускладнена ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='нормальні ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='ускладнене ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='проста ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='нормальні ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='висока ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='просте ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='проста ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='нормальні ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Таблиця 11 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Матриця знань для лінгвістичної змінної O (якість організації виробництва) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Тип виробництва ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='o1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Матеріали ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='(складність ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='опрацювання) o2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Тип ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='обладнання o3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Якість організації ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='виробництва O ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='одиничне ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='висока ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='ручне ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='низька ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='серійне ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='висока ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='ручне ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='серійне ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='середня ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='механічне ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='середня ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='серійне ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='середня ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='автоматизоване ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='серійне ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='низька ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='автоматизоване ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='висока ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='масове ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='низька ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='автоматизоване ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='119 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Таблиця 12 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Матриця знань для лінгвістичної змінної P (якість опрацювання видання) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Технологічні та економічні ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='розрахунки (ефективність ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='виробництва) p1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Схема ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='технологічного ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='процесу p2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Якість ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='опрацювання ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='видання P ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='низька ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='складна ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='низька ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='низька ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='ускладнена ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='середня ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='проста ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='середня ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='середня ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='ускладнена ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='висока ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='проста ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='висока ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='висока ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='ускладнена ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Нечіткі логічні рівняння для визначених термів матимуть вид: ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='– для лінгвістичної змінної «якість формування видання» ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='( ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=') ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='( ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=') ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='( ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=') ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='( ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=') ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='( ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=') ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='( ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=') ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='( ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=') ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' низька складне складна граничні складне складна робочі M m m m m m m µ = µ ∧ µ ∧ µ ∨ ∨µ ∧ µ ∧ µ ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 3 1 2 3 1 2 3 1 2 3 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' середня складне ускладнена робочі ускладнене ускладнена нормальні висока ускладнене проста нормальні просте проста нормальні M m m m m m m M m m m m m m µ = µ ∧ µ ∧ µ ∨ ∨µ ∧ µ ∧ µ µ = µ ∧ µ ∧ µ ∨ ∨µ ∧ µ ∧ µ – для лінгвістичної змінної «якість організації виробництва» ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 3 1 2 3 1 2 3 1 2 3 1 2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' низька одиничне висока ручне серійне висока ручне середня серійне середня механічне серійне середня автоматизоване висока серійне низька автоматизова O o o o o o o O o o o o o o O o o µ = µ ∧ µ ∧ µ ∨ ∨µ ∧ µ ∧ µ µ = µ ∧ µ ∧ µ ∨ ∨µ ∧ µ ∧ µ µ = µ ∧ µ ∧ µ ( ) ( ) ( ) ( ) 3 1 2 3 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' не масове низька автоматизоване o o o o ∨ ∨µ ∧ µ ∧ µ – для лінгвістичної змінної «якість опрацювання видання» ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 1 2 1 2 1 2 1 2 1 2 , , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' низька низька складна низька ускладнена середня середня проста середня ускладнена висока висока проста висока ускладнена P p p p p P p p p p P p p p p µ = µ ∧ µ ∨ µ ∧ µ µ = µ ∧ µ ∨ µ ∧ µ µ = µ ∧ µ ∨ µ ∧ µ 120 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Дефазифікація нечіткої множини Для встановлення інтегрального показника якості проєктуван- ня післядрукарських процесів здійснюється процес дефазифіка- ції, враховуючи розподілення якості за частковими показниками ( ) , , G G F M O P = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Слід зазначити, що дефазифікація є одним з ключових процесів не- чіткої логіки, який полягає у перетворенні значень нечіткої множини у кількісний показник.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Дефазифікація передбачає наявність сформо- ваних нечітких баз знань та нечітких логічних рівнянь досліджуваного технологічного процесу для подальшого формування таблиць на осно- ві терм-множин з пронормованими значеннями функцій належності у визначених точках поділу універсальної множини значень виокрем- лених лінгвістичних змінних та підставлення значень термів у нечіткі логічні рівняння.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для здійснення числових розрахунків у дослідженні обрано метод центру ваги, згідно з яким кількісне значення початкової змінної рівне абсцисі центру ваги площі, що обмежена графіком кри- вої функції належності аналізованої змінної [22;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 62;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 69;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідно до наведених тверджень формуються таблиці значень функцій належності для кожної лінгвістичної змінної за точками по- ділу універсальної множини значень та терм-множинами (табл.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6–13) [22;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 26;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 62;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Як приклад наведемо таблицю значень терм-множини ( ) 1 D m лінгвістичної змінної «Показники видання»: Таблиця 13 Функції належності терм-множини ( ) 1 D m (показники видання) iy ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' умовні одиниці 1 2 3 4 5 ( ) просте iy µ 1 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='778 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='556 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='333 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='111 ( ) ускладнене iy µ 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='124 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='624 1 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='374 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='124 ( ) складне iy µ 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='11 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='553 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='777 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='887 1 Наведемо нечіткі логічні рівняння для термів «низька»,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' «середня»,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' «висока» найвищого рівня G: ( ) ( ) ( ) 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='667 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='443 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='334 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='667 1 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='334 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='334,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='777 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='443 1 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='333 1 1 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='443,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='333 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='375 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='666 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='333 1 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='666 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='333.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' низька середня висока G G G µ = ∧ ∧ ∨ ∧ ∧ = µ = ∧ ∧ ∨ ∧ ∧ = µ = ∧ ∧ ∨ ∧ ∧ = 121 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визначення числового значення інтегрального показника якості На основі отриманих даних виконується дефазифікація нечіткої множини за формулою [22;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 26;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 62;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 72]: ( ) ( ) ( ) 1 1 1 1 m i i m i i G G G i G m G G = = \uf8ee \uf8f9 − + − µ \uf8ef \uf8fa − \uf8f0 \uf8fb = µ ∑ ∑ , (39) де G — найменше значення показника якості;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' G — найбільше значення показника якості;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' m — кількість нечітких термів [22;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 26;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 62;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Приймаються умовні межі для змінної G : 1% G = , 100% G = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Об- числення виконується за трьома точками поділу: 1 %, 50 %, 100 %.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У результаті обчислення встановлюється числове значення інтеграль- ного показника якості проєктування післядрукарських процесів: .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 0,334 50 0,443 100 0,333 50,256%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0,334 0,443 0,333 прогноз G ⋅ + ⋅ + ⋅ = = + + Опираючись на сформовану послідовність етапів дослідження, наведемо синтезовану структурно-функціональну модель інформа- ційної технології прогностичного оцінювання якості проєктування післядрукарських процесів (рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, розроблена структурно-функціональна модель складається з п’яти основних етапів, кожен з яких розділений на відповідні підетапи, що визначають окрему дію з отримання, мо- делювання, аналізу та синтезу інформації, задля визначення якості досліджуваного процесу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Така деталізація, внаслідок впровадження розробленої інформаційної технології в реальні виробничі умови уможливлює обдумане, прогнозоване формування проєкту реалізації післядрукарських процесів, підвищення економічної ефективності, доцільності операцій, спрощення післядрукарського опрацювання книжкової продукції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Використаємо методологію IDEF0 для функціонального моде- лювання інформаційної технології проєктування післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Побудуємо контекстну діаграму А-0, діаграму першого рів- ня декомпозиції А0, діаграми другого рівня декомпозиції А1, А2, А3, А4, А5, діаграми третього рівня декомпозиції А23, А24, А41, А42, А51, А52 [40;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 77].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 122 ЕТАП 1 Аналіз предметної області 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Узагальнений опис операцій та технологій післядрукарського опрацювання книжкової продукції 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Функціональне моделювання післядрукарського опрацювання книжкової продукції 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Аналіз факторів впливу на якість ППП.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розроблення онтології 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Функціональне моделювання ППП ЕТАП 2 Синтез моделей факторів ППП 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розроблення семантичної мережі взаємозв’язків між факторами проєктування післядрукарських процесів 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формалізація з’язків між факторами за допомогою предикатних формул 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Побудова моделі пріоритетного впливу факторів ППП за методом математичного моделювання ієрархій 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Побудова моделі пріоритетного впливу факторів ППП за методом ранжування ЕТАП 3 Оптимізація моделі факторів ППП 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формування матриці попарних порівнянь факторів 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визначення компонент головного власного вектора МПП 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визначення компонент нормалізованого вектора МПП 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Аналіз результатів оптимізації за максимальним значенням головного власного вектора МПП, індексом узгодженості та відношенням узгодженості 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Візуалізація співвідношень компо- нент вихідного та нормалізованого векторів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Побудова оптимізованої моделі пріоритетного впливу факторів на якість ППП ЕТАП 4 Визначення оптимальних альтернатив реалізації ППП 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Багатофакторний вибір альтернативи на основі лінійного згор- тання критеріїв 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Багатофакторний вибір альтернативи на основі нечіткого від- ношення переваги 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перевірка результатів ЕТАП 5 Визначення інтегрального показника якості ППП 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Фазифікація нечіткої множини 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Дефазифікація нечіткої множини 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визначення числового значення інтегрального показника якості Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Структурно-функціональна модель інформаційної технології прогностичного оцінювання якості проєктування післядрукарських процесів Контекстна діаграма зображена на рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому основною функцією системи є інформаційна технологія прогностичного оці- нювання якості проєктування післядрукарських процесів, а зв’язок системи із навколишнім середовищем зображується граничними стрілками: I1 — потреба у розробленні інформаційної технології, I2 — ETAII5Il IlI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Po3po6JeHH 0HToJoril1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' @yHKniOHaIHe MOeOBaHHIIIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='ETAII 2ETAII3ETAII4ETAIIAnals npedneot obndci1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' YaraHeH ollc oepain TaTexHOIOri icJpyKapcEEorO1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' DyHKnioHaIHe MOIeOBaHHLEHHKEOBoi poyEIii1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' AHalis bakTopiB BIJIHBy Ha kicTE123 погано структурована задача, C1 — нормативно-технічна та техноло- гічна документація, C2 — теорії, методи, методики, принципи, O1 — оптимальна альтернатива реалізації проєктування післядрукарських процесів, O2 — інтегральний показник якості проєктування післядру- карських процесів, M1 — апаратне та програмне забезпечення, M2 — дослідники, експерти з предметної області, інші зацікавлені особи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інформаційна технологія прогностичного оцінювання якості проєктування після- друкарських процесів Потреба у розробленні інфор- маційної технології Погано структурована задача Оптимальна альтернатива реалізації ППП Апаратне та програмне забезпечення Дослідники, експерти з предметної області, зацікавлені особи Теорії, методи, методики, принципи Нормативно-технічна та технологічна документація Інтегральний показник якості ППП Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контекстна діаграма А-0 моделі IDEF0 інформаційної технології прогностичного оцінювання якості проєктування післядрукарських процесів Опишемо кожну граничну стрілку, враховуючи поділ за типами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Граничні стрілки типу «Вхід» (Input): – 1I (потреба у розробленні інформаційної технології).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Потреба в організації інформаційних процесів з використанням засобів об- числювальної техніки, що пришвидшує опрацювання даних, пошук інформації та спрощує доступ до неї;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – 2I (погано структурована задача).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За глибиною пізнання роз- різняють три класи проблем: добре структуровані, неструктуровані та погано структуровані.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Останні характеризуються наявністю як якіс- них, так і кількісних показників, з явною перевагою маловідомих, не- достатньо досліджених якісних характеристик проблеми.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До погано 01120CM,M124 структурованих проблем відносяться великомасштабні задачі, яким притаманні значна кількість альтернатив, залежність від сучасних тех- нологій, невизначеність щодо тривалості виконання, кількості фінан- сових ресурсів та матеріалів, наявність ризиків.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Проєктування після- друкарських процесів належить до погано структурованих проблем.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Граничні стрілки типу «Контроль» (Control): – 1 C (нормативно-технічна та технологічна документація).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До нормативно-технічної документації належать технічні вимоги та за- конодавчі положення, зокрема: закони, стандарти, технічні умови, кодекси усталеної практики та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – 2 C (теорії методи, методики, принципи).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кожен інформацій- ний процес виконується на основі загальновідомих чи новітніх тео- рій, методів, методик та принципів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Так, наприклад, виокремлення та формалізація зв’язків між факторами проєктування післядрукар- ських процесів здійснюється за методами системного та матричного аналізу, теорією графів та семантичних мереж, логікою предикатів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' створення моделі пріоритетного впливу факторів відбувається за тео- рією ієрархічних багаторівневих систем і т.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' д.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' [58;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Граничні стрілки типу «Вихід» (Output): – 1 O (оптимальна альтернатива реалізації проєктування післядру- карських процесів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виконання будь-якого технологічного завдання передбачає наявність можливих альтернатив.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Важливим етапом є вибір найкращої альтернативи реалізації серед множини існуючих [25;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 79];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – 2 O (інтегральний показник якості проєктування післядрукар- ських процесів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основною метою виконання будь-якого процесу є отримання якісного результату.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому прогнозування якості уможливлює досягнення мети.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Встановлення кількісного показника якості проєктування післядрукарських процесів здійснюється за до- помогою методів та засобів нечіткої логіки [26;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 42;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Граничні стрілки типу «Механізми» (Mechanism): – 1 M (апаратне та програмне забезпечення).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Пошук, опрацюван- ня, зберігання та передавання інформації передбачає використання сучасних технічних та програмних засобів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – 2 M (дослідники, експерти з предметної області, зацікавлені особи).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Реалізація інформаційної технології прогностичного оціню- вання якості проєктування післядрукарських процесів передбачає проведення ряду досліджень із залученням фахових науковців, фор- муванням експертних висновків, апробацією та консультуванням із зацікавленими особами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 125 Діаграма першого рівня декомпозиції А0 моделі IDEF0 утворена шляхом декомпозиції контекстної діаграми та містить такі функціо- нальні блоки: – АПО (аналіз предметної області).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Здійснюється для означення теоретичної складової досліджуваного процесу та виокремлення по- слідовності операцій шляхом функціонального моделювання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому розглядається не лише створення проєкту, а й сам процес піс- лядрукарського опрацювання книжкової продукції, адже важливо розуміти особливості об’єкта проєктування;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – СМФ ППП (синтез моделей факторів проєктування після- друкарських процесів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Полягає у розробленні семантичної мережі та формалізації зв’язків між факторами, використовуючи елементи логіки предикатів, а також у визначенні рівнів домінантності факто- рів та побудові моделі пріоритетного впливу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Пріоритетність факто- рів визначається за методом математичного моделювання ієрархій і уточнюється за методом ранжування [58, 59];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ОМФ ППП (оптимізація моделі факторів проєктування піс- лядрукарських процесів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Передбачає встановлення оптимізованих вагових значень факторів досліджуваного процесу та побудову опти- мізованої моделі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Цей етап дозволяє деталізувати пріоритетність фак- торів і, за наявності, уникнути розміщення кількох факторів на одна- ковому рівні [68];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВОАР ППП (встановлення оптимальних альтернатив реалізації проєктування післядрукарських процесів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Здійснюється проєктуван- ня та дослідження можливих альтернатив реалізації аналізованого про- цесу та обирається оптимальна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому опрацювання здійснюється за двома методами, а результати порівнюються.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Збіжність отриманих результатів свідчить про адекватність розв’язку задачі [25;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 61];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВІПЯ ППП (встановлення інтегрального показника якості про- єктування післядрукарських процесів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На основі методів та засобів нечіткої логіки встановлюються прогнозовані числові параметри до- сліджуваного процесу та, відповідно до заданих умов, визначається інтегральний показник якості [26;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 42;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наступним етапом є побудова діаграм другого рівня декомпозиції, тобто декомпозиція діаграми першого рівня.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Діаграма А1 складається з чотирьох функціональних блоків: – ООТ ПОКП (опис операцій та технологій післядрукарського опрацювання книжкової продукції).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Описуються можливі операції та технології післярукарського опрацювання, умови їх вибору та реа- 126 лізації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такий опис уможливлює подальше моделювання та проєкту- вання;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ФМ ПОКП (функціональне моделювання післядрукарського опрацювання книжкової продукції).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Функціональне моделювання здійснюється за методологією IDEF0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Полягає у формуванні кон- текстної діаграми, де основною функцією системи є післядрукарське опрацювання книжкової продукції, декомпозиції контекстної діагра- ми (створенні діаграми першого рівня декомпозиції) та декомпозиції діаграми першого рівня (створенні діаграм другого рівня декомпози- ції).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формується деревовидна ієрархічна модель післядрукарського опрацювання книжкової продукції, яка ілюструє відношення між батьківськими та дочірніми вузлами моделі IDEF0 [40;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 77];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – АФВ та РО ППП (аналіз факторів впливу та розроблення онто- логії проєктування післядрукарських процесів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Означується інфор- маційна складова факторів впливу на якість досліджуваного процесу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Здійснюється деталізований опис виокремлених факторів: показни- ки видання, конструкційні особливості, умови експлуатації, тип ви- робництва, матеріали, тип обладнання, технологічні та економічні розрахунки, схема технологічного процесу [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розробляється онто- логія [33];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ФМ ППП (функціональне моделювання проєктування піс- лядрукарських процесів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Будується контекстна діаграма, діаграма першого рівня декомпозиції та діаграми другого рівня декомпозиції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основною функцією системи є проєктування післядрукарських про- цесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Також формується деревовидна ієрархічна модель, вершиною якої є контекстна діаграма [40;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 77].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Діаграма А2 містить такі функціональні блоки: – РСМ (розроблення семантичної мережі).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Модель семантичної мережі є основою для подальшого дослідження.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За структурою це орієнтований граф, сукупність вузлів якого відповідає множині фак- торів, а дуги — зв’язкам між ними [61];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ФЗФ (формалізація зв’язків між факторами).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формалізований опис зв’язків між факторами здійснюється з використанням елемен- тів логіки предикатів [59;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 61];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ПМПВФ за МММІ (побудова моделі пріоритетного впливу факторів за методом математичного моделювання ієрархій).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Метод математичного моделювання ієрархій полягає у встановленні рівнів пріоритетності факторів шляхом побудови матриці досяжності та іте- раційних таблиць [58];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 127 – ПМПВФ за МР (побудова моделі пріоритетного впливу факто- рів за методом ранжування).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Метод ранжування передбачає побудову ієрархічних дерев, що ілюструють зв’язки між факторами і встанов- лення пріоритетності факторів за ваговими значеннями [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для третього та четвертого функціональних блоків діаграми А2 до- цільно продовжити декомпозицію.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Діаграма А23 містить такі функці- ональні блоки: – СМД (створення матриці досяжності).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Матриця досяжності для зручності відображення даних будується у вигляді таблиці.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наявність прямого чи опосередкованого впливу позначається одиницею, а від- сутність — нулем;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – СІТ (створення ітераційних таблиць).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ітераційні таблиці містять чотири колонки: порядковий номер фактора у множині;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' порядкові номери факторів, на які впливає визначений фактор;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' порядкові номе- ри факторів, від яких залежить визначений фактор;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' спільні порядкові номери впливаючих та залежних факторів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кожна ітерація полягає у викресленні рядка (рядків) ітераційної таблиці, у якому співпали дані у третьому та четвертому стовпцях.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Фактор, що відповідає першому викресленому рядку, має найвищий рівень пріоритетності, а фактор, що відповідає останньому викресленому рядку, — найнижчий рівень пріоритетності;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – МПФ (моделювання пріоритетності факторів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Дані, отримані внаслідок ітерації, використовуються для побудови моделі пріоритет- ного впливу факторів [58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Діаграма А24: – СІД (створення ієрархічних дерев).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для кожного фактора мно- жини будуються ієрархічні дерева, що ілюструють прямі та опосеред- ковані впливи визначеного фактора на інші фактори та ієрархічні де- рева, що ілюструють прямі та опосередковані залежності;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВВЗФ (встановлення вагових значень факторів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За ієрархіч- ними деревами визначається кількість прямих та опосередкованих впливів і залежностей.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Приймаються умовні вагові коефіцієнти.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Об- числюються інтегральні вагові величини факторів за сумами ваг усіх типів зв’язків;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВРФ (встановлення рангів факторів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Згідно з інтегральними ваговими значеннями визначаються ранги факторів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому фак- тору із найменшим інтегральним значенням належить найнижчий ранг — перший.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кільком факторам можуть бути присвоєні однакові ранги;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 128 – ВРПФ (встановлення рівня пріоритетності факторів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Рівень пріоритетності встановлюється за рангом фактора.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Фактору з найви- щим рангом належить найвищий рівень пріоритетності — перший.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кілька факторів можуть бути однаковими за пріоритетністю;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – МПФ (моделювання пріоритетності факторів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На основі вста- новлених рівнів пріоритетності факторів, отриманих внаслідок іте- раційних процесів та уточнених шляхом ранжування, синтезується ієрархічна модель пріоритетного впливу факторів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому найви- щий рівень моделі відповідає фактору з найбільшим пріоритетом, а найнижчий — з найменшим пріоритетом серед виокремленої множи- ни [30;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розглянемо функціональні блоки діаграми А3: – ФМППФ (формування матриці попарних порівнянь факторів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На основі шкали відносної важливості об’єктів за Сааті формується матриця попарних порівнянь факторів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За критеріями порівняння обирається необхідна оцінка корисності від 1 до 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо об’єкти рів- ноцінні, оцінка корисності 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо один об’єкт абсолютно перева- жає інший — 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для опису проміжних відношень слугують інші оцін- ки в межах вказаної шкали [25;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 68];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВКГВВ (визначення компонент головного власного вектора).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Головний власний вектор визначається як середнє геометричне еле- ментів кожного рядка матриці попарних порівнянь;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВКНВ (визначення компонент нормалізованого вектора).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ком- поненти нормалізованого вектора визначають числові пріоритети факторів та дозволяють уточнити їх вагові значення;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – АРО (аналіз результатів оптимізації).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Здійснюється перевірка отриманих результатів за нормативними значеннями індекса узго- дженості, відношення узгодженості та максимальним значенням го- ловного власного вектора матриці попарних порівнянь;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВСКВ (візуалізація співвідношень компонент векторів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Буду- ються гістограма та порівняльний графік вагових значень компонент вихідного та нормалізованого векторів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вихідний вектор формується на основі моделі пріоритетного впливу факторів за присвоєними ва- говими значеннями.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для зручності візуалізації компоненти нормалі- зованого вектора адаптуються за довільним коефіцієнтом;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ПОМПВФ (побудова оптимізованої моделі пріоритетного впли- ву факторів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За перевіреними результатами оптимізації синтезується оптимізована модель пріоритетного впливу факторів на якість про- єктування післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Найвищий рівень моделі від- 129 повідає фактору з найбільшим пріоритетом, а найнижчий — з най- меншим.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Отримана модель є основою подальшого прогностичного оцінювання [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Діаграма А4 містить такі блоки: – БВА ЛЗК (багатофакторний вибір альтернатив на основі ліній- ного згортання критеріїв).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Встановлення оптимального варіанту ре- алізації проєктування післядрукарських процесів за методом ліній- ного згортання критеріїв полягає у лінійному об’єднанні часткових цільових функціоналів в один, а задача багатокритеріальної (багато- факторної) оптимізації — у знаходженні максимального значення функцій корисності [25;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 59];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – БВА НВП (багатофакторний вибір альтернатив на основі нечіт- кого відношення переваги).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Багатофакторний вибір альтернатив на основі нечіткого відношення переваги полягає у встановленні попар- них переваг між запроєктованими альтернативами факторів проєк- тування післядрукарських процесів та їх кількісному представленні;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ПР (перевірка результатів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Порівнюється, чи однаковими є встановлені оптимальні альтернативи за двома вищеописаними ме- тодами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тотожність результатів свідчить про адекватність розв’язку задачі [59;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 79].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для першого та другого функціональних блоків діаграми А4 до- цільно продовжити декомпозицію.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Діаграма А41 містить: – ФМП (формування множини Парето).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Множина Парето вклю- чає тільки фактори з суттєво вищою пріоритетністю, фактори з низь- кою пріоритетністю відкидаються;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ПА (проєктування альтернатив).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Проєктується необхідна кіль- кість альтернативних варіантів реалізації проєктування післядрукар- ських процесів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ОА (оцінювання альтернатив).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Здійснюється відсоткове виражен- ня міри впливу факторів множини Парето для кожної альтернативи;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – СМППФ (створення матриці попарних порівнянь факторів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Згідно із ваговими даними факторів множини Парето та за шкалою від- носної важливості об’єктів формується матриця попарних порівнянь;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – НГВВ (нормалізація головного власного вектора).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Внаслідок нормалізації головного власного вектора матриці попарних порів- нянь факторів множини Парето встановлюються вагові значення, необхідні для подальших обчислень;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВК та БОК (визначення корисності та багатокритеріальних оцінок корисності).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формуються матриці попарних порівнянь альтернативних 130 варіантів реалізації щодо кожного фактора множини Парето, за якими визначаються корисності альтернатив.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Багатокритеріальні оцінки ко- рисності кожної альтернативи обчислюються як суми добутків вагових значень факторів та корисності відповідних альтернатив [25];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВОА (вибір оптимальної альтернативи).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оптимальна альтернати- ва реалізації проєктування післядрукарських процесів обирається за максимальним значенням багатокритеріальної оцінки корисності [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Діаграма А42: – ОНВП на МА (оцінювання нечітких відношень переваги на множині альтернатив).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формуються відношення нестрогої переваги між альтернативами кожного фактора множини Парето;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ФМВФ (формування матриць відношень для факторів).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На основі відношень переваги формуються матриці відношень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Причо- му наявність переваги позначається одиницею, а непорівнюваність альтернатив між собою — нулем;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ПЗВ (побудова згорток відношень).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формується згортка від- ношень за усіма факторами множини Парето, де одиницею позна- чається наявність переваги між альтернативами для усіх факторів, а нулем — непорівнюваність альтернатив хоча б за одним фактором.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інший тип згортки відношень визначається за ваговими значеннями факторів та відповідних функцій корисності;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВПНА (визначення підмножин недомінованих альтернатив).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визначаються на основі згорток відношень та за відповідними фор- мулами;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВФНСМ (визначення функцій належності спільної множини).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визначається спільна множина недомінованих альтернатив та функ- ції належності;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВОА (вибір оптимальної альтернативи).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оптимальною є альтер- натива із максимальним значенням функції належності [25;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Діаграма А5 містить три функціональні блоки, а саме: – Ф (фазифікація).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Процес фазифікації полягає у зіставленні мно- жини значень її функцій належності;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Д (дефазифікація).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Процес дефазифікації є зворотним до фази- фікації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Дефазифікація нечіткої множини здійснюється за принци- пом центра ваги;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВЧЗІПЯ (визначення числового значення інтегрального показ- ника якості).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визначається для можливості прогностичного оціню- вання якості проєктування післядрукарських процесів за певних ви- значених умов.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виражається у відсотках [27–29;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 60;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 131 Подальшій декомпозиції підлягають перший та другий функціо- нальні блоки діаграми А5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідно діаграма А51 містить такі блоки: – ФЧПЯ (формування часткових показників якості).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для вста- новлення інтегрального показника якості проєктування післядру- карських процесів доцільно сформувати часткові показники якості лінгвістичних змінних та згрупувати її за спільними ознаками та при- значенням;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ВУМЗ та ТМАЗ (виокремлення універсальної множини значень та терм-множини аналізованих змінних).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для кожної лінгвістичної змінної формується універсальна множина значень зі встановленими межами та одиницями вимірювання і терм-множина, яка словесно описує градацію універсальної множини;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ПБМНЛВ (побудова багаторівневої моделі нечіткого логічного виводу).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Багаторівнева модель нечіткого логічного виводу будується для ієрархічного представлення залежності між якістю проєктування післядрукарських процесів та значеннями лінгвістичних термів ви- окремлених факторів [27];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ОФНЛЗ (опрацювання функцій належності лінгвістичних змін- них).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За відносними оцінками рангів лінгвістичних термів створю- ються квадратні обернені симетричні матриці, внаслідок обчислення яких встановлюються числові значення функцій належності у п’яти точках поділу універсальної множини.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Отримані нечіткі множини ві- зуалізуються за допомогою графіків [28;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 29];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ФБЗ (формування баз знань).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формується нечітка база знань для інтегрального показника якості та для кожної лінгвістичної змін- ної, враховуючи ієрархію, наведену у багаторівневій моделі нечіткого логічного виводу;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ФМЗ (формування матриць знань).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За сформованими базами знань синтезуються матриці знань для якості проєктування післядру- карських процесів та для кожного часткового показника;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ФНЛР (формування нечітких логічних рівнянь).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За сформова- ними матрицями знань будуються нечіткі логічні рівняння для кож- ного терму часткових показників якості та для термів лінгвістичної змінної «якість проєктування післядрукарських процесів» [50;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 60;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Діаграма А52 включає: – ФТЗФНЛЗ (формування таблиць значень функцій належності лінгвістичних змінних).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За терм-множинами з пронормованими зна- ченнями функцій належності у п’яти точках поділу універсальної мно- жини створюються таблиці значень для кожної лінгвістичної змінної;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 132 – ФНЛР (формування нечітких логічних рівнянь).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Здійснюється підстановка значень з таблиць значень у нечіткі логічні рівняння для термів «низька», «середня», «висока» кожної лінгвістичної змінної.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідно проводяться обчислення підсумкових значень функцій належності [22;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 26;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 62;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для відображення ієрархічної залежності функцій використаємо діаграму дерева вузлів, у якій верхній рівень відповідає контекстній діаграмі (батьківському елементу), а нижні — декомпозиції потоків (дочірнім елементам).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому взаємозв’язки між функціональ- ними блоками не відображаються, лише ієрархічна впорядкованість.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такий підхід уможливлює цілісний аналіз ієрархії функціональних блоків моделі IDEF0 [77].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Висновки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У дослідженні наведено розв’язання актуального науко- во-прикладного завдання розроблення інформаційної технології про- гностичного оцінювання якості проєктування післядрукарських про- цесів на основі дослідження домінантності виокремлених факторів і застосування нечіткої логіки для отримання інтегрального показника якості.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виокремлено основні етапи інформаційної технології.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наведено загальну характеристику реалізації та проєктування піс- лядрукарського опрацювання книжкових видань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виокремлено та описано фактори впливу на якість проєктування післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Здійснено моделювання функцій реалізації та проєктуван- ня досліджуваного процесу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Створено IDEF0-моделі, які складаються з сукупності ієрархічно впорядкованих та взаємопов’язаних діаграм: контекстної діаграми, декомпозиції контекстної діаграми (діаграми першого рівня декомпозиції) та декомпозиції функціональних блоків діаграми першого та другого рівнів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Описано основні підходи до ство- рення онтології та основні типи онтологій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Подано методологію побудови семантичної мережі, що відтворює зв’язки між факторами впливу на якість аналізованого процесу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За допомогою логіки предикатів здійснено формалізоване відображен- ня зв’язків між ними.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наведено особливості синтезу та оптимізації моделі пріоритетного впливу факторів на якість проєктування післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Критерії оптимізації становлять: власне значення матриці max 8,483 λ = , індекс узгодженості 0,069 IU = , відношення узгодженості 0,049 RU = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Критерії оптимізації знаходяться в допустимих межах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Визначено оптимальні альтернативні варіанти реалізації проєкту- вання післядрукарських процесів за методами багатофакторного ви- 133 бору альтернатив на основі лінійного згортання критеріїв та на основі нечіткого відношення переваги.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому за методом багатофак- торного вибору альтернатив на основі лінійного згортання критеріїв максимальне значення отримала оцінка корисності 3 0,414 U = аль- тернативи А3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За методом багатофакторного вибору альтернатив на основі нечіткого відношення переваги максимальне значення отри- мала функція належності ( ) [ ] 3 0,4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0,74;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1,26 нд Q x µ = , тобто оптималь- ним вважається третій варіант.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Порівняно результати пошуку опти- мальних альтернатив та встановлено тотожність варіантів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Отримано значення функцій належності лінгвістичних змінних аналізованого технологічного процесу шляхом обчислення матриць попарних порівнянь для кожної лінгвістичної змінної та відповідної їй терм-множини значень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Терми лінгвістичних змінних представле- но нечіткими множинами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Описано отримання значення оцінки якості проєктування піс- лядрукарських процесів шляхом дефазифікації нечітких множин за принципом центра ваги.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інтегральний показник якості за обраних умов становить .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 50,256% прогноз G = при максимальних значеннях 100%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розроблено структурно-функціональну модель інформаційної технології прогностичного оцінювання якості проєктування після- друкарських процесів, що враховує етапи дослідження та уможлив- лює апріорне забезпечення якості друкованої продукції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Створено IDEF0-моделі інформаційної технології: побудовано контекстну діа- граму А-0, діаграму першого рівня декомпозиції А0, діаграми другого рівня декомпозиції А1, А2, А3, А4, А5, діаграми третього рівня деком- позиції А23, А24, А41, А42, А51, А52 та діаграму дерева вузлів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' СПИСОК ВИКОРИСТАНОЇ ЛІТЕРАТУРИ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ДСТУ 3017:2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Видання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основні види.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Терміни та визначення понять.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Київ, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 38 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ДСТУ 4489:2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Видання книжкові та журнальні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вимоги до форматів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Київ, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Антонова С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Г.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Редакторская подготовка зданий: учебник.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Москва: Изда- тельство МГУП, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 468 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Барановський І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Яхимович Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' П.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поліграфічна переробка образо- творчої інформації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Київ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів: ІЗМН, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 400 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Бартіш М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Я.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Дудзяний І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Дослідження операцій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ч.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3: Ухвалення рі- шень і теорія ігор.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів: Вид.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' центр Львів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' нац.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ун-ту ім.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Івана Франка, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 278 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 134 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Брошюровочно-переплетный процесс в подробностях.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Арт-проект творческого коллектива Zen Designer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' URL: zen-designer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='ru/scio/767- broshurovochno-perepletnij-protsess 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Величко О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Скиба В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Шангін А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Проектування технологічних процесів видавничо-поліграфічного виробництва: навч.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' посіб.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' К.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=': НТУУ «КПІ», 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 235 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Волкова Л.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Издательско-полиграфическая техника и технология.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Мо- сква: Изд-во МГУП «Мир Книги», 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 224 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Воробьев Д.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Технология послепечатных процессов: учебник.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=': МГУП, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 394 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Гавенко С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ф.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Воржева О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Конюхова І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Мельников О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Прак- тикум з оцінки якості поліграфічної продукції / за ред.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Е.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Т.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Лазаренка.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів: Афіша, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 64 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Гавенко С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Лазаренко Е.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Мамут Б.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оздоблення друкованої про- дукції: технологія, устаткування, матеріали.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Київ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів : Ун-т «Україна», УАД, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 180 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Гавенко С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Корнілов І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Ничка В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Системний аналіз і методи керування якістю книжкової продукції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ужгород: Карпати, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 80 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Гавенко С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Кулік Л.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Мартинюк М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Конструкція книги.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Л.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=': Фенікс, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 256 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Гавриш Б.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Тимченко О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Методи опрацювання потоку цифрових даних в процесорах растрових перетворень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Моделювання та інформаційні технології.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 142–147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Голубник Т.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Піх І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Засади нечіткої логіки при забезпеченні якості формування монтажних спусків.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наукові записки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 1–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 77–83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Голубник Т.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Піх І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Петрів Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Побудова функцій належності факторів якості формування монтажних спусків.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Технологія і техніка друкарства.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' К.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=': ВПІ НТУУ «Київський політехнічний інститут», 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 3 (45).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20–29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Либау Д.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Хайнце И.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Промышленное брошюровочно-переплетное про- изводство.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ч.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=': МГУП, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 422 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 470 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Дурняк Б.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Піх І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інформаційні технології про- гнозування та забезпечення якості видавничо-поліграфічних процесів (методологія вирішення проблеми).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Технологічні комплекси.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 21–24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Жидецький Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ц.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Лазаренко О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Лотошинська Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Д.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поліграфіч- ні матеріали / за заг.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ред.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Е.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Т.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Лазаренка.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів: Афіша, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 328 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Заде Л.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Понятие лингвистической переменной и его применение к принятию приближенных решений.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Москва: Мир, 1976.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 165 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Заде Л.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Роль мягких вычислений и нечеткой логики в понимании, кон- струировании и развитии информационных интеллектуальных систем.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Новости искусственного интеллекта.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Москва, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 2–3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 7–11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 135 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зайченко Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' П.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Дослідження операцій: підручник.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сьоме видання, пере- роблене та доповнене.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Київ: Видавничий Дім «Слово», 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 816 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Карпенко В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Сисюк В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Г.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Друкарське і брошурувально-палітурне ви- робництво: проектування та розрахунок технологічних процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів: УАД, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 76 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кипхан Г.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Энциклопедия по печатным средствам информации.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Техноло- гии и способы производства: пер.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' с нем.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=': МГУП, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1280 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кудряшова А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Багатофакторний вибір альтернативних варіантів про- єктування післядрукарських процесів на основі лінійного згортання кри- теріїв.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поліграфія і видавнича справа.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 2 (78).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 45–50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кудряшова А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Литовченко Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формування інтегрального показни- ка якості процесу структурування видання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поліграфія і видавнича справа.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 82–89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кудряшова А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Модель якості проектування післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Технологічні комплекси.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Луцьк, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 1 (16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 44–48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кудряшова А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Опрацювання функцій належності лінгвістичних змін- них проєктування післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Частина 1: Створення ма- триць попарних порівнянь.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наукові записки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 1 (60).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 26–32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кудряшова А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Опрацювання функцій належнос- ті лінгвістичних змінних проєктування післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Час- тина 2: Візуалізація значень функцій належності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поліграфія і видавнича справа.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 1 (79).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 30–41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кудряшова А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Синтез моделі пріоритетного впливу факторів про- ектування післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наукові записки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 1 (58).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 48–54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Лазаренко О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' та інші.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Як вибрати технологію та устаткування для міні- друкарні?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів: НВП «Мета», 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 226 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Либерман Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' И.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Статистические методы контроля качества печатной продукции: по показателям несовмещения краски и точности фальцовки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Москва: Книга, 1977.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 119 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Литвин В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Технології менеджменту знань: навч.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' посібник.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів: Львів- ська політехніка, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 260 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Маїк В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Теоретичні основи процесів тиснення поліграфічної продукції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Квалілогія книги.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 43–62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Маїк В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Технологія брошурувально-палітурних процесів: підр.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' / за заг.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ред.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Лазаренка Е.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Т.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів: УАД, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 488 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Малышкин Е.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Мильчин А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Э.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Павлов А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Шадрин А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Е.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Настольная книга издателя.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Москва: АСТ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Агенство «КРПА Олимп», 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 816 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Малколм Дж.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кейф.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Послепечатные технологии / пер.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' с англ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' И.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Куп- цова;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' под ред.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' И.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Стефанова.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=': ПРИНТ-МЕДИА центр, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 280 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Небава М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Адлер О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Лесько О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Й.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Економіка та організація вироб- ничої діяльності підприємства: навчальний посібник.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ч.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2: Організація виробництва Вінниця: ВНТУ, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 131 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 136 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Новожилов А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Цифровий друк — шлях у майбутнє.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Палітра друку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 43–45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Овчинникова Е.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Моделирование бизнес-процессов с помощью AllFusion Process Modeler: учебно-методическое пособие.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Екатеринбург: УрГУПС, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 102 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Осінчук О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Козак Р.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нечітка логіка як засіб формування якості плану- вання книжкових видань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поліграфічні, мультимедійні та web-технології: матеріали II Міжнародної науково-технічної конференції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 49–51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Осінчук О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Литовченко О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Калиній І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формування інтеграль- них показників якості планування та художньо-технічного оформлення книжкових видань засобами теорії нечітких множин.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Моделювання та ін- формаційні технології.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вип.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 137–142.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Осінчук О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Сеньківська Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Є.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Побудова та розра- хунок функцій належності лінгвістичних змінних для процесів плануван- ня та художньо-технічного оформлення книжкових видань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поліграфія і видавнича справа.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 2 (76).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 57–63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Павлов А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Соколов Б.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Принятие решений в условиях нечеткой ин- формации: учебное пособие.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' СПб.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 72 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Пашуля П.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Л.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Стандартизація, метрологія, відповідність, якість у полігра- фії: підручник.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів: УАД, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 408 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Піх І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Дослідження параметрів книжкових видань Науково-технічна конференція професорсько-викладацького складу, наукових працівників і ас- пірантів: тези доповідей.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Піх І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Дурняк Б.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Голубник Т.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інформацій- ні технології формування якості книжкових видань: монографія.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів: Українська академія друкарства, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 308 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Піх І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Модифікована графічна модель параметрів книжкових сторінок.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Квалілогія книги: матеріали VI Міжнародної науково-практичної конфе- ренції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 19–22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Піх І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інформаційні технології моделювання ви- давничих процесів: навчальний посібник.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів: Українська академія дру- карства, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 224 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Піх І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Сеньківська Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Є.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Калиній І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Теоретич- ні основи забезпечення якості видавничо-поліграфічних процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Час- тина 4: Прогнозування та забезпечення якості засобами нечіткої логіки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наукові записки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 22–30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Предко Л.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Проектування додрукарських процесів: навчальний посіб- ник.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів: УАД, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 352 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Репета В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Б.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Гургаль Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Прогнозування якості процесу уф-флексографічного друку етикетки на основі нечіткої логіки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наукові записки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 1–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 84–89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 137 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ротштейн А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' П.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Интеллектуальные технологи идентификации: нечеткие множества, нейронные сети, генетические алгоритмы.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Винница: УНІ- ВЕРСУМ-Вінниця, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 320 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ротштейн О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' П.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Ларушкін Є.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' П.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Мітюшкін Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Soft Computting в біо- технології: багатофакторний аналіз і діагностика: монографія.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вінниця: УНІВЕРСУМ-Вінниця, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 144 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Саати Т.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Принятие решений (Метод анализа иерархий).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Москва: Радио и связь, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 278 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Самарин Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Технологические процессы автоматизированных про- изводств (Полиграфическое производство): учебник.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=': МГУП, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 556 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Свідоцтво про реєстрацію авторського права на твір № 41832.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Україна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Імі- таційне моделювання в системному аналізі методом бінарних порівнянь.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' [Комп’ютерна програма] / Авторські майнові права належать І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Гілеті, В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сеньківському, О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Мельникову.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зареєстровано 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Козак Р.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Автоматизоване проектування книжко- вих видань: монографія.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів: УАД, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 200 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Кудряшова А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Козак Р.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інформаційна техно- логія формування якості редакційно-видавничого процесу: монографія.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів: Українська академія друкарства, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 272 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Кудряшова А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Прогностичне оцінювання процесу проектування видань засобами нечіткої логіки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' International research and practice conference «Modern methods, innovations, and experience of practical application in the field of technical sciences»: Conference proceedings (Radom (Poland): Izdevnieciba «Baltija Publishing», December 27–28, 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Radom, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Р.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 28–32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Кудряшова А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формалізоване подання зв’язків між факторами проектування післядрукарських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поліграфія і ви- давнича справа.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 1 (77).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 70–77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Кудряшова А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формування інтегрального показ- ника якості реалізації процесу проектування видання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поліграфія і видав- нича справа.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 2 (74).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 11–18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Піх І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Гілета І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Петрів Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Функції належнос- ті параметрів паперу для плоского офсетного друку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Технологічні комплек- си.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 32–37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Піх І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Голубник Т.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нечітка база знань і нечіткі логічні рівняння в процесі реалізації монтажних спусків.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наукові записки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 111–119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Піх І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Голубник Т.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Калиній І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Структурно- функціональна модель інформаційної технології прогнозування якості проектування та реалізації монтажних спусків.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наукові записки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 2 (51).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 7–13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 138 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Піх І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Калиній І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інформаційно-технологічні моделі додрукарського процесу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Квалілогія книги.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вип.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5–9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Сеньківська Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Є.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Кудряшова А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Кали- ній І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Моделювання процесу забезпечення якості технології випуску книжкових видань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Квалілогія книги.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 26–31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Сеньківська Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Є.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Кудряшова А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оптимізація мо- делі пріоритетного впливу факторів на якість проєктування післядрукар- ських процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наукові записки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 2 (59).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 22–29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сеньківський В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Сеньківська Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Є.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Петрів Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Калиній І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ва- гомість функцій належності у забезпеченні якості друкарського процесу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поліграфія і видавнича справа.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' № 3–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 31–36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сокол О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ф.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Підготовка видання до поліграфічного оформлення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів: УАД, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Специальные виды печати.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Технологические инструкции.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Москва: Книжная палата, 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 350 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сявавко М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інформаційна система «Нечіткий експерт».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів: Видав- ничий центр ЛНУ імені Івана Франка, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 320 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Темникова Е.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Асламова В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Берестнева О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Г.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Онтологическое моде- лирование предметной области учреждения дополнительного професси- онального образования.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Онтология проектирования.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Том 5, № 4 (18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 369–386.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' URL: http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='ontology-of-designing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='ru/article/2015_4 %281 8 %29/2_ %D0 %A2emnikova.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='pdf 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Романо Ф.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Принт-Медиа Бизнес / пер.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' с англ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Бредис, В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вобленко, Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Друзьева;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' под ред.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Б.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кузьмина.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=': ПРИНТ-МЕДИА центр, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 456 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Хведчин Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Й.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Брошурувально-палітурне устаткування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ч.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1: Брошуру- вальне устаткування: підручник.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів: ТеРус, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 336 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Хведчин Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Й.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Брошурувально-палітурне устаткування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ч.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2: Палітурне устаткування: підручник.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів: УАД, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 392 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Шаховська Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Б.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Литвин В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Проектування інформаційних систем: на- вчальний посібник.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Львів: Магнолія-2006, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 380 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ontology Metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Protégé 5 Documentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' URL: http://protegeproject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='io/protege/views/ontology-metrics/ 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Senkivskyi V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Kudriashova A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Pikh I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Hileta I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Lytovchenko O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Models of Postpress Processes Designing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1st International Workshop on Digital Content & Smart Multimedia, DCSMart 2019, Lviv, Ukraine, December 23–25, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 259–270.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 139 THERMALLY STIMULATED PROCESSES AND PYROELECTRICITY IN FERROELECTRIC POLYMERS Sergeeva A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Стаття присвячена експериментальному дослідженню тонких плі- вок полівініліденфториду (ПВДФ), його сополімеру з тетрафторетиле- ном П(ВДФ-ТФЄ), а також композитів на основі ПВДФ та неорганічних керамічних матеріалів титанату барію BaTiO3 та титанату циркона- ту свинцю (ЦТС).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Всі ці матеріали є сегнетоелектриками.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вивчено їхню поведінку при різних температурних впливах, зокрема струми термо- стимульованої поляризації (ТСП) та деполяризації (ТСД), а також піро- електричний ефект у цих матеріалах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Встановлено, що термічний вплив є важливим при формуванні сегнетоелектричної поляризації та забезпечен- ня її стабільності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Встановлено важливу роль об’ємного заряду в сегнетоелектричних полі- мерах на величину та стабільність залишкової поляризації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Запропоновано методи поділу гомозаряду та гетерозаряду у полімерних плівках.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Отримані результати мають як наукове, так і практичне значення, оскільки сегнетоелектричні полімери широко використовуються для виго- товлення різних сенсорів і датчиків.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This article is devoted to the experimental study of polyvinylidene fluoride (PVDF) thin films, its copolymer with tetrafluoroethylene P(VDF-TFE), as well as composites based on PVDF and inorganic ceramic materials of barium titanate Ba- TiO3 and lead zirconate titanate (PZT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' All of these materials are ferroelectrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Their behavior was studied under different temperature influences, in particular, currents of thermally stimulated polarization (TSP) and depolarization (TSD), as well as the pyroelectric effect in these materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It was found that thermal action affects the formation of ferroelectric polariza- tion and its stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The important role of the space charge in ferroelectric polymers on the magnitude and stability of polarization has been established.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Methods for separating homocharge and heterocharge in polymer films were proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The results obtained are of both scientific and practical importance, since fer- roelectric polymers are widely used in the manufacture of various kinds of sensors and transducers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Introduction To measure the thermal relaxation of the residual polarization, the mea- surement of the thermally stimulated depolarization currents (TSD) is the most appropriate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Despite numerous experimental studies, there is still no theory of the TSD current method for the case of poled ferroelectric poly- mers like polyvinylidene fluoride (PVDF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Therefore, the description and 140 interpretation of measured current peaks are usually qualitative and hypo- thetical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' To detect the nature of the TSD current peaks, their connection with po- larization and pyroelectricity must be taken into account, as well as processes occurring in the amorphous and crystalline phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Such an attempt was made [1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2] by considering individual contributions to TSD currents of pyroelectric processes, polarization in the amorphous phase, “charge-induced interphase polarization” (called the Maxwell-Wagner effect) and the ferroelectric po- larization in the crystalline phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In qualitative description of the predicted processes, in addition to compensating charges, “injected surplus charges” were taken into account, that is, space charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Often it is considered as a self-evident that there is polarization in PVDF, compensating charges, and space charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' While there is no doubt about the existence of polarization, the existence of the space charge in addition to compensating charges is question- able, since PVDF has a sufficiently high specific conductivity about g = 10–11 Sm/m at room temperature [3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4] and the dielectric permittivity ε = 10–20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Therefore, any surplus charges will be neutralized with the Maxwell re- laxation time of approximately 0 13s g ε ε τ = ≈ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (1) This indicates that in the short-circuited sample, after about 40 seconds, any electric field caused by charges (other than compensating charges and polarization charges of the ferroelectric crystals) will disappear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Homogeneously polarized two-phase materials, like PVDF, consist of ferroelectric crystallites scattered in the amorphous matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Compensation of the depolarizing field in the ferroelectric crystallites is possible only due to the charges localized at two sides of the crystallites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Full compensation by the electrode charges, as in the case of single crystals or 100 % crystalline materials, is not possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In PVDF and other biphasic ferroelectric poly- mers, the accumulation of charge at the boundaries between the crystalline and amorphous phases only occurs to a small extent due to the difference in dielectric constant, and is the most likely due to presence of the ferroelec- tric polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' von Seggern and Fedosov proposed a model of a layered structure with alternating ferroelectric and non-ferroelectric layers for the description of initial poling [3, 4], switching of polarization [5], short circu- iting and the back switching [6] in PVDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The theory of the TSD method [7] was developed only for electrets with dipole and/or space charge polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is assumed that polarization or 141 space charge is initially thermally frozen, and then it defrosts under linear heating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' For application the TSD method to ferroelectric polymers, the the- oretical basis has not yet been constructed, since polarization in PVDF is not thermally frozen, but has the ferroelectric nature and can occur in high fields without heating during poling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In addition to the irreversible relaxation cur- rents, in the TSD experiments on ferroelectric polymers, there are reversible pyroelectric currents, and the separation of these components is not an easy task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, the TSD method, due to its informative and versatile nature, has been widely used for studying the polymer ferroelectric as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The TSD current peak at 50–60 °C has been observed by many research- ers in the non-ferroelectric α-PVDF and the ferroelectric β-PVDF poled in a wide range of temperatures, electric fields and times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The only common feature of all PVDF samples on which these experiments were carried out was the presence of the amorphous phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, this TSD current peak with high probability can be associated with processes occurring in the amor- phous phase of PVDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In many cases, it was assumed that the TSD current peak near 50–60 °C is associated with the so-called αc-process [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, data on the nature of the αc-process are still controversial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Moreover, an interrelation between structural transformations and TSD currents should be established, since the TSD currents are the result of electrical, but not always structural pro- cesses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Making assumptions about the nature of the TSD currents peaks, it is necessary to take into account not only structural transformations, but also fundamental electrical principles and laws.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Otherwise, a qualitative ex- planation without the corresponding formulas and equations may be false.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Two high-temperature peaks, in addition to the usual α- and β-processes in PVDF, were found by the TSD method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' One of the processes was attribut- ed to charges trapped on the boundary between the nonpolar crystalline α-phase and the amorphous region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The other was assumed to be related to charges on polar β-crystallites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The authors believe that both peaks are due to the positive homocharge injected from the anode, although it is quite probable that they are related to the poling temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Eliasson [9], studying the influence of the polarizing field, temperature, and electrode material on TSD currents, believed that the formation of a bulk charge was influenced by injection, although her results did not match with the position and magnitude of peaks in the data of Ieda and others [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The picture becomes even more complicated if we compare the data on the TSD obtained by different researchers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The variety of relaxation pro- cesses determined by the TSD method is due to the lack of clear methods 142 for identifying peaks (sometimes they take for relaxation peaks the smallest bends at the TSD current curve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Neagu and others [11] believe that the high influence on the TSD currents has the material of electrodes and the uncontrolled composition of the atmosphere, in particular presence of oxy- gen, nitrogen and water vapors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It follows from the theory of the TSD currents [12] that in a one-com- ponent homogeneously polarized dipolar sample, the measured current is equal to the displacement current dP/dt, so that the integral of the TSD current is equal to the value of the initial polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' As shown by von Seggern and Fedosov [5], the integral of the TSD current is smaller than the residual polarization in the case of a two-phase system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Possibilities of thermally stimulated research methods are extremely wide, since most relaxation processes are thermally activated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At the same time, these possibilities in the study of ferroelectric polymers have not yet been detected and have not been used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This relates to the study of the ef- fective conductivity dynamics in the process of the thermoelectret poling (TEP), the comparison of TEP and TSD currents, the separation of homo- charge and heterocharge contribution in the ferroelectric polymers to the relaxation current, the use of fractional TSD methods for separation of the pyroelectric and the relaxation components of the total current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The aim of the present article was to obtain additional experimental re- sults by using above mentioned methods for clarifying physical processes responsible for formation of the residual polarization in PVDF films, being a typical representative of the ferroelectric polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Another part of inves- tigation is related to finding interrelation between TSD currents and the py- roelectricity in this class of materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We also performed some experiments on P(VDF-TFE) copolymer and composites of PVDF with the inorganic crystals like barium titanate (BaTiO3) and lead zircanate titanate (PZT) in order to make the research more generalizing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The features of the Thermally Stimulated Depolarization Current method In the case of thermoelectret poling (TEP), unlike isothermal poling, the sample was initially kept at room temperature at constant voltage for some time necessary to decrease the absorption current to values of the or- der of 10–11 A, and then the temperature was linearly increased to 150 °C at a constant rate (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5–4 °C/min) with continuous measuring of the poling current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' After completion of poling, the samples were quickly cooled down without switching off the applied voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 143 Since many relaxation processes have the thermally activating nature, the TSD method [12] was used to predict the space charge and the residual polarization stability and to study the mechanism of their formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The sample electrodes were connected with each other through the electrometer having a sensitivity of 10–14–10–16 A by current and the current recording device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The temperature was raised at a constant rate in the range of 15–150 °C and measured by a chromel-copel thermocouple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The principle of the current TSD method is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We measured the thermally stimulated decrease in the electret potential by the vibration electrode method (Kelvin’s method).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Measurements in the range from -100 °С to +180 °С was carried out by using the relaxation spec- trometer Solomat-91000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Studies in the field of low temperatures from -170 to + 40 °C were performed by using the Kithley-6100 electrometer on the samples that were originally cooled in liquid nitrogen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Relaxation of homocharge and heterocharge during the TSD currents measurement A number of properties of the ferroelectric polymers can be explained within the framework of the modern theory of polar electrets [13] consid- ering relaxation of the homocharge and the heterocharge in a self-consis- tent regime without taking into account the ferroelectricity in the crystalline phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We consider the interrelation between the homocharge and the het- erocharge taking into account experimental data on thermally stimulated and isothermal relaxation of PVDF films poled in the corona discharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Four types of depolarization varieties were used to study the relaxation processes, namely thermally stimulated (T) and isothermal (I) depolariza- tion of short-circuited samples (S) and depolarization in the open circuit mode (O).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The modes were denoted as TS, TO, ISO, and IO, where the first letter indicated the temperature mode (thermally stimulated or iso- thermal), and the second was related to the electrical state (short-circuit or open circuit).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Additional experiments on the thermally stimulated electret potential (TP) kinetics were also performed after 24 hours of keeping in the open circuit configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A film of polytetrafluoroethylene (PTFE) with a thickness of 10 μm was used as a dielectric gap in TO and IO modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' All thermally stimulated experiments were performed at a constant heating rate of 3 °C/min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In isothermal experiments, the temperature was maintained constant after the required temperature value was achieved by rapid heating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The electret potential in the TP method was measured by the Kelvin meth- od and was continuously recorded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 144 Time External field Temperature TSD current Charging current Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The principle of the thermoelectret poling (1) and depolarization (2) methods During poling in a corona discharge, the excess charge is localized on the surface of the sample forming a homogeneous charge σ, which creates a homogeneous field in the sample volume, in which the internal dipolar polarization (heterocharge) is formed characterized by the surface density of the bound charge P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the case of the sample short-circuiting without a gap, only the heterocharge relaxes [12], and the equality σ = P and the zero internal field (E = 0) is supported due to the current redistribution in the external circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the presence of a dielectric gap and in the open circuit mode, the relaxation currents of the homocharge and the heterocharge flow in opposite directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In order to find separately components corresponding to the decay of the homocharge σ and the heterocharge P of the full depolarization current in the open circuit mode,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' we present the current density i(t) and the surface potential V(t) as ( ) ( ) ( ) dP t d t i t s dt dt σ \uf8ee \uf8f9 = − \uf8ef \uf8fa \uf8f0 \uf8fb ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (2) [ ] 1 0 1 ( ) ( ) ( ) sx V t t P t = σ − ε ε ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (3) 0 1 1 ( ) ( ) dV t i t x dt ε ε = − ⋅ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (4) E T TSDC145 where,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' t is time,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ε and xo are the dielectric constant and the thickness of the sample;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ε1 and x1 are similar parameters of the dielectric gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' For the con- ductivity current density, it is possible to write down 0 ( ) ( ) ( ) C g d t i t V t x dt σ = = − , (5) where 0 exp( / ) g g Q kT = − is the specific conductivity, k is Boltzmann’s constant, T is temperature, Q is the activation energy of the intrinsic con- ductivity, go is a pre-exponential factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Integrating (4) over time and replac- ing the variable t by T taking into account the linear heating 0 T T t = +β⋅ where β is the heating rate,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' То is the initial temperature of the experiment,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' we obtain from (5) the temperature dependences of the depolarization cur- rents and the electret potential 1 0 1 0 0 0 1 ( ) exp ( ) T x g d Q i T i T dT dt bT x kT ∞ σ \uf8eb \uf8f6 ′ = = − − \uf8ec \uf8f7 ε ε \uf8ed \uf8f8∫ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (6) 2 ( ) ( ) dP i T d i T dt s dt σ = = + ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (7) 1 0 0 1 ( ) ( ) T x V T i T dT bT ∞ ′ = ε ε ∫ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (8) All values in the right-hand sides of the equations (6–8) are known from the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, this technique allows to differentiate processes of ho- mocharge and heterocharge relaxation in different modes of TSD by using experimental i(T) curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Application of thermoelectret poling of PVDF films The thermoelectret poling method (TEP) has several advantages over isothermal poling, because it allows to obtain additional data on the mech- anism of the polarization formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is also possible to determine the op- timal temperature of poling, as well as to find the temperature, at which the ohmic conductivity becomes significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2 and Table 1 one can distinguish the following features: 1) The TEP curves contain three characteristic areas: a) the growth of the current irrespective of the corona discharge polarity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' b) decrease of the current (negative temperature coefficient of conduction);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' c) increase of the current at high temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 146 25 50 75 0 250 500 750 1000 2 1 Current density, \uf06dA/m 2 Temperature, oС Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Dependence of current on temperature during thermally stimulated poling in positive (1) and negative (2) corona discharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Heating rate is 2 °C/min Table 1 Effective activation energy during TEP in different temperature ranges (from the inclination of linear parts in lni-1/T curves) [9] Charge Polarity Heating Cooling Activation energy, eV Temperature range, °C Activation energy, eV Temperature range, °C + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='87 20–40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='82 40–50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='82 50–65 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='92 60–45 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='06 45–25 – 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='87 20–35 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 35–45 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='12 65–80 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='19 70–55 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='83 55–35 2) With negative corona discharge polarity, the second region is more pronounced than with positive polarity, and the decrease in conductivity begins at lower temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The difference in the currents of the TB pos- itively and negatively poled samples indicates different injection levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In a positive corona, it is likely that both positive charges and negative ones (from the rear electrode) are injected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the case of a negative corona, pos- itive charge carriers from the metal electrode are not injected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3) When thermoelectret poling of PVDF films occurs, the irreversible de- crease in the effective conductivity is due to the fact that the value of the ther- mal current when cooled is much smaller than the current during heating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In PVDF, the current peak during TEP (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2) cannot be considered to be due to polarization, as in the case of linear polar polymers, because its 147 integration gives an unrealistically great value of the polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Probably, the conductivity current in TEP ferroelectric polymers is much larger than the polarization component of the current, therefore the graphs in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2 reflect the nature of changing in the films effective conductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The mechanism and nature of conductivity in PVDF are unknown, but presence of the negative temperature coefficient of conductivity sections in curves Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2 suggests that, along with the thermally activated increase in the number of moving carriers, there is also likely to be a trapping by deep traps, and with certain ratios of field strength and temperature the second process prevails over the first process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The trapped charges play an important role by neutralizing the depolarizing field and contributing to the preservation of the residual polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' High polarization in a poled film and a sharp decrease in conductivity (the current passes through the maximum) are probably interconnected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The fer- roelectric polarization in crystallites creates conditions for trapping of charges at their boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The field of the trapped charges screens the polarization and contribute to its stabilization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, the processes of the polarization de- velopment and the charge trapping are interconnected and interdependent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At the current curve of TEP from room temperature to 30–40 °С, the dependence i(T) is exponential regardless of the corona polarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This can be related to the thermal generation of charge carriers in the volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The fur- ther course of the current graphs corresponds to the proposed model for the polarization formation and the charge trapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' There is again increase of the current in the third section that may be due to the internal thermoelec- tric detrapping of the previously trapped charges with partial destruction of the already formed polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' If this assumption is valid, then it is an important for practice conclusion that it is impractical to heat PVDF during TEP above the minimum temperature on the current-temperature curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Decrease of the current and the effective conductivity in the second sec- tion of the TEP curve may be due to the following reasons: 1) Depletion of the stock of own carriers due to their migration in the external field and trapping near the electrodes (electrode polarization);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2) Irreversible changes at the electrodes or near to them leading to lim- iting of the charge injection;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3) Generation of regions in the volume that do not conduct current, for example, polarized crystallites with layers of the trapped charges;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4) Changing the equilibrium between free and trapped charges due to the formation of new traps at the boundaries of the polarized crystallites and macroscopic polarized regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 148 The difference between TEP currents in positively and negatively charged samples is against the migration mechanism causing the reduction in con- ductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The second reason is also unlikely, because due to ionic impurities the field on the electrodes should increase, which together with the effect of the temperature would lead to increase in the injection level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The third reason is more probable, because the ordering in the crystalline phase of the poly- mers leads to decrease in localized states the density and decrease in conduc- tivity (the band gap width is of the order of 6–9 eV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, the ordering of the preferred orientation of dipoles in crystallites in the external field cannot substantially change their conductivity, because they already have the spon- taneous polarization as the higher degree of the internal ordering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Most likely, the conductivity of PVDF decreases as a result of the inten- sive trapping of carriers at the boundaries of polarized crystals and macro- scopic polarized regions, which create favorable conditions for localization of the charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We have found that similar processes at low temperatures and high fields lead to appearance of areas of negative dynamic resistance on volt-ampere characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' If the proposed hypothesis is correct, then there the relationship between the temperature and the field strength must be observed, in which high po- larization is formed and the irreversible decrease in conductivity appears.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Dependence of the effective conductivity on temperature in TEP mode at different constant voltages is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3, from which it is seen that the beginning of the negative temperature conductivity section moves to lower temperatures with increasing the polarizing voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is known that the high polarization in ferroelectrics occurs in fields above the coercive one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' From the data of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3 it follows that the value of the coercive field decreases with increasing temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3 and Table 1 it is evident that the acti- vation energy that provides the effective conductivity in not polarized and polarized samples is practically the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At the same time, the conductivity of the polarized films, and hence the concentration of free carriers in them is almost 100 times smaller than in not polarized films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Consequently, in the process of poling, there are redistribution of carriers and their additional trapping at the newly created traps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Let us analyze the shape of the TEP current curve taking into account that the conductivity current IS is proportional to the concentration of free charge carriers 0 c c U i n e x = µ⋅ , (9) 149 where μ is the mobility;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' U is the applied voltage;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' xo is thickness of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the presence of localized states in the forbidden zone, the concentration of trapped charges is determined by the Fermi-Dirac formula 1 {1 (1/ / exp[ ( ) / ])} t t t n N g F E kT − = + − − , (10) where Nt is the density of localized states;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' g is their statistical weight;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Et is the localized state energy;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' F is a quasi-level Fermi based on its own and injected carriers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We assume that the total concentration of carriers and the Fermi level remain constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2,9 3,0 3,1 3,2 3,3 3,4 2 1 0 1 2 3 Q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='8 eV Q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='8 eV Q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='8 eV 2 kV 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4 kV 1 kV ln[g(pSm/m)] 1000/T(K) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Temperature dependence of the effective conductivity during thermally stim- ulated poling in a corona discharge under different voltages at a control grid (electret potential) Increase in the density of the localized states with increasing polariza- tion can be represented as a linear function where the polarization P is a function of the field strength E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' For ferroelectrics, the function P(E) can be approximated by three rectilinear sections 0, , ( ) ( ) / ( ), , , , c c s s c c s s s E E P E E E P E E E E E P E E < \uf8f1 \uf8f4 = − − < < \uf8f2 \uf8f4 < \uf8f3 (11) where Ec is the coercive field;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Es is the field strength at which polarization reaches saturation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Consider the decrease of the coercive field with increasing temperature 150 0 c E E T = − γ ⋅ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (12) We will assume that the dynamic permittivity at Ec < E < Еs does not de- pend on T, that is equivalent to the constancy of the difference ΔЕ = Еs – Ес.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' From (10)–(15), taking into account the made assumptions, we obtain the dependence of the conductivity current on the temperature 1 0 0 ( / ) {1 (1/ )exp[ ( ) / ]} c t t i e V x n N g F E kT − = µ⋅ ⋅ − + − − , (13) where 0 1 0 0 0 2 0 0 0 0 0 2 1 ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( / ) / , ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( / ) / , ( / )[( / ) ( )], t c t s c t s c N N T T E V x N N P T T E E V x N N P E V x E T T T T = < = − γ = + α > = Δ + − γ = + α Δ − − γ > > .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (14) It follows from expressions (13) and (14) that with increasing tempera- ture in the range T < T1 the current ic increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Nt begins to increase at T > T1 provided 2 / ( / )exp( / ) sP E Q gkT Q kT α γ Δ > − , (15) where Q = F – Et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' There is a decrease in current ic despite the increase in temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The current increases again, if the saturation of polarization is reached, or if the condition (15) is violated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Reducing of the effective conductivity during TEP indicates the impor- tance of volume-charge processes, since the charge trapped on the bound- aries of the polarized regions compensates the depolarizing field and con- tributes to the long-term preservation of the residual polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A similar relation was established during isothermal poling in high fields [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, the increase of temperature and the field strength equally influ- ences on the generation and injection of moving charges, the large con- centration of which is a prerequisite for the emergence and development of the high local polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' As the polarization is formed, the conductivity of ferroelectric polymers is irreversibly reduced due to the trapping of the injected charge carriers at deep traps formed by the polarization of crys- tallites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' These trapped charge carriers stabilize the residual polarization by compensating local depolarizing fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thermally stimulated depolarization currents in PVDF Measurement of TSD currents is a powerful tool for studying relaxation processes [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Although the theory of TSD currents was developed only for the thermally frozen dipole polarization, this method is widely used to study 151 the ferroelectric polymers as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In PVDF, two peaks are the most import- ant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' One of them, related to the glass transition in the amorphous phase, is always observed at a temperature of about -45 °C and it is well-studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The nature of the second peak in the range of 50–80 °C (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4) is not fully understood, although it is clear that several processes, such as the reorien- tation of dipoles in the amorphous phase, the relaxation of the ferroelectric polarization, the displacement of the space charge, as well as interphase and piezoelectrode processes can be responsible for this peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is established that the temperature of about 60 °C is characteristic for PVDF, but its nature is not completely clear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Many researchers associate a peak at this tempera- ture with so called αc relaxation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Lacabane et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' [15] explain the appear- ance of the peak by shrinkage, that is, by a partial restoration after stretching carried out for obtaining the ferroelectric β-phase in PVDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We believe that this peak is associated with polarization in the amorphous phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ferroelectric polymers have the properties of ordinary polar electrets in addition to the ferroelectricity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Therefore, one can expect the presence of two components of the residual polarization: one associated with the fer- roelectricity in the crystalline phase, and another related to the amorphous phase, although there is currently no direct experimental confirmation of this phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Analysis of the relationship between TSD currents in PVDF and pyro- electricity was carried out in the work of von Seggern and Fedosov [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' They have found that the residual polarization decreases after heating to 60 °C, while the pyrocoefficient remains unchanged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' They concluded that the fer- roelectric polarization in the crystalline phase is partially offset by localized charges and partly by polarization in the amorphous phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Therefore, in the formation of the TSD peak in the ferroelectric polymers, several currents are involved caused by relaxation of the electret and the ferroelectric com- ponents of the residual polarization, and associated with the space charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We investigated polarized specimens subjected to TSD either in short-cir- cuit mode or in open-loop with PTFE film as a dielectric gap between the free surface of the sample and one of the electrodes [149–16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The period of time after poling to the TSD measurement was either one day or 16 months.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The samples were named “fresh” and “old” accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Similarly to the data reported in other papers, we observed one broad peak in the mode of the short circuit on fresh samples (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The direction of current at this peak corresponded to the residual po- larization relaxation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Because the crystallinity of PVDF is about 50 % and most of the molecular dipoles in the crystalline regions are in the ferroelec- 152 tric β-phase, the contributions of the electret and the ferroelectric compo- nents to the formation of this peak in fresh samples can be compared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' As for the bulk charging component, it is known that it either does not contribute to the TSD current in the mode of the short circuit, or its direction coin- cides with the depolarization current component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20 40 60 80 100 120 0,4 0,2 0,0 0,2 0,4 0,6 0,8 Current density nA/cm 2 Ioc(T) Temperature, oC 0 2 4 6 8 Current density nA/cm 2 Ic(T) Isc(T) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' TSD currents Іsc(T) and Іoc(T) measured on fresh polarized samples in short-circuit and open circuit modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The curve Ic(T) corresponds to the vol- ume-charge current 0 20 40 60 80 100 120 0,2 0,0 0,2 0,4 0,6 0,8 Current density nA/cm2 Current density nA/cm2 Ioc(T) Temperature, oC 0 1 2 3 4 Ic(T) Isc(T) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5 TSD currents Іsc(T) and Іoc(T) measured in polarized samples in short-circuit- ed and open circuited modes after exposure for 16 months.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The curve Ic(T) corre- sponds to the volume-charge current 153 Comparing the TSD currents of fresh and aged polarized samples, we observed a new phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' One broad TSD current peak in the mode of the short circuit was divided during the aging in two narrow peaks complete- ly separated from each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At the same time, two pairs of the oppositely directed peaks appeared in old samples instead of one pair of peaks typical for fresh samples (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This feature is likely to be common to all ferroelec- tric polymers and does not depend on the polarization conditions, because similar results were also obtained by us on samples poled by a non-focused electron beam at the accelerating voltage of 20 kV and in P(VDF-TFE) and PVDF films poled through a lime glass at the voltage of 7 kV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The depolarization current in the open circuit mode remains unchanged, while the TSD current due to the charge changes the direction to the op- posite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Therefore, the two peaks shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4 can be explained as the result of two partially overlapping and oppositely directed currents arising as a result of the relaxation of polarization and space charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In order to separate the depolarization current IP(T) from the space charge current Ic(T), it is reasonable to assume that the polarization is homogeneous in the direction of the thickness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Since the compensating charges trapped near the surface do not generate any current in the short circuit mode, then Isc(T) = IP(T), where Isc(T) is the experimentally mea- sured TSD current in the short circuit mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The current Ic(T) can be cal- culated from the experimental curves Isc(T) and Ioc(T) shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4 1 2 0 2 1 ( ) 1 ( ) 1 ( ) c c sc x I T T I T x \uf8ee \uf8f9 ε = + − \uf8ef \uf8fa ε \uf8f0 \uf8fb , (16) where ε1, x1, ε2 and x2 are dielectric permittivity and thickness of the sample and the dielectric gap, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In our calculations, we used ε1 = 12, ε2 = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1, x1 = 20 μm, x2 = 25 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is noteworthy that the peak Ic(T) is at the higher temperature than the peak of the depolarization, indicating that the trapped charges are more stable than the residual polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The obtained results can be explained qualitatively taking into account the different nature of the three components of the TSD current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The elec- tret polarization accounting for almost 50 % of the residual polarization in fresh samples decays in time faster than the ferroelectric component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' That is why the two peaks are overlapped in fresh samples, become completely sep- arated in the old films, as if the slow redistribution of residual polarization is going on for a long time after the completion of poling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Observed and calculated peaks are difficult to process quantitatively, since there is no TSD currents theory in ferroelectric polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, 154 as evident from the shape of the peaks, all three relaxation processes differ significantly from the ideal Debye case, corresponding to the absence of the relationship between the relaxing dipoles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This feature can be taken into account considering that the polarization relaxes over time in accordance with the law of the expanded exponent 0 ( ) exp 1 0 t P t P α \uf8eb \uf8f6 = − ≥ α ≥ \uf8ec \uf8f7 τ \uf8ed \uf8f8 , (17) where τ is a time constant, Po is the initial polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' If the sample is lin- early heated at the rate β = dT/dt, then 0 0 1 1 ( ) exp ( ) T T P T P dT T α \uf8f1 \uf8fc \uf8ee \uf8f9 \uf8eb \uf8f6 \uf8eb \uf8f6 \uf8f4 \uf8f4 ′ = −\uf8ef \uf8fa \uf8f2 \uf8fd \uf8ec \uf8f7 \uf8ec \uf8f7 ′ β τ \uf8ed \uf8f8 \uf8ed \uf8f8 \uf8ef \uf8fa \uf8f4 \uf8f4 \uf8f0 \uf8fb \uf8f3 \uf8fe ∫ , (18) where To is the initial temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is reasonable to assume that the tem- perature dependence of τ corresponds to the Arrhenius law 0 ( ) exp A T kT \uf8eb \uf8f6 τ = τ \uf8ec \uf8f7 \uf8ed \uf8f8 , (19) where A is the activation energy, k is the Boltzmann constant, τo is the char- acteristic time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The expression for the TSD current density is derived from the equations (17)–(19) [ ] [ ] { } 1 0 0 ( ) exp ( ) exp ( ) P A i T s T s T kT α− α \uf8eb \uf8f6 α \uf8eb \uf8f6 = − − − \uf8ec \uf8f7 \uf8ec \uf8f7 τ \uf8ed \uf8f8 \uf8ed \uf8f8 , (20) where 0 0 1 ( ) exp T T A s T dT kT \uf8eb \uf8f6 \uf8eb \uf8f6 ′ = − \uf8ec \uf8f7 \uf8ec \uf8f7 βτ \uf8ed \uf8f8 \uf8ed \uf8f8∫ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The results of computer fitting of the experimentally observed and cal- culated TSD peaks in equation (20) confirmed our assumptions about the nature and the thermal stability of the relaxation processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' They showed that the depolarization peak in fresh samples where the electret and the ferroelectric components are mixed, is wide (α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='24), because the two relaxation processes responsible for its formation are very different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The ferroelectric polarization is quite stable (A = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='7 eV), and the TSD peak due to its relaxation is relatively narrow (α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='52).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The parameters of the space charge peaks in the fresh and old samples are completely different, as if there are two types of the space charges, one probably associated with the ferroelectric polarization, and the other one with the electret component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It 155 is also likely that the small peak that occurs near the electret depolarization peak in open mode (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5) is due only to the electret component of the vol- ume charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Since the glass transition temperature is -45 °C in PVDF, the ordering of the dipoles in the amorphous phase is not thermally frozen, as in the ordinary polar electrets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The dominant orientation of dipoles in these conditions may be supported by the field of the trapped charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, it has been shown that in corona poled films of the ferroelectric polymers, there are two components of polarization, and both components are accompanied by corresponding space charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The electret-type ther- modynamically unstable component relaxes as long as the broad TSD peak observed in fresh polarized samples is not transformed into two completely separated narrow peaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The unstable electret component of the residual polarization can be re- moved by heating the poled sample to a specific temperature (about 60 °C in the case of PVDF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Apparently, the trapped charges always accompany the dipolar polarization regardless of its nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Pyroelectric effect in ferroelectric polymers and its nature Pyroelectric effect in PVDF films was discovered more than 40 years ago.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, despite the large number of works, the nature of pyroelec- tricity in PVDF still remains unclear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A series of papers was devoted to the pyroelectric properties of the ferroelectric polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is assumed in the first of the three most popular models that pyroelectricity results from the contribution of electrostriction, dipole fluctuations and changes in the size with temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the second model, only the change in the dimensions of the sample is considered and the crystals, while in the third model, the pyroelectricity is attributed to electrostrictions and to the change in size when temperature changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Under the pyroelectric effect, one means the range of phenomena as- sociated with reversible changes in the electric displacement vector (induc- tion) when the temperature changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the case of a free sample, the pyro- coefficient is determined by the following expression [13] , , , , , i j i i i i i j H E U E H E U D D D p T T U T \uf8eb \uf8f6 ∂ \uf8eb \uf8f6 ∂ ∂ ∂ \uf8eb \uf8f6 \uf8eb \uf8f6 = = + \uf8ec \uf8f7\uf8ec \uf8f7 \uf8ec \uf8f7 \uf8ec \uf8f7 \uf8ec \uf8f7 ∂ ∂ ∂ ∂ \uf8ed \uf8f8 \uf8ed \uf8f8 \uf8ed \uf8f8 \uf8ed \uf8f8 , (21) where Di is the component of the induction vector;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ui,j is the deformation tensor;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' H is the mechanical stress;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' E is the field strength, , i i j D U \uf8eb \uf8f6 ∂ \uf8ec \uf8f7 \uf8ec \uf8f7 ∂ \uf8ed \uf8f8 is the 156 piezo modulus;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,i j U T ∂ \uf8eb \uf8f6 \uf8ec \uf8f7 ∂ \uf8ed \uf8f8 is the thermal expansion coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The first term in (21) corresponds to the primary or true pyroelectric effect measured on the compressed sample, and the second term characterizes the secondary pyroelectric effect being the result of the piezoelectric induction changes due to the thermal expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Since the pyroelectric effect depends both on the internal polarization and on the space charge, in principle, it can be caused by the temperature dependence of both quantities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' If we neglect the influence of the space charge, then for the case of a flat short-circuited sample with homogeneous polarization P we obtain 0 ( / ) D P q S p T T T T ∂ ∂ ∂σ ∂ = = = = ∂ ∂ ∂ ∂ , (22) where q and σ are magnitude and density of the bound surface charge;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' S is the surface area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the experimental conditions, the current ( ) dq I T dt = occurring when the temperature change (dT/dt) is measured, and the pyrocoefficient is con- sidered to have the following value 1 1 ( ) / dq I T p S dT S dT dt = = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (23) Because ро ≠ р there are differences in the values of the theoretically cal- culated and experimentally measured pyrocoefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It has been proved that the pyroelectric effect can only be caused by a nonuniform distribution of the space charge (without taking into account polarization).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Investigating the pyroelectric effect in PVDF, Lines and Glass [17] came to the conclusion that this is a real pyroelectricity, but not a depolariza- tion effect observed in many polar electrets, because the crystalline phase of PVDF completely corresponds to the definition of a ferroelectric, as a py- roelectric with reversible spontaneous polarization under application of the electric field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A fundamental question was posed that has not been solved for the time being: is the pyroelectricity an equilibrium property of PVDF or a result of non-equilibrium polarization, that is, in some way it is a fixed orientation of dipoles?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In early works on PVDF, the effect of volume charge on the pyroelectric effect was considered decisive, but after the proof of the ferroelectric na- 157 ture of PVDF crystallites, the pyroelectric was more often associated with the spontaneous polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' So, in the model of Broadhurst and Davies [18] the behavior of rigid dipoles in thin crystalline plates (lamellae) dis- tributed in the amorphous phase is considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the model of Wada and Hayakawa [19], the presence of spherical ferroelectric particles scattered in the amorphous phase is assumed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Both models predict the influence of thermal expansion (dimensional effect) on the pyroelectric effect, as well as temperature dependence of the dielectric constant and the spontaneous polarization Psc(T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At the same time, there is no satisfactory correspondence between cal- culated and experimental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' drew Attention was attracted to the fact that the models of Broadhurst [18] and Wada and Hayakawa [19] ignored the contribution of the volume charge to the pyroelectric effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' An attempt to take into account the volume charge led to contradiction with the obtained data [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Estimated calculation of Lines and Glass [17] showed that the theoretical pyrocoefficient even at 100 % orientation of dipoles in PVDF is several times lower than the value measured in the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We believe that not only the crystalline, but also the amorphous phase contributes the pyroelectricity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Elling et al [20] found that the pyrocoefficient value is affected not only by the residual polarization, but also by the supra- molecular structure on which the mechanical properties of PVDF depend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is shown in the work of Fedosov and Sergeeva [21] that one of the components of the pyroelectric effect in the ferroelectric polymers is the electret component, that is, the pyroactivity of PVDF is due to the reversible temperature changes of the residual polarization closely related to those in equilibrium with trapped charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Fedosov and von Seggern [3, 4, 6] proved that compensating charges localized on the surface of crystallites are very important in two-compo- nent ferroelectric polymers of the PVDF type for obtaining high and stable polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' With periodic increase and decrease of temperature [21], the pyrocoefficient irreversibly decreases at temperatures much lower than the Curie point indicating the possible effect of charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is generally accepted that the pyrocoefficient in PVDF is directly pro- portional to the value of the residual polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, this relationship is more complicated, because the pyrocoefficient usually increases nonlin- early with increasing temperature, while there is no increase in polarization occurs in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Summarizing the above data, we can conclude that the pyroelectricity in PVDF is usually considered in isolation from other processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, 158 to understand the nature of this phenomenon, it is of interest to experi- mentally study the dynamics of its formation and changes simultaneously with other isothermal and thermally simulated processes, such as mea- surement of volt-ampere characteristics, thermoelectret poling and de- polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Measuring the pyroelectric coefficient in poled PVDF films The pyroelectric effect is usually investigated in quasi-static or dynamic mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the first case, the pyroelectric current is measured during the slow heating of the short-circuited sample, while in the second case, the variable component of the current is studied during a rapid change of temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The main difficulties of the quasi-static method are the separation of the py- roelectric (reversible) component of the thermal shock from the relaxation (irreversible) component in the TSD current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We measured the pyroelectric dynamic coefficient by the thermal pulse method developed by Collins [22] and used in a number of other papers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The light pulse of 50 μs duration was generated using the Metz 45 CT-3 flashlight and was used as a reproduced heat source that penetrates the sur- face of the poled films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The pyroelectric signal was recorded using a broad- band oscilloscope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This method is the dynamic one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' With the help of a highly sensitive pyroelectric sensor it was established that light pulses are characterized by a rather high reproducibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The av- erage energy scatter in measuring of 200 consecutive pulses was 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4 %.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The magnitude of the pyroelectric coefficient was judged by the maximum value of the electric signal;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' thus the results were obtained in relative units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Measurement of the pyrocoefficient by a quasi-static method was car- ried out by linear heating and cooling of polarized samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Dependence of the pyrocoefficient on temperature was calculated by the following formula ( ) ( ) p c I T p T A = β , (24) where IP(T) is the pyroelectric current measured during cooling, βc is the cooling rate, which is a derivative of the temperature over time, A is the sam- ple surface area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The heating rate was maintained constant 3 K/min, while the cooling rate depended on time and temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3 Switching of polarization and pyroelectric activity of PVDF films Pyroelectric studies of PVDF films have an independent value, since PVDF is widely used in pyroelectric sensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, it is interesting to study pyroactivity in conjunction with the residual ferroelectric polar- 159 ization, because it will allow to clarify the nature of the pyroelectricity in PVDF, and to ensure its stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Measurement of the pyroactivity by the Collins method was carried out immediately after the polarization switching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6 shows how the pyro- electric signal changes when the polarization is fully switched from a fully polarized state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Although the value of the pyrocoefficient can only be judged in relative units, it is evident that the sensitivity of the method is rather high and the signal a completely symmetric after the full switching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It appeared that full switching occurs only if the voltage pulse duration exceeds 100 s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At a shorter duration of the voltage pulse, there is only a partial switching of polarization judging from the data of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0 1 2 3 4 5 120 80 40 0 40 80 120 Direction of switching Initial state Pyrosignal voltage, mV Time, ms Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The pyroelectric signal after the polarization switching of PVDF film by ap- plying 2 kV voltage for 50 seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Pyroelectricity was measured after 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 min after the voltage switching off Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 7 shows the results of four series of experiments, in which the polar- ization switching was performed at different durations of the voltage pulse, but with the same magnitude in each series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At a voltage of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 kV (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 7) that provides a field strength of about 40 MV/m, being in the same order as the coercive field, even with a pulse duration of 50 s, only 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4 % of the polarization is switched, which in principle can be switched, and if the pulse duration is shorter than 50 ms, no switching is practically happening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At a voltage of 1 kV applied for 50 s, 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4 % of the residual polarization is switched, that is, the sample is almost converted to the state with zero mean polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At this voltage, the 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 % polarization is switched even within 50 μs of the switching voltage application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Increasing the voltage to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 kV 160 leads to the switching of 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4 % of the residual polarization by a 50 s appli- cation of voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At a voltage of 2 kV for 50 s, the polarization is completely switched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10 6 10 4 10 2 10 0 10 2 0 20 40 60 80 100 120 Pyrosignal voltage, mV Pulse duration, s 0 1 2 3 4 5 6 0 40 80 120 50 s 5 s 0,5 s Initial state Pyroelectric voltage, mV Time, ms Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 7 Dependence of the pyroelectric signal on the duration of the polarizing pulse in the range from 10 μs to 100 s during initial poling of the PVDF film by 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 kV voltage It is interesting to note the specific shape of the pyroelectric signal when switched polarization is more than 50 %, that is, when the direction of the average predominant orientation of the dipoles changes to the opposite di- rection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the electrode zone, which the thermal pulse passes during to = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 ms, when the polarity direction changes to the opposite, a non-symmetric in shape pyroelectric signal is formed in relation to the initial one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the vi- cinity of the electrode, the direction of the pyro-signal change is maintained during the switching polarization indicating the existence of a near-to-elec- trode layer of thickness about 0 x t = λ where λ is the thermal conductivity of PVDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' According to the literature, the coefficient of thermal conductivity of PVDF is λ = 6∙10–8 m2/s, thus the thickness of the electrode layer is of the order of 3 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We believe that the feature revealed by us is due to the fact that the originally formed polarization in this layer does not switch even in high fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is natural to assume that polarization near the electrode does not in- crease sharply, but there is some transition layer in which the polarization 161 grows from zero at the electrode to a maximum uniform value in the volume of the film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' According to the Poisson equation, inhomogeneous polariza- tion in any layer can be stable only with the presence of a compensating charge in this layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Apparently, this charge was trapped by deep traps and not released during the polarization switching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The revealed phenomenon is similar to the established by us feature about impossibility of improving the polarization uniformity if its initial formation took place in weak or medium fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10 6 10 4 10 2 10 0 10 2 0 20 40 60 80 100 120 Pyrosignal voltage, mV Pulse duration, s 0 1 2 3 4 5 6 0 40 80 120 50 s 5 s 0,5 s Initial state Pyroelectric voltage, mV Time, ms Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Pyroelectric signal at sequential polarization switching in PVDF films by pulses of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 kV voltage with duration from 5 ms to 50 s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The duration of the volt- age pulse is indicated near the curves It was found that polarization switched under the action of several suc- cessive short voltage pulses is much smaller than the polarization switched by one pulse of the duration equal to the total time of several short pulses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This indicates that there is some distribution of switching times, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' some dipoles are easily switched, while others require more time to be switched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Under the influence of short voltage pulses, only «fast» dipoles are switched, while during the continuous voltage application both «fast» and «slow» di- poles are switched, so the total switched polarization significantly increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In conclusion, polarization switching at different time and field strength is compared with the values of the pyrosignal under the same switching con- ditions (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The absolute similarity of the above experimental graphs indicates that there is a direct proportional relationship between the residual 162 ferroelectric polarization and the value of the pyroelectric coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This provision makes it possible to use the technically simple pyrocoefficient measurement to evaluate the polarized state of poled PVDF films, that is, to estimate the magnitude and the direction of the residual polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10 7 10 4 10 1 10 2 0,0 0,1 0,2 40 80 40 80 120 160 200 200 160 120 Time, s Pyroelectric signal, V Time, s 10 7 10 4 10 1 10 2 0 2 4 6 8 10 Polarization, \uf06dC/cm 2 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Evolution of pyroelectric activity and stable ferroelectric part of polarization obtained by sequential application of switching voltage pulses with increasing dura- tion from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 μs to 50 s and at different field strength 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Separation of TSD current components in PVDF Despite the fact that PVDF is considered as a ferroelectric polymer, some of its electrical properties can be explained within the framework of the theory of polar electrets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The phenomenological model of Gross-Swan- Gubkin [23] suggests the presence of two types of charges in the electret, namely, the homocharge σ(t), whose sign coincides with the polarity of the electrodes during poling, and the heterocharge P(t) (internal polarization), which is the result of the micro — and macro- displacements of own charges in the dielectric under the field action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the case of PVDF, the heteroch- arge is the dipole polarization, and the homocharge is formed by charges trapped on or near the surface [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Stability of the electret state in a polar dielectric depends on the mutual relaxation of the homocharge and the heterocharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Since the heterocharge (polarization) is usually the most important in PVDF, the role of the homocharge has not paid enough attention to the 163 present, although the stabilizing effect of the space charge on the residual polarization has already been discussed [4, 6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thermally stimulated depolarization (TSD) is a method used to identi- fy relaxation processes in polymer electrets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, it is very difficult to divide the effect of the homocharge and the heterocharge on TSD currents especially if the corresponding peaks are superimposed on each other in a wide range of temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We have developed a method for separating homocharge and heteroch- arge currents [24] by solving the inverse problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In addition, it has been shown that the application of various modifications of the TSD method, complemented by isothermal depolarization currents allows us to find such important parameters of relaxation processes as the activation energy, char- acteristic frequencies and the time constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The uniaxially oriented 25 μm thick PVDF films metallized on one side were poled in corona triode at the control grid voltage of 3 kV at room tem- perature and constant poling current density of 90 μA/m2 for 30 min and then shortened and held at room temperature for 24 h (except for specimens for measuring the electret potential kinetics).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Four modifications of the TSD method were used, namely thermally stimulated (T) and isothermal (I) depolarization of short-circuited (S) and open circuit (O) samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, the modifications are named TS, TO, IS and IO where the first letter indicates the temperature mode (thermally stimulated or isothermal), and the second indicates the electric state of the sample (short-circuit or open circuit).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Additional experiments on the thermally stimulated electret potential (TP) kinetics were performed after 24 h of being in the open circuit state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' As a dielec- tric layer in TO and IO modifications, PTFE film of 10 μm thickness was used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thermally stimulated experiments were performed at a heating rate of 3 K/min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In isothermal experiments, the temperature was maintained constant after its required value was achieved by rapid heating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The electret potential in TP modifications was measured by the Kelvin method and con- tinuously recorded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The main features of the experimental curves shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10 and 11 are as follows: – The depolarization current in the TS modification forms a broad «non-classical» peak with a maximum of 65 °C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – There is an inversion of the TSD current in the TO modification, while the current direction coincides with the direction of the current in the TS modification in the initial heating stage;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 164 20 40 60 80 100 120 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3 1 Current density, \uf06dA/m 2 Temperature, oC 3 1 2 0 100 200 300 3 2 Voltage, V 0 5 10 15 0 2 4 6 0 5 10 15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3 Current density, \uf06dA/m 2 Time, min (a) 3 2 1 Current density, \uf06dA/m 2 Time, min (b) 3 2 1 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thermally stimulated currents in the TS modification (1) and in the TO modification (2), as well as the electret potential in the TP modification 20 40 60 80 100 120 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3 1 Current density, \uf06dA/m 2 Temperature, oC 3 1 2 0 100 200 300 3 2 Voltage, V 0 5 10 15 0 2 4 6 0 5 10 15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3 Current density, \uf06dA/m 2 Time, min (a) 3 2 1 Current density, \uf06dA/m 2 Time, min (b) 3 2 1 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Isothermal transient currents at different temperatures in the IS mode (a) and in the IO mode (b);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1–45 °C, 2–55 °C, and 3–70 °C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – The electret potential in TP modification has a maximum at 40 °C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – The current slowly decreases over time in the IS modification at all temperatures, while the isothermal current changes the direction in IO mode at elevated temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 165 These features can be explained within the framework of the model, which implies existence in the samples of the homocharge and the hetero- charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' First, consider the processes of poling and relaxation qualitatively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is reasonable to assume that negatively charged particles (ions and/or elec- trons) generated by corona discharge are adsorbed and thermalized on the surface of the sample due to their low (thermal) energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Excessive charge in the near-to-surface layer or on the surface forms a homocharge that has a certain superficial density σ and creates a homogeneous field E in the vol- ume of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The high electron affinity of fluorine atoms facilitates the trapping of charges at traps and formation of the stable homocharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Homogeneous internal polarization P (heterocharge) is formed as a result of dipoles -CH2-CF2- orientation in the field created by a homo- charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The formation of polarization is equivalent to the formation of a bound surface charge P, which has a sign opposite to the sign of the homo- charge σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Of all the polarization processes in PVDF, the orientation of the CH2-CF2- dipoles is the most significant due to their large dipole moment of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 Debye [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' If the polarization P is zero, then the field is created by a complete su- perficial charge σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' When P begins to grow, the depolarizing field appears which is “neutralized” by a part of the surface charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, the field in volume is created by the difference (σ — P) between the surface charge and the polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Consequently, the surface charge σ consists of two parts σ = σ1 + σ2, the first of which is a charge that provides compensation of the depolarizing field (σ1 = P), and the second σ2 = σ – P creates the electric field in the volume of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' After the short circuiting of the poled samples (in TS and IS modes), the “excess” charge σ2 disappears.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The equilibrium between the homocharge and heterocharge (σ = σ1 = P), as well as the zero internal field (E = 0) are supported by the current in the external circuit, so that the measured current corresponds to the relaxation of the heterocharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, if after the short circuiting and the formation of equilibrium σ = σ1 = P, a non-conductive dielectric insert (in TO and IO modes) is introduced between one of the electrodes and the surface of the sample, then one can observe the relaxation currents both the heterocharge and the homocharge flowing in the opposite directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The field in the volume is no longer zero, so that the surface charge (homocharge) drifts in its own field through the entire thickness of the sample, or it is slowly neutralized by charge carriers responsible for its own conductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 166 In any case, the relaxation of the heterocharge occurs in a field other than zero and caused by thermal disordering of oriented dipoles [12, 13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We will show that both components of the depolarization current can be found from the dependence of i(T) in the TO mode (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10, curve 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is known [12,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13] that the TSD current i(t) and the electret potential V(t) in experiments with nonconductive insertion between the surface of the sam- ple and the electrode,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' depend not only on the relationship between the ho- mocharge and the heterocharge,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' but also on their derivatives,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' so ( ) ( ) ( ) dP t d t i t s dt dt σ \uf8ee \uf8f9 = − \uf8ef \uf8fa \uf8f0 \uf8fb ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (25) 1 0 1 ( ) [ (t) P(t)] sx V t = σ − ε ε ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (26) 0 1 1 ( ) ( ) dV t i t x dt ε ε = − ⋅ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (27) where 0 1 1 0 1 / ( ) s x x x = ε ε + ε ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' t is time,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ε and xo are the dielectric constant and the thickness of the sample,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ε1 and x1 are corresponding values of the dielectric gap,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' εo is the permittivity of a vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The full component ic(t) can be represented as 0 ( ) ( ) ( ) C g d t i t V t x dt σ = = − , (28) where 0 exp( / ) g g Q kT = − is the own conductivity, k is the Boltzmann con- stant, T is temperature, Q is the activating energy of its own conductivi- ty, go is a pre-exponential factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Integrating (27) and replacing the time t with temperature T in (25)–(28) according to 0(1 ) T T bt = + ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' where b is the heating rate,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' То is the initial temperature,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' we obtain the expressions for the temperature dependences of the homocharge current i1(T) and the hetero- charge current i2(T),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' as well as the voltage on the sample (potential) V(T) 1 0 1 0 0 0 1 ( ) exp ( ) T x g d Q i T i T dT dt bT x kT ∞ σ \uf8eb \uf8f6 ′ ′ = = − − \uf8ec \uf8f7 ε ε \uf8ed \uf8f8∫ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (29) 2 ( ) ( ) dP i T d i T dt s dt σ = = + ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (30) 1 0 0 1 ( ) ( ) T x V T i T dT bT ∞ ′ ′ = ε ε ∫ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (31) 167 20 40 60 80 100 120 0 2 4 6 8 0 10 20 30 40 2 Voltage, V 3 2 1 Current density, \uf06dA/m 2 Temperature, oC Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Temperature dependences of the homocharge (1) and heterocharge (2) re- laxation currents, as well as of the voltage on the sample (3) calculated according to the model All quantities at the right side of the equations (29)–(31) are known, or can be obtained experimentally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The results of calculations according to the equations (29)–(31) based on the data of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10, are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The values of the activation energy Q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='76 eV and the factor go = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='18 Sm/m were obtained from constant values of the isothermal poling current and voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' As one can see in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12, the homocharge and the heterocharge form two broad peaks with almost identical maxima.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The heterocharge relaxes faster in the low-temperature region where the homocharge is relatively stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This is probably the reason for the initial increase of the thermally stimulated potential (see curve 3 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10 and curve 3 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The current inversion in TO and IO modes is caused by a change in the ratio be- tween homocharge and heterocharge at high temperatures (curves 1 and 2 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is known that the inversion of the TSD current can be caused by the re-polarization, that is, it arises as a result of the appearance of an addition- al heterocharge in the field of a homocharge, and the voltage in this case should decrease [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, this was not observed in our case (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' On the other hand, the initial growth of the electret potential during heating cannot be caused by increase of the surface charge density σ, since charges in this case would 168 have to move against the electric field created by these charges, which is impossible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Therefore, the first peak of the TSD current and the increase of the electret potential (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10) are due to the faster disintegration of the heterocharge (polarization) compared with the homocharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is possible that in PVDF in the first stage of heating, not all polarization is destroyed, but only its least stable part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, the long-term conservation of the heterocharge in PVDF films is possible only in presence of the stabilizing field created by homocharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We believe that many special properties of PVDF are associated with successful combination of a large dipole moment of -CH2-CF2- (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 D) that contrib- utes to formation of heterocharge, and the high electron affinity of fluorine atoms (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='37 eV) that contributes to the creation of the stable homocharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Although the electret state in the PVDF is unstable, the self-balanced re- laxation of the homocharge and the heterocharge is slowed down due to the stabilizing effect of the homocharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the theory of electrets [23], it is assumed that homocharge and het- erocharge decay by the exponential law with the temperature dependent time constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Therefore, such expressions should be valid for IO and IS modes 0 1 1 1 ( ) exp s t i t \uf8eb \uf8f6 σ = − − \uf8ec \uf8f7 τ τ \uf8ed \uf8f8 , (32) 0 2 2 2 ( ) exp P t i t \uf8eb \uf8f6 = − − \uf8ec \uf8f7 τ τ \uf8ed \uf8f8 , (33) 0 1 0 ( ) exp Q T g kT ε ε \uf8eb \uf8f6 τ = \uf8ec \uf8f7 \uf8ed \uf8f8 , (34) 2 0 ( ) exp W T kT \uf8eb \uf8f6 τ = τ \uf8ec \uf8f7 \uf8ed \uf8f8 , (35) where W is the activation energy of the heterocharge relaxation, τ1 and τ2 are the corresponding time constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Applying the equations (32)–(35) to the experimental curve in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 11, we calculated the following relaxation parameters for homocharge and het- erocharge: activation energies (Q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='76 eV and W = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='54 eV), characteristic frequencies (f2 = 1/τo = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4 MHz and f1 = (go/εoε) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='7 GHz, time constants at 20 °C (τ1 = 31000 s and τ2 = 2800 s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The results indicate that the homo- charge is more stable than the heterocharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 169 Thus, we have developed a method for separating the depolarization currents of the homocharge and the heterocharge from the measured TSD current, and revealed the relaxation behavior of the both components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Application of various TSD modifications complemented with isother- mal depolarization currents allowed to find the most important parameters of the relaxation processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The developed method allows us to analyze the relationship between the homocharge and the heterocharge not only in PVDF but also in other polar dielectrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The introduction of polar groups with the simultaneous creation of deep traps could contribute to increasing of the residual polarization sta- bility in polar polymer dielectrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Therefore, if there are appropriate con- ditions for creating a homocharge, then a high level of the residual polariza- tion can also be provided for a long time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thermally stimulated and isothermal processes in composites Composite materials based on polymers with impurities of ferroelectric ce- ramics have a number of significant advantages over conventional ferroelectric ceramics, but the possibilities of using composite materials as active elements of piezoelectric and pyroelectric converters are not fully implemented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is known that most of the polarization in ferroelectric ceramics im- mediately switches back to its original state after switching off the applied voltage, and only 25–30 % of the domains remain oriented if no special actions are taken.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Therefore, the dominant orientation of domains should be somehow fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A similar problem exists in ferroelectric polymers, in which ferroelectric crystallites are distributed in the amorphous phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This structural similarity between composites and ferroelectric polymers can also determine the similarity of the electrical relaxation processes in these two classes of materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' PVDF data to verify the applicability of the concepts already proven for the case of the ferroelectric polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In addition, concrete data on the pa- rameters of the electrical relaxation in the specified composites were obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We considered the PVDF-BaTiO3 composite as a model material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The obtained results were compared with ыamples of PVDF-BaTiO3 composites with a thickness of 300 μm containing 0 %, 40 %, 50 % and 70 % of Ba- TiO3 were produced by hot pressing of a mixture consisting of PVDF powder and BaTiO3 particles with an average size of 10 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The composites were annealed at 140 °C and examined using a Solomat 91000 spectrometer for obtaining the general spectrum of TSD currents in the range from -80 °C to +180 °C (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 170 80 60 40 20 0 2 4 6 8 40 60 80 100 120 Temperature, оC 4 3 2 1 Current, 10 11A 4 3 2 1 (x50) Temperature, оC 0 40 80 120 1,0 1,2 1,4 1,6 3 2 1 Activation energy, eV Temperature, оC Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' TSD current curves of poled PVDF-BaTiO3 composites with different con- tent of BaTiO3: 0 % (1), 40 % (2), 50 % (3) and 70 % (4) 80 60 40 20 0 2 4 6 8 40 60 80 100 120 Temperature, оC 4 3 2 1 Current, 10 11A 4 3 2 1 (x50) Temperature, оC 0 40 80 120 1,0 1,2 1,4 1,6 3 2 1 Activation energy, eV Temperature, оC Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The activation energy of relaxation processes in PVDF-BaTiO3 composites containing 40 % (1), 50 % (2) and 70 % (3) of BaTiO3 171 The samples were prepoled at 150 °C in the electric field of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='25 MV/m for 15 min, and then cooled to –100 °C without disconnecting the electric field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The samples were then depolarized by heating in a short-circuit mode at the rate of 7 °C/min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The fractional analysis of relaxation processes was carried out by the method of thermal windows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The polarization temperature increased every time for 5 °C from 20 °C to 150 °C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The equivalent frequency of experiments was about 2·10–4 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' From these experiments, the activation energy of the relaxation processes was calculated (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It was found that thermal activation of the polarization process is nec- essary, since polarization is not formed at room temperature even in high electric fields of about 20 MV/m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This fact is confirmed by the lack of the TSD current after poling of specimens at room temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In addition, the VAC at 20 °C was superficial and typical for the space charge limited currents, but not N-shaped, as in the case of PVDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In all samples, including PVDF without ceramic additives, well-expressed low-temperature peaks near -40 °C can be seen on TSD curves (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This peak is near the glass transition temperature of the amorphous phase in PVDF and is usually attributed to the β-relaxation associated with the micro Brownian motion of molecular chains in amorphous regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Neither the peak nor its magnitude correlates with the amount of the filler in the com- posite, which indicates that this peak is associated with the properties of the polymer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The peak in the range 80–120 °C is structurally good only in the case of PVDF, but suppressed in composites by the exponentially increasing leakage current of unknown nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' To eliminate the parasitic currents, we periodically included a capacitor in series with the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' But even in this case, the unambiguous interpretation of the peaks was difficult, because the theory of TSD currents in composites has not yet been developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is assumed that in the thermal windows method each individual peak corresponds to a single Debye relaxation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Then the peak analysis gives the temperature-dependent relaxation time τ(T), which can be ap- proximated by the Arrhenius equation 0 ( ) exp( / ) T Q kT τ = τ ⋅ , (36) where τо is the pre-exponential factor;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Q is the activation energy;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' k is Boltz- mann’s constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' As can be seen from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 14, the activation energy slightly decreases in the range of 20–80 °C from 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='17 eV to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='09 eV regardless of the samples composition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Then it sharply increases reaching the maximum values of 172 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='23–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='55 eV at 105–110 °С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The amount of the activation energy cor- relates with the concentration of the ceramic filler and equals 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='23 eV at 40 %, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4 eV at 50 % and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='55 eV at 70 % of BaTiO3 in the composite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In addition, the peak temperature in the Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='10 is very close to Curie point of BaTiO3 confirming the fact that relaxation behavior of the composite near this temperature is determined by ceramics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It was found that the maximum temperature of the thermal window peak was about 15 °C above the polarization temperature for all fractions, regard- less of the composition of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The dielectric constant of the composites increased with temperature and was in a certain ratio with the percentage content of the filler equaling 20–250 at 40 %, 30–400 at 50 % and 40–1100 at 70 % of BaTiO3 in the composite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is known that the dielectric constant of pure PVDF was about 10–12, and in BaTiO3 it was equal to 1500–7000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The polarization field applied to the composites in the experiments (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='25 MV/m) was higher than the coercive field of pure BaTiO3 estimated as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3 MV/m, but it is unclear whether the ferroelectric polarization occurs, because the resistance the polymer matrix is much higher than that of ceramics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, it was established that the processes of the polarization formation and electrical relaxation in PVDF-BaTiO3 composites are similar to similar processes in the ferroelectric polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This can serve as a prerequisite for the creation of a generalized model that not only explains, but also predicts the electrical behavior of polymer-ceramic composites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We have established the influence of the polymer matrix conductivity and poling regime on the effective conductivity of the PVDF-PZT compos- ites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The research was carried out on flat plates of PVDF-PZT composite, made by hot pressing of a mixture of PVDF powders and PZT ceramics taken in a volume ratio of 60:40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Two types of the PVDF powder differing in concentration of ionogenic end groups that contribute to dissociation of impurities, and therefore have a specific resistance at room temperature 1010 Ω·m and 1012 Ω·m, were used to study the influence of the properties of polymer matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Specific resistance of the PZT had an order of 1010 Ω·m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Poling of the samples was carried out by the thermoelectret method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The samples were kept for 50 min at high temperature in the outer field, and then cooled without removal of the field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' As changing parameters, we used the poling temperature (70–130 °C) and the conductivity of the poly- mer component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It was assumed that there are different conductivities and dielectric permittivities in the layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In real ferroelectrics polymers the phenomenon of percolation and injection of carriers in volume should be 173 taken into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' From the theory of percolation, it is known that for three-dimensional two-phase systems the leakage threshold depending on the structural features of the phases is in the range of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='05–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the case of conventional ferroelectric polymers with the concentrations of the fill- er or crystalline ferroelectric phase of the order of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 it is very like- ly to find the mixture either in the critical region or in the region where the infinite cluster is formed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Therefore, known formulas for generalized electrical characteristics of mixtures exopessed by formulae of Lichteneker, Landauer-Brugemann, Odelevsky and others are unsuitable for ferroelec- tric polymers and composites because they assume relative proximity of the components properties and the small volume fraction of one of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is obvious that in the presence of contacts between particles of crystal- lites or ceramics, equivalent circuit diagrams should take into account not only sequential combinations of layers, but also parallel ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Consideration of the injection based on the Poisson equation should lead to the field het- erogeneity in the thickness of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The mentioned effects in ferro- electric polymers and composites have not yet been studied and the theory of these phenomena is absent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' As can be seen from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 15, change in the poling temperature affects the temperature dependence of the conductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The activation energy increas- es with increasing temperature both in low-conductive and high-conductive composites, and the value of the conductivity decreases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This corresponds to the proposed hypothesis that explains decrease of the conductivity by trapping a part of the carriers at the boundaries of the polarized crystallites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Indeed, residual polarization increases with increasing temperature and the specific conductivity decreases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The degree of the residual polarization and its stability in a ferroelectric ceramic essentially depend on the magnitude of the injected space charge that apparently compensates the depolarizing field occurring when dipoles in crystallites are oriented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Similar processes occur in the ferroelectric poly- mers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, in view of the morphological features, the conditions for maintaining the stable polarization in ferroelectric polymers are better than in ferroelectric composites where the incomplete polarization occurs due to boundaries scarcity, mechanical stress and restriction in free volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' There- fore, some of the residual polarization immediately relaxes after removing the external field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the ferroelectric polymer, the ferroelectric particles are free that creates favorable conditions for trapping the charge at their bor- ders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Although the particles are in contact with each other, they do not form a rigid grid and easily allow for volume changes during poling Large-scale 174 potential changes during poling contribute to deep trapping of charges, as well as to reduced molecular mobility in the interphase layer That is why the piezoactivity of polymer in ferroelectric polymers is higher than that of ceramics used as a filler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2,2 2,4 2,6 2,8 3,0 1 0 1 2 3 6 5 4 3 2 1 ln g (10 9 Ом 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='м 1) 1000/Т Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Temperature dependence of the specific conductivity of PVDF-PZT sam- ples poled at 70 °C (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4), 100 °C (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5) and 130 °C (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Specific resistance of the polymer is 1010 Ω·m (1, 2, 3) and 1012 Ω·m (4, 5, 6) In «polymer-ferroceramics» composites as in the ferroelectric polymers, one should not contradict the role of space charge and polarization in the appearance of high pyroactivity, but consider them in a relationship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the composites like as in PVDF, irreversible relaxation processes and reversible (pyroelectric) are interconnected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is known that pyroelectric currents are reversible, that is when switch- ing from heating to cooling they must change the direction to the opposite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, as can be seen from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 16, this is not always observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The imbalance of direct and reciprocal current is due to the influence of the relaxation component, which does not diminish instantaneously to zero with the termination of heating, but it relaxes with the time constant of order of tens and hundreds of seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' As a result, there is a delay in the pyroelectric current, which is observed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' With repeated heating and cooling of the samples, along with decrease of the current in the forward direction as a result of the relaxation processes annealing, the symmetry of the direct and the reverse current appears for the same reason (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 17) indicating predominance of the pyroelectric compo- nent over the relaxation component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 175 0 30 60 90 120 150 180 0 4 8 12 3 2 1 Current density, \uf06dA/m 2 Temperature, оС 0 30 60 90 120 150 180 2 0 2 4 6 8 3 2 1 Current density, \uf06dA/m 2 Temperature, оС Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thermal currents during primary (1) and repeated (2) heating of poled PVDF-PZT composites samples, and also cooling after the reheating (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The heat- ing rate is 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 °C/min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The thickness of the samples is 280 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Piezo modulus is 8 pC/N 0 30 60 90 120 150 180 0 4 8 12 3 2 1 Current density, \uf06dA/m 2 Temperature, оС 0 30 60 90 120 150 180 2 0 2 4 6 8 3 2 1 Current density, \uf06dA/m 2 Temperature, оС Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thermal currents when heated for the first (1) and the third (2) times, and also after cooling after the third heating (3) of PVDF-PZT samples poled by the thermoelectret method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The heating rate is 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 °C min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The thickness of the samples is 240 μm, the poling temperature is 100 °C 176 It is interesting to note that in the polymer-ceramic composite, as in PVDF, the maximum of pyroactivity coincides with the position of the TSD current peak indicating the interrelation of these processes, and possibly also their general nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Conclusions Application of the corona triode in most of our studies allowed to make the poling process fully controlled, to optimize the magnitude of the result- ing polarization and to perform a virtual short circuiting after the comple- tion of poling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Based on the multifactorial experiment, the best correlations of parameters such as temperature and time of poling, as well as the poten- tials of the corona electrode and the grid are established.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A new technique for studying the relaxation of homocharge and heterocharge processes in the ferroelectric polymers was developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The technique is developed for sep- aration of the complete electrical displacement components during PVDF films poling by voltage pulses for allocation and analysis of the polarization components and kinetics of their formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The commonality and similarity of electrophysical and polarization pro- cesses in ferroelectric polymers and composites have been experimentally proved considering their two-phase structure and the need to neutralize the depolarizing field by trapped charges at the interphase boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Phenomenological models of the polarized state formation and relax- ation processes under different conditions were proposed and calculated taking into account and explaining polarization heterogeneity, nonlin- ear dependence of polarization on the field and trapping of carriers at the boundaries of polarized regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A phenomenological model for the polarized state formation a ferroelec- tric polymer subjected to constant current poling was developed and ana- lyzed, in which an important role is assigned to injection of charges, which create a heterogeneous distribution of the space charge, the field strength and the residual polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Three-stage nature of the poling process of the ferroelectric polymer films is explained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Comparison of experimental and calculated kinetics of the electret potential showed their high degree of con- formity that allowed considering the reasonable assumption about deeply trapped injected charges, on the basis of which the model was constructed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A model of the polarization switching in PVDF in the mode of the con- stant applied voltage has been developed that took into account the follow- ing features: – Two-phase structure of the polymer,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 177 – Presence of the intrinsic conductivity and injection of charges from the electrodes,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Trapping of charges at the boundaries of polarized crystallites and their release depending on the stage of the process,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Partial recombination of the released charges and their secondary trapping,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Dependence of the polarization switching time on the field strength,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Nonlinear dependence of quasi-stationary polarization in crystallites on the field strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A system of differential equations describing the process of the polariza- tion switching was formulated and solved in which the following parameters were used as alternating variables: – Field strength in amorphous and crystalline phases, – Polarization in crystallites, – The effective conductivity and the surface charge density at the inter- phase boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' From comparison of the experimental polarization switching curve with the calculated curve, such parameters as the effective mobility, the charac- teristic polarization switching time and the activation field are found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Based on the model, the difference between the initial polarization formation in a two-phase polymer ferroelectric and the polarization switching was ex- plained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A model for explaining polarization profiles in PVDF films in the mode of the constant voltage creating either the middle field close to the coercive field, or the high field substantially exceeding the coercive field was developed and analyzed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The model took into account the monopolar injection of charges from a negative electrode, the nonlinear dependence of the quasi-stationary ferroelectric polarization on the field strength, the Poisson equation on interrelation between charges and the gradient of the field strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The character of the injected charges front motion was calculated, as well as the time dependence of the field strength in the zone adjacent to the positive electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Formation of the inhomogeneous polarization in the case of the middle fields was explained, as well as for- mation of the deeply trapped charge layer at the boundary of the polarized region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This layer is stable even when the polarization is switched lead- ing to distortion of the polarization uniformity profile and impossibility of its improvement by application of very high fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is shown why the uniform residual polarization is formed in the case of high applied fields during initial poling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 178 On the basis of the conducted research, practical recommendations for the modes of ferroelectric polymers and composites poling are developed, which provide high and stable residual polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' REFERENCES 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Rollik D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Bauer S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Gerhard-Multhaupt R.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' and Fedosov S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Diel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Elect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Insul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 11, 232 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 96, 2173 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Das-Gupta D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ), Ferroelectric polymers and composites — Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Sessler G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Das-Gupta D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', IEEE Trans.' 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 17, 866 (1949).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Fedosov S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Sergeeva A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', arXiv:0704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3993 5 p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 179 DISTRIBUTION OF FERROELECTRIC POLARIZATION IN POLED PVDF AND P(VDF-TFE) FILMS Fedosov S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У статті наведено результати експериментального дослідження рівно- мірності розподілу поляризації у сегнетоелектричних полімерних плівках за товщиною зразків.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Об’єктами дослідження обрані типові полімерні сегне- тоелектрики — полівініліденфторид (ПВДФ) та його сополімер з трифтор- етиленом П(ВДФ-ТФЕ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вимірювання виконані сучасним чутливим мето- дом п’єзоелектрично генерованої сходинки тиску.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Встановлено, що розподіл поляризації істотно залежить від величини прикладеної напруги у процесі первинної електризації плівок.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У разі слабких та середніх полів, близьких до коерцитивного, розподіл є неоднорідним з мак- симумом поблизу позитивного електрода.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому рівномірність поляриза- ції не можна поліпшити шляхом подальшого застосування дуже сильних полів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо первинна електризація проводиться у сильних полях, то розподіл поляризації однорідний.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Досліджено особливості сополімера, електризова- ного в коронному розряді.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розроблено феноменологічні моделі процесів, що відбуваються при формуванні поляризації в сегнетоелектричних плівках та сформульовані практичні рекомендації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This article presents the results of experimental study of the polarization distri- bution uniformity in ferroelectric polymer films over the thickness of the samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Typical polymeric ferroelectrics — polyvinylidene fluoride (PVDF) and its copoly- mer with trifluoroethylene P(VDF-TFE) were selected as objects of research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The measurements were carried out by a modern sensitive piezoelectric generated pres- sure step method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It was found that the distribution of polarization substantially depends on the value of the applied voltage during the primary electrification of the films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the case of weak and medium fields close to coercive, the distribution is inhomogeneous with a maximum near the positive electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, the uniformity of polarization cannot be improved even by the subsequent application of very strong fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' If the primary electrification is carried out in strong fields, then the polarization distribution is uniform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The features of the copolymer electrified in corona discharge have been investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Phenomenological models of the processes occurring during the formation of polarization in ferroelectric films have been developed and practical recommendations have been formulated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Introduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' State of the problem Spatial distribution of polarization in PVDF films is extremely import- ant both from scientific and practical points of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Even in earlier works [1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2] it was noted that the piezoelectricity and pyroactivity in PVDF films 180 near the positive electrode are higher than near the negative one that was erroneously associated with injection of holes and the formation of a non- uniformly distributed positive space charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Further studies [3–5] showed that in some cases not only the space charge, but also the polarization are distributed non-uniformly in the thickness direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' For the first time, heterogeneity of polarization in PVDF was detect- ed by Day et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' [1] by different values of the pyroelectric activity near two sides of polarized films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Sassner [2] found that from tightly pressed to each other three films only the film adjacent to the positive electrode was highly polarized It was found [6] that in the high field (E > 150 MV/m), the po- larization is almost homogeneous, while in the middle fields the maximum of polarization is either in the center of oriented films, or near the anode in the unoriented ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Gerhard-Multhaupt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' [7] investigating the distribution of piezoac- tivity by the method of a pressure pulse generated by a powerful laser con- firmed that during thermoelectret poling in the middle fields, the maximum polarization is near the anode, as in the case of poling in a corona discharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Authors of [8] believe that because of the high conductivity of PVDF, areas of excess charge cannot exist, and charge-compensated polar- ization zones are formed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At the same time, we have calculated Debye’s length of screening LD for the following PVDF characteristics: temperature T =300 K, the dielectric permittivity ε = 10, the mobility of charge carriers μ = 10–12 m2/(V∙s), the specific conductivity g = 10–12 Sm/m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We obtained LD = 170 μm that is much larger than the typical thickness of the films (10–50 μm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Therefore, the effect of screening by the space charge should be weakly expressed in PVDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Mopsik and de Reggi [9] found an increased value of the coercive field strength near the surface of the PVDF, and de Reggi and Brodhard [10] found that, in spite of the displacement of polarization to the anode, it is zero near the electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Sessler and Berraissoul [11] found that the piezo- activity near the electrodes and, consequently the polarization is very small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The weakening of the field, in our opinion, is an indication of the injec- tion of charge carriers and, on the contrary, the field and polarization near the blocking electrode are increased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In [4], the maximum polarization near the anode is reported after poling of PVDF in a positive corona discharge, although in the other work of the same authors it is indicated that the polarization in this case is concentrated in the central zone [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Bichler et al [3] found that the position of the maximum polarization depends on the mode of thermal and mechanical processing of 181 PVDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The authors of the paper [3] concluded that the polarization in the PVDF containing the α-phase was shifted to the anode, while the polarization was uniform in the presence of the β-phase although the heat-treatment and stretching changed both the crystalline structure of the films and their other properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In [12], the polarization attenuation near the anode is reported in corona poled PVDF films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Such contradictory data are explained by the fact that the selection of films for the study was random (various thicknesses, re- gimes of poling, annealing, and mechanical pre-treatment).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In addition, the research methodology was imperfect in some cases, so that there was a sub- jective factor in interpreting the measurement results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Direct measurements of the polarization profile are possible only by the method of the pressure step, while all other methods should be considered as non-direct ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The dynamics of the polarization profile in PVDF was studied only in a few works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, it was established [13] that polarization develops in the central zone in biaxially oriented PVDF films containing 70 % β-phase in the case of middle field (60 MV/m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, when changing the polarity of the voltage, the complete switching near the anode does not occur and a bimorph structure is formed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Fedosov and Sergeeva, investigating the distribution of polarization in films electrically charged in a corona discharge [5;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 14–16], found that the maximum polarization is near a positive electrode with a negative polarity of the corona discharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This indicates that injection of negative carriers takes place, while the positive electrode is blocking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' When charged in a positive corona there is a double injection: positive charges from the corona and negative charges from the electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It was found that the free surface of the film exposed to the corona discharge can be regarded as a virtual injection electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In a number of studies, the thermal stability of polarization and its dis- tribution in the thickness direction in PVDF and P(VDF-TrFE) [10], as well as in P(VDF-TFE) [16] were investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The charge and polarization distribution in PVDF films poled by the electron-beam method [17] was studied by the laser induced pressure pulse (LIPP) method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Fedosov and Sergeeva found that the trapped electrons in the volume are not concentrated in a thin layer at a certain depth, but are distributed with uneven density in a zone of the finite thickness [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' These electrons form a virtual negative electrode, from which injection of charges in a non-irradiated region takes place leading to increase in the imaginary penetration depth of the electrons and to inhomogeneity of po- larization in the non-irradiated region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 182 The importance of the injection processes, but not the distribution of intrinsic charges in volume was evidenced by Mitsutani and Ieda [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' They found that the poling current increases in 200 times, if a corona discharge is used instead of a metal electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The experimental results in papers [19;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20] have been explained by the injection of charge carriers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At the same time, some authors believe that the corona discharge forms an ideal block- ing contact with any dielectric [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, the question of the injection of charge carriers and their role in the formation of polarization remains open and controversial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The reasons of the fragmentary and contradictory nature of the literature data on the polarization profiles in PVDF are the complexity of experimen- tal methods and ambiguity in interpretation of the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The aim of this study is to clarify the situation with importance of the uniformity of the polarization distribution in polymer ferroelectrics by per- forming additions experiments and developing the corresponding phenom- enological models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Methods for studying polarization profiles in ferroelectric polymers Profile of polarization and space charge in thin polymer films is studied by one of the following three methods is used: 1) The method of the piezoelectrically generated pressure step (PPS);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2) The method of the thermal wave induced by a modulated laser (LIMM);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3) The method of the laser induced pulse pressure (LIPP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The analysis of the efficiency, sensitivity and resolution of these meth- ods showed that the measured current in the PPS method is proportional to the polarization or gradient of the space charge, whereas in the LIPP method the measured signal is proportional to the charge (if any) and the gradient of polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Given the features of the LIPP method, only zones where polarization changes in thickness direction is detect- ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Therefore, a high homogeneous polarization and complete absence of the polarization give the same signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Despite the resolution of the LIPP method is practically the same as the resolution of the PPS method, it should be recognized that the method of the pressure step (PPS) is more reliable and informative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the LIMM method, the depth of the thermal wave penetration de- creases with the increase of the modulating frequency, so at very high mod- ulation frequencies above 10 MHz it is possible to investigate very thin near- to-electrode layers of less than 1 μm in thickness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 183 However, the resolution of the LIMM method drastically decreases with increasing the distance from the surface to the depth of the sample, and this is a significant disadvantage of the LIMM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Taking into account the results of the analysis, we have chosen the PPS method, which provides a fairly high resolution of about 2–4 μm and the possibility of observing the real-time polarization profile on oscilloscope’s screen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It does not require complex calculations, assumptions, and solu- tions of incorrect inverse tasks as in the case of the LIMM method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The colossal advantage of the PPS method is the ability to study the dynamics of the polarization profile “in situ” directly in the process of poling, polariza- tion switching, and short-circuiting of the samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Most methods for measuring polarization and space charge profiles in dielectrics are applied to already polarized samples providing the informa- tion about the final state, while the process of the polarization development and its profile remained inaccessible for a direct experimental study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In this sense, a unique possibility is provided by the piezoelectrically generated pressure step (PPS) method, in one of the modifications of which there is the ability to measure the profile “in situ” directly when the polarizing voltage is applied or the specimen is short-circuited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Such measurements of the dynamics of the polarization profile are extremely important for under- standing the physical processes occurring in ferroelectric polymers during their poling and switching of polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The PPS method developed by Eisenmenger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' [6] was applied by us, and all measurements were performed in the laboratory of Prof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Eisen- menger at the Department of Physics of the Stuttgart University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The meth- od is based on the generation of an electric signal (a current pulse) when a pressure step generated by a piezoelectric crystal passes through the sam- ple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The piezoelectric pressure step results from a voltage step with a very steep front.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The front of the pressure wave extends with the sound speed of 2250 m/s creating a current pulse in the short-circuited sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It has been proved that the shape of the current pulse repeats the profile of the polariza- tion distribution in the thickness of the film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The block diagram of the installation using the PPS method is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The voltage step is formed by means of a constant voltage source (500 V) loaded with connected in series a resistance and a capacitor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This chain with a frequency of about 100 Hz is locked to a resistor of 50 Ω, in parallel with which a quartz crystal is connected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A sample is pressed to the back side of the piezoelectric crystal, to which a grounded copper electrode is connected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 184 Silicon oil Pressure step 1 50 Ω 50 Ω Conducting rubber Sample Signal І(t) Piezocrystal 2 Voltage step U(t) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Schematic diagram of the polarization profile measurement by the piezoelec- trically induced pressure step (PPS) method For better transferring of the pressure wave from quartz to the specimen, a thin layer of silicone oil is applied between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The electric signal is tak- en from the rear side of the sample with the help of a clamping conductive rubber electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The load is a 50 Ω resistor, the signal from which is fed to the broadband amplifier and then either to the spectrum analyzer, or to the oscilloscope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the case of thin specimens, a 23-μm thick polypropylene gasket was used to reduce the capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Measurements have shown that the steepness of the pressure step front is of the order of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4 ns, while the sound speed in PVDF at room tem- perature is about 2250 m/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, the time of the pressure wave passage through the sample at its thickness of 20 μm is of the order of 10 ns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The duration of one voltage pulse was 100 ns, that is, a step-by-step mode was implemented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' All used devices (amplifier, spectrum analyzer, and oscilloscope) had a bandwidth of more than 1 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The sensitivity of the PPS method was about 2 μm and was limited by the steepness of the pressure step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' An electri- cal signal in the spectrum analyzer was converted into a digital code to allow computer processing of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' To investigate the polarization profile, several series of experiments were performed on PVDF films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Aluminum electrodes of 5 mm in diameter on both sides were pre-deposited at the samples by vacuum evaporation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Initial poling and the polarization switching were carried out at room temperature by applying a constant voltage of certain magnitude and polarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' M185 The magnitude of the voltage was chosen so that average field was 60 MV/m in a series of polarizing and switching, which is slightly higher than the coercive field of PVDF according to the literature data [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Such a mode was named as «middle fields».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In another series, the polarizing field strength was 160 MV/m being much higher than the coercive value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Such regimes were classified as «high fields».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At the middle fields and at the high fields, full polarization cycles were investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' After each phase of polarization or switching, the speci- men was short-circuited for a time sufficient to establish a quasi-stationary state (from 200 to 2000 s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The polarization profiles were measured about 100 times per second and recorded from the oscilloscope screen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Then the analog information of se- lected frames was converted into digital and entered into the computer for further processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' All results are presented in the form of graphs of depen- dence of polarization on the distance in the sample from its surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Distribution of polarization in thin PVDF films Polarization profiles and the space charge give important information about their interrelation in the process of the polarized state formation and in ensuring of its stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This allows us to move from hypotheses and as- sumptions to concrete experimental facts, the analysis of which contributes to the deeper understanding of the ferroelectric polymers characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' That is why special attention was paid to the dynamics of polarization profiles in PVDF films not only during the process of poling but also during the polarization switching and short-circuiting both in the middle fields close to the coercive (50–60 MV/m) and in high fields with a strength of about 160 MV/m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The obtained results allowed constructing models, which take into ac- count the relation between injection and separation of charges, presence of deep charge trapping zones and its interrelation with the residual polar- ization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The impossibility of a complete switching of an inhomogeneously polarized ferroelectric polymer [22] discovered by us is of great practical importance for the choice of poling modes and shows how strong is relation between the ferroelectric polarization and the surface charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Poling field near the coercive value From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2 it can be seen that, with the average field strength close to the coercive value Ec = 50 MV/m [23], the dynamics of the polarization profile is characterized by the following: At the initial stage of poling, af- 186 ter 8 seconds after the voltage application, the polarization distribution is uniform, but its value is very low (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 μC/cm2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Over time, the distribution of polarization in in the thickness direction becomes non-uniform with the maximum near a positive electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' After poling of PVDF in the average field for 2000 s, a sharply heterogeneous asymmetric distribution of the re- sidual ferroelectric polarization appears with a layer of about 5 μm thickness near the negative electrode, in which the residual polarization is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' When the voltage is disconnected and the sample is short-circuited, the character of the polarization distribution does not change and the polarization re- mains heterogeneous, but its magnitude decreases from 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='31 to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='71 μC/cm2 in the region of the maximum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0 5 10 15 20 0 1 2 3 4 2 4 6 8 10 Polarization, \uf06dC/cm 2 Stage Depth, \uf06dm Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Distribution of polarization in P(VDF-TFE) film during its poling in the field of 60 MV/m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The stage number corresponds to different times after the starting of poling: 1–8 s, 2–70 s, 3–100 s, 4–150 s, 5–250 s, 6–350 s, 7–450 s, 8–750 s, 9–1000 s, 10–1510 s, 11–2000 s The resolution of the method for measuring the polarization profile is of the order of 2–3 μm, which leads to appearance of smooth polarization profiles in near-to-electrode regions and in other places of the virtually sharp polarization change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' For example, it was shown [5] by measuring the polar- ization profile near the electrode by the LIMM method having the resolu- tion near the electrodes of the order of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 μm that the polarization changes 187 sharply from the maximum value to zero within about 1 μm in the vicinity of the positive electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the vicinity of the negative electrode where po- larization is absent, distortion of the profile due to the finite resolution does not occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The effect of resolution, probably, also affects the boundary between the first and the second zones where the polarization changes more sharply than it follows from the curves in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0 5 10 15 20 2 1 0 1 2 3 4 0 2 4 6 8 10 Polarization, \uf06dC/cm 2 Stage Depth, \uf06dm Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Polarization profiles in the P(VDF-TFE) film during the polarization switch- ing in the field 60 MV/m after initial poling and the short-circuiting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The stage corresponds to different times from the starting of the switching: 1–0 s, 2–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 s, 3–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 s, 4–1 s, 5–5 s, 6 –50 s, 7–200 s, 8–500 s, 9–1000 s, 10–1500 s, 11–2000 s After changing the voltage polarity (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3) a minimum is formed in the place of the former maximum at a depth of about 16 μm, because the po- larization in this place is not completely switched, but even does not reach zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At the same time, the oppositely directed polarization is formed to the right and to the left of this intersection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' High polarization is formed again only near the positive electrode now connected to the opposite side of the film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It should be noted that the polar- ization switching is faster than initial poling, and the residual polarization in the peak area is almost 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 times greater than after initial poling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 188 Comparison of polarization profiles after several switchings showed that with even number of switchings, practically identical profiles are appeared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the case of odd number of switchings, the profiles are also the same, ex- cept for the profile after the first charging when there is no reverse polariza- tion near the negative electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, the profile is determined by whether the number of switchings is either even, or odd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In both cases, the distribution of polarization is sharply heterogeneous and asymmetrical with respect to the center of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The main polarization maximum, regardless of the parity of the phases, is always near the electrode, which was positive in the last previous experi- ment, and the magnitude of this maximum is almost 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 times greater than in the case of an odd number of switchings than with the even number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The time for quasi-stationary state formation decreases with increase in the number of voltage switchings from 2000 s during initial poling to 250– 500 s during the subsequent transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In some studies, for example [10, 24], the information that the coercive field near the surface is greater than that in the volume are incorrect, in our opinion, because the incomplete switching is, most likely due to heteroge- neity of the field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Due to injection of charge carriers, the field near the sur- face is smaller than in the volume, and therefore the polarization is poorly switched there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Attempts to improve properties of non-uniformly polarized films It is seen from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3 that in the middle fields (60 MV/m) po- larization is heterogeneous at any polarity of the voltage, and the complete switching does not occur in any section of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The formed bimorph structure is stored regardless of the direction of the external switching field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At the same time, as will be shown below, homogeneous polarization is formed in high fields (160 MV/m), which then remains homogeneous with any changes in the magnitude and sign of the applied voltage up to complete depolarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In this regard, it was interesting to investigate behavior of the polymer ferroelectric films in high fields, originally poled in middle fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' If the initial polarization inhomogeneity is due to the fact that the field is not high enough, homogeneity should increase after applying a high field, due to expansion of the polarized region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, we have found that the polarization does not become homogeneous, and the polarized region does not expand under the action of a high field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Experiments were carried out as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' PVDF films were placed in a field of 60 MV/m and polarization profiles were measured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' As can be seen 189 from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2 and 3, the spatial distribution of polarization was sharply het- erogeneous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Further, without interrupting the measurements of the polar- ization profile we increased the voltage to 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 kV by steps of 200 V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The field strength at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 kV is several times greater than the coercive value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0 5 10 15 20 0 1 2 3 4 5 6 7 2 4 6 8 10 Polarization, \uf06dC/cm 2 Stage Depth, \uf06dm Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Polarization profiles in the P(VDF-TFE) film during the stepped voltage in- crease from 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 kV (primary poling) to 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 kV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The value of the voltage step is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 kV, the exposure time at each voltage is 50 s However, as it follows from the graphs in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4, the increase in the field strength did not lead to the expected improvement of the polariza- tion uniformity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Only the magnitude of the maximum increased, while the non-uniform character of the polarization distribution remained un- changed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, in order to obtain the high and homogeneous residual polar- ization, it is not enough to apply a high field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is necessary to take into account the conditions in which the sample was poled for the first time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' If initial poling was carried out in the high field, then the residual polar- ization will be homogeneous at any applied forward poling or switching voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' If initial poling was carried out in medium or weak fields, then the het- erogeneity of the residual polarization cannot be corrected or eliminated by 190 applying the high field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In this case, for obtaining the uniform profile of the residual polarization, we recommend a complete thermal depolarization of the sample and its annealing in the short-circuited condition at about 160 °C for several hours, so that the trapped charges in the volume will be com- pletely dissipated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' After cooling the sample, it is necessary to re-pole it, but necessarily in the high field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Poling and switching of polarization in high fields In the case of high fields (160 MV/m), (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5), polarization is much more uniform than in the case of middle fields, and the polarization uni- formity appears even after initial poling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' When polarity of the polarizing voltage changes, the symmetric switching of polarization occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' By apply- ing the voltage of the opposite polarity, and by increasing it in small steps, it is possible to almost completely depolarize the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The field strength at which this occurs corresponds to a value of 60 MV/m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Namely this value can be considered as a real coercive field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is interesting to note that the subsequent application of an external field of 60 MV/m of any polarity provides homogeneous residual polariza- tion, which cannot be obtained after initial poling in such a field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The com- plete depolarization of a highly polarized sample irrespective of the polarity of the external field occurs at field strength of 60 MV/m, which indicates the symmetry of the hysteresis loop if initial poling was carried out in high fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, the main features of poling and switching in high fields are as fol- lows: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Polarization in the sample volume is homogeneous and symmetric with respect to the central section;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' There is no difference in the shape of the profile and the magnitude of polarization at different polarizing voltages;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Polarization is easily switched over the entire volume, and full depo- larization is possible;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Homogeneity of polarization is stored not only in high but also in middle fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Of great importance to practice, we have the effect of “formatting” or “conditioning” in a high field, after which homogeneous polarization is provided at any field strength, including the coercive field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This enables, if necessary, to change the magnitude and sign of the re- sidual polarization in a wide range from zero to saturation that cannot be achieved without this formatting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 191 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Phenomenological model of polarization profile formation at constant poling field It follows from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2 that in the initial stage of poling at 8 seconds after the application of a constant voltage creating average field strength of 60 MV/m the polarization is uniform and corresponds to about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 μC/cm2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0 5 10 15 20 25 4 2 0 2 4 6 2 4 6 8 Polarization, \uf06dC/cm 2 Stage Depth, \uf06dm Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Polarization profiles in the P(VDF-TFE) film initially poled at 3 kV after applying the opposite polarity voltage of different values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Stages: 1 — initial state, 2 — 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 kV, 3 — 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='6 kV, 4 — 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=',0 kV, 5 — 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4 kV, 6 — 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='8 kV, 7 — 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 kV This indicates a uniform distribution of the field strength and absence of injected charges [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At the same time, the stationary value of polarization, can be calculated by the formula corresponding to initial poling [26] taking into account its non-linear dependence on the field strength, the presence of the coercive value Ec and at 50 % crystallinity ( ) 2 ( ) r st c s c P P E E E E = − ⋅ − .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (1) Substituting in (1) the value of Pr = 13 μC/cm2 [27], Es = 200 MV/m [23], Ec = 50 MV/m, E = 60 MV/m, we obtain Pst = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='43 μC/cm2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The re- versible polarization component Pcap is proportional to the field strength and the dielectric permittivity Рcap= εо(ε–1)Е.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (2) 192 Assuming ε = 10 [21] and taking into account that εо = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='85∙10–12 F/m and E = 60 MV/m, we obtain Pcap = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3 μC/cm2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' From the graph of the po- larization profile dynamics, it is seen that the value of polarization after 8 s of the voltage action is about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 μC/cm2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, all polarization is reversible, that is, the ferroelectric component during this time is not yet formed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' With further application of the field, the polarization becomes non-uni- form (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2) indicating appearance of inhomogeneous distribution of the field strength with its weakening near the negative electrode and the increas- ing near the positive electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' According to the Poisson equation, inhomo- geneous polarization of this kind is possible only in the presence of excessive negative charge in the place of the field heterogeneity 0 ( , ) ( , ) E x t x t x ∂ ε ε = ρ ∂ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (3) This charge is likely to be injected from a negative electrode and is pres- ent near this electrode extending with time to the sample depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Without taking into account the formation of the ferroelectric polarization, it can be assumed that the charge distribution is close to the rectangular [13], and the speed of the charge front motion is determined by mobility μ and the field strength E1 at the boundary x1 between the zone with the space charge and the zone free of excess volume charge [ ] 1 1 ( ) ( ), v t E x t t = µ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (4) Since the applied voltage remains constant (Uo = const), the normaliza- tion condition is fulfilled 0 0 0 ( , ) x E x t dx U = ∫ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (5) The expression (5) is simplified when the rectangular distribution of the injected charge is assumed, since in the region from 0 to x1, the field accord- ing to the Poisson equation (3) depends linearly on the coordinate, while in the other part of the sample it is constant and equal to E1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, for finding the x1(t) function and the field strength E1(t) we have the following system of equations 1 1 (t) ( ) dx E t dt = µ , (6) 1 0 1 0 1 ( ) ( ) 2 E t x x t U \uf8ee \uf8f9 − = \uf8ef \uf8fa \uf8f0 \uf8fb .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (7) 193 0 200 400 600 800 1000 0 5 10 15 20 25 60 80 100 120 Depth, \uf06dm 1 2 Field strength, MV/m Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Estimated graph of the front of injected charges motion after application of a constant voltage to a PVDF film under the charge mobility of 3⋅10–16 m2/V·s (1) and the time dependence of the field strength at the boundary, to which the front of the injected negative charges reached (2) The equations (6) and (7) were solved by numerical methods, and the graphs x1(t) and E1(t) are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6 at xo = 23 μm, μ = 3·10–16 m2/V·s, Uo = 1380 V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' From the above graphs it follows that there is some acceleration of the motion of the injected charges front in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At the same time, the field strength in the part of the sample which the injected charges have not yet reached increases with time exceeding the initial strength more than 2 times after 1000 s of poling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The polarization switching time depends on the field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Let us explain this in more detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' If we consider that the switching time of the ferroelectric polarization in PVDF is about 5 μs at E = 200 MV/m, and the dependence of the switching rate on the field strength is of the following form 0 exp A E E \uf8eb \uf8f6 τ = τ \uf8ec \uf8f7 \uf8ed \uf8f8 , (8) where τo has an order of 20 ns, then for the activation field EA we will get the following value: 0 ln 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 A E E τ = = τ GV/m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (9) 194 The polarization switching time in the field of 60 and 120 MV/m should be τ60 ≈ 2 s, τ120 ≈ 2·10–4 s in accordance with the formula (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, the increase of the field strength by 2 times leads to decrease of the switching time by 4 orders of magnitude, but both values are small compar- ing to the time scale of the experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This allows assuming that the pro- cess of the ferroelectric polarization formation is quasi-stationary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In this case, we can disregard the dependence of the switching time on the field strength, but use the field dependence of the ferroelectric polarization (1) assuming that at any given time Pfe = Pst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It was shown [16] that in the PVDF, in addition to the capacitive Pcap and the ferroelectric Pfe component of polarization, there is also a revers- ible component Prev of the definitely not established nature, the presence of which is associated with dipole polarization in the amorphous phase of the polymer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The correlation between the components of polarization can be established by analyzing the evolution of the polarization profile after the voltage is switched off and the sample is short-circuited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the process of poling, when the voltage is applied, there are all three components of polarization Р1 = Рcap+Рfе+Рrev, (10) where P1 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='31 μC/cm2 at the point of maximum polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the case of the shortening, the components of Pcap and Prev disappear and only the ferroelectric component remains, that is, P2 = Pfe with P2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='71 μC/cm2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Since the polarization formation process is rather slow, the experiment time is much greater than the Maxwell relaxation time 0 3 M s g ε ε τ = ≈ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (11) At own conductivity of PVDF g = 3∙10–11 Sm/m [16], there is no reason to assume that there is a partial back switching of the ferroelectric polariza- tion due to insufficient compensation of the depolarizing field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Therefore, Pfe does not change with the short-circuiting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' By the formula (1) we can find the corresponding polarization maximum of (Pst = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='71 μC/cm2) and the field strength E = 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 MV/m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The capacitive component of the polariza- tion Pcap = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='79 μC/cm2 according to the formula (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Then the reversible component of the polarization will be equal to Prev = P1 — Pcap — Pfe = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='81 μC/cm2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Since the reversible polarization most likely, is due to the dipole struc- ture of the amorphous phase, it can be taken into account by introducing 195 the effective dielectric permittivity of the amorphous phase, which includes all the reversible processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The obtained value of the same order (19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='6) was used in the works of von Seggern and Fedosov [15;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 28] in calculations of the two-stage forma- tion of the ferroelectric polarization in PVDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The dynamics of polariza- tion in four cross sections (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 7) shows that the degree of heterogeneity increases, because the polarization of about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 μC/cm2 near the negative electrode at the depth of about 5–6 μm does not increase in time, as it does in the second part of the sample, but it gradually decreases to zero (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At the same time, the maximum near the positive electrode located initially at a depth of 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 μm, and then shifted to a coordinate of 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4 μm increases with time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0 1000 2000 0 1 2 3 Polarization, \uf06dC/cm 2 Time, s 5 10 15 20 \uf072 Е Р 0 х х х 2 х х х о Е Е Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Dynamics of polarization in the P(VDF-TFE) during initial poling in the field of 60 МV/м at different distances from the film surface (depth): 5, 10, 15 and 20 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This suggests that the ferroelectric polarization is not formed near the negative electrode, but there is a decrease of the field and polarization to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is known from the theory of injection currents [25] that the field strength at the injecting electrode is very small or equal to zero, but near the electrode where excessive charge is located, the field is non-zero increasing linearly in the case of the homogeneous charge distribution, as follows from the formula (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' If the charge density decreases in the direction of depth, the graph of the E(x) dependence will be convex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' That is, only injection of charges cannot explain the presence of a zone in the thickness of about 196 5–6 μm, in which the field and polarization are almost zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Obviously, there is another phenomenon that leads to decrease of the field strength and polarization near the negative electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0 ( ) / 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 a cap rev P P E ε = + ε = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (12) 0 1000 2000 0 1 2 3 Polarization, \uf06dC/cm 2 Time, s 5 10 15 20 \uf072 Е Р 0 х х х 2 х х х о Е Е Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Scheme of processes occuring during poling of PVDF films in middle fields and leading to formation of a heterogeneous three-layer structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Also the distribu- tion of the injected charge along the thickness, the field strength and polarization are shown It is known that the effective conductivity decreases sharply during formation of the ferroelectric polarization in PVDF [17], that is, it can be assumed that the conductivity of the polarized part of the sample is much smaller than that of the not polarized part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In this case, the distribution of the total applied voltage Uo between the not polarized and polarized parts occurs as between two connected in series resistors of different values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The voltage, and hence the field strength, is small in the not polarized part, it is higher in the polarized part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This distribution of voltages con- tributes to the formation of even greater heterogeneity of the residuals polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, equations (6) and (7), which do not take into account the depen- dence of the effective conductivity on the ferroelectric polarization Pfe, only valid until the beginning of the Pfe formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' After this, the uniform motion 197 of the injected charge is stopped, because its localization on the boundary of the polarized and not polarized regions occurs in accordance with the Pois- son equation (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Chargers only partially penetrate into the polarized region or do not penetrate at all, that is, the effective conductivity of the polarized region decreases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' There is a redistribution of the applied voltage, so that it decreases at the not polarized part, and increases at the polarized part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' As a result, the field strength and reversible polarization decrease in the adjacent to the injection electrode region, while they increase in the polarized region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Exactly this is observed on the experimental curves of the polarization pro- file evolution (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This phenomenon leads to the formation of a three-layer structure, schematically shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0 х2 х1 хо Е2 Е1 х Е Е1=0 Е2=0 (а) (b) (c) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Scheme of processes occurring in PVDF poled in middle fields at the mo- ment of the short-circuiting (a), distribution of the field strength at the moment of cut-off (b), and state of the sample after aging in the short-circuited condition In the area adjacent to the negative electrode, there is a high concentra- tion of injected charges, high conductivity, low field strength and very low reversible polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At the boundary of the not polarized and polarized regions, a layer of localized negative charges is formed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Within this layer, the field is heterogeneous and polarization sharply increases from zero to the 198 maximum value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the third zone, there is the homogeneous field and the homogeneous polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' When the sample is short-circuited after the completion of poling, the average field strength becomes zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At the same time, the direction of the field strength vector in the not polarized part of the sample E1 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 9) be- comes such that excess free injected charges from the first zone are “blown” through an electrode that was negative during poling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The reversible com- ponents of polarization in all zones are reduced to zero, the excess non-lo- calized charges are dispersed due to their own conductivity, and the field strength at all points of the sample becomes zero with a time constant equal to the Maxwell’s relaxation time (11), as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' According to the experimental data of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2, the first zone occu- pies an area from x= 0 to x1 = 6 μm, the second zone is from x1 = 6 μm to x2 = 14 μm, and the third zone is from x2 = 14 μm to xo = 23 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' As it follows from the experimental polarization profiles, the boundaries of the zones do not change with time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the second zone, the excess negative charge is dis- tributed almost uniformly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This is confirmed by the presence of practically linear sections of the polarization profile in this zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is essential that the polarization profile changes with time at a constant voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This indicates that slow processes of transfer and redistribution of the space charge are involved in formation of the polarization and in its switching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the general case, as follows from our data, the polarization is a complex function of the field, coordinates in the volume of the dielectric and time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The obtained results correspond to the model, which provides an im- portant role of the volume charge in the formation of the polarized zones in PVDF and the injection of charge carriers from electrodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Experimental data indicate that the level of injection of negative charges from the met- al electrode is higher than from the positive electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is also possible that the mobility of injected negative charges is much higher than positive charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Intrinsic free carriers play a minor role in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, in the case of initial poling, the homogeneity of the field is dis- turbed by injection of negative charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In a large part of the sample near the injectable electrode, the field is attenuated and smaller than the coercive field, so the ferroelectric polarization is not formed there and the residual polarization is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At the same time, the field exceeds the coercive val- ue near the positive electrode, and the high residual polarization is formed there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The polarization heterogeneity is fixed by negative charges trapped in the region where the gradient of polarization exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The depolarizing field 199 on the opposite side is compensated by positive charges located either at the electrode or in the near-to-surface layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' After poling and short circuiting, the field in the peak area supports po- larization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' There is also a redistribution of moving charges: in the vicinity of the negative electrode, they move in the opposite direction to the injection until the field at all points of the volume becomes zero (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Uncom- pensated trapped charges remain only at the slopes of the polarization peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The massive trapping of injected charges at the boundary of the polar- ized region begins immediately as soon as a zone of the high polarization appears.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This charged layer divides the volume into two parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the first part, adjacent to the negative electrode, there is no high polarization, and the concentration of free injected carriers is rather high.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This results in a high apparent conductivity and, accordingly, in a weakened field in this zone in the process of poling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At the same time, the polarized region ap- pears separated from the injection electrode by a layer of the trapped charge carriers, and its apparent conductivity becomes considerably smaller than in the first zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This phenomenon can be considered as the Maxwell-Wagner effect induced by the non-homogeneous polarization, which leads to in- creasing field in the polarized region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' That is why, with the passage of time, the polarized region does not expand, and the value of polarization increas- es.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Phenomenologically, trapping of charges and division into two zones is manifested in reducing the charging current at constant voltage, that is, in reducing the effective conductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' When polarity of the applied voltage is changed, the preferred injection of negative charge carriers is again takes place, but they are injected from the opposite electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' As a result, the region of the high field appears where the residual polarization was zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This leads to the high polarization formation in new direction in this zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the area where residual polarization was strong, the field is weakened due to the injection of negative charges and presence of the negative bulk charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Therefore, switching of polarization does not occur here, but a part of the residual polarization of the former direction remains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the zone of the negative space charge localization (8–15 μm), the direction and value of the polarization gradient do not change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This indi- cates that the negative charges trapped during initial poling are still in place, despite the fact that the polarization direction in the zone where they are located changes to the opposite direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This unusual phenomenon is completely consistent with the Poisson equation for the case of a zero field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is also possible that there is a delocalization of previously trapped carriers 200 and their re-trapping without a significant change in the spatial position of localization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, after the switching, an asymmetric bimorph structure is formed, which is stored at subsequent transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The negative charge layer, judging by the polarization gradient in the region of 8–15 μm, is preserved as if it is fixed in the sample volume during all its transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The presence of this layer explains the faster formation of the polarization profile during switch- ing compared to initial poling when this layer is not yet present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This same layer prevents formation of the homogeneous polarization even in the case of high applied fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The effect of impossibility to improve the profile of polarization by in- creasing the applied voltage to the films initially poled in the middle fields can be explained by the influence of the injected and trapped charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 7 it is seen that the polarization gradient at the boundary of the polar- ized region in the sample volume does not change the sign when the polarity of the switching external voltage changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This indicates that in the volume there is a layer of deeply trapped negative charges, which plays the role of a barrier preventing the expansion of the polarized region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This layer is stable because it compensates for the depolarizing field in the regions lying at one and the other side of it (at different polarities of the external field).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Since this layer obstructs the free motion of injected negative charges, their con- centration in the region between this layer and the cathode is much greater than between the charged layer and the anode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Accordingly, the effective conductivities of these regions are different, and the applied voltage is dis- tributed unevenly, so that a significant part of the voltage is applied to the already polarized region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, increase in voltage cannot widen the polarized region because of the blocking layer, that is, it does not improve polarization homogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' So, the initial inhomogeneous polarization remains inhomogeneous in high fields of any magnitude and polarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The phenomenon discovered by us is of fundamental importance from scientific, methodological and practical points of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' First, it further clar- ifies the mechanism of interrelation of the polarization with the trapped space charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It would seem that a high field 3 times higher than the coercive field, should provide uniform polarization regardless of the initial condi- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, this is not the case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The influence of the trapped charge is so significant that even high fields cannot suppress it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Secondly, in the study of switching and hysteresis phe- nomena in ferroelectric polymers, it seemed self-evident to start electrifying 201 from a weak field gradually increasing the applied field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' That is how the hys- teresis measurements are performed “at the infra-low frequencies”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Taking into account our data it turns out that such measurements are incorrect, because the magnitude and, most importantly, the profile of polarization, depends not only on the field strength, but also on the pre-history of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It was established by studying poling and switching in high fields that po- larization is homogeneous in this case and it is easily switchable over the en- tire volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the case of high field initial poling, a complete depolarization is possible, and the polarization homogeneity persists not only in high but also in middle fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' These features can be explained by the fact that, given the presence of a high field, the polarized region quickly occupies almost the entire volume, which leads to blocking the movement of charges and a sharp weakening of the injection of charges role.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The processes of compensation and neutralization of the depolarizing field occur in this case, either on the electrodes, or near the surface, so that the entire main volume remains free of injected and trapped charges, which could disrupt the field’s uniformity and polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The change of the polarization gradient near the electrodes during the polarization switching indicates that the sign of the trapped com- pensating charges also changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This is only possible if these charges are not trapped too deep, so they can be “shaken” from their traps under action of a high field with the subsequent localization in the same region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Uniformity of polarization in corona poled P(VDF-TFE) copolymer Polarization profiles in P(VDF-TFE) have not been studied before, and the data obtained on other corona-charged ferroelectric polymers are rather fragmentary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' For example, it was found that polarization occupies the cen- tral zone of a positively charged PVDF [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In another sample of PVDF, which was in similar conditions, the peak of polarization was found near the positive surface, while the biaxially stretched PVDF showed more or less uniform polarization [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The polarization profiles in polarized PVDF films that were poled in a negative corona turned out to be bell-shaped [31], while a significant decrease in polarization was observed near the positive side of a biaxially stretched PVDF poled in a positive corona [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Distor- tion of polarization homogeneity is usually considered as a consequence of the injected charge presence [29–32], but the details of this mechanism are still only partially clear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In [5], we report on measurements of polarization profiles obtained by applying a piezoelectrically generated pressure step (PPS) method to films 202 P(VDF-TFE) that were charged in a negative corona discharge under dif- ferent conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The samples were films from experimental batches of 20 μm thick P(VDF-TFE) consisting of 95 % VDF and 5 % TFE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The films were extrud- ed from the melt and stretched unilaterally by the supplier (Plastpolymer, Russia) and contained approximately 90 % of the ferroelectric β-phase crys- tals according to the IR spectroscopy measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Aluminum electrodes with a diameter of 20 mm and a thickness of 150 nm were deposited at one surface of the samples by thermal evaporation in vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Non-metallised films were also sometimes used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Poling was carried out in a corona triode [33] with a bare surface of the sample subjected to a negative corona discharge initiated by a sharpened tungsten electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The ions and electrons passed through a control grid, which was held at a constant negative potential in relation to the grounded rear electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The polarization field was generated by charges adsorbed on the surface of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The grid was made vibrating to allow simultane- ous measurement of the surface potential by the Kelvin method and the DC poling current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Six combinations with three poling parameters were investigated by maintaining the field strength at two levels (50 MV/m and 100 MV/m), temperatures (25 °C and 85 °C), and electrical mode (constant current and constant voltage).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Moreover, we conducted experiments with a multi-lay- ered sample formed from identical films, in which only the lowest film was metallized that was in contact with a positive electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Immediately after completion of poling all samples were short-circuited for 15 minutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The short circuiting was carried out by the non-electrode grounding of the bare sample surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' To do this, polarity of the corona was changed from negative to positive with the simultaneous grounding of the control grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, the sample was short-circuited, because its upper surface, now bombarded with positive corona discharge ions, received a grid potential equal to the poten- tial of the rear electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The duration of the short circuit was long enough to provide a zero field everywhere in the main part of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' After the short circuiting, the samples were stored in an open circuit conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Polarization profiles were measured at room temperature using a piezo- electric-induced pressure step (PPS) method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The full description of the method is given elsewhere [29], and only its basic principle is described here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The pressure step is generated by an electrically controlled quartz crystal connected to the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Pressure waves propagate at a sound speed (~ 2000 m / s) through a sample in the direction of the thickness causing an 203 electrical signal measured by an oscilloscope with a bandwidth of 1 GHz and then digitized for further processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It was shown [30;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 34] that the reaction of the short-circuit current to the pressure step provides a direct image of the spatial distribution of the piezoelectricity in the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is also known [26] that piezoelectric coefficients in ferroelectric polymers are proportional to the level of the residual polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, the magnitude of the current at any time was proportional to the residual polarization in the corresponding point of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Therefore, the measured signal was calibrated directly in polarization units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A 23 μm polypropylene film was in- serted between the sample and the measuring electrode to reduce the input capacitance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' To obtain reliable data, we measured the polarization profiles twice on each sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We found that the residual polarization is distributed non-uniformly in P(VDF-TFE) films under constant current conditions, regardless of tem- perature, as can be seen from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10 and 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The polarization peaks in the samples poled at room temperature are shifted to the positive side leaving almost half of the thickness not polarized (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In samples heated to 85 °C, the peak is higher and closer to the positive surface than at room temperatures (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Another small peak is observed near the surface bombarded with corona discharge ions in all samples poled by the constant current, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10 and 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0 4 8 12 16 20 0 2 4 6 8 10 P, \uf06dC/cm 2 x, \uf06dm 0 4 8 12 16 20 0 2 4 6 8 10 P (\uf06dC cm 2) x (\uf06dm) 0 4 8 12 16 20 0 2 4 6 8 10 (a) x (\uf06dm) P (\uf06dC cm 2) x (\uf06dm) 0 4 8 12 16 20 0 2 4 6 8 10 (b) 0 4 8 12 16 20 0 2 4 6 8 10 P (\uf06dC cm 2) x (\uf06dm) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Distribution of polarization in P(VDF-TFE) films after poling at 25 °C and the DC current density of 80 μA/m2 for 15 min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The field at the end of poling was 100 MV/m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The coordinate x = 0 corresponds to the sample surface bombarded by negative corona ions 204 0 4 8 12 16 20 0 2 4 6 8 10 P, \uf06dC/cm 2 x, \uf06dm 0 4 8 12 16 20 0 2 4 6 8 10 P (\uf06dC cm 2) x (\uf06dm) 0 4 8 12 16 20 0 2 4 6 8 10 (a) x (\uf06dm) P (\uf06dC cm 2) x (\uf06dm) 0 4 8 12 16 20 0 2 4 6 8 10 (b) 0 4 8 12 16 20 0 2 4 6 8 10 P (\uf06dC cm 2) x (\uf06dm) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Distribution of polarization in P(VDF-TFE) films after poling at 85 °C and the DC current density of 160 μA/m2 for 15 minutes and cooled to 25 °C in the ap- plied field of 100 MV/m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The x = 0 coordinate corresponds to the negative side of the sample Multilayer samples were poled at constant voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The field strength was either moderate (50 MV/m) or high (100 MV/m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The first value was close to the coercive field of PVDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The polarizing field in the multilayered samples was not the same in two-layer films from which the sample was composed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At the average field of 50 MV/m, only the film having direct contact with the positive rear electrode had residual polarization (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The upper film did not show any residual polarization indicating that the voltage was applied mainly to the lower film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, both films are polarized in the case of a high field, as can be seen from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13 The distribution of polarization in the lower («pos- itive») film is rather uniform (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13 (b)), whereas in the upper film there are two asymmetric peaks with the higher one located near the surface that was bombarded by the corona ions (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13 (a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Three-lay- er and four-layer specimens were poled in the average nominal field of 50 MV/m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The results shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 14 and 15 differ significantly from the results obtained on the two-layered samples (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12 and 13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Of the three films in the sample, the upper film, which was subjected to the ac- tion of ions, was not polarized at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The distribution of polarization in 205 the film attached to the positive electrode is not uniform and similar to that in the case of constant current poling (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10 and 11), while in the middle film there are two symmetric peaks separated by a saddle (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 14 (a)) In the case of four films, only two films at the positive side of the sample are polarized, but not uniformly (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Polarization peaks in both films are shifted to the positive side, and the magnitude of the po- larization is much higher in the film, which contacts the electrode (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 15 (a) and (b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0 4 8 12 16 20 0 2 4 6 8 10 P, \uf06dC/cm 2 x, \uf06dm 0 4 8 12 16 20 0 2 4 6 8 10 P (\uf06dC cm 2) x (\uf06dm) 0 4 8 12 16 20 0 2 4 6 8 10 (a) x (\uf06dm) P (\uf06dC cm 2) x (\uf06dm) 0 4 8 12 16 20 0 2 4 6 8 10 (b) 0 4 8 12 16 20 0 2 4 6 8 10 P (\uf06dC cm 2) x (\uf06dm) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Distribution of polarization in the lower film of a two-layered sample poled at 85 °C in the constant field with the average intensity of 50 MV/m for 15 minutes and cooled to 25 °C in the applied field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Coordinate x = 0 corresponds to the neg- ative side of the film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The upper film bombarded by corona discharge ions did not have any residual polarization Distribution of polarization in the middle and the lowest films of a three-layer sample poled at 85 °C in the average field of 50 MV/m and cooled to 25 °C in the applied field have shown the similar results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Coor- dinate x = 0 corresponded to the negative side of each film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The upper film that was bombarded with corona discharge ions did not have any residual polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' From our experiments on multilayer samples, it should also be antici- pated that the polarization peak near the positive electrode with a large de- pleted polarization region near the negative electrode occurs in the case of one thick film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A similar phenomenon was observed in corona poled PVDF films with a thickness of 120 μm [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 206 0 4 8 12 16 20 0 2 4 6 8 10 x (\uf06dm) P (\uf06dC cm 2) x (\uf06dm) 0 4 8 12 16 20 (b) (a) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Distribution of polarization in (a) upper and (b) lower films of a two-layer sample poled at 85 °C with the constant average field of 100 MV/m for 15 minutes and cooled to 25 °C in the applied field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Coordinate x = 0 corresponds to the nega- tive side of each film Polarization and injection of charges The heterogeneity of polarization in the direction of thickness in homo- geneous specimens may obviously be due to the non-uniform distribution of the applied field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' According to the Poisson equation, the inhomogeneity of the field strength E(x,t) is due to the presence of either a real uncompen- sated charge ρ(x,t) or the polarization charge dP(x,t)/dx: [ ] 0 ( , ) / ( , ) ( , ) / E x t x x t P x t x ε ε ∂ ∂ = ρ − ∂ ∂ , (13) where ε is the dielectric constant, εо is the permittivity of a vacuum, P is the ferroelectric polarization, x is the coordinate in the direction of the film thickness, t is time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Since the polarization P itself depends on the field strength E, the initial heterogeneity of the poling field should be attributed only to the effect of real charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' There are two main sources of the space charge in a dielectric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It can be caused by the spatial separation of already existing intrinsic positive and negative charge carriers, or by injection of charges to the volume from the outside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' To show how to use equation (13) to distinguish the effects of in- jected and internal carriers, we first assume that the external voltage V is 207 applied to a sample of thickness xo, when the density of the injected charges is much lower than that of the intrinsic carriers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' From equation (13) it follows that the field increases near both surfaces of the sample and accordingly decreases in the central region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' If the applied field Ep = V/xo is equal to or close to the coercive value Ec, then two peaks of the ferroelectric polarization will appear in front of the electrode sections separated by a non-polarized zone, as shown schematically in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 16 (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Now suppose that the same voltage V is applied to another sample where monopolar injection of negative carriers takes place, and their density is much higher than that of the intrinsic charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The injection charge does not affect the average Ep field, but creates heterogeneity of the field, as shown schematically in Figure 16 (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The field at the injecting electrode is almost zero, but it increases in the direction of x in accordance with equation (13) until it reaches the Ec value at a certain depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is clear that the peak of the residual polarization will be shifted to a positive electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus, one can determine the dominant phenomenon from the position of polarization peaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' For example, profiles in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13 (a) and 14 (a) indicate that the level of injection was low in these samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, injection of negative charges in many cases is more important than the separation of the intrinsic carriers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The consequence is visible, for example, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10, 11, 14 (b), 15 (a) and 16 (b), in which polarization peaks in all these cases are observed near the positive electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Spatial neutrality inside the sample will be distorted due to the predom- inant movement of positive charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The charges injected during poling do not remain there after a short circuiting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' They form a spatial charge that cor- responds to the slope of the residual polarization profile, since dP(x)/dx = = ρ (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' E(x) = 0 under short circuit conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The contribution of the space charge to the measured signal cannot be experimentally separated from the residual polarization, but it can be con- sidered as insignificant, since the piezoelectricity in ferroelectric polymers, to which the PPS method is sensitive [30;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 34] is caused by the residual po- larization, but not by the space charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Our results obtained for P(VDF-TFE) films are consistent with the data on the polarization profiles observed in the case of other ferroelectric poly- mers that have been poled in a corona discharge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The depletion of polariza- tion near the negative side due to the charge injection was detected in PVDF and P(VDF-TrFE) [30–32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Moreover, a similar phenomenon was observed in ferroelectric polymers, poled by the thermoelectret method [29;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 30], by direct application of a high field and the electron-beam polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 208 0 4 8 12 16 20 0 2 4 6 8 10 x (\uf06dm) P (\uf06dC cm 2) x (\uf06dm) 0 4 8 12 16 20 0 2 4 6 8 10 (b) (a) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Distribution of polarization in (a) penultimate lowest and (b) the last lowest film of a four-layer sample that was poled at 85 °C in the average field of 50 MV/m for 15 minutes The charge injection is most likely appears from a virtual electrode formed on a surface bombarded by electrons and ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Our results show that homogeneity of polarization is more severely distorted by injection, if low or moderate fields are used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' For example, the field in the case of a constant voltage gradually increases from zero to about 100 MV/m, and the resulting polarization distribution is highly heterogeneous (Figs 10 and 11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Almost a quarter of the sample thickness is not polarized, since the field in this area is too low for the formation of the ferroelectric polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the case of two-layer samples poled in the average field of 50 MV/m, charges are main- ly injected into the film under action of the corona that causes increase of the film conductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We assume that the conductivity corresponds to the following equation [ ] ( ) n n g e n + − + + − − ′ ′ = µ + µ + µ + µ , (14) where e is the elementary charge, n is the density of the carriers, n+ and n- are injected charge densities, μ+, μ-, μ’+ and μ’- are mobilities of intrinsic and injected carriers (they may be different).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This expression implies that the conductivity increases if injection takes place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' As a result, the applied 209 voltage is redistributed, so that its main part is applied to a film attached to the positive electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The distribution of polarization in such a film is quite homogeneous (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12), although the effect of the negative charge injec- tion is still considered as a thin non-polar layer near the negative side of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The top film was completely not polarized because there was a very low field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Similarly, one film in a three layer and two films in four-layered experiments are also not polarized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' a) Polarization Charge Ec Field Charge After short-circuiting b) Charge Charge After short-circuiting Ec Field Polarization Polarization Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Schematic diagram showing distribution of volume charge, field strength and ferroelectric polarization during corona poling in the case of (a) monopolar in- jection of negative charges and (b) separation of internal positive and negative charge carriers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The average field strength is equal to the coercive field Ec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Also shown is the distribution of localized charge after completion of poling and short circuiting of the sample The results of our measurements on P(VDF-TFE) films coincide with the results obtained from multilayered experiments on PVDF films poled by the thermoelectret method [35], but the explanation of this phenomenon is 210 different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The increase of the pyroelectric and piezoelectric activities near the positive electrode was attributed [35] to the effect of the positive charge injection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We believe that, according to the theory of injection currents [25], the heterogeneity of the field and hence polarization is due to injection of the negative charges, but not the positive ones, as previously thought [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This is considered normal if the charge is injected either from a real met- al electrode, or from a virtual electrode formed on the surface of the sam- ple bombarded by electrons and ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, our results indicate that the virtual injecting electrode can also be formed on a surface that was neither metallized nor bombarded by ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Exhaustion of polarization at the nega- tive side of the samples shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12, 14 (b), and 15 (b) proves that in all these cases, a negative charge is injected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Transition zones It is worth analyzing the behavior of the space charge after the com- pletion of poling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Immediately after a short circuiting, the average field in the sample becomes zero, but the local field still exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Therefore, mobile charges are redistributed under the action of this field until the field be- comes zero at any point of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The characteristic Maxwell relax- ation time for this process is given as 0 / g τ = ε ε , (15) where g is the explicit conductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Considering the typical values of g = (10–11–10–12 Sm/m [12]) for PVDF and its copolymers, we obtain τ ≈ 10–100 s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The real value of τ is even lower, since additional carriers are introduced during poling, and the apparent conductivity increases accord- ingly, as can be seen from equation (14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' From equation (13) it follows that under conditions of equilibrium (E(x) = 0), the spatial charge ρ(x) can be localized only at the boundaries of the polarized zones where the derivative dP/dx ≠ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) ( ) / (t ) x dP x dx ρ = > τ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (16) It is clear from equation (16) that thickness of the transition zone where the polarization decreases from its maximum value to zero, depends on the density of the charge, therefore, the higher the density of the charge, the narrower the transition zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The thickness of the transition zone cannot be measured with a high pre- cision by the PPS method, since its resolution (2 μm) is comparable to the thickness of the zones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, these values can be estimated by compar- 211 ing the growth time of the measured electrical signal and the pressure step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The first in all cases was longer than the last, indicating that the transition zones are thicker than 2 microns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' For example, the most delicate transition zones (4–5 μm) are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12 and 13 (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The corresponding times of the electrical signal grows and the pressure step are 2–3 ns and 1 ns, re- spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is known that any polarization heterogeneity creates a polarization charge with the density of dP(x)/dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This charge creates a depolarizing field, which tends to switch the ferroelectric polarization back to its original state after the completion of poling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The residual polarization can be stable only if the depolarization field is compensated or neutralized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We believe that in the case of the ferroelectric polymers, the compensation is carried out by the spatial charge ρ(x) trapped in the transition zones, by which the polarized part of the sample is separated from the not polarized part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Since the po- larization charge dP(x)/dx and the real charge ρ(x) are equal to each other (according to equation (16)), the depolarizing field is completely compen- sated, so that E(x) = 0 everywhere in the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We consider the existence of the transition zones in conjunction with compensating spatial charges as a general feature of poled P(VDF-TFE) and, probably, of all other ferro- electric polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Presence of the spatial charge in the transition zones is a guarantee of a high stability of the residual polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Near-to surface regions We observed two types of polarization profiles in near-to-surface zones of P(VDF-TFE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The residual polarization was zero to a certain depth, as can be seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10, 11, 14 (b), 15 (a) and 15 (b) near the negative sur- face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In other cases, Pr = 0 near the positive surface, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10, 11, 12, 13 (b), 14 (b), 15 (b) or near the negative surface in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12, 13 (a), 13 (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is clear that zones of the first type are created due to the massive injection of negative charges during poling, because the field near the injec- tion surface is reduced and the ferroelectric polarization is not formed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The thickness of the not polarized zone depends on the depth of the injected car- riers’ penetration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The zones are particularly wide in the case of moderate poling fields, as can be seen from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10, 11, 15 (a) and 15 (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' On the other hand, if the polarizing field strength is high, the near-to-surface zones are very narrow if the negative charges are not injected deeply into the volume (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12, 13 (a), 13 (b), 14 (a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In some cases, the separation of the intrinsic charge carriers dominates over the external injection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Then there are two polarization peaks at the two 212 sample surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Not polarized near-to-surface zones are either very narrow or not observed at all (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13 (a) and 14 (a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' According to our results, it can be concluded that a certain time is required for the injected charge for deep penetration into the bulk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This can only be done if the pre-poled regions are not polarized, for example in the case of low or moderate electric fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, if the ferroelectric polarization is already formed near the surface, as in the case of a high field, the injected charge cannot easily pass through a polarized region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It seems that the effective conductivity of the polarized regions is much lower than that of not polarized ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The second type of near-to-surface zones with rather high polarization can be seen near a met- allized surface attached to a positive electrode during poling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The role of a positive electrode in the accumulation and distribution of polarization has been widely discussed since the discovery of the inhomogeneous distribution of piezoelectricity and pyroelectricity in PVDF [35], and many contradic- tory explanations of this phenomenon were proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Our measurements show that the maximum polarization appears in all metallized samples near the positive electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This means that the conditions are favorable both for the rapid development of ferroelectric polarization, and for its stabilization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Positive charges are either not injected or deeply trapped very closely to the surface creating good conditions for compensating the depolarizing field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' At the same time, the trapped charges do not allow the attachment of a highly polarized zone directly to the electrode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The PPS method with a resolution of about 2 μm cannot provide more information about the fine structure of near-to-surface zones, but this can be achieved by using the LIMM method [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Polarization profiles in uni- formly electrified P(VDF-TFE), measured by this method, are present- ed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We used the same specimens as those for which the results obtained by the PPS method are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13 (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is known that the resolution of the LIMM method is about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 μm near the illuminated electrode [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' As can be seen from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 17, the polarized zones are not directly at- tached to the positive and negative surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The transition zones consist of thin layers where the polarization drops from maximum to zero and is supplemented by a completely not polarized layer of about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 μm thick- ness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The applied voltage is distributed non-uniformly between layers in the case of multilayered samples poling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Only the film near the positive electrode shows a high and fairly uniform polarization, while the upper films remain not polarized indicating that the injected charge permeates 213 the entire thickness of the film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Therefore, to obtain a uniformly polarized P(VDF-TFE) copolymer film in a moderate field, it would be advisable to cover the main sample during poling with another auxiliary film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the case of high poling fields, the residual polarization is homogeneous, since injections of charges are suppressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' But even in this case, the po- larized part of the volume is separated from the sample surfaces by transi- tion zones where compensating charges are trapped.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A thin layer of about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 μm thickness always remains completely not polarized near the sample surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Distribution of polarization measured by the method of the modulated intensity of laser radiation in near-to-surface regions of a nominally well-poled P(VDF-TFE) film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The conditions for poling were the same as for the sample shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Coordinate x = 0 corresponds to the negative side of the film 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Effect of temperature on distribution of ferroelectric polarization Recently, it has been shown that a high stability of the residual polariza- tion in PVDF and P(VDF-TrFE) is due to interaction of the polarization with the injected charge trapped at the boundaries of crystallites or macro- scopic polarized regions [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In both cases the polarization and the space charge form a stable and a self-consistent system in which the latter plays a decisive role.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Assum- ing Debye’s approximation for relaxation and the continuous distribution (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' units) 12 16 20 x (μm)214 of activation energies for the charge trapping, Eisenmenger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' received such a distribution for PVDF and P(VDF-TrFE) [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Our purpose was to find out how the bulk charge affects the thermal stability of the residual polarization in P(VDF-TFE) copolymer which also belongs to the class of the ferroelectric polymers, but is much less studied than PVDF and P(VDF-TrFE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' To do this, we measured the polarization profiles in P(VDF-TFE) sam- ples as a function of temperature by performing the linear heating from 20 °C to the melting point of crystallites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The activation energy was calcu- lated by applying our experimental data and the theoretical model proposed in [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The obtained results were compared with those that are known for PVDF and P(VDF-TrFE) copolymer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The samples were cut from experimental batches of P(VDF-TFE) 20 μm thick copolymer films containing more than 90 % of the ferroelec- tric β-forms in the crystalline phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Aluminum electrodes with a diameter of 5 mm and a thickness of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='15 μm were deposited on both sides of the samples by thermal evaporation in vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Poling was carried out either by direct application of high voltage (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 kV at 20 °C for 2 min) or by thermo- electret method (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 kV at 85 °C for 10 min and fast cooling to 20 °C under the applied voltage).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The polarization of the field in both cases was three to four times greater than the coercive field, which is 35–40 MV/m in P(VDF-TFE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The resid- ual polarization profiles in the direction of the sample thickness were mea- sured with a repetition rate of about 100 Hz using the PPS method, while the temperature was linearly increased at a rate of 3 K/min from 20 °C to the melting point of the crystallites, which turned out to be 134 ± 2 °C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is established that the distribution of polarization in the thickness direction is rather uniform, except for areas close to the electrode zones, where the polarization decreases from the maximum to the low value (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The profiles of polarization at all temperatures were slightly asymmet- ric, with a maximum located near the positive electrode, similarly to that observed in other ferroelectric polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We used these maximum values for evaluating the thermal stability of the residual polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' From the data presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 19, it is clear that the polarization in P(VDF-TFE) breaks down with the temperature throughout the studied range almost lin- early decreasing from the maximum at room temperature to zero at a melt- ing point (134 ° C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This behavior is significantly different from PVDF and P(VDF-TrFE) where the polarization decreases only when the temperature exceeds 90 °C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 215 0 5 10 15 20 25 0 1 2 3 4 5 (a) 136 119 98 81 63 47 32 18 Pr (\uf06dC cm 2) x (\uf06dm) 0 5 10 15 20 25 0 2 4 6 8 10 (b) 134 126 113 101 84 72 61 49 37 18 Pr (\uf06dC cm 2) x (\uf06dm) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Spatial distribution of polarization at different temperatures in P(VDF-TFE) films poled (a) by direct application of the high field and (b) by the thermoelectret method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Zero on the axis of the thickness corresponds to the negative surface of the sample during processing It is advisable to use the Debye approximation for the relaxation of po- larization with the temperature dependence of the decay constant corre- sponding to the Arrhenius law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Then, the current of depolarization ia(T) in the case of one activation energy is [38]: [ ] 0 0 0 0 ( ) / exp( / ) exp exp( / ) a T T i T dP dT h f a T P h f a T dT = − = \uf8ee \uf8f9 = ⋅ − ⋅ − ⋅ − \uf8ef \uf8fa \uf8f0 \uf8fb ∫ , (17) where h is the heating rate, fo is the proper frequency, Po is the initial value of polarization at To, a = A k, where A is the activation energy, k is Boltzmann’s constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Taking into account that energy is continuously distributed on the surface of the polarized crystallites surrounded by a disordered amorphous phase, one can conclude that the energy spectrum of traps is, most likely, continuous, rather than discrete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Therefore, the total depolarization current i(T) is a superposition of all relaxation components: 0 ( ) ( ) ( ) a i T g a i T da ∞ = ∫ , (18) 216 where g(a) is the distribution function of activation energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It was shown that the depolarization current i(T) calculated from the experimental curve P(T) is an image of the distribution function g(a): 0 40 80 120 160 0 2 4 6 8 10 (b) (a) Pr (\uf06dC cm 2) T ( 0C) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The value of residual polarization in P(VDF-TFE) obtained experimentally (points) and theoretically (solid lines) depending on (a) poling in a high field and (b) b the thermoelectret method The results of calculations based on experimental data of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 19 are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is clear that the high-temperature behavior of the P(VDF-TFE) copolymer is regulated by two relaxation processes characterized by signifi- cantly expanded energy levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The low-temperature peak in thermoelectret samples is slightly shifted to lower energy, whereas the high-temperature peak does not affect by the heat treatment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The relationship between the values of the two peaks in P(VDF-TFE) differs from PVDF [38] where the second peak is more advanced than the first one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Comparing the curves in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20 (a) and 20b, one can see that there is no significant difference in values and distribu- tion of the activation energies in the samples polarized in a high field strength and by the thermoelectret method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This indicates that the residual polariza- tion in P(VDF-TFE) is not thermally frozen, as in the case of ordinary polar 217 thermoelectrets, but it is stabilized, most likely, by the field of the trapped charges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' P(VDF-TFE) has two components of polarization, namely: a ferro- electric component and an electret component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The first one is concentrated in the crystalline phase, and the second is localized in the amorphous phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Therefore, the two peaks shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20 can be related to the relaxation of these polarization components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A similar behavior was observed in PVDF and P(VDF-TrFE) copolymer [38] indicating that this phenomenon is likely to be common in the whole class of the ferroelectric polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) ( ) i T g mT ∝ , (19) where m is a constant value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It is known that the ferroelectric polarization is stable only when the de- polarizing field is somehow neutralized or compensated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In the ferroelectric polymers, this compensation is performed by trapped charges [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0 30 60 90 120 150 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='06 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='6 g(A) (x10 3) (a) A (eV) dP/dT (nC cm 2 K 1) T ( 0C) 0 30 60 90 120 150 0 40 80 120 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='6 g(A) (x10 3) A(eV) (b) dP/dT (nC cm 2 K 1) T ( 0C) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The temperature dependence of the depolarization current i (T) = dP / dT and the distribution function of the activation energy in P(VDF-TFE) calculated depending on (a) poling in a high field and (b) Since the charge is deeply trapped and the binding energy is in the range of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='65–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='35 eV, as can be seen from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20, the spatial charge effectively compensates the depolarizing field in the crystals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' This explains the high polarization stability at room temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' According to our calculations, based on the data of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20, polarization is expected to decrease to 90 % of its initial value for about one year.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 218 The model of the continuous distribution of activation energies was ver- ified by calculating the dependence P(T) by using the data given in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The results of the calculations shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 19 by solid lines agree with the experimental data indicating that the thermal stability of the residual polar- ization in P(VDF-TFE) and, probably, in other ferroelectric polymers, is indeed controlled by the trapped volume charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Conclusion Results of experimental study of the polarization distribution uniformity in ferroelectric polymer films over the thickness of the samples are presented in this article presents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' We selected typical polymeric ferroelectrics, namely, polyvinylidene fluoride (PVDF) and its copolymer with trifluoroethylene P(VDF-TFE) as objects of the study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The measurements were carried out by a modern sensitive piezoelectric generated pressure step method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It has been found that the polarization uniformity substantially depends on the value of the applied electric filed during initial poling of the films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' the distribution of polarization was inhomogeneous with a maximum near the positive electrode in the case of weak and medium applied fields close to coercive value of the field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A very important feature has been discovered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It appeared that the uni- formity of polarization cannot be improved even by the subsequent applica- tion of very strong fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' However, if the initial poling of a fresh sample has been carried out in strong fields, then the uniform polarization distribution has been formed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The features of the P(VDF-TFE) copolymer electrified in corona discharge have been investigated as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Phenomenological models of the process- es occurring during the formation of polarization in ferroelectric polymer films have been developed for clarifying physical processes responsible for the formation of the polarization distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' REFERENCES 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Day G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Hamilton C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 44, 65 (1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' De Reggi A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Broadhurst M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Ferroelectrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 194, 351 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Sessler G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Berraissoul A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Ferroelectrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 206, 489 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Sessler G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (еd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ), Electrets — v.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Sergeeva A E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Marat-Mendes J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Ferroelec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 294, 93 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 7, 543 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Sessler G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Das-Gupta D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' et al.' 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Fedosov S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Solidi, Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 114, 435 (1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 83, 5870 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Fedosov S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Solidi, Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 114, 435 (1989) 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Sessler G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Das-Gupta D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Electr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Insul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 27, 872 (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Fedosov S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Butenko A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 9th Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' & Techn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thin Films, Ivano-Frankivsk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 45 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Furukawa T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Colloid Interface Sci.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Lines M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Glass A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Principles and Applications of Ferroelectrics, Oxford University Press, (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 28.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Gerhard–Multhaupt R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', IEEE Annual Report CEIDP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 68 (1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Giacometti J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Lang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' and Das-Gupta D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 59, 2151 (1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ploss B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Bianzano O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 8th Intern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Symp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Electrets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 211 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Kussner B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 8th Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Symp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Electrets, 594 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 220 Розділ ІІ АВТОМАТИЗАЦІЯ ТА УПРАВЛІННЯ ТЕХНОЛОГІЧНИМИ ПРОЦЕСАМИ ТЕХНОЛОГІЧНИЙ РОЗВИТОК СУДНОПЛАВСТВА, СИСТЕМ ШВАРТУВАННЯ СУДНОПЛАВСТВА МАЙБУТНЬОГО Пунченко Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Цира О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Водний транспорт був і існує як провідний елемент системи світової еко- номки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Існує постійне збільшення морського та річкового перевезення, а та- кож вимоги до якості вантажного перевезення шляхом водного транспорту (своєчасність, безпека, надійність), які змінюються у напрямку поліпшення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розвиток відбувається з метою використання автономних систем, які є од- нією з найбільш вагомих змін, що спостерігаються в морській промисловості.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У роботі наведено огляд систем управління безекіпажними суднами (кора- блями), де людський фактор не впливає на рішення, що приймаються.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Пред- ставлені переважаючі складові інтелектуальної системи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наведено види ав- томатизованих систем швартування: лазерні, вакуумні, магнітні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Системи швартування знижують ризик перевищення швидкості судна за рахунок зни- ження впливу людського чинника при швартуванні, знижують вплив оцінки поточної ситуації зближення судна з причалом, обирають режими і наочно відображають робочий процес за визначеною ситуацією, підвищуючи тим самим ефективність системи в цілому.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В результаті огляду зрозуміло, що у світі немає галузі економіки, яка в останні роки не вплинула б на цифрову трансформацію, а телекомунікаційні компанії зробили достатньо, щоб розширити цей спектр послуг.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тим часом у морській промисловості у світі цифрова трансформація робить лише перші кроки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основою для цього є канали зв’язку, без яких передача даних у принципі неможлива.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На воді це завдання є найбільш складним, оскільки волоконно- оптичний кабель не може бути підведений до судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тому на річці та морі є необхідним супутниковий зв’язок, існує суттєва потреба його використання не тільки для комунікацій та цифрових розваг на борту, а й для моніторингу стану судна та вантажу, можливості дистанційного управління, контролю бункерних суден, питання безпеки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Звідси випливає, що безекіпажний флот буде використовувати інтегровані автономні системи управління, які мо- жуть керуватися оператором на березі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Water transport has been and exists as a leading element of the world economy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' There is a constant increase in sea and river transport, as well as requirements for 221 the quality of freight transport by water transport (timeliness, safety, reliability), which are changing in the direction of improvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The development is taking place with the aim of using autonomous systems, which is one of the most signif- icant changes observed in the maritime industry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The paper provides an overview of control systems for unmanned vessels (ships), where the human factor does not affect the decisions made.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The predominant components of the intellectual system are presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The types of automated mooring systems are given: laser, vacuum, magnetic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Mooring systems reduce the risk of over-speeding of the vessel by reduc- ing the influence of the human factor during mooring, reduce the impact of assessing the current situation of the ship’s approach to the berth, select modes and visually reflect the working process according to the current situation, thereby increasing the efficiency of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' As a result of the review, there is no industry in the world that has not affect- ed digital transformation in recent years, and telecommunications companies have done enough to expand this range of services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Meanwhile, in the marine industry, in the world, digital transformation is only taking its first steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The basis for this is communication channels, without which data transmission is, in principle, impos- sible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' On the water, this task is most difficult because the fiber-optic cable cannot be connected to the vessel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Therefore, on the river and sea, satellite communication is necessary, its use not only for communications and digital entertainment on board, but also for monitoring the condition of the vessel and cargo, remote control capa- bilities, control of bunker vessels, security issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' It follows that the unmanned fleet will use built-in autonomous control systems that can be operated by the operator ashore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для програми розвитку перспективних шляхів підвищення за- гальної безпеки мореплавання, в умовах зростання інтенсивності морського судноплавства спостерігаються тенденції збільшення кіль- кості смертельних випадків від морських аварій [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Однією з причин цього є людський чинник.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оскільки в інноваційному суспільстві така галузь як судноводіння при зародженні визначила себе як інновацій- на.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такому визначенню є підтвердження, а саме група MariNet, яка створена в рамках Національної технологічної ініціативи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Група змо- гла об’єднати великі компанії і невеликі стартапи у галузі морських високих технологій, наукові центри, офіційні органи і внз [3], що представлені соціуму як інтелектуальні автономні системи, які є ра- дикальними змінами в судноплавній індустрії.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це інтелектуальні сис- теми, які приймають рішення без втручання ззовні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інтелектуальні системи стали базисом для створення такого напрямку як безекіпаж- не судноводіння, де використовується комбінація дистанційного й автономного управління, яке зводить до мінімуму людський чинник у безпеці судноводіння.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 222 Основи теоретичних та практичних наукових досліджень у галузі інформаційних технологій та систем судноплавства дуже детально представлені в роботах таких вчених: A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сазонова (математич- не та програмне забезпечення автоматизованих систем управління суднами), С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Смоленцева (основи будівельних систем інтелек- туального управління), С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Руда (системи моніторингу та управ- ління суднами технічного та допоміжного флоту), I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Г.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Малюгіна, В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' І.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Комашинського (питання будівництва транспортних сис- тем), Д.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Скорошодова (інтегровані системи управління судном), A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сикарева (стійкі системи радіозв’язку), A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Диди (складні системи), а також іноземних вчених, таких як Ch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Liu (автоматизо- вані системи управління кораблем), М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Хойхтяя (автономні системи управління, супутникові зв’язки), Е.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Топп (дистанційне управлін- ня системами), Р.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Польвара (системи технічного бачення) та інші.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У своїх роботах автори заклали теоретичну та практичну базу, яка сприяє підвищенню ефективності функціонування та розвитку вод- ного транспорту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вважається, що судна без екіпажу будуть дешевшими, безпечні- шими і будуть менше забруднювати навколишнє середовище.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' А ідея і обґрунтування ідей їх створення базується на кількох основних по- ложеннях: Положення 1 — за відсутності екіпажу вартість підтримки судна може бути зменшена на 30–40 %;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Положення 2 — за відсутності екіпажу макет і архітектура судна значно спрощуються, що тягне за собою зменшення вартості будів- ництва та обслуговування судна;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Положення 3 — вартість підготовки фахівців судна може бути зна- чно зменшена;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Положення 4 — досягнення науки та технологій свідчать, що з тех- нічної точки зору фундаментальних обмежень завдання не має;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Положення 5 — розробка та реалізація забезпечення кораблів на- лежить до нового напрямку науки і техніки, який об’єднує та сприяє зростанню творчої діяльності наукових, дизайнерських, освітніх та промислових організацій галузі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Положення 6 — будівництво та реалізація військових суден, зда- ється, є довгим багатоступеневим процесом, що включає поступову зміну структури флоту, яка складається з традиційних суден, що об- слуговуються екіпажами, і що є контрольованими віддалено або по- вністю автономно заданою програмою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 223 Перевага — це давня професія, яка має багато століть.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зрештою, в доісторичні часи люди подорожували до інших берегів на човнах, таким чином поступово зміцнюючись на землі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основи доставки стародавніх артефактів були на практиці, тому що у них не було сучасної теоретичної бази, підручників та карт.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Першими людьми- навігаторами були фінікійці, знання яких починають свій шлях з 15 століття, наприклад, лоцманом Васко да Гамы Ибн Маджид був накопичений досвід: кожен, хто хоче впоратися з елементами моря, повинен розбиратися в румбах та фазі місяця, відстанях та напрямках.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Величезна частина нашої планети покрита водою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тому можна впевнено сказати, що морський транспорт ніколи не стане застарі- лим, незалежно від того, як розвивається наземне та повітряне облад- нання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Щоб подолати моря та океани, потрібні грамотні судноводії, яким добре відомі пристрої їхнього судна, а також характер нестійко- го елемента води.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В даний час безпілотні судна відповідно до міжнародних конвен- цій є незаконними.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Щоб підтвердити таке твердження, ми дамо неве- лику оцінку міжнародно-правовим актам, які встановлюють вимоги до стану транспорту та флоту, а також його експлуатації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Найбільші зусилля в цьому напрямку були зроблені Міжнародною морською організацією та Міжнародною організацією праці.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Почи- наючи з сорокових років, ці організації розробили цілий ряд міжна- родних конвенцій безпеки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При розробці і застосуванні зазначених конвенцій функції управління залежать від двох відповідних вимог.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перш за все, це стан плавання судна в залежності від прапора.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Другий координуючий орган повинен бути спеціалізованою організацією — класифікаційним товариством.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідальність за виконання вимог конвенції покладається на власника судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Однак практика пока- зала, що всі суворі вимоги до суден були розроблені міжнародними організаціями, ці вимоги не були виконані.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Держава прапора з одно- го боку, зацікавлена особа і намагається забезпечити судновласників найбільш сприятливими умовами праці з економічної точки зору, з іншого боку, держава прапора не завжди має можливість здійсню- вати ефективний контроль стану її судна і його роботи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідно до вищесказаного був введений нагляд з боку класифікаційних това- риств різних країн.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для цієї мети був розроблений Міжнародний ко- декс з управління безпекою (ISM-Code).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Його головна мета полягає в тому, щоб забезпечити безпеку на воді.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 224 Міжнародні організації, що регулюють безпеку судноплавства Після Другої світової війни і створення ООН суспільство прийшло до висновку про необхідність впровадження авторитетної міжнарод- ної організації в області безпеки судноплавства.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' І саме такою органі- зацією в 1948 році стала Міжнародна морська консультативна органі- зація.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У 1973 році організація отримала назву Міжнародної морської організації (ІМО).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вона функціонує в рамках ООН.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Її штаб-квартира знаходиться в Лондоні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Міжнародні організації безпеки судноплавства: ILO — Міжнародна організація праці;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ICF — Міжнародна палата доставки;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ISF — Міжнародна федерація судновласників;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' INSA — Міжнародна асоціація судновласників;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' МАК — Міжнародна асоціація класифікаційних товариств;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' IALA — Міжнародна асоціація маячних служб;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' IPH — Міжнародна асоціація портів та гаваней;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' МСЕ — Міжнародний телекомунікаційний союз;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' CIRM — Міжнародний комітет морського радіозв’язку;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' IMPA — Міжнародна асоціація морських лоцманів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' IFSMA — Міжнародна федерація асоціацій морських капітанів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ICFTU — Міжнародна конфедерація профспілок вільної торгівлі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' WMO — Всесвітня метеорологічна організація;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ISO — Міжнародна організація стандартизації;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ICAO — Міжнародна організація цивільної авіації;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ІМО — Міжнародна морська організація.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Верховний орган Міжнародної морської організації — Асамблея, яка регулярно відбувається кожні два роки і в якій беруть участь всі чле- ни організації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Рада проходить між зборами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виконує функції Асамблеї та має право надавати урядам рекомендації щодо безпеки доставки та запобігання забрудненню.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Крім того, Рада організації має такі функції: 1) координація всіх органів організації;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2) надання робочих програм та бюджету для затвердження Асамб- леєю;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3) приймає і удосконалює обов’язкові до виконання і рекоменда- ційні міжнародні конвенції, кодекси, резолюції, протоколи, цирку- ляри і рекомендації;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4) звернення Генерального секретаря до Асамблеї;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5) запрошення та організація зустрічі з представниками інших ор- ганізацій для участі в Асамблеї.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 225 Призначення до Ради Міжнародної морської організації відбува- ється відповідно до правил: а) десять країн, що мають найбільший інтерес до міжнародної на- вігації;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' б) десять країн, що демонструють найбільший інтерес до міжна- родної морської торгівлі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' в) двадцять країн, які не включені до категорій а) та б), і ті, хто за- цікавлені морським транспортом або навігацією та представляють всі географічні райони світу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Комітети Міжнародної морської організації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На постійній основі працюють такі комітети: 1-й Комітет з питань безпеки (MSC — Maritime Safety Committee) є найважливішим у Міжнародній морській організації, він включає всіх членів організації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2-й Комітет з охорони навколишнього природного середовища (MEPC — The maritime Environment Protection Committee) включає всіх членів організації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Він був організований як збори, а в 1985 році отримав повний правовий статус незалежного.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ці два комітети допомагають у роботі 9 підкомітетів: – BLG — транспортування рідини та газів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – DSC — перевезення небезпечних та загальних вантажів та кон- тейнерів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – FP — захист від пожежі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – COMSAR — радіозв’язок, пошук та порятунок;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Nav — безпечна навігація;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – модернізація та обладнання кораблів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – SLF — стабільність, вантажний бренд, безпека риболовних су- ден;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – STW — стандарти навчання та навігаційні вимоги;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – FSI — впровадження держави.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3-й Юридичний комітет (Legal Committee) включає всі країни- члени Міжнародної морської організації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4-й Комітет з технічного співробітництва (Technical Co-operation Committee) — включає всі країни-члени Міжнародної морської ор- ганізації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5-й Комітет формальностей (Facilitation Committee) — відкритий для всіх країн-членів Міжнародної морської організації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Організовано в 1972 році як дочірнє відділення Ради з полегшення формальностей у міжнародній навігації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У 1991 році видав Додаток до 226 Конвенції Міжнародної морської організації як стандартного коміте- ту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Однак додаток ще не набув чинності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Секретаріат Міжнародної морської організації — складається з зо- внішніх співробітників та 300 співробітників головного офісу в Лон- доні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' IACS Міжнародна асоціація класифікаційних суспільств.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Міжнародну асоціацію класифікаційних суспільств організовано за рекомендацією Конвенції про вантажні морської конвенції 1930 року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У 1968 році вона отримала консультативний статус у Міжнарод- ній морській організації як неурядової організації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Члени Міжнародної асоціації класифікаційних товариств: ABS — Американське бюро доставки;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' BV — Бюро Верітас (Франція);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' CCS — Китайська спілка класифікації;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' DNV — Det Norske Veritas (Норвегія);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' GL — Німецький Ллойд;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' KR — Корейський реєстр суден;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' LR — Регістр судноплавства Ллойда (Англія);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' NK — Ніппон Кайджи Кіокай (Японія);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' RINA — Італійський морський регістр;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' RS — Російський морський реєстр судноплавства.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Асоційовані члени: CRS — Хорватське судноплавства;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' IRS — Індійський реєстр судноплавства.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основні цілі: – забезпечення безпеки людського життя в морі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – забезпечення плавання в безпеці;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – забезпечення надійного перевезення вантажів морем та вну- трішніми водними шляхами;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – запобігання забруднення навколишнього середовища.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для досягнення цих цілей правила, засновані на наукових дослі- дженнях, розробляють та вдосконалюють вимоги міжнародних кон- венцій та кодів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ITU — Міжнародний телекомунікаційний союз.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 24 травня 1844 р.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Самуїл Морзе надіслав перше повідомлення телеграфною лінією між Вашингтоном та Балтімором.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 17 травня 1865 р.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перша Міжнародна телеграфна конвенція була підписана в Парижі між 20 країнами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На підставі цієї Конвенції було створено Міжнародний телеграфний союз.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Через заснування союзу ця конвенція зазнала знач них змін — в 227 1876 році увійшов телефон, у 1896 р.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' — радіолокація.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зміни включе- ні до Конвенції 1903 року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У 1906 р.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перша радіотелеграфна конвен- ція була підписана в Берліні на першій конференції з радіотехніки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У Додатку до цієї Конвенції прийняті перші правила для радіозв’язку, які пізніше були оновлені і тепер відомі як «Правила переміщення».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У 1920 році почалися перші радіопередачі, а в 1927 році міжнародні радіослужби схвалили розподіл частот та правил між різними країна- ми та користувачами радіозв’язку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У 1932 році на Мадридській кон- ференції були поєднані міжнародні конвенти.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Об’єднана конвенція була названа міжнародною конвенцією телекомунікацій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Також з 1 січня 1934 року союз був перейменований на Міжнародний теле- комунікаційний союз (МСЕ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У 1947 році на МСЕ (ІТU) вступив до Егіди ООН, а головний офіс організації був переведений з Берна до Женеви.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У 1963 році був запущений перший супутник Synk-1, і почалася епоха супутникового зв’язку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На позачерговій конференції в Же- неві було представлено комунікацію з космічного спілкування, де було передбачено не тільки частоти супутникового зв’язку, а й ор- біти супутників зв’язку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У 1992 році ця комунікація була доповнена у зв’язку з новими особливостями цифрового зв’язку та викорис- танням негеостаційних супутників.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На пленарному засіданні додат- кової конференції ITU була реорганізована.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тут трьома секторами стали: — телекомунікаційна стандартизація (ITU-T), — радіозв’язок (ITU-R), — розробка телекомунікацій (ITU-D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На Кіотській конфе- ренції 1994 року був затверджений перший стратегічний план розви- тку союзу та комунікації у світі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Крім того, на цій конференції орга- нізовано глобальний телекомунікаційний політичний форум (WTPF) для вирішення політичних питань між країнами зв’язку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перший WTPF пройшов у Женеві у 1996 році з питань глобальних мобільних супутникових комунікацій, а другий — у 1998 році для надання теле- комунікаційного обслуговування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ILO — Міжнародна організація праці.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Міжнародна організація праці була заснована в 1919 році на базі Версальського договору в інтересах соціальної справедливості.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ця організація має структуру тризіркової моделі, яку представляють уря- ди, роботодавці та працівники (профспілки).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Цілі та завдання Між- народної організації праці були підтверджені в Декларації у Філадель- фії, прийнятій Конференцією Міжнародної організації праці в 1944 році.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Декларація містить принципи: 228 – робота не є товар;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – свобода думки та право Асоціації є важливим елементом для підтримки процесу;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – бідність в будь-якому місці створює небезпеку для загального процвітання;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – всі люди незалежно від раси, переконань та статі мають право шу- кати матеріального добробуту та духовного розвитку в контексті поваги до свободи та гідності, економічної підтримки та рівних можливостей.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У 1946 р.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Міжнародна організація праці стала першою спеціалізо- ваною організацією, яка взаємодіє з ООН.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У 1969 р.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Міжнародна орга- нізація праці була нагороджена Нобелівською премією миру.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перша конференція Міжнародної організації праці відбулася у жовтні–лис- топаді 1919 року у Вашингтоні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вона прийняла шість рекомендацій та 8 конвенцій, включаючи № 1 про 8-годинний робочий день.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Спочатку організація включала 42 держави, зараз — 175.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Конференції проводяться щорічно.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кожні два роки конференція приймає дворічну програму та бюджет.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Між конференціями адміністративна рада включає 28 представників урядів, 14 від працівників та роботодавців.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Секретаріат та штаб-квартира розташовані в Женеві.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основні стратегічні цілі: – розробка та впровадження норм та фундаментальних принципів та трудових прав;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – створення більш широких можливостей для жінок та чоловіків, щоб забезпечити гідну зайнятість;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – розширення охоплення та підвищення ефективності соціально- го захисту для всіх;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – зміцнення тристоронньої структури та підтримки соціального діалогу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Способи досягнення цілей: – розробка міжнародних заходів та програм для полегшення ре- алізації фундаментальних прав людини, вдосконалення роботи та життя, розширення можливостей зайнятості;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – розробка міжнародних стандартів праці (підтримка унікальної системи контролю за їх застосуванням), яка служить керівним прин- ципом національних органів у здійсненні цих заходів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – комплексна програма міжнародного технічного співробітни- цтва, розроблена та впроваджена з активним партнерством із засно- вниками, щоб допомогти країнам у здійсненні цих заходів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – підготовча, освітня та видавнича діяльність, сприяння реалізації всіх цих зусиль.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 229 З 1919 р.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Міжнародна організація праці прийняла 184 Конвенції та 194 рекомендації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основні міжнародні конвенції безпеки судноплавства.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перший досвід у створенні міжнародних домовленостей виник на підставі правил запобігання зіткненням, що з’явилися на почат- ку XIX століття.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Пізніше, з розвитком флоту та глобальними пере- везеннями, вони неодноразово переглядалися.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Остання конвенція MPPSS-72, затверджена 20 жовтня 1972 року, набрала чинності лише 15 липня 1977 року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Після трагічної смерті пасажирського лайнера «Титанік» була при- йнята перша міжнародна конвенція про захист людського життя на морі 1914 року, потім 2-га конвенція про захист людського життя на морі — була прийнята в 1929 році, 3-тя у 1948 році, 4-ту прийнято 17 червня 1960 року — набрала чинності 26 травня 1965 року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тепер чинна Конвенція Solas-74/78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вперше про забруднення навколишнього середовища світо- ва спільнота підіймає це питання у другій половині ХХ століття.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У 1954 р.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' з ініціативи Великобританії була проведена конференція з нафтового забруднення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вона прийняла Конвенцію OILPOL-54, яка вступила в дію 26 липня 1958 року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ця конвенція охоплювала два основних напрямки світового судноплавства, стосується тільки забруднення наф тою та її компонентами, корекція пройшла в 1962, 1969 і 1971 роках.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Після катастрофи танкера «Торрі Каньйон» в Ла-Манші в 1967 році світове співтовариство, оцінюючи суму збитку (попадання близько 120 000 тонн нафти в море), прийнли ряд різних міжнарод- них конвенцій: Основні міжнародні конвенції з безпеки і запобігання забруднен- ня навколишнього середовища: СОЛАС-74/88;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' SOLAS-74/88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Міжнародна конвенція з охорони людського життя на морі 1974 з додатковим Протоколом 1988 року: МАРПОЛ-73/78;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' MARPOL-73/78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Міжнародна конвенція з запобігання забруднення з суден 1973 року з додатковим Протоколом 1978 року: ПДНВ-78/95;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' STCW-95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 230 Міжнародна конвенція про підготовку і дипломування моряків та несення вахти 1978 року з Кодексом 1995 року: МППСС-72;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' COLREG-72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Міжнародні правила запобігання зіткнення суден на морі — 1972 року: САР-79;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' SAR-79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Міжнародна конвенція для збереження і порятунку — 1979 року: КГМ-66/88;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' LL-66/88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Міжнародна конвенція про вантажну марку — 1966 року зі зміна- ми 1988 року: ФАЛ -65;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' FAL-65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Конвенція про формальності в Міжнародних морських переве- зеннях вантажу — 1965 року: КНА-88;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' SUA-88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Конвенція про боротьбу з незаконними актами, спрямованими проти безпеки морського судноплавства — 1988 року: КСИ-89;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' SALVAGE-89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Міжнародна Конвенція про порятунок майна — 1989 року: КГО -69;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' CLC-69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Міжнародна конвенція про цивільну відповідальність за шкоду, заподіяну забрудненням нафтою — 1974 року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Конвенція СОЛАС-74/88 (SOLAS-74/88).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Конвенція була прийнята 1 листопада 1974 року на Міжнародній конференції з охорони людського життя на морі, а протокол до неї 10 листопада 1988 року на міжнародній конференції з гармонізованої системи експертизи та сертифікатів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Також 11 листопада 1988 року було прийнято низку виправлень до SOLAS -74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Комітет з питань безпеки на морі постійно працює над покращен- ням та вдосконаленням SOLAS-74/78, внесення змін до неї.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Конвенція СОЛАС (SOLAS) та протокол 1988 року до неї були підписані англійською, іспанською, китайською, російською та французькою мовами, а всі тексти рівноцінні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Офіційною мовою за- 231 лишається англійська, отже з розбіжностями англійська версія при- ймається як основа.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Конвенція СОЛАС (SOLAS) спочатку мала 8 розділів: I — загальні положення II-1 — конструкція — поділ на відсіки та стійкість, механічні та електричні установки II-2 — конструкція — захист від вогню, виявлення та пожежога- сіння.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нове видання було прийнято у грудні 2000 року, набрало чин- ності 1 липня 2002 року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' III — рятувальні інструменти та пристрої.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нове видання в 1996 році набрало чинності з 1 липня 1998 року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' IV — радіозв’язок.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нове видання затверджено в 1988 році.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Введен- ня чинності через запровадження ГМССБ з 1 лютого 1992 по 1 лютого 1999 року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' V — безпека мореплавання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нове видання було затверджено в груд- ні 2000 року, набрало чинності 1 липня 2002 року (стосується АІС).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' VI — перевезення вантажів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' VII — перевезення небезпечних вантажів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Затверджено Міжна- родною морською організацією у 2002 році, набрала чинності з 1 січ- ня 2004 року (була підсумована Кодексом перевезення небезпечних вантажів морем — UMDG-code).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' VIII — ядерні судна — затверджені Асамблеєю Міжнародної мор- ської організації в 1981 році.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наступні глави були додані пізніше: IX — управління безпечною експлуатацією суден.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Затверджено в травні 1994 року, набуло чинності 1 липня 1998 року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' X — заходи безпеки для високошвидкісних суден.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Затверджено в травні 1994 року, набуло чинності 1 січня 1996 року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' XI — спеціальні заходи щодо підвищення безпеки на морі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Затвер- джено в травні 1994 року, набуло чинності 1 січня 1996 року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' XII — додаткові заходи безпеки для навалочних суден.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За- тверджена в листопаді 1997 року, набуло чинності 1 липня 1999 року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основна мета конвенції SOLAS полягає в об’єднанні і зменшен- ні кількості стандартів для будівництва, обладнання та безпечного управління морських суден.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Головне управління з виконання вимог Конвенції лежить на урядах країн, під прапором яких кораблі пла- вають.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Конвенція СОЛАС також зобов’язує держави контролювати судна в портах навігації (Правило 4 глави XI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 232 MARPOL-73 / +78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Міжнародна конференція з запобігання забруднення моря, склика- на Міжнародною морською організацією в 1973 році, прийняла кон- венцію з запобігання забруднення з суден, яку в 1978 році було змінено відповідно до Протоколу на Міжнародній конференції з питань безпе- ки та запобігання забрудненню танкерами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В результаті вона була на- звана: «Міжнародна конвенція з запобігання забруднення з суден 1973 року, змінений в 1978 році протокол» або скорочено МАРПОЛ-73/78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Конвенція набула чинності 2 жовтня 1983 (Додатки I і II).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Правила, що охоплюють різні джерела забруднення з суден, ви- кладені в шести додатках до MARPOL -73/78: I Правила для запобігання забруднення нафтою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Чинні з 2 жовтня 1983 року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' II Правила для запобігання забруднення шкідливими рідкими ре- човинами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вступ в силу з додаванням 1985 на 6 квітня 1987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' III Правила запобігання забруднення шкідливими речовинами, що перевозяться морем в упаковці, вантажних контейнерах, знімних танках, автомобільних і залізничних цистернах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Чинні з 1 липня 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' IV Правила запобігання забруднення стічними водами із суден.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Чинні з 27 вересня 2003 року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' V Правила для запобігання забруднення сміттям з суден.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Чинні з 31 грудня 1988 року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' VI Правила запобігання забруднення атмосфери з суден.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Затвер- джена в вересні 1997 року, але в силу ще не вступила.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Деякі важливі правила та положення Додатку І MARPOL (правила запобігання забруднення нафтою).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У правилі 1 надано визначення: – «Нафта» означає мастило у будь-якій формі, включаючи сиру нафту, рідке паливо, мастило, що містить осади, масляні залишки та очищені нафтопродукти;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – «Нафто-вмісна суміш» означає суміш з будь-яким вмістом мас- тила;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – «Нафтове паливо» означає будь-яке мастило, що використо- вується як паливо для основних двигунів та допоміжних механізмів судна;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Танкер нафти «означає судно, побудоване або адаптоване для транспортування нафти оптом у вантажних приміщеннях;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – «Комбінований вантажний корабель» означає судно, призна- чене для транспортування нафти оптом або твердого вантажу оптом;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 233 – «Спеціальний округ» означає морську зону, де відповідно до ви- знаних технічних причин, що належать до його океанографічних та екологічних умов, специфіка доставки на ній вимагає прийняття спе- ціальних обов’язкових методів запобігання забруднення моря з мас- тилом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Спеціальні райони — це райони, перелічені у правилі 10 цього Додатку;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – «Інтенсивність миттєвого розливу» означає інтенсивність роз- ливу нафти в літрах на годину в будь-який час, поділена на швидкість судна в вузлах;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – «Танк» означає закрите приміщення, призначене для транспор- тування рідин;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – «Бортовий танк» означає будь-який резервуар, що прилягає до бортової обрізки судна;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – «Центральний танк» означає будь-який резервуар, розташова- ний всередині судна з поздовжнім пересуванням;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – «Стійкий грязьовий танк» означає будь-який резервуар, спеці- ально розроблений для збору залишків з танків, промивання води та інших масляних сумішей;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – «Чистий баласт» означає баласт у танку, який після останньо- го перевезення в ньому був очищений таким чином, що стік з цього танка, з нерухомого судна в чисту, спокійну воду в ясний день, не ви- кликає видимих слідів нафти на поверхні води;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – «Ізольований баласт» означає водяний баласт, прийнятий у тан- ку, який повністю відокремлений від вантажу або паливної системи;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – «Проникність приміщення» означає співвідношення об’єму приміщення, який може бути заповнений водою до загального обся- гу приміщення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Правило 9 показує обмеження для скидання нафти: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З урахуванням положень відповідно до правил 10 і 11 цього До- датка і пункту 2 цієї статті, заборонити скидання в море нафти або нафто-вмісних сумішей з суден, до яких цей додаток застосовується, за винятком випадків: а) з нафтового танкера, за винятком випадків, передбачених у підпункті (б) цього пункту: — танкер знаходиться за межами особливого району;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' — танкер знаходиться на відстані біль- ше 50 морських миль від найближчого берега;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' — танкер на своєму шляху;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' — миттєва швидкість скидання нафти не перевищує 30 літрів на морську милю;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' б) з судна валовою місткістю 400 рег.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' т або більше тонн валової місткості, крім нафтових танкерів, а також від машин- них приміщень нафтового танкера, відділень вантажного насоса, за 234 винятком тих пір, поки вміст нафти в стоці не змішується з мастилом та залишками вантажу нафти: – судно знаходиться за межами особливого району;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – судно знаходиться в дорозі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – вміст нафти в стоці без розведення не перевищує 15 частин на мільйон;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – на борту експлуатується устаткування для фільтрування нафти, що задовольняє пункт 17 правила 16 цього Додатку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Стосовно судна валової місткості менше 400 рег.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' т, крім нафто- вих танкерів, якщо судно знаходиться в особливому районі, адміні- страція повинна забезпечити, щоб воно було обладнане, наскільки це доцільно і практично можливо, пристроєм для зберігання залишків нафтопродуктів на борту і їх скидання в приймальні споруди або в море відповідно до вимог пункту I (б) цього правила.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У всіх випадках, коли в безпосередній близькості від судна або його сліду на поверхні води виявлено видимі ознаки нафти, уряди Сторін Конвенції повинні без зволікання розслідувати цей факт.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вуглеводневі радикали, які не можуть бути скинуті в море відпо- відно до пунктів 1 і 2 цього правила, зберігаються на борту і виванта- жують в прийомні об’єкти.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У правилі 10 Додатку I наведені методи запобігання забруднення нафтою з суден при плаванні в особливих районах: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це райони Середземного моря, Балтійського моря, Чорного моря, Червоного моря, район Затоки, Антарктична область і Аден- ська затока.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У спеціальній зоні забороняється викид в море нафти або сумі- ші, що містить нафту, з будь-якого нафтового танкера або судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Додаток V конвенції MARPOL (правила запобігання забрудненню сміттям з суден).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У правилі 1 визначено: – «сміття» означає всі види харчових, побутових та операційних відходів (усунення свіжої риби та її залишків), які утворюються в процесі нормальної роботи судна та підлягають постійному або пері- одичному видаленню, за винятком речовин, визначення або список яких наведено в інших додатках до цієї Конвенції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – «найближчий пляж».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вираз «від найближчого берега» означає оригінальну лінію, з якої, за даними міжнародного права, відрахо- вуються територіальні води відповідної території, за винятком пів- 235 нічно-східного узбережжя Австралії, де початкова лінія наведена в Конвенції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – «спеціальний округ» означає морську зону, де відповідно до ви- знаних технічних причин, що стосуються його океанографічних та екологічних умов, специфіка доставки на ній вимагає прийняття спе- ціальних обов’язкових методів запобігання забрудненню моря сміт- тям.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Спеціальні райони — це райони, перелічені у правилі 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У правилі 3 додатку V MARPOL наводяться умови для видалення сміття за межами спеціальних територій: а) заборонено викид у море всіх видів пластмас, включаючи син- тетичні кабелі, синтетичні риболовецькі мережі та пластикові пакети для сміття, але не обмежуючись ними;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' б) жодна шкідлива речовина, що перевозиться в упаковці, не може бути скинута за борт за жодних умов.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 25 морських миль від берегу для плаваючих і пакувальних мате- ріалів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12 морських миль для харчових відходів та іншого сміт- тя, включаючи паперові вироби, ганчірки, скло, метал, пляшки, осколки та аналогічне сміття;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' в) кидати в море сміття, зазначене в підпункті (b) (ii) цього правила, може бути дозволено, якщо таке сміття проходить через подрібнювач, і це зроблено до меж від най- ближчого берега, але в будь-якому випадку заборонено, якщо від- стань до найближчого берега становить менше 3 морських миль.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таке подрібнене сміття повинне проходити через поверхню з отво- рами не більше 25 мм.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідно до пункту 1 правила 4, забороняється використовува- ти будь-які матеріали, які підлягають застосуванню зі стаціонарними або плавучими платформами, розробкою та пов’язаних з ними про- цесами обробки в морі морських притулків мінеральних ресурсів, а також від всіх інших суден, зв’язаних з такими платформами або зна- ходиться в межах 500 м від них.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо сміття змішане з іншими відходами, видалення або скидан- ня яких підпадає під інші вимоги, то жорсткіші вимоги.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Скидання в море пластику й зол із пластику заборонене всюди.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У правилі 5, додаток V MARPOL наведені спеціальні зони для за- побігання забруднення сміттям: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для цілей цієї заявки спеціальні зони є областю Середземного моря,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' в районі Балтійського моря,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ак- ваторії Чорного,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' району Червоного моря і райони Затоки,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' морські ра- йони Північного моря і Антарктична територія,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' басейн Карибського 236 моря,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' в тому числі в Мексиканській затоці і Карибському морі,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ви- значення якого дано нижче: a) район Середземноморського моря означає Середземне море із затоками і морями,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' розташованими в ньому,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' обмежено з Чорно- го моря з паралельним 41º північної широти,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' а на Заході — Meridian 5º36’ Західної довготи перетину Гібралтарської протоки;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' b) район Балтійського моря означає Балтійське море саме по собі з Botnik і фінських бухт і з проходом в Балтійське море, обмеже- не паралельно 57° 44,8’ північної широти мису Скаген в Скагеррак протока;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' с) район Чорного моря означає саме Чорне море, межує з Серед- земним морем з паралельно 41º північної широти;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' d) район Червоного моря означає фактичне Червоне море з Су- ецьким, обмежене з півдня прямою лінією, що проходить між Рас- SI-ANS (12° 8,5’ північної широти, 43° 19,6’ східної довготи) і Husner Murad (12° 40,4’ ’північної широти, 43° 30,2’ східної довготи);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (Е) Район затоки означає морський район, розташований на північний захід від прямої лінії, що проходить між Рас-Ель-Хадда (22°30’ пів- нічної широти, 59°48’ східної Lension) і Рас-Ель-Fast (25°04’ північної широти, 61° 25’ східної довготи).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' e) район зони Північного моря: в Північному морі обмежено: (I) від Північного моря на південь — паралелі 62° північної широти, а на сході — Meridian 4° західної довготи;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (Ii) протоку Скагеррак, пів- денна межа якого визначається паралельно 57° 44,8 північної широти на схід від мису Скаген;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' і (W) Манш і підходи на схід від меридіана 5° західної довготи і на північ від Parallel 48° 30’ північної широти;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' g) Антарктичний район означає морський район, розташований на південь від паралельної 60’ південної широти;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' h) район Карибського басейну, як визначено в параграфі I статті 2 Конвенції про захист та розвиток морського середовища Карибсько- го басейну (Картахена та Індіас, 1998), означає Мексиканську затоку та Карибський басейн з бухтами та морями в них.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перегляд, зміну та доповнення MARPOL-73/78 доручено Коміте- ту захисту морського середовища.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' STCW-78/95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Конвенція STCW стала першим міжнародним документом з осно- вних правил про підготовку та дипломування моряків та несення вах- ти.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вона була прийнята 7 липня 1978 року, набрала чинності 28 квітня 1984 року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 237 Стаття II STCW-78 містить визначення, головні з яких: – «Партія» означає державу, за яку набрала чинності Конвенція;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – «Адміністрація» означає уряд, під прапором якого корабель має право плавання;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – «Диплом» означає дійсний документ, незалежно від того, як це було названо, виданий адміністрацією або її повноваженними, або визнаний адміністрацією на право його власника займати позицію, зазначену в цьому документі або дозволену національними прави- лами;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – «Власник диплому» означає особу, яка володіє дипломом на правовій основі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – «Організація» означає міжнародну морську організацію;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – «Морське судно» означає судно, відмінне від тих, що плавають виключно у внутрішніх водах у межах захищених вод або в безпосе- редній близькості від них, або в межах правил порту;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – «Риболовецьке судно» означає судно, що використовується для риболовлі, китів або інших живих ресурсів моря.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Правило I/1 Додаток до Конвенції 1978 року містить наступні визначення: «Капітан», «Старший помічник капітана», «Поміч- ник капітана», «Механік», «Старший механік», «Другий механік», «Механік-статер», «Радіооператор», «Особа звичайного складу».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це правило повинно бути виключено для безекіпажних суден.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Меморандуми про взаєморозуміння.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інститут контролю іноземних судів у портах, з метою встановлен- ня дотримання цими судами до звичайних вимог, виник на початку 80-х років у формі регіональної угоди ряду країн (Паризький Мемо- рандум взаєморозуміння щодо контролю суден державного порту).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Світ підписав та експлуатує наступні регіональні угоди про управ- ління портом: – Паризький меморандум — 01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='82 у Парижі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Латиноамериканська угода — 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='92 у Vina Del Mar (Чилі) (Винья-дель-Мар);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Меморандум Токіо — 01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='93 в Токіо;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Карибський меморандум — 09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='96 в Крісчех (Барбадос);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Середземноморський меморандум — 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='97 у Валетті (Мальта);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Меморандум Індійського океану — 05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='98 у Преторії (Півден- на Африка);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Меморандум Центральної та Західної Африки — 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='99 в Абу- джа (Нігерія);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 238 – Чорноморський меморандум — 07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2000 в Стамбулі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Регіональні угоди порту: – перевірка іноземних суден у портах;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – використання ідентичних засобів керування;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – застосування узгоджених процедур контролю;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – застосування домовленостей;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – взаємний обмін інформацією.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основні засоби контролю: – SOLAS 74/88;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – MARPOL 73/78;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – STCW 78/95;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – COLREG-72;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – LL-66/88;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – CLC-69;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Конвенція ILO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Особлива увага приділяється наступним кораблям: – пасажир, bulk;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – кораблі для перевезення небезпечних вантажів та забруднюю- чих речовин;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – відвідування порту вперше, або через 12 місяців та більшу пере- рву;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – прийшов з іншого порту з зауваженнями PSC;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – під прапором країн, що належать до «чорного списку».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' «Чорний список» — це список країн, судна яких після перевірки PSC були затримані в портах, що дозволяє адміністрації порту не об- тяжувати суда надмірними інспекціями.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У той же час таки суди бу- дуть перебувати під пильним контролем для запобігання можливим порушенням.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Постанова Міжнародної морської організації A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='787 (19) «Проце- дури контролю судів державою порту» була прийнята 23 листопада 1995 року, і є основним документом, що регулює процедуру перевірки суден у портах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Глава 1, Визначення, глава 2 регулює перевірки судових інспекцій у портах, глава 3 забезпечує процедури для більш детальної перевір- ки, глава 4 — арешти кораблів у порту навігації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Міжнародна конвенція для пошуку та порятунку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' SAR-79 Міжнародна система пошуку та рятування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Спочатку захоплене морем судно ставало видобутком прибережних мешканців і безжа- лісно грабувалося.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Світова спільнота вперше прийняла міжнародну 239 угоду про надання порятунку людям у морі в 1914 році в Конвенції про захист людського життя на морі, після катастрофи «Титаніка».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ця Конвенція була довірена судам, що знаходяться поруч.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тому частота 500 кГц та сигнал SOS були прийняті.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Окрім того, 3 хвилини мовчання були встановлені кожні 30 хвилин у радіо, а світовий оке- ан поділяється на 13 зон, через прослуховування ефіру в будь-який момент є безперервним.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наприкінці ХХ століття така система за- старіла, крім того на кораблях та літаках з’явилося нове радіооблад- нання, набравши чинності ГМССБ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тому постанова Міжнародної морської організації A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='406 (X) від 17 листопада 1977 року рекоме- дувала скликати конференцію для прийняття рятувальної конвен- ції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Конференція відбулася в Гамбурзі з 9 по 27 квітня 1979 року, де світова спільнота прийняла пошукові та рятувальні конвенції про море (SAR-79).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За рішенням 69-го засідання КБМ у травні 1998 року було прийнято нову заяву до Конвенції САР-79, яка набрала чинності з 1 січня 2000 року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За даними Конвенції SAR-79 голо- вна роль у пошуку та порятунку приділяється прибережним послу- гам — центрам рятувальних координацій (RCC), які повинні бути організовані в кожній країні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Терміни, що використовуються в SAR-79: пошук, пошукові та рятувальні зони, центр порятунку, рятувальні підцентри, продукт та рятувальний інструмент, аварійний етап, стагінальна невизначеність, стадія тривоги, стадія катастрофи, координатор у пункті дії.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Глава 2 Додатків до Конвенції SAR-79 регулюються міжнародни- ми стандартами для координаційних пошукових послуг та порятунку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При отриманні інформації про будь-яку особу, що страждає на ка- тастрофу у морі, або, страждає на морі, влада повинна вживати тер- мінових заходів для забезпечення необхідної допомоги.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На підставі цієї допомоги вона зобов’язана самостійно організувати або разом з іншими державами пошукові та рятувальні послуги, які повинні мати наступні основні елементи: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Правова база;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Призначення відповідального органу;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Організація наявних коштів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Засоби зв’язку;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Координаційні та виконавчі функції;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Процеси покращення послуг, включаючи планування, відноси- ни на національному та міжнародному рівнях;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Підготовка персоналу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 240 Пошукові послуги та рятувальні роботи в рамках пошукового та рятувального майданчика, межі яких узгоджуються між зацікавле- ними сторонами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сторони надають допомогу будь-якій людині, що потерпає від катастрофи у морі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вони виконують це незалежно від національної приналежності або статусу такої особи або обставин, в яких ця особа знаходиться.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Генеральний секретар надсилає інфор- мацію про рятувальну службу, яка повинна бути своєчасно скори- гована: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інформація про національні органи, відповідальні за пошукові та рятувальні послуги на морі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розташування CRS або інших центрів для забезпечення координа- ції пошукових та рятувальних операцій та засобів спілкування з ними;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інформація про межі пошукової та рятувальної зони та прибе- режних комунікацій у катастрофі та безпеки;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Введення основних пошукових та рятувальних методів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для забезпечення ефективності сторони забезпечують найбільш повну координацію з повітряними послугами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Там, де можна створи- ти RCC та JSC для цілей навігації та літака.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сторони забезпечують ви- користання єдиних процедур для цілей як морського та повітряного пошуку, так і порятунку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Координація в пункті дії, коли виникає інцидент: призначається координатор пошукових та рятувальних дій (SMC), який, як прави- ло, діє з RCC Rescue Center або Центр RSC RSC, який забезпечує ко- ординацію.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Обов’язки координатора (OSC): – координує дії всіх пошукових та рятувальних інструментів у пункті дії;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – планує пошукові та рятувальні операції, якщо план не був отри- маний від координатора дій (SMC);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – змінює план пошукових та рятувальних операцій відповідно до ситуації, інформує SMC;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – координує зв’язок у пункті дії;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – моніторинг виконання дій іншими засобами;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – забезпечує повне виконання операцій, приділяючи особливу увагу поділу всіх фондів як в ефірі, так і в морі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – періодично передає повідомлення SMC, відповідно до стан- дартної форми SITREP: – проводить детальний запис операції;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – інформує координатора дій (SMC) про можливість появи ко- штів, що більше не потрібні;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 241 – повідомляє координатору дій (SMC) кількість збережених;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – надає координатору дій (SMC) імен та точок призначення ко- штів по збереженню людей;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – звіт, який зберігається по кожному крокові;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – запитує додаткову інформацію з (SMC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідальність ко- ординатора на місці дії (OSC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Координатор на сайті Action (OSC) повинен отримати план дій якомога швидше від SMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тим не мен- ше, ОСС може розвивати свій власний план (залежно від обста- вин).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виконавці також повинні змінити план пошуку відповідно до екологічно змінної атмосфери, зокрема, коли вони виникають: прибуття додаткових засобів допомоги;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' отримання додаткової ін- формації;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' зміни погодних умов, видимості, умов освітлення тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Пошукові операції повинні починатися відразу після прибуття до місця порятунку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У разі виникнення мовних труднощів слід використовувати міжнародні сигнали та стандартні фрази Міжнародної морської організації для спілкування на морі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Запитуючи обов’язки, ОСВ повинен інформувати відповідну прибережну радіостанцію (CRS) або службу управління повітряним рухом (ATS), а також коорди- натора дій (SMC) з регулярними інтервалами або коли змінюється ситуація.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Національні пошукові послуги та рятувальні послуги.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кожна сто- рона розробляє відповідні процедури для загальної організації, ко- ординації та вдосконалення пошукових та рятувальних послуг.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для забезпечення ефективності пошукових та рятувальних операцій сто- рони повинні: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Забезпечити координацію використання наявних засобів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Встановити тісну співпрацю між організаціями в таких сферах, як операції, планування та підготовка персоналу, навчання та дослі- дження.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Співпраця між державами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сторони повинні координувати робо- ту своїх координаційних центрів, а також їх пошукові та рятувальні операції з сусідніми державами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При необхідності, координувати на- ціональні закони, сторони зобов’язані визнати їх територіальні води, територію та повітряний простір над ними для пошуку та порятунку людей.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сторонам, особливо якщо їх пошукові та рятувальні ділянки перекривають одна одну, необхідно укласти угоди про прийом ряту- вальних підрозділів на їх території або повітряному просторі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо не існує ніякої угоди між сторонами, якщо це необхідно, надається 242 запит, до якого сторони, відповідальні органи зобов’язані якомога швидше відповісти: – Негайно підтвердити отримання запиту;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Вказати умови, якщо такі є, згідно з якими рятувальні одиниці допускаються до території держави.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кожна сторона повинна автори- зувати свої процедури пошуку: – Просити допомогу з інших центрів координації, включаючи суд- на, авіацію, персонал, постачання тощо, які можуть знадобитися;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Дати будь-який дозвіл на доступ до своєї території або повітря- ного простору таких суден, авіації, персоналу або пропозиції;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Координувати з митними, імміграційними, санітарними та ін- шими органами влади необхідні заходи для прискорення рятування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кожна сторона гарантує, що такі центри координації забезпечують негайну допомогу іншим центрам, включаючи допомогу авіаційних суден, персоналу, постачання тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Системи суден для повідомлень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сторони надають на цілодобовій основі швидке та надійне отримання сповіщень про лиха в межах по- шуку та рятувальних районів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Будь-яка країна або декілька країн, що отримують повідомлення про страждання, зобов’язані: – негайно транслювати повідомлення відповідному центру ряту- вальної координації або рятувального підключення, а потім, наскіль- ки це можливо, допомагати забезпечити зв’язок у пошуках та поря- тунку;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – підтвердити сповіщення, якщо це необхідно.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для полегшення операцій пошуку та порятунку сторони можуть створювати систему суден, бажано на основі рекомендацій Міжнародної морської органі- зації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Система повинна надавати користувачам інформацію про рух кораблів: – план переходу;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – розташування судна;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – кінцеве повідомлення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У випадку катастрофи: – скоротити час між моментом втрати зв’язку з судном та почат- ком пошуку та порятунку, без сигналу катастрофи;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – швидко визначити судна, які можуть бути залучені до допомоги;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – вміти встановити меншу область пошуку;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – сприяти наданню термінової медичної допомоги або консуль- тації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Система суден повідомлень повинна задовольнити положення: – надавати інформацію про місцезнаходження, плани переходу;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 243 – дозволити відправити рух суден;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – отримувати повідомлення від учасників за певними інтерва- лами;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – бути простим у намірах і в операційних відносинах;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – дозволити стандартні формати, загальноприйняті на міжнарод- ному рівні та стандартному порядку повідомлення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Список національних контактних адрес.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Контактні адреси наці- ональних центрів, відповідальних за безпеку моря та запобігання за- брудненню від кораблів, публікуються Міжнародною морською орга- нізацією та оновлюються щорічно.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нова версія та адрес, як правило, затверджується на засіданнях Комітету з питань безпеки та Комітету з охорони морського середовища та поширюється циркулярно.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зазви- чай список складається з двох частин: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Короткий список національних органів влади (раніше MSC/ CHERC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='630), місцеві підрозділи національних інспекційних послуг, офіційні послуги, що працюють від імені держави, а також органів, відповідальних за розслідування аварій (раніше MSC/Цик542), та секретаріату Меморандумів про взаєморозуміння щодо контролю су- ден державою порту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перелік контактних адрес існуючих національних центрів, від- повідальних за прийом, передачу та обробку термінових повідомлень від кораблів зі шкідливими речовинами, включаючи мастило.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Список 1 повинен бути на кожному судні та в компанії в докумен- тації СУБ (план дій у надзвичайних ситуаціях).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Список 2 має бути на кожному судні в аварійних засобах, щоб запобігти забруднення мастилом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Коректування контролюється реєстром з річним обсте- женням.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Форма аварійного повідомлення про аварійні події в плані дій су- ден про надзвичайні ситуації: План дій судна в надзвичайних ситуаціях.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Форма початкового повідомлення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' SS (координати, широта, довгота) / DD (відстань до прибережно- го знаку).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' N С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' град.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' хв.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' E W град.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' хв.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' / град.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' мор.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' мілі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' EE курс град.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' / FF (швидкість, вузли) 1/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' L L (передбачуваний шлях).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ММ (слухаюча радіостанція).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' NN (дата та час наступного повідомлення, UTC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' День.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Години.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' хв.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' PP (вид та кількість вантажу/палива на борту).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 244 QQ (коротка інформація про недоліки/пошкодження).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' RR (коротка інформація про забруднення, включаючи оцінку втраченої кількості).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' SS (коротка інформація про погоду та морський стан).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Напрямок, вітер швидкість (на масштабі Бофорта) / напрямок, висота хвиль (м).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ТТ (дані для зв’язку з судновласником / оператором / агентом).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' UU (розмір і тип корабля).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Довжина: (м) / ширина: (м) / осад: (м) / тип.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' X X (додаткова інформація).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Коротка інформація про інцидент.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Необхідність допомогти ззовні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Дії вжиті.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кількість екіпажу та інформація про будь-які тілесні ушкодження.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інформація про страхову компанію.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інша інформація.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Коли можуть виникнути труднощі та обмеження, що обумовлені нерозумінням мови, повинні включати англійську мову з викорис- танням, коли це можливо, стандартних фраз міжнародної морської організації морських перевезень на морі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для того, щоб передавати детальну інформацію, англійська мова може бути використана на свій розсуд, а також використані міжнародні сигнали.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При їх вико- ристанні в тексті повідомлення відразу після літерного індексу необ- хідно внести відповідні вказівки про це.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нижче наведені додаткові дані для заповнення спеціальної таблиці.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' AA — назва судна, позивний або ідентифікаційні дані суднової ра- діостанції і прапор судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ВВ — група з 6 цифр, яка вказує день (перші дві цифри), години і хвилини (останні чотири цифри).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' СС представляє собою групу з чотирьох цифр, що вказує на ши- роту в градусах і хвилинах, а також знаки N (північ) або з S (південь), і групу з 5 цифр, яка вказує довготу в градусах і хвилинах, а також зна- ки Е (схід) або W (захід).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' DD є істинний пеленг (перші 3 цифри) і відстань в морських милях від чітко визначеної прибережної позначки (вказати берегову позначку).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' EE — істинний курс.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' FF — швидкість у вузлах і десятих вузла.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' LL є оцінений шлях.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При описі шляху необхідно давати ши- роту і довготу кожної поворотної точки, як і в СС із зазначенням 245 типу передбачуваного шляху між цими точками, наприклад, RL (по Loccodromia), ГК (на великій дузі окружності) або уздовж берегової лінії в разі прибережного плавання, очікуваної дати і часу характер- них точок у вигляді групи з шести цифр, як у ВВ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ММ — повністю вказати назви прослуховування станцій / частота.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' NN — група із зазначенням дати і часу, як і в ВВ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' PP — найменування і кількість вантажу (бункер) на борту судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' QQ — резюме несправностей / недоліків / пошкоджень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Короткі звіти про стан судна та можливості концентрації палива.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' RR — коротка інформація про забруднення навколишнього се- редовища.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Назва мастила або палива витоку в море;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' оцінка величини;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' оцінка руху скидання мастила / палива;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо це можливо, оцінити поверхню області розливу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Місце дається як в СС або DD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' SS є короткий опис переважаючих погодних і морських умов.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' TT — ім’я, адреса, номер telemet і телефон судновласника і пред- ставника (фрахтувальник, власник або оператор судна або їх агент).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' UU — інформація про довжину, ширину, осадку і тип судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' XX — додаткова інформація: короткий опис інциденту;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' необхідність допомоги ззовні, допомога, яка була запрошена або була надана іншими суднами;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' вжиті заходи щодо скидання і руху судна;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' кількість членів екіпажу та відомості про будь-які тілесні ушко- дження;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' інформація про страхову компанію: інша інформація.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Після передачі вихідного повідомлення в обсязі таблиці, додатко- ве повідомлення повинно бути передано так, що воно містить інфор- мацію, важливу для безпеки судна і захисту морського середовища.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наступна додаткова інформація повинна бути спрямована на судновласника або оператора в можливо короткий час після перших внесень інформації: – додаткові деталі пошкодження судна і обладнання;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – вказується існуючий збиток;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – оцінка пожежної небезпеки і попереджувальних заходів, що вживаються;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – розміщення вантажу на борту і його номер;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – число нещасних випадків;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – пошкодження та збитки, завдані іншим суднам;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 246 – час (GMT), коли була запрошена допомога, і час, протягом яко- го очікується допомога;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ім’я рятувальника і тип аварійно-рятувального обладнання;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – чи було прохання про додаткову допомогу;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – вимоги до запасних частин та інших матеріалів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – будь-яка інша важлива інформація.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зв’язок в точці дії.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сигнал лиха: – MAYDAY використовується для вказівки того, що судно знахо- диться в стані загрози безпосередньої небезпеки і вимагає негайної допомоги;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – має перевагу перед усіма іншими повідомленнями.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Терміновий сигнал.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – PAN-PAN використовується, коли безпека мобільних засобів знаходиться під загрозою;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – терміногенний сигнал PAN-PAN повинен бути використаний, коли існує небезпечна ситуація, яка, в кінцевому підсумку, може спричинити необхідність залучення допомоги;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – має перевагу над усіма повідомленнями, за винятком сигналу катастрофи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сигнал безпеки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – SECURITE використовується для повідомлень, пов’язаних з безпекою судоводіння або передачею важливих метеорологічних по- переджень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Будь-які повідомлення, передані після цих сигналів, мають прі- оритет перед звичайними повідомленнями.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Як правило, сигнал по- вторюється тричі на початку повідомлення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Командир літака або капітан визначеного корабля повинен оголосити стан катастрофи за допомогою сигналу MAYDAY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основні слова для радіопроцедур, пошуку, які рятувальні співробітники повинні використовувати та розуміти: AFFIRMATIVE означає, що те, що передається, є правильним;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' BREAK використовується для відокремлення частини повідо- млення або одного повідомлення від іншого;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' FIGURES вимовляються безпосередньо перед номерами в пові- домленні;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' I SPELL використовується для вимовляння слів по буквам;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' NEGATIVE засобів немає;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' OUT кінець передачі, коли відповідь не очікується або не по- трібна;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 247 OVER кінець передачі, коли очікується негайна відповідь;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ROGER означає, що прийняте повідомлення задовільне;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' SILENCE вимовляється тричі і означає «зупинити негайно всі програми»;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' SILENCE FINI означає скасування тиші, використовується для позначення кінця надзвичайної ситуації та відновлення нормального радіообміну;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' THIS IS вимовляється до назви станції або позивного сигналу;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' WAIT означає, що «я повинен призупинитися на кілька секунд, очікую подальшу передачу».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Більш детальний перелік процедурних слів наведено в «стан- дартних фразах міжнародної морської організації для спілкування на морі» та MCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Передача повідомлення катастрофи від морського судна: – 156,8 МГц (УКВ, канал 16);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – 156,525 МГц (УКВ ЦИВ 70 канал);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – 2182 кГц (радіотелефонія);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ПВ/КВ ЦИВ (2187,55 кГц, 8414,5 кГц вахта несеться обов’яз- ково) та ще на одній з частот 4207,5 кГц, 6312 кГц, 12577 кГц, 16804,5 кГц;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Інмарсат 1644.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3–1644,5 МГц (АРБ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Інмарсат 1626,5–1646,5 МГц — АРБ 406–406,1 МГц.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо існують сумніви щодо прийому невідповідності повідо- млення, його слід надсилати на будь-яку існуючу частоту, яку можна використовувати в місцевих районах, і на яких увага може бути отри- мана негайно.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З метою створення сигналів катастрофи можна ви- користовувати рятувальне радіо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Передача сигналів тривоги з літака здійснюється: – зазвичай літак повідомляє блок керування рухом (АТС), який повинен повідомити RCC;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – 121,5 МГц;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – 4125 кГц (радіотелефонія);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – радар-респондент встановлюється при 7700 МГц;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – літак під час невизначеної катастрофи може використовувати будь-які засоби у своєму розпорядженні, щоб привернути увагу, по- відомляти про своє місцезнаходження та допомогу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Додаткове радіотехнічне обладнання, встановлене на морських та літальних апаратах відповідно до вимог Конвенції SOLAS-74/88 і з яким можна відправити невідповідність повідомлення: 248 – аварійний радіобуй (EPIRB), який, якщо вводиться або коли вмикається вручну, надсилає закодований сигнал, індивідуальний для кожного буя, на прибережні станції;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – радар-респондент (SART), після включення вручну, діє автома- тично, приймаючи радіолокаційні імпульси РЛС.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Надсилає імпульси, які видно на екрані РЛС, як групу розшире- них точок, як сигнали респондентських маяків.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зазвичай на екрані РЛС респондент бачиться на 6–8 миль — на переносних УКВ-радіо- станціях VHF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Повідомлення з судна про лихо повинно включати такі важливі компоненти: – Ідентифікація та координати судна;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Тип природної катастрофи та тип допомоги;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Погода в безпосередній близькості, напрямок вітру, хвилі, ви- димість;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Час залишення судна та кількість екіпажу, що залишився на борту;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Кількість і тип рятувальних засобів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Надзвичайні інструменти для розміщення на рятувальному агенті або в морі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Кількість серйозно поранених.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У початковому повідомленні стільки інформації включено як практично доречну, але цілий ряд коротких повідомлень більш до- цільніший, ніж одне довге.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сигнали візуальної катастрофи наведені в МППСС-72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Скасування повідомлення стихійного лиха повинно бути зроблено, як тільки буде надана допомога, або якщо допомога не треба.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Будь-яке помилкове сповіщення слід скасувати, щоб не ви- користовувати марно сили рятувальних послуг.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ISM-code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Світові стандарти.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Незважаючи на покращений тех- нічний стан флоту та сучасного навігаційного та радіотехнічного обладнання, відділ надзвичайних ситуацій світового флоту залиша- ється на тому ж рівні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вина покладається в основному на некомпе- тентність або непідготовленість екіпажів кораблів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За результатами розслідування надзвичайних справ на морі людство зазначило, що нещодавно «людський чинник» відіграє вирішальну роль.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тому було вирішено регулювати та стандартизувати людські відносини на бор- ту суден.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вимоги до безпечної експлуатації кораблів наведено в міжнарод- ному кодексі з питань управління безпекою та забрудненням (ISM- code), який був прийнятий Міжнародною постановою Міжнародної 249 морської організації A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='741 (18) 4 листопада 1993 року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вона включає в себе такі пункти: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Загальні положення;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Політика у сфері безпеки та охорони навколишнього середовища;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідальність та повноваження компанії;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Призначена особа (особи);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідальність та повноваження капітана;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ресурси та персонал;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розвиток планів проведення операцій на кораблях;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Готовність до надзвичайної ситуації;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Звіти про невідповідності, аварії, небезпечні ситуації та їх аналіз;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Технічне обслуговування та ремонт судна;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Документація;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перевірка, огляд та оцінка, зроблена компанією;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Експертиза, перевірка та контроль.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Конвенція SOLAS-74/78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Комітет з безпеки на морі в 1994 році прийняв постанову IX до- давання до конвенції SOLAS-74/88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Правило 1 «Визначення»: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ISM-code — означає Міжнародний код для управління безпеч- ною експлуатацією суден та запобігання забрудненню, прийнятий Організацією А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='741 (18) Постановою (18), з поправками, які можуть бути зроблені Організацією;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Компанія означає власника судна або будь-якої іншої органі- зації, або людину, таку як менеджер, який взяв на себе відповідаль- ність за роботу судна від власника судна, погодившись прийняти всі обов’язки та всю відповідальність, встановлену міжнародним кодом управління безпекою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Обладнання — це судно, конструкція якого включає в себе один корпус, бортові шлери та бортові танки в вантажних приміщеннях і призначені переважно для транспортування насипних вантажів або рудозних або комбіновані судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Море-мобільна бурова установка — це судно, здатне виробляти бурові операції для розвідки або розвитку ресурсів, таких як рідкі або газоподібні вуглеводні, сірка або сіль.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нафтовий танкер означає судно, побудоване або адаптоване, головним чином, для перевезення нафти оптом у своїх вантажних приміщеннях, і включає в себе комбіновані вантажні судна та будь- 250 який танкер-хімічний транспорт, якщо він транспортує нафту оптом як вантаж або частину вантажів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Швидкий корабель — це судно, здатне розвивати максимальну швидкість в метрах за секунду, рівну або більше: 3,7 V0,1667, де V 7 — розрахункове зміщення, м3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Танкер Himovo — означає вантажне судно, побудоване або при- стосоване і використовуване для транспортування оптом будь-якого рідкого продукту, зазначеного в Міжнародному кодексі Хемноса.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Банзор — означає вантажний корабель, побудований або адап- тований та використовуваний для транспортування оптом будь-якого скрапленого газу або іншого продукту, зазначеного в Міжнародному кодексі для газових транспортних засобів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Риболовецьке судно — означає судно, що використовується для риболовлі, ловлі морських тварин та морепродуктів, рибного госпо- дарства.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' DSC (доступний документ) — означає документ, виданий ком- панією, адміністрацією прапора, що підтверджує, що судно відпові- дає вимогам Кодексу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' SVUB (свідоцтво про управління безпекою) — це документ, виданий адміністрацією компанії, після генерації служби управління судном та підтверджуючий, що служба управління безпекою корабля відповідає вимогам правила 2 «Кодексу» — MCUB є Введено для всіх судновласників та кораблів, незалежно від дати будівництва, вчасно: – 01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='98 — швидкісні, масляні танкери, хімічні носії, газові но- сії, масові та вантажні високошвидкісні кораблі з валовою місткістю 500 або більше тонн;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – 01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='02 — інші вантажні судна та морські бурові установки ва- ловою потужністю 500 або більше тонн.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ця глава не застосовується до державних суден, які працюють у некомерційних цілях.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Постанова Міжнародної морської організації A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='787 (19) «Проце- дури контролю над кораблями держави порту».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Судно повинно мати непрострочений сертифікат управління, виданий адміністрацією порту прапора судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо є підстави для більш детальної перевірки, зареєстровані наступні запитання ISM-code (посилання на елемент ISM-code).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ISM-code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Загальні положення (ISM-code).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основна ланка сис- теми управління безпекою, відповідно до стандартів Міжнародної морської організації та Кодексу, є власником або оператором судна 251 (компанії).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Система управління безпекою (SUB) повинна бути реалі- зована у діяльності компанії для ефективних та професійних дій з ін- формацією судового управління та є невід’ємною частиною основної системи управління виробничою компанією.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Код вимоги до системи управління безпекою компанії: А) Стандарти якості безпеки та запобігання забрудненню: – дотримання системи обов’язкових правил та стандартів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – гарантії впевненості в тому, що система приймає кодекси, керів- ні принципи та стандарти, рекомендовані Міжнародною морською організацією та організаціями морської промисловості;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Б) Загальні цілі компанії: – забезпечення якості наданих послуг;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – забезпечення безпечної експлуатації суден та безпечних умов роботи та навколишнього середовища;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – організація захисту від усіх виявлених ризиків;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – постійне вдосконалення навичок управління безпекою та суд- ном, включаючи надзвичайну готовність, пов’язану з запобіжним за- собами запобігання небезпеки і ризиків, пов’язаних із забрудненням.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В) Функціональні вимоги до системи управління безпекою: – політика безпеки та екології;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – інструкції та процедури для забезпечення якості наданих по- слуг, безпечної експлуатації судна та охорони навколишнього серед- овища;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – кількість повноважень та зв’язків між узбережжям та персоналом судна, а також внутрішніми лініями спілкування на березі та з суднами;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – забезпечення взаємодії з радіостанціями та портів для організа- ції надійних щоденних обліків кораблів компанії;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – процедури при аваріях та випадках невідповідності вимогам Ко- дексу;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – процедури підготовки до надзвичайних ситуацій та дій щодо їх- нього усунення;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – процедури проведення внутрішніх аудитів та процедур розгляду керівництва.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='ISM-code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інститут у сфері безпеки та охорони на- вколишнього середовища (пункт 2 ISM-коду).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кожна компанія повинна мати політику у сфері безпеки та охоро- ни навколишнього середовища, яка полягає в: – досягненні загальних цілей, передбачених Кодексом;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – забезпеченні безпечної експлуатації суден на рівні міжнародних та національних стандартів (правил та норм);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 252 – підвищенні, на цій основі конкурентоспроможності своїх суден на світовому ринку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У той самий час компанія проголошує свою прихильність і дає пріоритет, насамперед, забезпечуючи безпеку та запобігання забруд- ненню та повинна забезпечити основну мету політики.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Безпека на морі, запобігання смерті та травм людей, пошкоджен- ня навколишнього середовища, особливо морського середовища та майна, а також дотримання правил проведення комерційних опера- цій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це досягається: – дотриманням міжнародних та національних стандартів (правил та норм) щодо безпеки запобігання навігації та забруднення;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – стійким та надійним двостороннім спілкуванням кораблів з бе- регом;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – звітами капітанів за станами кораблів, проблем на борту та за- ходів для їх вирішення, необхідну підтримку узбережжя;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – наявністями взаємопов’язаних планів дій у надзвичайних ситу- аціях та розробкою цих планів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – здатністю компанії швидко і адекватно реагувати на небезпеку, яка може виникнути на кораблі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – забороною приносити, зберігати та використовувати алкогольні напої та наркотики на борт суден;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – дослідженням аварій та надзвичайних ситуацій на кораблі та вживанням заходів щодо їх запобігання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На підставі вищесказаного компанія здійснює: – кадрову політику — збирання кваліфікованого персоналу;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – технічну політику — забезпечення проектно-технічної, техно- логічної та екологічної безпеки суден;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – соціальну політику — створення умов в інтересах персоналу для забезпечення безпечної експлуатації кораблів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Політика затверджується підписом Генерального директора.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ко- пія політики компанії, підписана Генеральним директором, викладе- на на визначеному місці в кожному підрозділі компанії, на судні — на місці, найбільш відвідуваному екіпажем, та в кабіні капітана.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Всі співробітники компанії повинні бути знайомі з політикою компанії для її виконання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Політика компанії складається з трьох рівнів документації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Політика — цілі та завдання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Загальна структура системи управління: – опис стратегій системи управління та цілей;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 253 – визначення діапазону системи управління;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – опис організаційної структури;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – визначення відповідальності потужних повноважень ключових працівників системи управління;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – перехресні посилання елементів посібника, використовуючи використані стандарти.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Процедури — що робити: – метод управління системою;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – процедури, що описують перелік різних заходів щодо системи управління;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інструкції — як це зробити: – задокументовані завдання;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – опис робіт (інструкції з роботи);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – форми звітів та шаблонів, які використовуються в системі управління безпекою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ISM-code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідальність та повноваження компанії (пункт 3 ISM-коду).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Стандартна структура СУБ будь-якої компанії повинна включати: – Вище керівництво;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Загальні збори акціонерів / засновників;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Рада директорів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Генеральний директор;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Рада, яку очолює Генеральний директор та включає всіх сво- їх депутатів та інших працівників, визначених зборами акціонерів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Прибережні одиниці: – служба безпеки (СБМ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – технічна експлуатаційна служба (корабель або MCC);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – відділ персоналу (OK) або служба управління персоналом;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – видобуток;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – виробнича служба;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – комерційний відділ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – юридичний відділ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – служба зв’язку;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – департамент експлуатації;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – департамент логістики (ОМТС).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Мінімальні вимоги до структури компаній відповідно до рекомен- дацій галузевого стандарту є такими: Маленька: – Генеральний директор;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 254 – призначена особа, за умови її заміни під час відсутності відпо- відного спеціаліста, прийнятого за угодою про зайнятість;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – технічний спеціаліст (механік, електромеханік), за умови її заміни на період відсутності фахівцем, прийнятим тимчасово.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Примітка: договір для забезпечення системи управління безпекою невеликої компанії не звільняється від зобов’язання призначати осіб.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Середня: – Генеральний директор;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – призначена особа;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – технічний фахівець: – служба безпеки (один капітан-наставник для шести суден, включаючи призначену особу, та один фахівець з комунікацій та SPI на 12 суден);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – механік та судноплавна служба (1 менторний механік для шести суден, включаючи технічного спеціаліста).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Велика: – Генеральний директор;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – призначена особа;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – головний інженер;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – служба безпеки (1 наставник для 6 кораблів);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – механік та судноплавна служба (1 наставник для 6 кораблів);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – радіотехнічне обслуговування (може бути частиною СБМ — 1 наставник для 12 кораблів);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – всі інші прибережні одиниці, наведені вище.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Склад та кіль- кість працівників кожного відділу визначаються керівництвом компанії.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ISM-code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Призначена особа.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (Пункт 4 ISM-code).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Безпека суден та якість послуг повинна бути під постійним контролем керівництва компанії.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для цих цілей керівник компанії встановлює призначену людину.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Згідно з офіційною посадою, призначена особа будь-якої компанії може працювати в компанії на постійній основі або заступ- ником керівника морської безпеки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Під час відсутності призначеної особи обов’язки виконуються за- ступником.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Призначена особа повинна бути затверджена: – у великій компанії — у Державному комітеті;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – у середній та невеликій компанії — у ГА порту реєстру.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Призначена особа будь-якої компанії може бути фахівцем, який має морську базову освіту, диплом та всі сертифікати, включаючи 255 ISM-код, що і дозволяють капітану працювати на найбільшому кора- блі компанії, щонайменше 3 роки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Призначена особа виступає від імені керівника компанії її ін- струкцій щодо безпеки навігації та запобігання забрудненню, що є обов’язковими для всіх працівників компанії.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Щоб виконати це як частину системи управління безпекою, при- значена особа: – організовує та координує діяльність системи управління безпе- кою;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – підтримує цю систему, включаючи нормативні документи;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – підтримує постійне спілкування з суднами, контролює їхню безпеку та забезпечує їх прибережну підтримку, необхідну для вико- ристання безпечної експлуатації;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – має прямий доступ до ресурсів та управління компанією;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – забезпечує контроль за дотриманням стандартів (правил та норм) безпеки та ефективності системи управління безпекою;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – забезпечує судна та прибережні ресурси, що виділяються на без- пеку;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – своєчасно і негайно реагує на повідомлення про невідповіднос- ті, небезпечні ситуації та аварії;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – організовує систематичні внутрішні та зовнішні перевірки сис- теми управління безпекою, виправлення невідповідностей та вико- нання коригувальних дій;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – призводить до нормативно-правової документації (розповсю- дження, налагодження, бюлетень тощо);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – проводить навчання для систематичних оглядів (аналізів) стату- су безпеки в компанії та розробляє основні пропозиції щодо системи регулювання політики та системи управління безпекою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ISM-code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ресурси та персонал (пункт 6 ISM-code).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До ресурсів безпечної роботи належать: – Нормативні документи;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Матеріальні ресурси;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Довкілля;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Фінанси;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Підготовлений персонал.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Центральною ланкою системи управління безпекою є персонал, який має кваліфікований, компетентний та професійно підготов- лений рівень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Весь прибережний персонал, що забезпечує систему управління безпекою, повинен мати морські назви та досвід роботи 256 з командними позиціями не менше 3 років.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вимоги до персоналу пе- редбачає посадовий опис, з якими вони знайомі до початку роботи ISM-code).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Готовність до надзвичайної ситуації (пункт 8 ISM-коду).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Підготу- вати та забезпечити постійну готовність компанії та суден до надзви- чайних ситуацій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Компанія є операційним штабом з надзвичайних ситуацій, затвер- джених Генеральним директором, та на чолі з призначеною особою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Склад аварійної штаб-квартири компанії узгоджується з ГА портом реєстру.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ISM-код.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Звіти про невідповідності, нещасні випадки, аварії, не- безпечні ситуації та їх аналіз (параграф 9 МКУБ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' СУБ компанії по- винні забезпечити систему негайних звітів про всі інциденти, прямо або опосередковано впливати на безпеку навігації — звіти про не- відповідності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Форму звіту про невідповідності наведено у докумен- тації суб’єкта.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Звіти про невідповідності складають команду верфі з підписом капітана або головою прибережної одиниці у таких ви- падках: – відбулися аварії, нещасні випадки;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – створені небезпечні, ризиковані та непередбачені ситуації;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – претензії, що виникли для рибного господарства, органів нагля- ду, портових органів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – невідповідності (невідповідність вимогам) у системі управління безпекою;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – претензії та відгуки вимог до підсвічування;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – немає жодних пропозицій щодо модернізації та вдосконален- ня підтвердження: якщо невідповідність усунута самостійно, і допо- мога компанії не потрібна, звіт про невідповідність не складається.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Звіт про невідповідність складається в 2 примірниках.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1-й направ- ляється на ім’я призначеної особи відповідно до схеми суб’єкта, на- веденої у документації, а другий залишається на кораблі / підрозділі компанії, яка написала звіт.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Після отримання звіту про невідповід- ність служба безпеки морського моря назначає призначену особу, що повинна: – зареєструвати доповідь, включаючи число на класифікацію до- кументації суб’єкта;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – організувати дослідження та аналіз звіту;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – розробити рішення про це;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – моніторинг виконання коригувальних дій;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 257 – проводити постійний рух доповіді та контролювати виконання коригувальних дій;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – встановити період для виконання коригувальних дій;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – призначити відповідальну особу за виконання коригувальних та профілактичних заходів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Коригувальні дії зроблено у формі рішення про звіт про невід- повідність, одна копія надсилається на адресу пристрою / судна, який написав звіт, а 2-га копія людині, відповідальній за виконання коригувальних дій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' СБМ (призначена особа) контролює виконан- ня цього рішення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Коригувальні та запобіжні заходи повинні бути спрямовані на забезпечення безпеки навігації та охорони навко- лишнього середовища, а ні в якому разі не зменшують рівень без- пеки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Коригувальні дії: – виправлення відповідних процедур та інструкцій;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – розробка нових процедур та інструкцій;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – розподілення досвіду серед суден та прибережного персо- налу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Звіт про невідповідність буде закрито після отримання призна- ченою особою інформації від голови підрозділу, який написав звіт, звітував про усунення невідповідностей у формі суб’єкта, наведеної у документації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ISM-code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Документація (Пункт 11 МКУБ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Система управління безпекою будь-якої компанії регулюється безліччю документації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Її склад та порядок відліку кожна компанія встановлює самостійно, але це повинно охоплювати всі сфери компанії та кораблі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кожне судно повинно мати повний пов’язаний з ним набір документації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За при- значенням документація поділяється: 1) Розтягнутий — поставляється з суднобудівельного заводу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Міні- мальна композиція безпеки Marigold включає: – Технічний паспорт судна (vessel information book), що містить основні ТТД (основні зменшення, призначення, танкова ємність, кількість вантажів, ваги та інше).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Інформація за стабільністю та схемами розрахунку (stability and trim book) — містить початкові дані для розрахунку стабільності та діаграм статичної та динамічної стабільності при різних завантажу- вальних діаграмах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Рисунки суднових конструкцій, механізмів та систем (draw- ings) є життєво важливими для забезпечення безпечної експлуатації судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 258 2) Регуляторно-правова — це ключова документація.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це набір обов’яз кових стандартів (правил та норм) для безпечної експлуатації судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='МКУБ (ISM-code).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Пункти 4–6 та 8 Кодексу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ISM-код.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При- значена особа (особи) (Пункт 4 МКУБ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Безпека суден та якість по- слуг мають бути під постійним контролем керівництва компанії.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для цього керівник компанії своїм наказом засновує призначену особу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За службовим положенням, призначеною особою будь-якої ком- панії може бути людина, що працює в компанії на постійній осно- ві, заступник керівника з безпеки мореплавання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Під час відсутності призначеної особи обов’язки виконує її заступник.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Призначена особа має бути затверджена: – у великій компанії — у Державному комітеті з рибальства;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – у середній та малій компанії — у ГА порту приписки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Призначеною особою будь-якої компанії може бути фахівець, який має морську базову освіту, диплом та всі відповідні свідоцтва, включаючи МКУБ, які дозволяють працювати капітаном на най- більшому судні компанії, досвід роботи капітаном найбільшого судна компанії не менше трьох років.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Призначена особа діє від імені керівника компанії та її вказівки щодо безпеки мореплавства та запобігання забруднення обов’язкові для всіх працівників компанії.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для виконання цього в рамках СУБ призначена особа: – організує та координує діяльність системи управління безпекою;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – здійснює ведення цієї системи, зокрема нормативно-правових документів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – підтримує постійний зв’язок із суднами, контролює їхню безпе- ку та надає їм берегову підтримку, необхідну для забезпечення без- печної експлуатації;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – має прямий доступ до ресурсів та керівництва компанії.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – забезпечує контроль за дотриманням стандартів (правил і норм) безпеки та ефективності системи управління безпекою;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – надає суднам та береговим підрозділам ресурси, виділені на за- безпечення безпеки;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – своєчасно та оперативно реагує на доповіді про невідповідності, небезпечні ситуації та нещасні випадки;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – організовує проведення планомірних внутрішніх та зовнішніх аудиторських перевірок системи управління безпекою, виправлення невідповідностей та виконання коригуючих дій;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 259 – веде нормативно-правову документацію (розподіл, коригуван- ня, розсилку тощо);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – проводить підготовку систематичних оглядів (аналізів) стану безпеки в компанії та розробку на їх підставі пропозицій щодо кори- гування політики та системи управління безпекою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідальність та повноваження капітана (Пункт 5 МКУБ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідно до вимог МКУБ, КТМ та Статуту служби на суднах капітан є вищою посадовою та довіреною особою компанії на судні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Капітан керує судном на основі єдиноначальності, підпо- рядковується Генеральному директору та призначеній особі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ніх- то, ні суднова рада, ні судновий комітет, ні партійна організація, ні комітет з безпеки, ні будь-який працівник компанії, включаючи Генерального директора та призначену особу, не мають права ска- сувати рішення капітана з будь-якого питання виробничої та по- бутової діяльності судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Усі члени екіпажу призначаються лише за згодою капітана.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Капітан видає накази по судну та має право усунути будь-якого члена екіпажу від виконання його обов’язків або списати з судна, вказавши підстави у наказі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Капітан несе від- повідальність за: – підтримання та підвищення престижу та авторитету компанії;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – проведення на судні політики безпеки та розуміння її судновим персоналом;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ефективне функціонування суднової СУБ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – створення в судновому колективі моральних та матеріальних передумов для підвищення суднової СУБ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – наявність та своєчасне підтвердження всіх суднових свідоцтв та документів суднового персоналу;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – організацію служби на судні, розподіл обов’язків, відповідаль- ності та повноважень екіпажу, включаючи аварійні ситуації;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – складання та затвердження посадових інструкцій суднового персоналу, причому в праві відступити від статутних вимог підпри- ємства;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – організацію зв’язку з компанією та внутрішньобортового зв’язку;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – передачу в компанію повідомлень про аварійні заходи та недо- тримання положень Кодексу;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – контроль за дотриманням персоналом судна міжнародних та на- ціональних стандартів, включаючи стандарти компанії, для забезпе- чення безпечної експлуатації судна;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 260 – проведення занять, навчання та тренувань з відпрацювання суд- новим персоналом дій в аварійних ситуаціях, включаючи забруднен- ня довкілля;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – ведення суднової документації та суднових журналів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – надання до компанії оглядів (аналізів) щодо ефективності судно- вих СУБ та пропозицій щодо її вдосконалення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Капітан має виняткові повноваження в прийнятті рішень щодо забезпечення безпечної екс- плуатації судна та звернення до компанії за допомогою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Він не обме- жений у праві прийняття рішень щодо забезпечення безпеки судна та суднового персоналу, запобігання забрудненню навколишнього серед- овища, збереження вантажу та майна і компанія підтримує його в цьому.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='ISM-код.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ресурси та персонал (Пункт 6 МКУБ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До ресурсів для забезпечення безпечного ведення робіт належать: – нормативні документи;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – матеріальні ресурси;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – довкілля;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – фінанси;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – підготовлений персонал.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Центральною ланкою СУБ є персонал, який має бути кваліфіко- ваним, компетентним та професійно підготовленим.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Весь береговий персонал, що забезпечує СУБ компанії, повинен мати морські зван- ня та досвід роботи на командних посадах не менше трьох років.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ви- моги до персоналу викладаються у посадових інструкціях, із якими вони знайомляться під розпис на початок роботи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Комплектування суднового персоналу здійснюється відповідно до чинного законодав- ства, з обов’язковим узгодженням із призначеною особою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Капітан зобов’язаний знати: – національне та міжнародне законодавство та нормативно-пра- вові документи;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – параметри непотоплюваності, міцності, стійкості, живучості судна та його особливості;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – міжнародні угоди щодо безпеки мореплавства;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – морське право, закони, правила та звичаї портів заходу;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – правила класифікаційного суспільства;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – правила, норми, рекомендації, інструкції компанії в частині експлуатації судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Судновий персонал повинен: – мати морську базову освіту, дипломи, сертифікати та свідоцтва, що засвідчують його кваліфікацію;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 261 – знати структуру судна та її особливості;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – мати достатній досвід роботи (при призначенні вперше на ко- мандні посади пройти відповідне стажування);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – вміти орієнтуватися в будь-яких умовах експлуатації, включаю- чи аварійні;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – знати умови експлуатації та галузь діяльності судна;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – знати режим роботи, робочі навантаження, розпорядок на судні;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – виконувати правила техніки безпеки;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – знати свої посадові обов’язки та суднову систему управління безпекою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Береговий персонал повинен: – мати спеціальну базову освіту, що відповідає призначенню;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – мати відповідні дипломи та свідоцтва, що підтверджують квалі- фікацію;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – знати сферу діяльності підприємства та її СУБ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – мати достатній досвід практичної діяльності;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – знати міжнародне морське право, відповідні міжнародні догово- ри, національне морське законодавство;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – знати міжнародні та національні нормативно-правові стандарти з безпеки мореплавання та ПЗМ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – знати міжнародні та національні правила ведення фінансових операцій;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – знати правила класифікаційних товариств.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для підтримки кваліфікації персоналу на належному рівні компанія повинна здійснювати його планомірне навчання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Осно- вними видами навчання суднового персоналу, передбаченими ПДМНВ-78/95, є: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Експлуатаційне навчання (in-service training) — проводиться на судні з виконання суднових операцій, але на березі перед призначен- ням на судно для підготовки та перевірки знань, майстерності, квалі- фікації, компетентності та професійної підготовленості.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сертифікаційне навчання (training for certification) — прово- диться для підготовки та сертифікації командного складу за відпо- відними міжнародно визнаними стандартами, кваліфікованими ін- структорами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виробничо-ознайомче навчання (shipboard familiarization) — проводиться з персоналом, який призначається на судно, з озна- йомленням зі своїми обов’язками, влаштуванням судна та суднових приміщень, входів та виходів, включаючи аварійні, судновими при- 262 строями, системами та обладнанням для нормальних та аварійних умов експлуатації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інше навчання (other training requirement applicable to all ships) — проводиться на всіх суднах з основним та тимчасовим судновим пер- соналом за способами та технікою виживання в аварійних ситуаціях, порядком залишення судна в кризових ситуаціях, а також методами індивідуального захисту (протипожежна безпека, техніка безпеки, перша невідкладна допомога тощо).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Спеціальне навчання (ship type specific training) — проводиться з судновим персоналом специфічних типів суден (добувні, обробні, приймальні, з небезпечними вантажами тощо).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Загальноосвітнє навчання — проводиться із судновим та бе- реговим персоналом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Навчання проводиться на березі та на судні у вигляді лекцій, курсів підвищення кваліфікації, тренувань на трена- жерах, стажувань як дублери тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Програми навчання на березі та на суднах узгоджуються та коригуються за результатами аварійних випадків, виявлених невідповідностей СУБ, зовнішніх та внутрішніх аудиторських перевірок.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відділ кадрів веде облік навчання кожного працівника.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На судні навчання відображається в судновій документа- ції та пред’являється наглядовим органам на їхню вимогу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Готовність до аварійної ситуації (Пункт 8 МКУБ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для під- готовки та забезпечення постійної готовності компанії та суден до аварійних ситуацій створюються: у компанії — оперативний штаб з аварійних ситуацій, затверджений наказом Генерального директора та очолюваний призначеною особою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Склад аварійного штабу ком- панії узгоджується з ГА порту приписки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На судні — судновий комітет із безпеки (мінімальний склад капітан, старпом, стармех).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Порядок дій аварійного штабу та суднового комітету з безпеки наводяться у взаємопов’язаних береговому (shore based emergency plan) та судново- му планах дій в аварійних ситуаціях.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Компанія має проводити підго- товку до дій у потенційно можливих аварійних ситуаціях.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Мета такої підготовки — постійна готовність компанії швидко та ефективно ре- агувати на аварійні ситуації, які можуть виникати на суднах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відпові- дальним за готовність суден та їх екіпажів до дій у аварійних ситуаціях є призначена особа.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Підготовка повинна передбачати: – ідентифікацію та опис аварійних ситуацій, що можуть виникну- ти на суднах;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – розробку планів дій берегового та суднового персоналів у потен- ційно можливих аварійних ситуаціях;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 263 – складання програм навчання та тренувань з відпрацювання бе- реговим та судновим персоналом дій в аварійних ситуаціях, запобі- гання аваріям, локалізацією та зведенням до мінімуму наслідків (ма- ють наводитися в положенні з тренувань та навчання).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – методи та підтримання контактів та зв’язку між судном та берегом, переданих в аварійних ситуаціях.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Бажано використову- вати рекомендації ІМВ (Резолюція А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 648(16) «Про основні за- сади системи суднових повідомлень та вимоги, що висуваються до них»).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Плани дій у аварійних ситуаціях.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Береговий повинен відображати: – склад, посади, службові та домашні телефони основного персо- налу штабу;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – порядок та місце збору штабу;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – обов’язки штабу та його взаємодію із зацікавленими партнера- ми, порядок запиту допомоги;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – методи та порядок повідомлень з судна на берег і назад;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – чек-листи, що ідентифікують аварійні ситуації, та буклети про- цедур для дій суднового персоналу у цих ситуаціях;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – взаємодія з оперативним штабом ГА порту;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – довідкова інформація про аварійно-рятувальні організації та центри в районах плавання суден компанії;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – порядок прийняття та виконання рішень та контроль їх вико- нання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Суднові вимоги повинні додатково включати: – склад, посади, телефони суднового комітету з безпеки;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – взаємодію та зв’язок із зацікавленими партнерами та суднами, що знаходяться в районі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідно до конвенції МАРПОЛ-73/78 на судні має бути «Суд- новий план надзвичайних заходів щодо боротьби із забрудненням на- фтою (shipboard oil pollution emergency plan)».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За структурою та побу- довою він аналогічний до плану дій в аварійних ситуаціях.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Компанія повинна проводити регулярні тренування та навчання суднового та берегового персоналу за вказаними вище планами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До програм під- готовки повинні включатися: – індивідуальні інструкції та навчання суднового персоналу щодо використання рятувальних та протипожежних засобів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – заняття, тренування та навчання суднового персоналу щодо бо- ротьби за живучість та дій у потенційно небезпечних аварійних ситу- аціях;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 264 – перевірки стану, надійності та готовності до дії суднового ава- рійного майна та обладнання, включаючи радіообладнання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ISM-код.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Доповіді про невідповідності, аварії, нещасні ви- падки, небезпечні ситуації та їх аналіз.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (Пункт 9 МКУБ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' СУБ ком- панії повинна передбачати систему негайних доповідей про всі події, що прямо чи опосередковано зачіпають безпеку мореплавства, — до- повіді про невідповідності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Форма доповіді про невідповідність на- водиться у документації СУБ компанії.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Доповіді про невідповідності складаються судновим командним складом (обов’язково підписує капітан) або керівником берегового підрозділу у таких випадках: – нещасних випадках, аваріях, аварійних пригодах;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – створених небезпечних, ризикованих та непередбачених ситу- аціях;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – претензій рибоохорони, наглядових органів, влади портів;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – невідповідності (недотримання вимог) у системі управління безпекою;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – претензій клієнтури та зворотних претензій до субпостачальни- ків;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – пропозицій щодо модернізації та вдосконалення СУБ, що з’яви лися: якщо невідповідність усунена самотужки і допомоги компанії не вимагає, доповідь про невідповідність не складається.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Доповідь про невідповідність складається у двох примірниках.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1-й прямує на ім’я призначеної особи за схемою, наведеною в докумен- тації СУБ компанії, а 2-й залишається на судні/підрозділі компанії, що написали доповідь.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Після отримання доповіді про невідповід- ність служба безпеки мореплавства, а де її немає, призначена особа повинна: – зареєструвати доповідь, надавши їй номер за класифікацією до- кументації СУБ компанії;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – організувати вивчення та аналіз доповіді;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – виробити рішення щодо неї;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – проконтролювати здійснення коригувальних дій;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – вести постійний рух доповіді та контроль виконання коригу- вальних дій;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – встановити термін виконання коригувальної дії;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – призначити відповідальну особу за виконання коригувальних та запобіжних дій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Коригувальна дія оформляється у вигляді рішення за доповіддю про невідповідність і один примірник надсилається на адресу підрозділу/судна, що написав доповідь, а другий примірник 265 особі відповідальній за виконання дії, що коригує.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' СБМ (призначена особа) контролює виконання цього рішення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Коригувальна та запо- бігаюча дія повинна бути спрямована на забезпечення безпеки море- плавства та захисту навколишнього середовища, та жодним чином не знижувати рівень безпеки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Коригувальні дії здійснюються шляхом: – виправлення відповідних процедур та інструкцій;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – розробки нових процедур та інструкцій;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – поширення досвіду серед суднового та берегового персоналу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Доповідь про невідповідність закривається після отримання призна- ченою особою від керівника підрозділу, який написав доповідь.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' До- несення про усунення невідповідності за формою, наведеною в до- кументації СУБ компанії.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0 МКУБ (ISM-code).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розробка планів проведення операцій на суднах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Пункт 7 Кодексу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основна відповідальність за розробку планів суднових операцій покладається на організацію.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Керівництво компанії має визначити, які суднові операції найбільш важливі для функціонування її суден.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Плани компанії: – річний план, що передбачає огляд (аналіз) пропозицій промис- лової (судноплавної) діяльності;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – підготовчий план, який передбачає підготовку суден до рейсу, відповідно до завдання;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – експлуатаційний план, що передбачає здійснення промислу/ вантажоперевезень, відповідно до рейсового завдання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Річний план виробничої діяльності, та аналіз його виконання здійснюється бе- реговими службами підприємств.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Підготовчий план здійснюється береговими службами підприємств, разом із судновим.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Компанія розглядає та виконує різні договори/контракти (ремонт, сервісне об- слуговування суднового обладнання, зв’язок, постачання, портові формальності та багато іншого), необхідні для успішної роботи судна в морі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На основі договірних (контрактних) умов основними видами підготовки судів є: – Навігаційна — здійснюється службою безпеки щодо гаранту- вання безпечного промислу (прогноз гідрометеобставин, забезпечен- ня морськими картами, укомплектованість судна аварійним та ряту- вальним обладнанням, наявність планів дій в аварійних ситуаціях та підготовка екіпажів до дій в аварійних ситуаціях);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Технічна — здійснюється механіко-судновою (технічною) служ- бою (виконання планового технічного обслуговування, ремонту та 266 докування, забезпечення технічної та технологічної готовності до промислу, перевірка строків дії суднових документів, проведення чергових оглядів, організація бункерування суден, перевірка якості палива, організація матеріально-технічного постачання);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Кадрова — здійснюється відділом кадрів (комплектація судно- вого персоналу, перевірка медичної придатності, перевірка дипломів та сертифікатів, організація заміни суднового персоналу);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Експлуатаційна (промислова) — здійснюється службою мо- реплавства та відділом видобутку/комерційним/експлуатаційним (планування роботи в промислових районах, призначення агентів, забезпечення суден вантажною та експлуатаційною інформацією, за- безпечення документами за правилами ведення промислу, організа- ція зв’язку та диспетчерських зведень, перевірка знарядь постачання необхідного промислового постачання);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Фінансова — здійснюється комерційним відділом та бухгалте- рією, з виділенням повноважень капітана (забезпечення суден не- обхідними засобами, оплата експлуатаційних послуг, встановлення порядку використання виділених коштів, контроль фінансових опе- рацій, дотримання комерційної таємниці підприємства, контроль руху готівки та майна);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Страхування — здійснюється юридичним відділом (забезпе- чення всіх видів страхування, встановлення порядку надання допо- відей про нещасні випадки та аварії, за результатами яких можливі ризики, статистичний облік збитків від виплат за претензіями та по- зовами).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Суднові операції — під час експлуатації суден компанія здій- снює розробку планів суднових операцій відповідно до ISM-code, враховуючи рекомендації ІМО та ґрунтуючись на національній сис- темі організації суднової служби багатьох країн.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Суднові операції, за можливими наслідками, поділяються на: – спеціальні — помилки у виконанні яких призводять до небез- печних ситуацій або виявляються після того, як аварія сталася;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – критичні — помилки у виконанні яких одразу породжують аварію або створюють загрозу для суднового персоналу, судна чи забруднення (наприклад: аварійні постановка та підйом зна- рядь лову, портові операції (лоцман, швартовка, якір та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ), ван- тажні операції в морі та портах, бункерувальні операції, аварійні тощо).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Критичні суднові операції мають виконуватися під суво- рим контролем.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому має бути повна переконаність у квалі- 267 фікації, компетентності та практичній підготовленості суднового персоналу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Суднові операції об’єднуються у послідовності процесу промислу та/або вантажоперевезень у такому порядку: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Загальні суднові операції: організація служби на судні — по- садові обов’язки суднового персоналу — доповіді/рапорти судново- го персоналу за підпорядкованістю — зв’язок судна з компанією — інспекції та контроль,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' що здійснюються капітаном та командним складом — суднова документація (склад,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' утримання,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' реєстрація) — медичне обслуговування — придатність до виконання посадових обов’язків та уникнення перевантажень суднового персоналу — ал- коголь,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' медикаменти,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' наркотики (судова політика,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' контроль вико- ристання та обстеження) — організація технічного обслуговування та ремонту — інструкції з експлуатації та обслуговування суднового обладнання — охорона праці та техніка безпеки — запобігання за- бруднення навколишнього середовища — перевірочні листи — про- мисловий розклад.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Операції під час перебування судна у порту: судова вахтова служба (стоянкова) — взаємодія з владою порту — перевірка,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' випро- бування та підготовка до дії протипожежних засобів — навантаження та вивантаження — контроль розміщення вантажу,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' міцності та стій- кості — вивантаження нафтовмісних вод та шкідливих речовин на берег — організація здачі харчових відходів,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' сміття та стічних вод — ремонтні роботи в порту — випадкові розливи рідких вантажів із суднового бункера — відповідальність за випадки забруднення — дії,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' якщо судно тимчасово затримується в порту — отримання промисло- вого та виробничого спорядження.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Операції з підготовки судна до рейсу: перевірка та реєстрація судна — перевірка міцності та стійкості — перевірка надійності за- криття всіх люків та отворів у корпусі — перевірка надійності крі- плення промислового устаткування — визначення/прогноз гідроме- теообставин — підготовка навігаційних карт та планування переходу до підготовки документації — перевірка,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' коректура карт та посібни- ків — бункерування судна — отримання продуктів,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' води та запасних частин — завершення ремонту та перевірка виконання — перевірка та підготовка ГД та механічного обладнання судна — перевірка та підго- товка систем управління судном — перевірка та підготовка систем та механізмів забезпечення безпеки (засоби навігації,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' якір,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' навігаційні вогні та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=') — перевірка та підготовка засобів зв’язку — перевірка та 268 підготовка обладнання та пристроїв ПЗМ — перевірка та підготовка промислового та виробничого обладнання та пристроїв.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Операції при знаходженні судна в морі та на промислі: суд- нова ходова навігаційна вахта — спеціальні вимоги при плаванні в складних умовах — радіозв’язок — спостереження за навколишнім середовищем — спостереження за станом та режимами експлуатації судна та основного обладнання — готовність судна до маневруван- ня — постановка знарядь лову — ведення промислових операцій — виробнича діяльність рибцехів та обробка риби — швартові операції (бункерування,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' розвантаження) — готовність до непередбачених/ екстремальних ситуацій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Операції з підготовки судна до приходу в порт: перевірка ГД, рульового пристрою, засобів навігації та зв’язку, якірного при- строю — проводка судна (лоцманська) — зв’язок судна з портом та інформація — визначення/прогноз гідрометеообставин — обмежен- ня з плавання в районі порту, сезонні таблиці та карти, настанови — баластування судна — контроль міцності, стійкості та водонепро- никності — перевірка та підготовка швартовного пристрою судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Документування суднових операцій здійснюється та оформляється у вигляді процедур та інструкцій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Процедура — це комплекс об’єднаний спільністю мети, дій (функцій), викладених у формі документа, що визначає призначення та завдання цього комплексу, склад, зміст та порядок виконання дій (функцій), що входять до нього, та їх кінце- вий результат.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основу процедур складають суднові операції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Процедура може ві- дображати суднову операцію повністю або її складові.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інструкція — це розвиток та деталізація процедури.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вона є документом, що визна- чає технологію виконання передбачених процедурою дій (функцій).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основний склад процедур наводиться у положенні щодо процедур документації СУБ компанії.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вимоги міжнародних та національних нормативних документів виконуються в компаніях та на суднах без дублювання їх у документах нижчого рівня.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У документації СУБ пра- вомірно лише посилювати чи деталізувати вимоги документів най- вищого рівня, прив’язуючи їх до конкретних особливостей роботи своїх суден.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У процесі роботи документація СУБ має коригуватися та доповнюватися на основі розслідувань (аналізів) аварій, невідпо- відностей, нещасних випадків тощо.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Найбільший відсоток важких аварій світового флоту падає на людський фактор, пов’язаний з на- вігаційною вахтою на містку та машині.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для полегшення дій судно- 269 водія та механіка значного поширення набули суднові перевірочні листи (чек-листи).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ці чек-листи наводяться у документації СУБ кожної компанії та рекомендуються для використання при повсяк- денній виробничій діяльності судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За рекомендацією ІМО (резо- люція А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='864(20) від 27 листопада 1997 року), при проведенні робіт, пов’язаних з підвищеним ризиком (на висоті та за бортом, у закри- тих та погано вентильованих приміщеннях, вогневі роботи тощо), судна повинні використовувати відповідні чек-листи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При викорис- танні чек-листів під час вахти судноводій/механік повинен врахову- вати наступне: – заповнений чек-листів суднової операції не звільняє осіб, які несуть ходову навігаційну вахту, від відповідальності за невірні дії;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – чек-лист є юридичним документом і поряд із записами в судно- вому/машинному журналі може бути доказом правильних дій судно- водія/механіка в екстремальних ситуаціях;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – про заповнення чек-листа необхідно зробити запис у судново- му/машинному журналі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – чек-листи заповнюються тільки ручкою синім або чорним чор- нилом, забороняється використовувати олівець;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – на всі пункти чек-листа має бути відповідь ТАК;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – якщо якийсь із пунктів чек-листа не виконаний, суднова опера- ція не повинна проводитися, а про ситуацію необхідно негайно допо- вісти капітану/старшому механіку за належністю;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – часто заповнювані чек-листи (зміна вахт, постановка трала тощо) кожен судноводій/механік заповнює один раз за рейс, а потім тільки робить відмітку в судновому/машинному журналі про його ви- користання;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – чек-листи при плаванні у складних умовах необхідно заповню- вати одразу;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – на кожному заповненому чек-листі повинні стояти дата, підпис та прізвище особи, яка заповнила його;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – всі заповнені чек-листи повинні зберігатися на судні щонай- менше два роки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У разі невідповідності чек-листа судновим умовам необхідно направити призначеній особі компанії доповідь про не- відповідність з обґрунтуванням коректури відповідного чек-листа.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Список усіх чек-листів, використовуваних під час роботи судна, має бути вивішений на видному місці містка/машинного відділення (над штурманським столом, над пультом управління головним двигуном) [4–10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 270 На підставі огляду нормативних документів випливає, що, поки безпілотні судна не дотримуються правил Міжнародної морської організації, вони будуть розглядатися як не судоходні, як такі, що не підлягають страхуванню.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Але час не стоїть на місці і вже є для без- екіпажних суден ескізи регулювання правових відносин.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для пов- них автономних суден, якщо ступінь автоматизації судна дозволяє виконувати плавання без екіпажу на борту при постійному спосте- реженні за судном та управляти його рухом персоналом за межами судна, або без постійного моніторингу та керування персоналом поза судном.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Суднові документи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оскільки багато суднових документів мають відношення до екіпажу судна та його функцій, необхідно замінити айсклоуз, що наявність або підтримка частини суднових документів для автономних суден у прийнятому тлумаченні повинні бути заміне- ні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для автономного судна необхідно консолідувати право не мати на борту суднових документів, а їх інспекційний контроль органи влади зможуть здійснити через судновласника в електронній та альтерна- тивній формі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Капітан судна, екіпаж судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Існуючі стандарти передбачають, що основною функцією капітана судна є управління суднами у сенсі на- вігації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У випадку автономного судна функція управління навігацією судна автоматизована та забезпечується або повністю судновою тех- нічною системою, або під керівництвом судновласного прибережно- го персоналу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Функції управління суднами, включаючи відправлен- ня, щодо напівавтономного судна можуть бути виконані судовими автоматичними пристроями або фахівцями судновласників, розта- шованими за межами автономного судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Мінімальний судновий екіпаж.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для повністю автономних суден ця вимога не застосовується взагалі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сертифікат мінімального складу напівавтономного судна повинен враховувати ступінь автоматизації (автономії) судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оскільки повністю автономне судно не має на бор- ту екіпажу, документ, що встановлює кількість екіпажу є безглуздям.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вимоги до кваліфікації персоналу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Управління автономним суд- ном, а також у присутності екіпажу і при його відсутності слід підтри- мувати або здійснюватися за допомогою фахівців поза автономним судном.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' А до членів екіпажу автономного судна та фахівців з управ- ління автономними судами повинні розробляти та встановлювати кваліфікаційні вимоги.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Найбільш відповідним правовим інструмен- том для встановлення кваліфікаційних вимог до зазначених членів 271 екіпажу та фахівців є положення про дипломи членів екіпажу мор- ських суден.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Управління судном.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідальність за безпечне управління ав- тономним судном може бути покладена на судновласника, який повинен мати спеціалістів, компетентних у сфері управління авто- номними суднами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такі фахівці виходять за межі автономного судна, контрольованого ними (на березі або на іншому судні або кораблі), але повинні мати всі необхідні інструменти технічного та організа- ційного характеру для управління суднами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Судновласник також має обов’язок призначити особу, відповідальну за управління автономним судном щодо кожного автономного судна (прибережного капітана).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ця відповідальна людина може одночасно керувати кількома судна- ми.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оскільки управління автономними суднами є дуже конкретним завданням, яке вимагає концентрації спеціальних компетенцій, про- понується надати право судновласнику укласти угоду про управління автономним судном зі спеціалізованою організацією, компетентною в управлінні автономним суднам.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У той самий час, відповідальність за безпечну роботу автономного судна, як і раніше, лежить на суд- новласнику.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такі коригувальні коментарі для запровадження нових технологій вже введені в морське законодавство.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У 2018 році DNV GL розробив документ «Autonomus and remotely operated ships», у 2020 р.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' РМРС ви- дав «Положення щодо класифікації морських автономних та дистан- ційно керованих суден (МАНС)».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вимогами до систем автономних та дистанційно керованих суден є надійність, безпека та ступінь авто- матизації, що є не гіршими, ніж у суднах з екіпажем.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Автономні судна повинні мати мінімальну кількість споруд, а також корисний простір судна та рекреаційних відділів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На автономних суднах ставка робиться на локальну мережу суд- на та системи зв’язку.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Локальна мережа повинна бути реалізована з можливістю функціонування в будь-якому агрегаті, тоді як несправ- не обладнання повинно бути виключено з мережі під час усунення невдачі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Однією з опцій інтегрованої системи є обчислювальна система, яка відповідає за управління суднами, повинна бути спроектована за мажоритарним принципом, з обчислювачем, який видає некоректні значення, що повинні бути відключені від загальної системи під час перезавантаження та перевірки, після чого він повинен бути реінте- грованим.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 272 Неможливо відхилити такий аспект, як реалізація автономних суден з можливістю участі у рятувальних операціях, для яких необ- хідно обладнати судно штучним інтелектом у формі робототехніч- них засобів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У разі відмови працювати з автономним та дистанційно керова- ним судном воно повинно бути доставлене до найближчого порту або ремонтні роботи проводити на борту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У той самий час повинні бути вирішені такі завдання: перевезення до найближчого порту;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' організація доступу до судна;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' оцінка доцільності ремонту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Рішення цієї проблеми полягає у створенні товариства порятунку автономних та віддалено керованих суден, під егідою Міжнародної морської організації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наявність людини на борту віддалено керованого судна вимагає роботи професійного психолога з медичною освітою, вирішення пси- хологічних проблем, таких як галюцинації, розвиток депресії, а також інші порушення людського організму.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Також не можна забувати про такий аспект морської діяльності, як піратство, який у різних формах існує з моменту зародження суд- ноплавства.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У випадку фізичного захоплення центру дистанційного управлін- ня повинна бути реалізована система передачі повноважень управ- ління на резервно-керовані структури, розташовані в інших центрах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перехоплення суднового управління може здійснюватися на спеці- ально відібраних цілях — суднах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Крім того, такі атаки можуть бути замасковані як «піратська атака».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Передача помилкових даних може бути безпосередньо спрямована на захоплення управління судном, але може побічно дозволити роботу судна на основі алгоритмів та не- правильних рішень у центрі пульта дистанційного управління.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Особливості дизайну та експлуатації автономних та віддалено ке- рованих суден вимагають: – Впровадження суворих вимог до правових аспектів відносин транспортних операцій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Використання сертифікованого обладнання та програмного за- безпечення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Впровадження модульного принципу обладнання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Можливості «гарячої заміни» обладнання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Уніфікація органів управління [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 273 Але виробничі технології не стоять на місці, і багато іноземних компаній не очікують створення та затвердження нормативної бази для безпілотних суден та швидко розвиваються та створюють повну модель автономних суден та самого автономного судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такими ком- паніями є: – Англійська Rolls-Royce Convice, яка разом з Finferries у грудні 2018 року, поблизу Турку, спеціально перетворені під автономний ре- жим 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 8-метрового типу порому «Falco».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Проект називався SVAN (Safer Vessel with Autonomous Navigation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тести були успішними, по- ром контролювався з командного пункту, розташованого за 50 км від експерименту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – Норвезька компанія Yara та Kongsberg Gruppen у жовтні 2017 р.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' завершили розробку повністю електричної автономної вантажівки, що називається Yara Birkeland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Як пише газета The Wall Street Journal перший у світі автономний вантажний корабель Yara Birkeland було введено в експлуатацію наприкінці 2018 року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Після спуску на воду розробники тестували системи автопілотів приблизно півтора року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Цей процес відбудеться в три етапи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На першому етапі судном управ- ляє команда на борту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На другому етапі оператор дистанційно кон- тролює тести, які здійснюються на маршруті довжиною 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 милі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наступний етап — електроход керується власним комп’ютером, ви- користовуючи GPS та численні датчики, щоб визначити положення інших морських об’єктів, а також для безпечного причалювання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Все вищезгадане про безпілотні судна та їх випробування доводить, що прогрес у розвитку безпілотних технологій не стоїть на місці, але з розвитком будь-якої технології, особливо в галузі морського тран- спорту, потрібно ретельно розробити нормативну базу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Але, на жаль, про досконале опрацювання ще рано говорити.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основною проблемою, яка вирішується для суден без екіпажів, є дотримання вимог безпеки навігації та запобігання забруднен- ню навколишнього середовища, а також відповідальність судно- власників як частина використання безпілотних суден.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В даний час безпілотні морські дослідження MAS проходять в «комфортних» умовах: – тестування судноплавства дронів відбувається на достатній від- стані від берега з впевненим, безперервним, безперебійним сегмен- том зв’язку з безпілотним судном;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – за відсутності близькості до інших суден;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – якщо є хороша зона супутникового покриття;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 274 – з повною відсутністю тіньових секторів для суднових РЛС;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – забезпечено безперебійну роботу АІС, GPS, гірокомпаса, лага, ехолота, за винятком помилок у переданій інформації;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – за наявності достатніх орієнтирів, глибин, СНО можливо дуб- лювати позиціонування суден у просторі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – при низькій швидкості маневрування;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – з повною відсутністю складних гідрометеорологічних чинників (штормовий вітер, хвилювання моря з високою бальністю, сильна те- чія, наявність значного льоду, айсбергів, інородних вільно плаваючих предметів з низьким коефіцієнтом відбиваючого сигналу).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Варто звернути увагу на ряд проблем, які в майбутньому виник- нуть з суднами без екіпажу: 1) як боротьба за життєздатність судна без екіпажу у разі аварії будь-якого виду (защемлення, зіткнення, пожежа, контроль води та інше);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2) у випадку повного блок-ауто відмова всього джерела живлення, включаючи резервні джерела живлення;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' хто може відремонтувати і за який час;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3) дії безпілотника в піратських водах;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4) екстрена віддача якоря, хто буде бігти на бак, щоб віддати якір;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5) плавання в льодових умовах (в льоду не йдуть прямо).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Потрібні постійні маневри та часті реверси мають підтримувати безпечну від- стань попереду рухомого судна, льодоколу, несподівано до відкритих перешкод.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6) виникнення ситуації невизначеності при дотриманні правил МППСС-72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Невизначеність є вираженою рисою морського тран- спорту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З усією ретельністю вивчення питань навігації фактор не- визначеності присутній і буде присутній навіть при вищому ступені автоматизації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, основні напрямки у сфері безпілотних технологій на морському транспорті повинні розглядатися як про- блема вирішення невизначеності сприйняття інформації під час роз- бігу суден, котрі рухаються в складних умовах, у причалі, перегляду правил для запобігання зіткнення та законодавчої бази у разі аварій- ної ситуації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На підставі вище викладеного розробка технології безекіпажного судоводіння та його застосування ведеться багатьма країнами, орга- нізаціями та компаніями, які здійснюють дослідження, технологічні та транспортні проекти.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інтенсивні розробки ведуть як установи, так і університети — Массачусетський інститут технології, Колумбійський 275 університет, Плімутський університет, Учоанський університет тех- нологій та транснаціональні корпорації та класифікаційні суспіль- ства.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Взаємне використання технологічних проектів може дозволити впровадженню у майбутньому повністю перейти до будівництва без- екіпажних суден, а також значно розширює можливості для розвитку суднобудівної промисловості.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Детальне вивчення проектів у сфері безекіпажного судноплавства дозволить створити техніко-економіч- не обґрунтування будівництва таких суден та визначити необхідний та остаточний набір технологій для їх реалізації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Телекомунікації тех- нології, електронні датчики та системи, технологія електронної на- вігації вже вводяться у секторі морської промисловості.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Економічні судна є найбільш складним технічним транспортом, в якому осо- блива роль призначена для автоматичної системи управління.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Най- ближчим часом неможливо уявити цивільний флот без автономних безекіпажних суден.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В роботі розглянуто, насамперед, регуляторні та правові аспек- ти, але не можуть бути відкинуті технічні, пов’язані з описом та аналізом існуючих проектів безекіпажних суден.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Безекіпажні суд- на відрізняються за ступенем обладнання засобами вимірювальної техніки та устаткування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На безекіпажних суднах не існує ходового містка, надбудови, житлових приміщень та системи життєдіяльнос- ті екіпажу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У травні 2018 року в рамках секретаріату Міжнародної морської організації була створена міжгалузева цільова група на морських ав- тономних поверхнях суден.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На 99-й сесії Комітет морської безпеки розпочав обговорення постійного регулювання сегмента автоном- ного перевезення, включаючи людський фактор, систему безпеки, взаємодію з портами, пілотною проводкою, ліквідацією наслідків аварій та захисту морського середовища для кораблів різних рівнів автономності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Слід також зазначити, що в рамках єдиного морського європей- ського проекту до 2025 року планується створити єдину «екосистему» логістики автономної доставки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У той самий час проект реалізується на принципах державно-приватного партнерства за участю провід- них гравців морської промисловості: Wartsila, Rolls Royce, Abb, Meyer Turku, Finnferries, Ericsson, Cargotec та ін.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' [12] Дефіцит часу на прийняття рішення щодо забезпечення безпеки судна призводить до необхідності виділення тільки тієї інформації, яка потрібна для виконання основного завдання управління і при- 276 йняття рішень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виникає проблема попереднього відбору та аналізу інформації, необхідної для реалізації механізму логічного висновку і вироблення практичних рекомендацій [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З такою проблемою справляються інтелектуальні системи, розраховані на експлуатацію в контексті певних невизначеностей протягом тривалого періоду часу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відзначається, що для того, щоб система відповідала інтелектуальній автономії, вона повинна володіти однією або декількома наступними можливостями: навчання;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ситуаційна обізнаність;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' міркування;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' пла- нування;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' людино-машинні інтерфейси;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' прийняття рішень;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' приве- дення в дію.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Під «автономним судном» розуміється — «морське судно з датчиками, автоматизованою навігацією, руховими і допоміжними системами, з логікою прийняття рішень для проходження по планам місії, налаштуванням виконання місії і роботи без втручання лю- дини», — представлено у звіті американського бюро судноплавства (ABS) про автономні судна (Autonomous Vessels: ABS ’Classification Perspective) за 2016 рік [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідно до звіту ABS про автономні судна (Autonomous Vessels: ABS’ Classification Perspective) за 2016 рік існують такі рівні авто- матизації систем [14]: людський контроль (human control), деякі функції автоматизації (some functions automated), звичайні операції автоматизації, людина готова взяти на себе відповідальність (normal operations automated;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' human ready totake over), критичні функції без- пеки автоматизації, людська присутність (safety-critical functions automated;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' human present), повна автономія критичних функцій без- пеки і моніторингу навколишнього середовища на час рейсу (full autonomy of safety-critical functions and environmental monitoring for duration of trip), повна автономія без доступних для людини інтер- фейсів управління (full autonomy with no human-available control interfaces).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В даний час безпілотні засоби — це концепт-проект, в якому увагу зосереджено на інтегрованій сенсорній технології і попередженні зі- ткнень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Основні елементи інтелектуальної системи, що використо- вується, забезпечують управління безекіпажним судном: автономна навігаційна система, система попередження зіткнень, система мо- ніторингу та управління двигуном, автоматизовані системи шварту- вання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Швартовні операції суден (рисунок 1) входять до складу небез- печних процесів судноплавства.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Прогрес в безпеці швартування суден досягається в результаті використання інноваційних техно- 277 логій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На багатьох причалах існує досвід роботи таких технологій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Але статистика свідчить, що такі системи швартування ще не ді- йшли до такої досконалості, щоб повністю виключити небезпечні ситуації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Застосування інноваційних технологій швартування суден Міжнародна морська організація схвалила вимоги до безпеки швартування суден та дизайну обладнання [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нові вимоги включатимуть оцінку повної лінії причалів, включаю- чи новий режим технічного обслуговування та швартове обладнання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На 102-му засіданні Комітету з питань безпеки моря Міжнародної морської організації було прийнято пакет обов’язкових вимог, у тому числі щодо безпеки еквівалентних операцій, повідомляє прес-реліз Міжнародної морської організації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На засіданні Міжнародної морської організації одна із прийнят- них вимог пов’язана з причалами, що повинні і забезпечити захист праці та безпечне пришвидшення суден, а також зменшити кількість наслідків аварій, які відбуваються під час роботи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Можливо, що ре- зультати цієї зустрічі матимуть значний вплив на проектування судна, зокрема на пристрої швартовних лебідок та відповідного обладнання на палубі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В даний час інструкції SOLAS (II-2 / 3–8) вважаються правила- ми для палубного обладнання, що використовується для причальних 278 операцій, шляхом визначення максимально допустимого наванта- ження для кожної одиниці обладнання та оснащення.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інструкції спрямовані на запобігання обмеженню доступу до ро- бочої області та мінімізацію обмеження видимості пропорційної зони, щоб уникнути впливу динамічних навантажень швартування персоналу, що бере участь у причалюванні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це правило II-2 / 3–8 додає нові предмети до вимог дизайну.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Спе- ціальна інформація повинна бути включена в так званий план бук- сирування та причалювання, описаний у нових інструкціях для про- ектування Міжнародної морської організації 1/1620 «Рекомендації щодо проектування причальних пристроїв та вибору відповідного швартового обладнання та оснащення для безпечного причалюван- ня».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У той самий час затвердження плану не вимагається адміністра- цією порту прапора.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Що стосується інспекції та технічного обслуговування, Комітет прийняв нові положення для всіх суден, незалежно від розміру та дати будівництва судна, вимагаючи перевірки обладнання причалу, включаючи кабелі та мотузки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перевірка Shridge зараз включає кіль- кість, силу, розмір, довжину, характеристики та обмеження.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Подаль- ші стандарти містяться в новому посібнику MSC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 / CHERC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1621 «Рекомендації щодо інспекції та обслуговування вологого обладнан- ня, включаючи швартування».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вимоги до швартовних пристроїв є особливо актуальними для конструкторів суден та суднобудівників, і їх слід обговорювати з клі- єнтом-судновласником.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вимоги до перевірки технічного обслугову- вання та заміни зіпсованого обладнання в основному важливі для судновласників та операторів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поправки набирають чинності з 1 січня 2024 року.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Процес швартування можливо розділити на кроки: 1) підхід судна на бажану відстань до причалу з поворотом у пра- вильному напрямку;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2) підхід судна за допомогою буксирів до певної позиції по відно- шенню до причалу та утримування у цьому положенні під час подан- ня швартування;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3) затягування судна до причалу за допомогою спеціального об- ладнання [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кожен з цих етапів причального процесу індивіду- альний.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Захід судна в порт призначення, з точки зору складності навігації, забезпечення радіоелектронного контролю та контролю інформацій- 279 ного навантаження, може бути диференційованим на ряд етапів, які можна назвати фазами судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такий поділ дозволяє більш чітко ви- сунути вимоги до точності визначення місця розташування судна у порту, а також дозволить оцінити безпеку суднобудівництва та заходи щодо зменшення впливу на можливі надзвичайні ситуації на кожно- му етапі судноплавства.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таке розділення забезпечується в 1983 році постановою Міжнародної морської організації A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='529 (13), але це сто- сується вузького аспекту судноплавства: точність розташування [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У той же час безпека суднозаходу залежить від великої кількості фак- торів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виходячи з вищезазначеної практики суднових вод, можливо окремо розібрати чотири етапи суднозаходу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перший етап суднозаходу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідно до Резолюції A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='529 (13) «Компенсаційні стандарти» рейс судна можна розділити на вхід до гавані та підходи до неї, а та- кож воду, яка має обмеження маневру та інші води.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для цього поді- лу майже всю відстань першого етапу суднозаходу відносить до етапу «інших вод».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для цього місця шлях руху точність навігації не повинна бути гіршою, ніж 4 % від відстані небезпеки, але не більше 4 морських миль [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На цьому етапі рейсу говоримо про відстані до небезпеки, що розраховуються десятками миль.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тоді порядок необхідної точнос- ті є долі та одиниці миль.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Саме цей етап суднозаходу, як показують статистичні дані, харак- теризується відносно низькою ймовірністю інцидентів та катастроф, що пояснює вказаний знижений рівень запиту до точності визначен- ня координат судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Слід зазначити, що перераховані параметри систем спостеріга- ються в ідеальних умовах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Але на практиці існують особливості, які обмежують можливості перелічених систем, такі як обмеження здат- ності діапазону узбережних РЛС (± 75 м), наявності зон та «радіоті- ні», а також екранування великим судном навколо розташованого невеликого судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Аналіз зазначеної інформації, а також параметрів суднових наві- гаційних інструментів дає можливість зробити висновок: у першій ін- формаційній фазі суднозаходу перераховані засоби навігації, залежно від їх ідеальної роботи, задовільно забезпечують необхідну точність визначення розташування судна, що заходить у порт.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Другий етап суднозаходу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Другий інформаційний етап суднозаходу відноситься до стадії рейсу, визначеного в «стандартах оцінки» [15], як «вхід до гавані та 280 підходів до неї, а також воду, в якому свобода маневру обмежена».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідно до [15], «вартість допустимої похибки місця залежить від місцевих умов, а його визначення є функцією відповідних адміні- страцій».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зрозуміло, що в умовах обмеженого маневру підходу до воріт фар- ватера потрібна більша точність місцезнаходження, ніж це було на першому етапі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ця заява є актуальною, оскільки періодично спосте- рігаються навали суден на воротах фарватера.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, з точки зору інформаційного модуля для визначен- ня точності навігації на третьому етапі суднозаходу, як у другому, іс- нуючі системи задовільно виконують свої функції, але в критичних ситуаціях їх ненормального функціонування на судні необхідно мати резерв для автономного визначення простору з точністю щонаймен- ше 10–15 л.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Четверта фаза суднозаходу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ця фаза характеризує причальний процес швартування судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Особливість цієї фази носія судна полягає в тому, що підхід судна до причалу здійснюється, як правило, коли двигун швартовного судна вимкнено, що призводить до повної практично неконтрольованої поведінки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тому завдання безаварійного швартування багато в чому визначається оператором, який контролює технологію швартування [16;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Більшість надзвичайних ситуацій у причалі пояснюються від- сутністю технічних засобів об’єктивного контролю підходу судна до пристані.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Аналізуючи навали суден на причали та їх об’єктах, можна стверджувати, що існує точне знання не тільки розташування суд- на щодо причалу, а й облік впливу найбільш складного компонента будь-якого технологічного процесу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зростаючі вимоги до безпеки навігації на кожному з етапів судно- заходу висуваються не тільки для покращення технічного обладнання суден, а передусім зміцнення технічного контролю за діями опера- тора [18;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тому Міжнародна морська організація та адміністрація морських портів світу в останні роки здійснюють активну роботу зі створення [20]: – розділення шляхів суднопроходів в місцях з інтенсивним ру- хом;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – зон з обов’язковими або добровільними радіоповідомленнями між суднами, коли вони наближаються один до одного або прохо- дять;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 281 – удосконалення системи управління рухом суден (СУРС) у пор- тах та підходів до них з поступовим збільшенням автоматизації конт- ролю за якістю судноплавства, доставки в морських районах;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – забезпечення засобами високоточного розташування суден у прибережних водах, використовуючи контрольні та коригувальні ди- ференціальні станції глобальних навігаційних супутникових систем (ДГНСС) ГЛОНАСС та GPS-типу;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – суцільного радіочастотного покриття (виключити тіньові зони) прибережні смуги морських територій — глобальної морської кому- нікаційної системи та забезпечення безпеки (ГМСЗБ) з цілодобовим надійним УКВ-зв’язком;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – супутникової морської системи зв’язку ІНМАРСАТ, що забез- печує глобальне та ефективне спілкування з суднами, розташовани- ми в будь-якій частині світу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Як частина роботи, проведеної в Міжнародній морській організа- ції, щоб переглянути главу 5 «Навігаційна безпека» Конвенції про за- хист людського життя на морі (SOLAS), передбачається найближчим часом вставити принципово нову автоматичну інформацію (іденти- фікацію) системи (AIS) на морському флоті.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перша версія AIS, вве- дена у всьому світі, виконує три основні функції: – автообмін навігаційними даними між суднами, коли необхідна розбіжність у морі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – передача даних про судно та його вантаж до прибережних по- слуг, коли воно плаває в контрольованих областях, з обов’язковими повідомленнями;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – перенесення навігаційних даних з судна до прибережних СУДС, забезпечуючи більш точну та надійну проводку в зоні дії системи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' автоматична інформаційна система — це морська навігаційна система,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' в якій взаємний автоматизований інформацій- ний радіообмін використовується як між суднами,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' так і між суднами та прибережними службами,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' під час яких вони передають інформа- цію про позивний та назву кожного судна (для їх ідентифікації),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' їх координати,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' параметри (розміри,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' навантаження,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' осадка тощо),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' цілі рейсу,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' параметри руху (курс,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' швидкість тощо) для вирішення про- блем попередження зіткнень суден,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' моніторингу дотримання режиму плавання та загального моніторингу статусу безпеки в контрольова- ному морському районі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Серед найважливіших компонентів розвитку мережі АІС слід розглядати введення служби диференціальної підсистеми глобаль- 282 них навігаційних супутникових систем (ДГНСС) типу американ- ського GPS, додавання яких діфпідсістемами вирішує пробле- му високоточного визначення місця судна з підводною точністю (d5 M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, незважаючи на широке впровадження високоточ- них навігаційних систем (ГНСС ГЛОНАСС, GPS), а також засобів автоматичної ідентифікації суден (АІС), проблема забезпечення без- пеки швартування залишається на останньому етапі суднозаходу [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Четвертий етап швартування є найскладнішим та відповідальним, що вимагає безперервного радіоелектронного контролю процесу набли- ження судна до причалу, а вимірювання до причалу потрібно визна- чити з точністю долі метра.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Аналіз літератури показує, що основний резерв вдосконален- ня потребує вдосконалення інтелектуально-інформаційних систем швартування різних типів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Потрібно враховувати, що кожна шварто- ва робота має свої особливості відповідно до погодних, кліматичних, структурних особливостей суден [21], незалежно від того, яка ситуа- ція, надзвичайна ситуація або вантажна робота: – швартування до судна, що лежить у дрейфі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – швартування до судна, що рухається;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – швартування до судна, що стоїть на якорі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – швартування кормою до причалу в портах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Автоматизовані системи швартування раціоналізують експлу- атацію причалу і забезпечують максимальну віддачу роботи порту.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Швартування в автоматичному режимі гарантує надійне кріплення судна і надає переваги з точки зору технічної та екологічної безпе- ки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Функції сигналізації таких систем використовуються в режимі реального часу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для проникнення в сутність автоматизованих процесів шварту- вання і стикування виділяють основні автоматизовані пристрої швар- тування і стикування: магнітний;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' лазерний і вакуумний.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо аналізувати швартувальні операції, побачимо, що прийняті заходи, хоча зменшують рівень аварійності, але проблема безпеки за- лишається актуальною завдяки багатьом факторам, включаючи слаб- ке інформування судноводія про поточні параметри швартування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для покращення управління та прийняття належного рішення судно- водію потрібні спеціальні технічні засоби швартування, що оперують даними вимірювань реальних параметрів розташування, швартуваль- ного судна за допомогою системи, яка отримує та обробляє поточну 283 інформацію про зміну цих параметрів, що видає оператор судноводію в зоровій формі небезпечної ситуації та що сигналізує звуковим сиг- налом, кольоровим сигналом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Технічним варіантом такого рішення може бути система аналізу швартування та контролю над підходом судна до причалу з попередженням поточного середовища — інди- катор безпеки, наприклад, який є технічним інструментом, який виконує прийом, обробку та зберігання інформації, необхідної для швартування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідно до використання розробленої прогностич- ної математичної моделі та програмного забезпечення цей пристрій повинен відображати результати обробки даних на екрані індикато- ра, як у формі ймовірнісної картини підходу судна до причалу, так і рекомендації судноводію у формі резервного часу та прогнозованої відстані.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ці вимоги на вищому технічному рівні застосовуються до безекіпажного судноплавства.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розглянемо характеристики систем швартування, які прийняті для безекіпажного судноплавства: Магнітна система автоматичного швартування (рисунок 2) конт- ролює процес за комплексом динамічних впливів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Система склада- ється зі здвоєних мертвих якорів, носових і кормових, оснащених магнітними подушками для надійного і міцного кріплення до будь- якого корпусу, плоского або вигнутого, пофарбованого або покрито- го корозією.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Подушки можуть пересуватися за корпусом з урахуванням змін по висоті.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Магнітна система має жорсткі обмеження: дорожнеча експлу- атації (енергоспоживання, професійне обслуговування), додаткове навантаження на корпус (вітри можуть деформувати борт) — подуш- ки потрібно ставити в районі шпангоутів, що означає пристосовува- тися під конкретний корпус.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У надійності є сумніви, оскільки трос, що лопнув, замінюється, а подушка, що вийшла з ладу, — не має замі- ни.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Дана система знайшла своє застосування на швидкому прийнятті рішення судном — пороми.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Є заборона використання системи авто- матичного навантаження на танкерах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Така заборона випливає з того, що система при поздовжньому «протягуванні» корпусу вздовж при- чалу, під дією хвилі або проходить поруч судна, змінює навантаження в шпринг і поздовжніх з системою контролю натягу кінців.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Така дія призводить до деформації корпусу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Застосування технології вакууму в швартових операціях і її роз- робки ведуть багато компаній, які здійснюють науково-дослідні, тех- нологічні системи швартування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 284 Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Конструкція системи швартування «The intelligent Dock Locking» Вакуумні системи автоматичного швартування (рисунок 3) для утримання судна біля причалу замість канатів використовують ва- куумні подушки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У кожної подушки є своє контрольоване робоче навантаження, яке може забезпечити надійне фізичне з’єднання судна з причалом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вакуумні подушки випробовуються і класифіку- ються під наглядом міжнародного класифікаційного товариства Det Norske Veritas (DNV), результати якого суміщені з сучасними триви- мірними апаратними засобами, показують діапазон ходів і пружну еластичність автоматичних систем на рівні швартування за допомо- гою канатів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інформація про навантажені утримання надходить від вимірювання рівнів вакууму і поперечних сил в носовій і кормовій тумбах.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оскільки вакуумна система може тримати судно ближче до причальної стіни, ніж перехрещений канат, ця система має причаль- ну продуктивність.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Маючи інформацію про всі умови швартування в режимі реального часу, оператор повністю контролює швартуваль- ний стан судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ManipulatorArmHydraulics HydraulicsPowerUnit MagnetPadsincluding HydraulicCyiinder PadEyeConnoction Framo285 Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вакуумна система швартування «Auto Moor» Такі системи високоефективні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тисячоліття для швартування су- ден використовують канати, але протягом багатьох років процедура не стає менш небезпечною.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Автоматичні вакуумні швартові системи вирішують проблему на- тиском однієї кнопки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' І менше ніж за 1/4 хвилини дозволяє спрацю- вати.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такі системи тримають судна всіх розмірів у одному місці в пор- тах, де присутні брижі та довгі хвилі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Лазерна система швартування (рисунок 4) яка відноситься до кла- су інструментальних систем, безперервно веде розрахунок дальності до судна кожним далекоміром.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На основі отриманих даних система обрисовує візуальне положення судна з розрахунковим кутом щодо пірсу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Крім дальності і кута, система розраховує швидкість зближення або віддалення з пірсом як носа, так і корми.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У разі наближення суд- на на близьку відстань з перевищенням зазначених в налаштуваннях швидкостей, відразу сигналізує про це через індикацію в інтерфейсі, а також через сирену на пірсі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оцінюючи характеристики систем швартування, розробники без- екіпажних судів схильні до використання лазерних систем.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Осно- вною особливістю другого етапу швартування є зближення судна з причалом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При швартуванні часто неминучий контакт судна з при- TRELLEBORG 01286 чалом з ненулевою швидкістю, який називається навалом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Класифі- кують навали як навмисні, так і випадкові, що виникають при кон- такті судна з причалом, іншим стаціонарним об’єктом або з іншим судном, розташованим на відстані або паркуванні [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Оскільки роз- міри судна фіксуються, єдиним способом уникнути навалу судна на причалі є ретельне вимірювання швидкості підходу судна та відстані до причалу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розміщення судна до причалу, як правило, здійснюєть- ся за допомогою буксирів [15;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З початку етапу зближення вони розгортають судно правою стороною паралельно причалу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Завдання буксирів включає підводку судна близько до причалу і тримання його в цій позиції, доки не будуть заведені та обтягнуті швартові.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поста- новка судна до причалу є небезпечною технологічною операцією, яка вимагає кваліфікованих та своєчасних дій судноводія, який управляє технічними засобами судноводіння, доставки та буксирів при збли- женні судна з причалом [15;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Концепція лазерної системи швартування Відмітна характеристика лазерної системи — сканування лазерно- го променя у вертикальній площині і отримання профілю відстаней з подальшою обробкою і визначенням відстані до причалу чи іншого об’єкта.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо аналізувати особливості лазерної дальнометрії, вона покаже, що експлуатація дальнометрії на причалах виявила свою на- LEO screen Wind speed, wind direction Monitor screen Temperature Distance (m) Distance (m 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='8 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='9 sis Speed 19 19 Acouisitoncontrolcabinet Laser senso DCd computer Sea level, flow rate Quick release hook287 дійність, легкість експлуатації, мінімум технічного обслуговування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Однак ця система не може вирішити всі проблеми порушення пра- вил, які найчастіше встановлюються адміністрацією порту під час швартування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тому необхідно більш глибоко розглянути можливість інформаційної підтримки причального процесу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Аналіз показує, що для забезпечення безпеки швартування використовується не весь ін- формаційний потенціал цих систем.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виявилося, що лазерна система швартування, що формується програмним забезпеченням для лазер- ної системи, дозволяє розширити інформаційну підтримку процесу швартування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Така система працює на підставі відстані з двох датчи- ків, розраховує швидкість і прискорення щодо цього об’єкта, а також можливо і визначення центру обертання судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За рахунок застосу- вання в пристрої датчика кута нахилу при розрахунках будуть ком- пенсуватися качка корабля і різні розмірені параметри суден і при- чалів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У цих системах виробляються точні вимірювання в реальному часі, дані про відстані і швидкості судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інформаційні потоки даних за параметрами зближення судна з причалом, виміряні лазерною швартовою системою великотоннажних суден (ЛСШКС), переда- ється до телеметричного пристрою за допомогою інтерфейсу модуля, призначеного для поєднання цих технічних засобів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Через переда- вальну антену поточна інформація надходить у радіопристрій, розта- шований на судні.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перетворена для подальшої обробки інформація через інтерфейс надходить у блок обчислення, де параметри розра- ховуються протягом всього швартування судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Індикатор забезпечує такі режими візуалізації: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відображає розраховану ймовірність перевищення швидкості судна під час контакту з причалом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Хронологія зближення судна з причалом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Комбінований режим відображення фактичної швидкості суд- на та ймовірність перевищення швидкості на момент контакту з причалом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Автоматичний режим включення аналізу поточної ситуації з прогнозними оцінками підходу судна до причалу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Найбільш інфор- мативним є автоматичний режим включення аналізу поточної ситуа- ції з передбачуваними оцінками підходу судна до причалу, що дозво- ляє попередити судноводія про те, яка ситуація може виникнути під час першого дотику судна до причалу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' «Trelleborg», «Strainstall», «A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' & Marine (Thai) Co.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='» і «MARIMATECH» є ключовими розробниками автоматизованих 288 систем швартування в світі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Система «Smart Dock», розроблена «Trelleborg», складається з двох лазерних датчиків, контролера і центрального персонального комп’ютера.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Дані про процес стиков- ки, а також аварійні сигнали при досягненні ризику критичних меж подаються декількома способами, в тому числі за допомогою вели- кого екрану на причалі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Персональний комп’ютер в центрі управ- ління реєструє дані і забезпечує графічне представлення всього процесу [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Система швартування «MARIMATECH» використовує два лазе- ри, які встановлені на пристані і міряють відстань до сторони набли- ження суден, далі обчислює швидкість і кут нахилу судна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Концепція системи «MARIMATECH» заснована на дистанційній передачі да- них.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Дані відображаються на встановленому на причалі цифровому великому екрані, бездротових пристроях, таких як портативні пей- джери або кишенькові персональні комп’ютери, на комп’ютерних моніторах диспетчерської.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Лазерна система швартування «Dock Aler» від «Strainstall» ви- користовує блоки безпечного для очей лазера, встановлені по оби- дві сторони від головки причалу, для вимірювання відстані від носа до корми щодо причалу, а також забезпечує швидкість і кут нахилу судна до причалу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Дані від цих лазерів надходять в центральну сис- тему управління, де вони можуть відображатися в диспетчерській, і передаватися переносним пейджерам, кишеньковим персональним комп’ютером і / або дисплеєм [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Висновки: Світові концерни, дослідницькі компанії роблять спро- би для втілення концепції безекіпажного судноводіння в реальність.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для цього необхідно поєднати безаварійну експлуатацію судна та за- конів держави прапора, рішення портових органів загальної міжна- родної юрисдикції.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Застосовувані інновації, що використовуються в безекіпажному судноводінні, дали привід для дискусій в журналах, на конференціях і семінарах з розвитку судноплавства.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У судноплав- стві одна з фундаментальних змін — це реалізація концепт-проектів безекіпажного судноводіння.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Цей напрямок включає одну з пере- ваг — підвищення безпеки судноводіння за рахунок використання інновацій.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У роботі представлено огляд рівнів управління автономними сис- темами в судноплавстві.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наголос зроблено на системи швартування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наведено характеристики вакуумних, лазерних, магнітних систем.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Безекіпажне судноводіння схиляється до використання систем ла- 289 зерного швартування за рахунок розширення можливостей інформа- ційного забезпечення швартування із застосуванням системи, яка ви- дає рекомендації у вигляді резервного часу і прогнозованої дистанції, що знижує ймовірність помилок.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Як підсумок — безпека швартуван- ня підвищується.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Стикувальна система «Dock Aler» [23] СПИСОК ВИКОРИСТАНОЇ ЛІТЕРАТУРИ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Pipitsoulis C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The EU eMaritime initiative — Single Window, with a view to the near future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' In Logious Conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Rotterdam, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Пунченко Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Праксеологія безекіпажних засобів водного транспор- ту, ризики автономни систем.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інформаційні технології та комп’ютерне моделювання ІТКМ-2021: міжнародна науково-практична конферен- ція.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5–10 липня 2021 року, Івано-Франківськ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Івано-Франківськ, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 35–36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Strelbitskyi V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Punchenko N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Tsyra O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Shaping the future of the marine in- dustry as a condition for adaptation in an innovative society.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Інтелектуальні системи та інформаційні технології ISIT-2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13–19 вересня 2021 року Одеса.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Одеса, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 116 –120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ISBN 978–617–7711–43–7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Медународная конвенция по охране человеческой жизни на море, SOLAS 74/88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' СПБ ЗАО ЦНИИМФ, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 720 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Международная конвенция о подготовке и дипломированию моряков и несению вахты.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1978 г.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' з Кодексом 1995 года.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ЗАО ЦНИИМФ, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 552 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 290 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Международная конвенция по предотвращению загрязнения MARPOL 73/ 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ЗАО ЦНИИМФ, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 720 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Международная конвенция по поиску спасания SAR-79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ЗАО ЦНИ- ИМФ, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 64 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Международное авиационное и морское наставление по поиску и спаса- нию.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='ЗАО ЦНИИМФ, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 448 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Процедура контроля судов государством порта (Резолюция ИМО А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 787(19)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ЗАО ЦНИИМФ, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 237 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' МППСС72, Лондон, ИМО, 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 56 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Морские суда без экипажей — реальность и перспективы : сборник на- учных докладов по итогам «круглого стола», проводимого совместно кафедрой «Морское право» Юридического института Российского уни- верситета транспорта (РУТ) и Ассоциацией междуна-родного морского права/под редакцией В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Гуцуляка.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Москва : Юридический институт РУТ (МИИТ), 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 41 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Титов А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Баракат Л.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Морские интеллектуальные технологии.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Пер- спективы технологического развития и внедрения безэкипажных судов.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 94–104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Пунченко Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На шляху до індустрії 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0: інформаційні технології, мо- делювання, штучний інтелект, автоматизація.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вплив нейронних мереж на достовірність прогнозу дрейфу судна, як напрямок безпеки судноводіння: кол.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' монографія за заг.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ред.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Котлика.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Одеса: Астропринт, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 544 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ISBN 978–966–927–702–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Jorgensen J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Autonomous Vessels: ABS’ Classification Perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Discussion Issues in Technology, Safety and Security for the Marine Board, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Лицкевич А.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' П.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Росторгуева Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Надежность системы управления дви- жением судов с резервом времени.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Известия высших учебных заведений Северо-Кавказский регион.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Технические науки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Проблемы водного транс- порта.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ч.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ростов-на-Дону: РГУ, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 118–120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Росторгуева Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Юсупов Л.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Демьянов В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Статистическая база для оценки влияния человеческого фактора при швартовке судна к при- чалу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Стратегия развития транспортно-логистической системы Азово- Черноморского бассейна: материалы международной научно-технической конференции совместно с секционными заседаниями VI региональной НТК «Проблемы безопасности морского судоходства, технической и коммерческой эксплуатации морского транспорта».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Новороссийск: МГА имени адмирала Ф.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ф.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ушакова, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 175–177.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Росторгуева Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Юсупов Л.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Демьянов В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Синтез вектора воз- мущения скорости швартовки судна полиномиальной аппроксимацией её тренда.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сборник научных трудов.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Новороссийск: МГА имени адмира- ла Ф.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ф.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ушакова, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вып.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 97–100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Росторгуева Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Анализ и количественные оценки статистической базы параметров швартовки лазерной системы дальнометрии.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сборник 291 научных трудов.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Новороссийск: МГА имени адмирала Ф.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ф.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ушакова, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вып.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 100–104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Росторгуева Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Статистическое исследование распределения вре- менной базы циклов регулирования скорости швартовки вероятностной модели отказа системы «человек — машина».' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сборник научных трудов.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Новороссийск: МГА имени адмирала Ф.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ф.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ушакова, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вып.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 94–97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Росторгуева Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ю.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Юсупов Л.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Н.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Демьянов В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Компьютерное моде- лирование аварийной ситуации при швартовке судна в условиях дестаби- лизирующих возмущений.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сборник научных трудов.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Новороссийск: МГА имени адмирала Ф.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ф.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ушакова, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вып.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' С.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 92–94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Бурханов М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=', Ермолаев Г.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Г.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' и др.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Справочник капитана дальнего пла- вания.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' М.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=': Транспорт, 1988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 248 с.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' SmartDock® Laser Docking Aid System [Електронний ресурс].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' URL: http:// www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='trelleborg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='com/en/marinesystems/products--solutions--and--services/ docking--and--mooring/docking--aid--system/smart--dock--laser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (дата обращения: 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Jetty monitoring and management systems [Електронний ресурс].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' URL:http:// www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='strainstall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='com/files/9214/9693/6079/43917_James_Fisher_Jetty_Moni- toring_V1_WEB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' pdf (дата обращения: 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' АВТОМАТИЧНИЙ СИНТЕЗ МЕРЕЖ ПЕТРІ ПРИ РОЗРОБЦІ АЛГОРИТМІВ ЛОГІЧНОГО УПРАВЛІННЯ Гурський О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' О.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У роботі розглядається актуальна задача, пов’язана з розробкою мето- дів автоматичного синтезу мереж Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Важливість розробки цих методів обумовлена розвитком інтелектуальних систем, що забезпечують автома- тизацію трудомістких процесів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Запропоновано принцип автоматичного синтезу мереж Петрі та певних алгоритмів логічного управління на основі функціонування штучної нейрон- ної мережі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Представлений математичний опис методу зміни коефіцієнтів міжнейронних зв’язків мережі при синтезі мереж Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У програмному середовищі Matlab/Simulink 2012a були проведені експе- рименти, пов’язані зі спільним функціонуванням штучної нейронної мережі і мереж Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Функціонування мереж Петрі в середовищі Matlab/Simulink було представлено за допомогою Statflow діаграм.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У результаті експери- ментів були отримані часові характеристики функціонування штучної не- йронної мережі, яка забезпечує композицію мереж Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На основі часових 292 характеристик була встановлена принципова придатність застосування штучної нейронної мережі для забезпечення автоматичної композиції мереж Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В результаті було вирішено задачу, яка пов’язана з розробкою системи спільного функціонування нейронної мережі і мереж Петрі для формування алгоритмів та послідовних обчислень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тим самим одержали подальший роз- виток методика автоматичного синтезу мереж Петрі та методика роз- робки певних алгоритмів на основі функціонування нейронної мережі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The important task was solved during the scientific research related to the de- velopment of the methods for automatic synthesis of Petri nets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The importance of development of these methods is due to the evolution of intelligent systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' These systems provide the automation of labor intensive processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The principle of automatic synthesis of Petri nets and the implementation of cer- tain algorithms for tuning complex control systems based on the functioning of an artificial neural network are proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The mathematical description of the method for changing the coefficients in neural connections of network in the synthesis of Petri nets is presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The experiments were conducted in the Matlab\\Simulink 2012a environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' These experiments were bound to the joint functioning of an artificial neural network and Petri nets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The functioning of Petri nets was presented in the Matlab \\ Simulink environment using Statflow diagrams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' As a result of the experiments we have obtained the temporal characteristics of the functioning of artificial neural network providing the composition of Petri nets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The fundamental suitability of using artificial neural network to provide the auto- matic composition of Petri nets was determined on the basis of analysis of temporal characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' The problem linked to the development of system for the joint functioning of neu- ral network and Petri nets for the formation of algorithms and sequential calcula- tions was solved in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Thus the method of automatic synthesis of Petri nets and the method of developing of the certain algorithms based on the functioning of a neural network were further developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Мережі Петрі як прикладний математичний апарат досить відомі в області моделювання і аналізу дискретних динамічних або логіко- динамічних систем.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Також мережі Петрі відомі як форми представ- лення паралельних алгоритмів і обчислень [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Актуальність розробки принципів автоматичного синтезу мереж Петрі лежить в області автоматизації процесу розробки алгоритмів логічного управління.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Як приклад варто відзначити так звану задачу про «розумну мурашку», яка представлена в роботах [2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Мураха за допомогою проб та помилок, мутації будує автомат своєї поведінки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Але безсумнівно, що процес синтезу алгоритму носить інтелектуаль- 293 ний характер, в даному випадку можливо задіяти відповідну інтелек- туальну технологію, пов’язану зі штучними нейронними мережами і їх алгоритмами навчання [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, нами вирішується задача, пов’язана з розробкою принципів синтезу алгоритмів і відповідних композицій мереж Петрі на основі певної інтелектуальної технології.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У роботі представлено етап розвитку певної інтелектуальної сис- теми до застосування штучної нейронної мережі та алгоритми на- строювання штучних нейронних мереж, пов’язаних з автоматичним синтезом мереж Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відомо, що можливість автоматичного синтезу та існування ме- тодів автоматичної побудови мереж Петри відзначалися ще в роботі Джеймса Пітерсона [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З того часу з’явився ряд наукових публіка- цій, пов’язаних з автоматичною генерацією і композицією мереж Петрі, у яких відображаються особливості побудови мереж Петрі, засновані на певних методах [6–9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Аналогічно з’явилася робо- та [10], у якій автоматичний синтез мереж Петрі здійснюється на основі методу перевірки досяжності дискретно-безперервних мереж [11;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо метод перевірки досяжності деякого стану в просторі змінних пов’язаний з перетворенням дискретно-безперервної мере- жі (ДБ-мережі) до одного переходу (елемента мережі Петрі), то при автоматичному синтезі мережі Петрі процес зворотний, з одного переходу перетворюється мережа Петрі, яка представляє досяжність деякого стану гібридної системи (з керованою структурою — СКС) [13;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Досяжність стану СКС можна забезпечити при наявності відпо- відного алгоритму логічного управління.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такий алгоритм дозволить реалізувати k-процес функціонування СКС ∑I+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У даному випадку повинна існувати послідовність запусків переходів ДБ-мережі, що представляє модель системи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, засоби ДБ-мереж дозво- ляють досліджувати досяжність системи на основі правил редукції мережі, а правила редукції мережі і методи перевірки досяжності віді- грають важливу роль у розробці формуючого автомата, синтезуючого мережу Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Далі розглянемо формування алгоритмів на базі методу перевірки досяжності ДБ-мереж.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формування алгоритмів на базі методів перевірки досяжності дис- кретно-безперервних мереж.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перевірка досяжності системи шля- хом редукції безперервної і дискретної частин ДБ-мережі полягає 294 в «згортці» мережі за певними правилами до макропереходу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, при формуванні алгоритму дискретну мережу Петрі також можна розгорнути — сформувати аналогічно, як згорнути до макро- переходу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для формування мережі Петрі, що представляє алгоритм логічно- го управління, були виділені такі правила формування матриці інци- дентності W: – рядок повинен починатися з 0 або +1 і значення в рядках повин- ні чергуватися — 0, +1, 0, -1, 0 і т.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' д.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – поява хоча б однієї +1 у стовпці повинна супроводжуватися по- явою хоча б однієї -1 у тому ж стовпці;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – у рядку не може йти підряд дві та більше +1 або -1 навіть через нулі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' – для виключення формування занадто складних алгоритмів в одному рядку не може бути більше двох пар +1, -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Фрагмент алгоритму формування матриці інцидентності згідно з вищенаведеними правилами представлений у вигляді Stateflow діа- грами на рисунку 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З рисунка 1 видно, що автомат представлений паралельними станами StateC4, StateC5, StateC6 … StateCN, де N — кількість рядків формованої матриці інцидентності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перехід з підста- ну State19 або State24 у підстани State20 або State25, тобто поява –1, супроводжується переходом з підстану State22 або State26 у підстани State23 або State27 (появою +1 у тому ж стовпці).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Слід зазначити, що перехід зі State19 або State24 в State20 або State25 може супроводжуватися залежно від умови data01> -10 з ви- тримкою за часом або без умови.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У цьому випадку формується мере- жа Петрі, у якій мають місце переходи з наступними умовами спра- цьовування: 0 ( ): ( ) 1& & i j i j k p I t p J g t t ∀ ∈ µ = < < , ( ): ( ) 1& i j i k p I t p t t ∀ ∈ µ = < , де μ(pi) — маркування вхідних позицій переходу tj;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' g — граничне зна- чення J0j деякого критерію якості роботи системи;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' tk — час витримки по спрацьовуванню переходу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Переходи з різними умовами спрацьовування вибираються за- лежно від значення сигналу формування алгоритму data14 або data15 і т.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' д.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Сигнали формування алгоритму V1 ….' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Vn відіграють важливу роль у визначенні динаміки станів автомата формування матри- 295 ці інцидентності мережі Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Поява тієї або іншої одиниці +1 реалізується залежно від значення сигналів V1 ….' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Vn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наприклад, перехід зі стану State22 в State23 може здійснюватися за умовою [data24>0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5&data15>2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5], де data24 — локальна змінна Stateflow-діа- грами, а data15 — значення сигналу V1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Stateflow-діаграма, що представляє автомат формування матриці ін- цидентності (зв’язків між елементами мережі Петрі) Таким чином, дана Stateflow-діаграма здатна представляти вели- ку кількість усіляких алгоритмів, навіть можливо непередбачуваних експертом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Створення алгоритму визначається залежно від сигналів V1 ….' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Vn, а ці сигнали можливо коректувати, якщо алгоритм є неза- довільним.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Як показано на рисунку 2, залежно від установлених сигналів V1 ….' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Vn і за значеннями показників — J01, J02, J03 автомат формування StateC4 after(2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='tick [data28>0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5&data14≤0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='9] [data02>-10] [data14<0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='9] State 18 State19 State 20 State 21 State 17 after(50,tick) data4=0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' data4= -1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' after(50,tick) data4=0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' data4=0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' data4=1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' exitdata24=1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' exit:data24=0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' [data14>0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='9] [data22>0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5&data14≤0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='9] after(2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='tick) StateC5 after(2000,tick) [data26>0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5&data15<2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2] [data02>-10] [data15>0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5] State 23 State: 24 State 25 State 31 State 22 after(50,tick) data5=0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' data4= -1, after(50,tick) data5=1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' data5=0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' data5=0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' exit:data25=1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' exit:data25=0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' [data15<0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5] [data22>0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5&data15<2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2] after(2000,tick) [data240.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5&data15<2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5] StateC6 after(2000,tick) [data25>0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5&data16<2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2] [data02>-10] [data16>1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2] State 27 State:28 State 29 State 30 State 26 [data15<0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5] after(50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='tick) data6= -1, after(50,tick) data6=1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' data6=0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' data6=0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' data6=0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' exitdata26=1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' exitdata26=0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' [data16<1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2] [data25>0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5&data16<1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2] after(2000,tick)296 матриці інцидентності виробляє послідовність значень, з яких скла- дається матриця інцидентності мережі Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Структурна схема, що відображає модель формування мережі Петрі Однак виключення експерта в побудові мережі Петрі та у визна- ченні деякого алгоритму управління веде до того, що представляється відсутність прикладного характеру синтезованої мережі Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У та- кому випадку в роботі [15] була запропонована автоматична компо- зиція мережі Петрі на базі функціонування нейронної мережі, яка представляє інтелектуальну технологію у визначенні деякого алго- ритму логічного управління.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Надалі модуль визначення сигналів V1 ….' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Vn буде представляти- ся нейронною мережею, а Stateflow-діаграми показані на рисунку 1, можуть бути представлені відповідними синхронно функціонуючими мережами Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формування алгоритмів на базі функціонування штучної нейронної мережі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, синтез мережі Петрі на основі функціонуван- ня штучної нейронної мережі становить область формування й авто- матичного синтезу мереж Петрі [5;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Як показано на рисунку 3, у цьому випадку нейронна мережа взаємодіє на принципах зворотного зв’язку із синхронно функціонуючими мережами Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Із цих син- хронно функціонуючих мереж можливо сформувати композицію, яка буде відображати певний алгоритм дій, реалізованих штучною нейронною мережею.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Матриця коефіцієнтів міжнейронних з’єднань вихідного шару нейронної мережі має певну аналогію з матрицею ін- цидентності мережі Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, нейронна мережа генерує ABToMaTopMyBaHHMaTpML MoAynbMepekeTpi iHUMAeHTHOCTi Step8 +fata1i tp1 Step7 d=t=12 l=t=1 Outz tp2 u(o) Step8 Hd=t=13 d=ts2 tp3 n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3 Out3 u(og) Step5 d=t=14 dst=3 In.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4 Out4 data15 tp4 μ(P4/ Step4 l=t=4 Out5 Step3 data16 tp5 μ(Ds) Step2 d=t=17 d=t=5 Qut?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' μ(Pg) tp6 Step1 d=t=18 d=t= 1- 7 Out7 MoAynb BM3HayeHHAcWrHaniB tp7 u(p) Step d=t=01 d=t=7 n8 Quts tp8 u(pg) cbopMyBaHHanropMTMy d=t=02 datasl ns Qut?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' tata03 Chart3 n10 Out10 b Subsysteme 01, 202 J03297 вихідні сигнали, аналогічні матриці інцидентності синтезованої ме- режі Петри.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Схема синтезу штучної нейронної мережі і мереж Петрі при форму- ванні відповідних алгоритмів логічного управління в системі, w11,… wnj — ко- ефіцієнти міжнейронних з’єднань;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' t7,…t12 — дискретно-безперервні переходи, що забезпечують зв’язок між штучною нейронною мережею і мережами Петрі Функціонування мережі Петри можна описати рівнянням: 1 1 | | k k k M M A U − − = + ⋅ , де 0 | ( ),.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='. ( ) |T k n M p p = µ µ — вектор маркування мережі Петрі на k-му кроці;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 k M − — вектор маркування мережі Петрі на k–1 кроці;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' | | A — матриця інцидентності, яка визначає взаємозв’язок позицій і пере- ходів у мережі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 k U − — управляючий вектор.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому для даного випадку, якщо ( ) 1 ip µ = , де i=1…n, то зміню- ється значення відповідного параметра, наприклад, при настроюван- ні системи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Згідно зі схемою, представленою на рисунку 3, нейронна мережа представляє частину виразу 1 | | k A U − ⋅ та генерує матрицю ін- цидентності | | A синтезованої мережі Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо певний алгоритм дій при функціонувані деякої системи не- задовільний, то треба указати, на якому переході мережі Петрі була виявлена помилка в системі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це необхідно для перенастроювання ней ронної мережі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такий принцип автоматичного синтезу мереж Петрі неодноразово розглядався у наукових роботах [15–17], у яких показані різні експе- W11 10 S W12 M 13 Wnj n 10 WTyyHa HeИpoHa MepeKa /.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Artificial neural networks Mepexi eTpi /Petri Nets/298 рименти для підтвердження принципової придатності такого методу формування певних алгоритмів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Синтез мереж Петрі може бути заснований на композиції і деком- позиції мереж Петрі, тому що будь-яка мережа Петрі може складатися з однотипних функціональних підмереж [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Як показано на рисунку 4, при декомпозиції мережі Петрі N1 можна виділити функціональ- ні підмережі, які виконують різні логічні операції (АБО, І, операцію умовного переходу).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Декомпозиція мережі Петрі N на функціональні підмережі N1, N2, N3 При реалізації зв’язків між функціональними підмережами фор- мується мережа Петрі яка представляє певний алгоритм логічного управління.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У відомих роботах синтез мереж Петрі реалізуєтся на основі композицій і декомпозицій певних функціональних підмереж [18;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Однак такі функціональні підмережі можуть функціонувати ра- зом зі штучною нейронною мережею.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У цілому штучна нейронна мережа, що взаємодії з функціональними підмережами, може пред- ставляти роботу різних мереж Петрі як композицію роботи окремих підмереж.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, згідно зі схемою, представленою на рисунку 3, ДБ- мережа містить дискретні підмережі, пов’язані дискретно-безперерв- ними переходами ti 3, ti 4, де i=1…N [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кожна така підмережа є мере- жею Петрі, яку можна розглядати незалежно від усієї ДБ-мережі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' p N?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' p 10 N P11 Onepauia yMoBHoro nepexoAy Onepain AbO299 Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формування мережі Петрі при взаємозв’язку функціональних підмереж Нейронна мережа формує сигнали Vs=|V1 ….' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' V5|Т, згідно з якими здійснюється рух маркерів у мережах Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому рух маркерів носить погоджений характер.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наприклад, вихід маркера з позиції Р2 супроводжується появою маркера в позиції Р3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Погоджений характер зміни маркування в мережах Петрі дає мож- ливість виконати композицію цих мереж в одну загальну мережу Пе- трі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Як показано на рисунку 6 а, для композиції мережі Петрі необ- хідно об’єднати переходи, які одночасно спрацьовують у конкретний момент часу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На рисунку 6 а переходи t1, t3, t7, t8, t9 поєднуються пунк- тирними кривими.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наприклад, переходи t3, t7 поєднуються в один пе- рехід t3,7, який спрацьовує в окремому випадку в момент часу t2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' За допомогою такого об’єднання можна перетворити різні мережі в одну загальну мережу Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Згідно з рухом маркерів у мережах Петрі забезпечується фор- мування значень матриці інцидентності мережі Петрі, так само, як послідовна активізація підстанів Stateflow-діаграми, фрагмент якої представлено на рисунку 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Як показано на рисунку 6 б, з кожним кроком формується мережа Петрі згідно із процесом формуван- ня матриці інцидентності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Слід зазначити, що в окремому випад- ку поява переходу t1 була помилковою, тому що, наприклад, зміна маркування спричинила небажану зміну критерію якості роботи системи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У цьому випадку деякий блок автонастроювання повинен L Pm 10300 Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Візуалізація автоматичного формування мережі Петрі Step No 1 Step No 2 StepNo4 t10 D p a) Composition of Petri net b) Generation of Petri net301 випадковим образом змінити відповідні коефіцієнти міжнейронних з’єднань, зміна яких надалі дозволила би сформувати необхідну ди- наміку маркування, відповідну до мережі Петрі, організованої напри- клад на 4-му кроці.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Формування алгоритму при роботі нейронної мережі із синхронно функціонуючими підмережами Петрі здійснюється при зміні коефі- цієнтів міжнейронних з’єднань.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Зміна коефіцієнтів міжнейронних з’єднань тягне за собою коректування відповідного алгоритму.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У цьому випадку деякий алгоритм має місце як при наявності пев- ної локальної штучної нейронної мережі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Слід врахувати, що може бути деяка кількість вихідних алгоритмів при синтезі системи логічного управління і відповідно можна виділи- ти деяку кількість локальних штучних нейронних мереж, як показано на рисунку 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У процесі класифікації алгоритмів запускається відповідна ло- кальна нейронна мережа, яка вже безпосередньо буде брати участь у формуванні певного алгоритму.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У такому випадку автоматичний синтез мереж Петрі можна пред- ставити у два етапи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На першому етапі вибір певного алгоритму і відповідної мережі Петрі з можливих варіантів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На другому етапі ко- ректування обраного алгоритму і мережі Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Послідовність фор- мування такого алгоритму можна представити у вигляді рисунку 8, де відображені відповідні етапи синтезу мережі Петрі, що представляє формований алгоритм.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ці два етапи, які представлено на рисунку 8, можна реалізувати за допомогою штучної нейронної мережі та її тренування.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У цьому випадку необхідно представити інтелектуальну систему, що формує алгоритми логічного управління при автоматичному синтезі і компо- зиції мереж Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Надалі необхідно представити структурну схему та- кої інтелектуальної системи і при цьому визначити метод тренування штучної нейронної мережі при автоматичному синтезі мереж Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Алгоритми настроювання штучних нейронних мереж при автоматич- ному синтезі мереж Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Штучна нейронна мережа, як обчислювальна схема, що включає безліч обчислювальних одиниць — нейронів, може представити пев- ну інтелектуальну систему при наявності певного методу зміни ко- ефіцієнтів міжнейронних зв’язків.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Саме подібна зміна коефіцієнтів міжнейронних зв’язків, яка має місце в процесі навчання нейрон- ної мережі, може відігравати важливу роль у прояві інтелектуальних 302 Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Фрагмент схеми, що представляє візуалізацію автоматичного формування мережі Петрі на основі функціонування Xp1 Xp2 CMrHaMAA@OpMyBaHHA Xo Ta6WLi iHLMAeHTHOCTi C Xp3 W11 W12 W 11 13 KoMno3Muig, °23 nepexoAyMepexki 12 M nj WTyyHaHeMpoHaMepeKa /-Artificialneuralnetworks Xo p 10 W11 10 Xpn W12 W 03 11 13 MepekieTpi/PetriNets303 Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Схема формування алгоритму логічного управління і відповідного синтезу мережі Петрі особливостей нейронної мережі при розв’язані певних задач.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В окре- мому випадку такі задачі можуть бути пов’язані з автоматичним син- тезом мереж Петрі, а також з синтезом алгоритмів логічного управ- ління деяких об’єктів [3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Автоматичний синтез і композиція мереж Петрі припускає використання відповідних певних методів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Однак для того щоб сформована мережа Петрі була застосовна для розв’язку певно- го завдання, необхідне застосування інтелектуальних технологій, здатних замінити експерта в області формування певних алгорит- мів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наприклад, заміна експерта в області формування алгоритмів настроювання різних багаторівневих систем автоматичного управ- ління [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Особливості функціонування нейронної мережі при автоматичній генерації мережі Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Спочатку було встановлено, що автоматична генерація мережі Петрі повинна виконуватися при функціонуванні ней ронної мережі, що визначає інтелектуальну технологію форму- вання алгоритму управління деяким об’єктом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Така нейтронна мережа є багатошаровою і прямонаправленою.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кожний шар нейронної мережі несе певне функціональне наван- таження.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перший шар нейронної мережі забезпечує класифікацію ETan 1 AnropuTmnoriyHoro Bu6ip AnropuTm oriyHoro ynpaBiHH N1 ynpaBniHHANk neBHoro anropuTMy AnropuTM oriHoro ynpaBniHHN2 OuiHKa AnropuTm oriyHoro npWAaTHOcTi yNpaBniHHANen ETan 2 KopMryBaHH KiHeb o6paHoro epeBipkayMoB anropuTMy 3aBepWeHHA304 Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Спрощена структурна схема системи,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' що формує алгоритми логічного ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='управління при автоматичній композиції мережі Петрі на базі функціонуван- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='ня штучної нейронної мережі ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Mepexki leTpi /Petri nets/ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='IPn ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content="06'EKT " metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='yNpaBniHHA ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='V ' metadata={'source': 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+page_content='/ Synthesis and analysis ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='/ Tuning unit / ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='of Petri nets / ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3aBAaHHA ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='W61(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='(i(s) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='W21(7) ' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='W13(3) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='y2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='fy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='W14(4) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Kacwbikatop ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='(s) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='W15(5) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Y: ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='((s) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='AropTM 1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='「eHepaTop ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='iMnybciB ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='(s AnropuTM 2 IHTeeKTyabHa HeipoHHa Mepexa / Neural network / CWCTeMa305 можливих алгоритмів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Внутрішній шар визначає алгоритми управлін- ня.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вихідний шар забезпечує формування певної матриці інцидент- ності мережі Петрі, що представляє алгоритм логічного управління об’єктом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Як показано на рисунку 9, нейронну мережу можна розді- лити на сектори, кожний сектор представляє певний алгоритм управ- ління і відповідну матрицю інцидентності мережі Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У зв’язку з тим, що формування алгоритму представляється як покроковий — поетапний процес, кожний крок при формуванні алгоритму супро- воджується активізацією певного нейрона, названого початковим.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Найперший початковий нейрон можна назвати командним, тому що після його активізації локальна нейронна мережа починає функціо- нувати.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вибір командного нейрона для його активізації здійснюється на етапі класифікації алгоритмів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Такий процес класифікації також можна реалізувати за допомогою штучної нейронної мережі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Слід за- значити, що відправні нейрони W є в кожному секторі відповідної ло- кальної нейронної мережі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перенастроювання вагових коефіцієнтів міжнейронних з’єднань, пов’язаних з початковими нейроном, спри- чиняє коректування відповідного алгоритму, якщо він не задоволь- няє певним вимогам.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нейронна мережа як обчислювальна схема визначає матрицю інцидентності мережі Петрі набором коефіцієнтів міжнейроних з’єднань ( ) ij k w , пов’язаних з початковими нейронами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Матриця інци- дентності розглянутої мережі,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' представленої на рисунку 9,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' має такий ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='вигляд: ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='11(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='12(2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='13(#) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='14(4) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='15(5) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='16(6) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='21(7) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='22(8) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='23(9) ' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='p ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кількість стовпців матриці інцидентності W визначається кіль- кістю початкових нейронів, а кількість рядків визначається кількістю вихідних нейронів n-го (вихідного) шару нейронної мережі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 306 Певні умови спрацьовування відповідних переходів мережі Петрі визначаються ваговими коефіцієнтами вхідних з’єднань початкових нейронів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Набір вагових коефіцієнтів вхідних з’єднань початкових ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='нейронів також можна представити у вигляді матриці: ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 ' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='64(19) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='65(25) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='66(31) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='N ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='w ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У цій матриці N кількість рядків N1 ….' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' N6 відповідає різним умо- вам спрацьовування переходів, а кількість стовпців відповідає кіль- кості кроків формування алгоритму.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Згідно з рисунком 3 процес формування елементів матриці інци- дентності мережі Петрі здійснюється на базі вихідних сигналів y1…y8 нейронної мережі, що забезпечують паралельне — синхронне функ- ціонування відповідних мереж Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це дає можливість представити деяку композицію з відповідних мереж Петрі, яка відображає алго- ритм логічного управління певним об’єктом [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо алгоритм логічного управління об’єктом не відповідає за- даним вимогам, при яких здійснюється відповідна зміна значень критеріїв якості роботи системи, то блок автонастройки (Tuning unit) повинен змінити певні коефіцієнти міжнейронних з’єднань згідно з інцидентною матрицею синтезованої мережі Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Особливості архітектури нейронної мережі, що здійснює синтез ме- реж Петрі і формування алгоритмів логічного управління.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виходячи з вищерозглянутої схеми, представленої на рисунку 9, можна виділити деяку певну архітектуру нейронної мережі, яка може застосовуватися при формуванні алгоритму управління, відображеного відповідною мережею Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Така архітектура нейронної мережі, зображена на ри- сунку 10, представляється двошаровою зі зворотними зв’язками і з елементами затримки сигналів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Особливість функціонування такої нейронної мережі полягає в тому, що в будь-який момент часу може бути активним тільки один нейрон з n можливих нейронів у вхідному шарі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому активіза- 307 ція лише одного нейрона у вхідному шарі може викликати активіза- цію N нейронів у вихідному шарі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Архітектура нейронної мережі, що використовується при формуван- ні інцидентної матриці мережі Петрі Розрахунки синаптичних коефіцієнтів вихідних нейронів обчис- люються на основі синаптичних коефіцієнтів вхідних з’єднань почат- кових нейронів мережі за формулою: ( ) ( ) 1 1 m nk u nk k u nk nk n w w b w w = \uf8eb \uf8f6 = ⋅ − + − \uf8ec \uf8f7 \uf8ed \uf8f8 ∑ , де ( ) nk u w — синоптичний коефіцієнт n-го входу вхідного k-го нейрона;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' nk w — синоптичний коефіцієнт k-го входу вихідного n-го нейрона;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) k u b — величина зсуву вхідного k-го нейрона.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Ця формула розрахунків коефіцієнтів міжнейроних зв’язків ви- значена з умови активізації лише одного вхідного нейрона з n мож- ливих нейронів, у будь-який момент часу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Кількість відправних ней- ронів мережі повинна бути такою, щоб не повторювалися комбінації значень сигналів виходів Y1 … Yn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для перевірки принципової придатності розглянутої архітекту- ри нейронної мережі в програмному середовищі MATLAB/Simulink була реалізована відповідна схема, що представлена на рисунку 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2 Xo 以 M (s 11 W21 W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 11() X1 Y2 Ow, 5 M 22 W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' M 21(u) n+12 Wn+1le W2k Wik (u) X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='k Yn Wk M n+1k- f(s) k LWnk(u) n+1308 Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Структурна схема нейронної мережі з початковими нейронами Y1 Y4 X1 0 1 W11 HeipoH4 Constanto 事 Add Gain9 Gain10 本术本 Scope3 0 2 t, sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Unit Delay4 HoyaTKoBMM Gain11 netsum3 hardlim3 HeMpOH1 Gain1 netsum hardlim Scope2 W13 Y2 Gain15 Y5 Gain2 T Constant2 0 Constant3 X2 W HeipoOH 5 0 t, sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' H Scope4 Y2 Gain14 W21(u) 22 netsum4 hardlim4 netsum1 hardlimt Scope1 Gain4 Ws1(u) m T- 1 HoyaTKoBWM .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4 1 Y6 Gain5 0 Constant7 HeMpOH 2 Gain16 Constant Constant4 X3 W W31 0 2 HeMpOH 6 t, sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2/u) Scope5 Y3 Gain19 H 0 hardlim5 netsum2 hardlim2 Scope netsum5 Gain7 2 4 t, sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Y5 1 b3 HoyaTKoBWM 4 Gain8 0 HeMpOH 3 Constant1 Constant5 Gain20 2 t, sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Y6 TI N Unit Delay1 2 Unit Delay2 t, sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Unit Delay3309 Як вид но з рисунку 11, представлена схема нейронної мережі, що складається з 3 відправних і 3 вихідних нейронів, має зворотні зв’язки з елементами затримки сигналу.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Згідно з вищенаведеною формулою представимо наступні розра- хунки деяких коефіцієнтів міжнейронних з’єднань відповідної ней- ронної мережі: 3 32( ) 32 2( ) 2 32 1 1 1 (| 4 | (1 1 1)) 1 1 1 u u n n w w b w w = \uf8eb \uf8f6 = ⋅ − + − = ⋅ − − + + + − = \uf8ec \uf8f7 \uf8ed \uf8f8 ∑ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3 31( ) 31 1( ) 1 31 1 1 1 (| 4 | (1 0 0)) 1 1 3 u u n n w w b w w = \uf8eb \uf8f6 = ⋅ − + − = ⋅ − − + + + − = \uf8ec \uf8f7 \uf8ed \uf8f8 ∑ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' З відповідних часових діаграм активізацій нейронів, представ- лених на рисунку 11, видно, що в будь-який момент часу активний тільки один нейрон з 3 початкових, при цьому кількість активних вихідних нейронів різна.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тому що в кожний момент часу активний лише один нейрон у вхідному шарі, то розрахунки коефіцієнтів між- нейронних з’єднань були виконані вірно.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Алгоритм настроювання нейронної мережі за дозволеними комбіна- ціями.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розглянутий алгоритм настроювання нейронної мережі відпо- відає алгоритму навчання з послідовним підкріпленням знань, при якому мережі не надаються бажані значення вихідних сигналів, а за- мість цього мережі ставиться оцінка, гарний вихідний сигнал або по- ганий [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Передбачається, що в нейронній мережі в певний момент часу може бути активний лише один нейрон, названий початковим, з n можливих нейронів у шарі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виходячи із цього, сутність настро- ювання нейронної мережі можна відобразити в такий спосіб: якщо активність початкового нейрона привела до небажаної ситуації, то зв’язки із цим нейроном W повинні притерпіти зміни (рисунок 12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому зміна зв’язків з початковим нейроном повинна відбува- тися таким чином, щоб не порушити правила формування мережі Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При обліку правил формування мережі Петрі коефіцієнти міжней- ронних з’єднань, пов’язаних з вихідним нейроном, повинні зміни- тися певним чином залежно від сформованої матриці інцидентності.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Отже,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' якщо при активізації певних нейронів була отримана небажана реакція деякої системи,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' то вагові коефіцієнти зв’язків цих нейронів wij слід змінити у такий спосіб: 310 (0) 1 1 1 n n ij ij im ij ik i j j w w S w f F = = \uf8eb \uf8f6 \uf8eb \uf8f6 = η⋅ ⋅ + − ⋅ ⋅ \uf8ec \uf8f7 \uf8ec \uf8f7 \uf8ec \uf8f7 \uf8ed \uf8f8 \uf8ed \uf8f8 ∑ ∑ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) ( ) ( ) ( ) 1 1 0 0 1 0 T T ij im ij ik i T T ij im ij ik npu w S w f F npu w S w f \uf8f1 ⋅ ⋅ − ⋅ > \uf8f4 = \uf8f2 ⋅ ⋅ − ⋅ = \uf8f4\uf8f3 ∑ ∑ ∑ ∑ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) ij i ih w n = η⋅ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' де 1 2 0 11 12 1 1 22 2 2 1 1 2 j j ij j j i i i ij ij t t t w p w w w w p w w W w p w w w w − = ⇒ ∑ ∑ ∑ ∑ \uf04b \uf04b \uf04b \uf04b \uf04b \uf04b \uf04b \uf04b \uf04b \uf04b \uf04b — матриця інцидентнос- ті формованої мережі Петрі і сформований вектор 1 T j ij w w w = ∑ ∑ ∑ \uf04b 1 T j ij w w w = ∑ ∑ ∑ \uf04b ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ij w ∑ сума всіх значень i-го рядка матриці W ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' , im ik S f — вектори дозволених комбінацій ваг міжнейронних з’єд- нань, що не порушують правила формування мережі Петрі;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 2 3 4 5 6 7 8 1 2 3 1 1 2 2 3 3 1 1 4 4 5 5 6 6 7 7 8 8 1 2 3 1 2 2 1 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 1 0 , ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='0 ' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 1 i i i i i i i i k k k m k m k m k m k m k m f f f f f f f f f f f s f f s f s f s f s f s = ih n — вектор комбінацій вагових коефіцієнтів вхідних зв’язків ви- хідного нейрона;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 2 3 4 1 1 2 3 4 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 i i i i h h h h n n n n n N n n n = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Схема, що відображає зв’язки початкового нейрона з позначеними вагами міжнейроних з’єднань W 22(i8) w 32(i9) W 82(o44) Wi(i) W21(u) W: ij(o) W ij(u)312 Представлені вище вектори можливих комбінацій синоптичних коефіцієнтів зв’язків нейронів дозволяють нейронній мережі в про- цесі функціонування виконати композицію лише певних мереж Пе- трі, тому що не всі можливі комбінації коефіцієнтів міжнейронних зв’язків представлені.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Очевидно, що ці мережі Петрі можуть відоб- ражати суто певні алгоритми управління об’єктами або, в окремому випадку, алгоритми настроювання певних систем управління.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Однак слід зазначити, що розглянута архітектура нейронної мережі, що ви- користовується при автоматичному синтезі мереж Петрі, має певну особливість, необхідну при формуванні різних алгоритмів управління.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Представлений нами алгоритм настроювання певної ней ронної мережі з вихідними нейронами дає можливість виконати певний крок у розробці інтелектуальної системи, що формує алгоритми ло- гічного управління об’єктами при автоматичному синтезі і компо- зиції мереж Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Автоматично синтезована мережа Петрі дозволяє представити результат формування алгоритму управління об’єктом і тим самим дозволяє фахівцеві виробити, при необхідності, потрібне коректування алгоритму.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Слід зазначити, що в даній інтелектуальній системі, яка пов’язана з автоматичним синтезом мереж Петрі, була представлена спроба використання принципу навчання з підкріпленням, яка відображає область штучного інтелекту, нейромережевого моделювання і управ- ління, що активно розвивається.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тим самим інтелектуальна система, що розробляється, пов’язана із синтезом мереж Петрі і з формуван- ням, наприклад, алгоритмів настроювання особливого класу систем управління, достатньою мірою вписується в рамки сучасного розви- тку інтелектуальних технологій, особливо актуальних в наш час.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Далі розглянемо ще один алгоритм настроювання нейронної ме- режі, що виключає наявність дозволених комбінацій коефіцієнтів міжнейронних зв’язків нейронної мережі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Алгоритм настроювання нейронної мережі по перебору можливих ва- ріантів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Принцип настроювання нейронної мережі з перебору мож- ливих варіантів аналогічний вищенаведеному алгоритму за винятком його формалізації.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У цьому випадку, якщо певний алгоритм дій не- задовільний, то необхідно вказати, на якому з переходів мережі Пе- трі була виявлена помилка в системі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це необхідно для перенастро- ювання штучної нейронної мережі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Так, якщо значення показників якості роботи деякої системи збільшується, то необхідно відповідно зв’язок між переходом ti і позицією pi ліквідувати.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Але при цьому не- 313 обхідно додати новий зв’язок між переходом ti і сусідньою позицією pi+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, наприклад, мережа Петрі, що представлена на ри- сунку 13 a, змінюється в мережу Петрі, представлену на рисунку 13 b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповідно повинні змінитися коефіцієнти міжнейронних зв’язків штучної нейронної мережі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Математично це можна формалізувати в такому виді: ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 1 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 1 ( ) ( ) (1 | ( ) ( ) | ) ( ) | ( ) ( ) | i j k i j k i j k i j k i j k i j k i j k w t w t w t w t w t w t w t + + + + + + = ⋅ − ⋅ ⋅δ + × × ⋅ ⋅δ (1) при i=2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='6… ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 1 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 1 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 1 ( ) ( ) (1 | ( ) ( ) | ) ( ) | ( ) ( ) | i j k i j k i j k i j k i j k i j k i j k w t w t w t w t w t w t w t + + + + + + + + + = ⋅ − ⋅ ⋅δ + × × ⋅ ⋅δ (2) при i=2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='6… ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 1 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 1 ( ) ( ) (1 | ( ) ( ) | ) ( ) | ( ) ( ) | i j k i j k i j k i j k i j k i j k i j k w t w t w t w t w t w t w t + + − − − + = ⋅ − ⋅ ⋅δ + × × ⋅ ⋅δ (3) при i=1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5… ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 1 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 1 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 1 ( ) ( ) (1 | ( ) ( ) | ) ( ) | ( ) ( ) | i j k i j k i j k i j k i j k i j k i j k w t w t w t w t w t w t w t + + + + − + − − + = ⋅ − ⋅ ⋅δ + × × ⋅ ⋅δ (4) при i=1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5… де ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) i j k w t — коефіцієнт міжнейронного з’єднання,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' який визначає від- повідний зв’язок у мережі Петрі,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' що формується на кроці tk;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' , 1 ( ) i j k w t + , відповідний коефіцієнт міжнейронного з’єднання на кроці tk+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Матриця коефіцієнтів міжнейронних зв’язків N має певну анало- гію з інцидентною матрицею мережі Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наприклад, з інцидент- ною матрицею W1 мережі Петрі, представленої на рисунку 13 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При помилці на переході t1 інцидентна матриця W1 змінюється відповідно в матрицю W2 у такий спосіб: 314 Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Алгоритми логічного управління, що представлені мережами Петрі, які відображають процеси поетапного настроювання багаторівневої системи 3HayeHHA V0 3HayeHH9 0 3HaYeHH 0 pyxaeTbco Hy pyxaeTbc o Hy pyxaeTbc o Hy 3 p p p 5 Y 3HayeHH napaMeTpa 3HayeHH napaMeTpa 3HayeHHA 3pocTae 个k,3pocTae napaMeTpa 个k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 3pocTae p p p 4 6 3HayeHH napaMeTpa 3HayeHH9 napaMeTpa 3HayeHH9 napaMeTpa 3MeHWyeTbcq 1k, 3MeHWyeTbcq k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' (KoopWHyroyw piBeHb (CTaini3yroywM piBeHb (KoopHyrOywi piBeHb ynpaBiHH) ypaBJiHHg) ynpaBiHH) 0 p CTON lyck omwka a Ha nepexoni 3HayeHH 3HayeHHA, 3Ha4eHH9 J 903 902 01 pyxaeTbc o max pyxaeTbc o max pyxaeTbc o max 0 p 3HayeHH napaMeTpa : 3HayeHH9 napaMeTpa 3HayeHH9 3pocTae 个k,3pocTae napaMeTpa k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 个k, 3pocTae p6 p p 4 2 3HayeHH apaMeTpa 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='= ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='⇒ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='= ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Рядки р1 і р2 матриці W1 були змінені згідно з виразом (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Відповід- но, якщо на переході ti виявлена помилка, то 1 1 δ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У цьому випадку, якщо є зв’язок між переходом ti і позицією pi то , , 1 ( ) ( ) 1 i j k i j k w t w t + ⋅ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Отже, згідно з виразом ( ) , , 1 1 1 ( ) ( ) 0 i j k i j k w t w t + − ⋅ ×δ = і коефіцієнт між- нейронного зв’язку, на кроці 1 kt + стане також рівним нулю , 1 ( ) 0 i j k w t + = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, відповідний зв’язок у мережі Петрі, що формується, зникне.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В іншому випадку, якщо відсутній зв’язок між переходом ti і позицією pi, то , , 1 ( ) ( ) 0 i j k i j k w t w t + ⋅ = , ( ) , , 1 1 1 ( ) ( ) 1 i j k i j k w t w t + − ⋅ ×δ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' При цьому, якщо був присутній сусідній зв’язок між переходом ti і позицією pi+1, то 1, 1, 1 1 ( ) ( ) 1 i j k i j k w t w t + + + ⋅ ⋅δ = і, отже, коефіцієнт між- нейронного зв’язку збільшиться на одиницю , 1 , ( ) ( ) 1 i j k i j k w t w t + = + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, з’явиться відповідний зв’язок у мережі Петрі, що формується.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо на переході ti помилка не виявлена, то 1 0 δ = , ( ) , , 1 1 1 ( ) ( ) 1 i j k i j k w t w t + − ⋅ ×δ = і, отже, , 1 , ( ) ( ) i j k i j k w t w t + = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Експерименти.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У програмному середовищі MATLAB/Simulink 2012 були проведені експерименти, пов’язані зі спільною роботою нейронної мережі з мережами Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Функціонування мереж Петрі у програмному середовищі MATLAB/Simulink було реалізовано за допомогою Statflow-діаграм.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Фрагмент Stateflow-діаграм, що пред- ставляють роботу мереж Петрі, представлено на рисунку 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' State1, State2, State3 і State4 є станами однієї мережі Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нейронна мережа пов’язана з роботою відразу трьох таких мереж Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Це показано на рисунку 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 316 Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Stateflow-діаграми, що представляють роботу мереж Петрі StateA StateC1 [data01>0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='9] [data01-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='9] after(9,tick) State1 State2 State3 State4 data1=0 data1=0: data1=1: data1=1: data2=1 data2=1 data2=0 data2=0 after(9,tick) StateC2 [data02>0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='9] [data02<-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='9] after(9,tick) State5 State6 State7 State8 data3=0: data3=0 data3=1: data3=1: data4=1 data4=1 data4=0 data4=0317 Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Структурна схема нейронної мережі, що синтезує мережу Петрі Xt1 Xp1 0 +1 0 2 uo +t2 Xp2 Constant47 P 0 Constant4g Scope9 :18 Add1 dotprod21 2 Unit Delayg t3 Xp3 2 0 0 2 Scope9 :2r ++1 0 2 2: 1 C onstant44 t, sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2 t, sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' dotprod29 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4 0 Constant3g Xp1 u(p Constant45 p + hardlim2 dotprod20 netsum12 dotprod30 4 data1 0 Constant48 tansig7 Scope9 :19 P Scope9 :27 Constant48 1 0 dotprod32 netsume +data01 dotprod31 Constant34 Constant50 JΛ ！' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='！！' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Xt2 dotprod33 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 Constant27 Constant55 ScoDe9 :28 dotprod40 Constant56 Xp2 μ(p: 0 Scope9 a3 Constant5 Constant37 P dotprod34 dotprod23 4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 Constant52 + hardlim1 tansig9 Scope9 :25 Scope9 :29 Constant38 netsum8 P dotprod35 netsumg dotprod24 +?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 0 1 Constant29 0 Constant40 p Constant35 dotprod36 Constant28 dotprod25 Scope9 ±30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 u(p t3 口 0 0 Constant53 ZF Constant32 sdx Scope9 :23 Constant54 0 dotprod39 口 0 Constant41 Scope9 331 Constant33 tansig10 Scope9 26 dotpro d26 事 P 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='5 Lw dotprod38 netsum10 hardlim Constant42 netsum11 H!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Constant31 data6 P 0 dotprod27 0 dotprod22 Scope9 :17 Constant30 C onstant43 Constant36 Chart2 dotpro d28 Unit Delay10 Unit Delays Unit Delay7318 На рисунку 15 також представлена засобами середовища MATLAB/ Simulink двошарова штучна нейронна мережа, що складається з шес- ти нейронів із вихідними сигналами Xp1, Xp2, Xp3, пов’язаними з ме- режами Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Структурна схема цієї нейронної мережі і мереж Петрі аналогічна спрощеній схемі, яка представлена на рисунку 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На рисунках 14 і 15 наведені всі необхідні параметри системи, яка представляє спільне функціонування нейронної мережі і мереж Петрі для автоматичного формування мереж Петрі і певних алгоритмів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Система, структурна схема якої наведена на рисунку 4, здатна представити функціонування різних мереж Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Рівняння (2) описує таке спільне функціонування мереж Петрі і штучної нейронної мережі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо матриця інцидентності A мережі Петрі має певну анало- гію з матрицею коефіцієнтів міжнейронних з’єднань вихідного шару ней ронної мережі, то штучна нейронна мережа генерує вихідні сиг- нали 1 k V A U − = ⋅ , відповідні значенням матриці інцидентності мере- жі Петрі, що формується.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На рисунках 15 і 16 представлені часові діаграми функціонуван- ня мережі Петрі, що складається із трьох позицій і трьох переходів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Функціонування такої мережі Петрі представляє система спільної ро- боти штучної нейронної мережі і Stateflow-діаграм.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Вихідні сигнали штучної нейронної мережі Xp1, Xp2, Xp3 відповідають матриці інци- дентності мережі Петрі, що формується.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' А вихідні сигнали μ(р1) μ(р2) μ(р3) представляють зміну маркування мережі Петрі в часі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В окремо- му випадку представляється робота мережі Петрі, показаної на ри- сунку 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Як видно з часових діаграм, якщо присутній сигнал на вході J1 (J01 >0), то спрацьовує перехід t2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Якщо з’являється сигнал на вхо- ді J2 (J01 >0), то спрацьовує перехід t3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Одночасне спрацьовування переходів t2 і t3 відповідає конфліктній ситуації в роботі мережі Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Аналізуючи часові характеристики, наведені на рисунках 15 і 16, можна зробити висновок про принципову придатність розглянутої системи представляти роботу різних мереж Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Важлива складова такої системи — це наявність штучної нейронної мережі, тренування якої пов’язане з автоматичним синтезом мережі Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, зміна коефіцієнтів міжнейронних зв’язків при тренуванні мережі пов’язана зі зміною синтезованої мережі Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 319 Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Процес функціонування синтезованої мережі Петрі Xp1 2 Xt2 Xp2 0 2 2 Xp3 ,sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' sec320 Математичний опис зміни коефіцієнтів міжнейронних з’єднань при тренуванні мережі було представлено як одну зі спроб реалізації перебору можливих варіантів з’єднань у мережі Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У цьому ви- падку сформована мережа Петрі є візуальним відображенням набору коефіцієнтів міжнейронних з’єднань штучної нейронної мережі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Висновки.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Нами було вирішено задачу, пов’язану з розробкою системи спільного функціонування нейронної мережі і мереж Пе- трі для формування алгоритмів і послідовних обчислень.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Тим самим одержали подальший розвиток методики автоматичного синтезу мереж Петрі і розробки певних алгоритмів на основі функціонуван- ня нейронної мережі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Був представлений математичний опис змі- ни коефіцієнтів міжнейронних зв’язків мережі при синтезі мережі Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Розроблені методики синтезу мереж Петрі дозволяють підійти до вирішення практичної задачі, пов’язаної з автоматизованим настро- юванням складного класу багаторівневих автоматичних систем коор- динуючого управління.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У цьому випадку синтезована мережа Петрі дозволяє представити процес і алгоритм настроювання відповідної системи управління.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Автоматизоване настроювання автоматичної системи координуваль- ного управління при синтезі мереж Петрі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Практичне застосування розглянутих методів автоматичного синтезу мереж Петрі може бути в області автоматизації процесів настроювання певного класу багато- рівневих автоматичных систем координувального управління [22;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' На основі відомих наукових праць можна зробити висновок, що спочатку при синтезі координувальну систему автоматичного управління треба розглядати як однорівневу, тобто необхідно вико- нувати синтез системи, починаючи з нижнього рівня, а потім пе- реходити до синтезу верхніх рівнів [22–25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Але в деяких випадках можливі й інші варіанти.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Наприклад, синтез координувальної сис- теми автоматичного управління (КСАУ) приводами робота-мані- пулятора доцільно було починати з контуру регулювання верхнього рівня, потім необхідно було налаштувати нижній рівень, а потім па- раметри настроювання верхнього рівня необхідно було коректува- ти.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Було встановлено, що можливі різні варіанти алгоритмів синтезу координувальних системи, а кожний з алгоритмів може приводити до різних результатів.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Таким чином, виникає задача формування, отже, пошуку алгоритму, який дозволить досягти бажань значень показників якості роботи координувальної системи.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У цьому випад- 321 ку виникає задача, подібна до задачі досяжності системи в гібрид- ному (дискретно-безперервному) просторі станів, яка розглядалася в роботах [14;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' В даному випадку розробляється система параметричного синтезу КСАУ на базі математичного апарата дискретно-безперервних мереж (ДБ-мереж), яка дозволяє досліджувати властивість досяжності сис- теми шляхом редукції безперервної і дискретної частин мережі [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Перша спроба розробки такої системи була запропонована в роботі [27], у якій мережею Петрі представлявся алгоритм самонастроюван- ня певних параметрів нейро-нечіткої системи управління.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У цьому випадку запропоновано в системі, що розробляється, реалізувати формування алгоритму параметричного синтезу на основі методів перевірки досяжності ДБ-мережі.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Виконана розробка автомата в се- редовищі MATLAB/Simulink формує матрицю інцидентності мережі Петрі дискретно-подійної частини ДБ-мережі, отже, формує мережу Петрі, що представляє алгоритм параметричного синтезу координу- вальної системи автоматичного управління.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Мета роботи є зниження необхідних обчислювальних і часових ресурсів на розробку складних багаторівневих систем автоматичного управління.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для досягнення поставленої мети потрібно було розробити сис- тему, яка здатна сформувати необхідний алгоритм параметричного синтезу і виконати необхідний порядок дій згідно зі сформованим алгоритмом.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Координувальна система автоматичного управління приводами робота-маніпулятора представляється як дворівнева система [28;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Структурна схема моделі такої системи, що реалізована засобами се- редовища MATLAB/Simulink, представлена на рисунку 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Верхній рівень управління системи пов’язаний з відпрацьовуванням помилок регулювання за положенням зхвату Lm і за кутом повороту маніпуля- тора αm, а нижній рівень пов’язаний з відпрацьовуванням неув’язок співвідношень змінних, що представляють траєкторію руху зхвату в циліндричній системі координат.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Дворівневий закон цієї системи управління можна представити так: [ ] 1 2 T q p Lm m u u u u u α = + = ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' де 1 2 21 2 3 31 (1 ) ( ) (1 ) q q q u k k p u t u k k p ⋅ + ⋅ \uf8ee \uf8f9 \uf8ee \uf8f9 = = ⋅ψ \uf8ef \uf8fa \uf8ef \uf8fa ⋅ + ⋅ \uf8f0 \uf8fb \uf8f0 \uf8fb — закон управління нижнього рівня;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 322 1 1 11 2 4 41 ( ( ) ( )) (1 ) ( ( ) ( )) (1 ) p mz m p p mz m u L t L t k k p u u t t k k p − ⋅ ⋅ + ⋅ \uf8ee \uf8f9 \uf8ee \uf8f9 = = \uf8ef \uf8fa \uf8ef \uf8fa α − α ⋅ ⋅ + ⋅ \uf8f0 \uf8fb \uf8f0 \uf8fb — закон управління верхнього рівня;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) ( ) ( ) ( ) m m m t f L L t k t b ψ = ⋅ + ⋅α − — відхилення (неув’язка) від спів- відношення параметрів у момент часу t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' ( ) m L t , ( ) m t α — регульовані зміни;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' f(Lm) — нелінійна залежність, що відображена в системі у вигляді ланки NU (рисунок 17), що описує траєкторію руху зхвата в коорди- натах Lm – αm;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' k1, k11, k2, k21 k3, k31, k4, k41 — параметри налаштування системи які необхідно визначити з урахуванням прояву ефекту поділу руху;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' αm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Z(t), Lm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Z(t) — задаючі впливи за кутом повороту і положенням маніпулятора в площині F;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' p — оператор диференціювання.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' У даній роботі об’єкти системи координувального управління описуються такими передатними функціями: 1 1 1 ( ) ( ) ( ) ( ) L L X p k W p u p p Q p = = ⋅ , 2 2 2 ( ) ( ) ( ) ( ) k X p W p u p p Q p α α = = ⋅ , у яких kL, kα — коефіцієнти передачі, QL(p), Qα(p) — деякі поліноми, такі, що QL(0)=1, Qα(0)=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Рівняння кінематики робота встановлює зв’язок між різними ко- ординатами.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Рівняння Xi=F(q1, q2), де q1, q2 — координати Lm, αm від- творюючих систем, визначають математичну модель механічної час- тини робота.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Для параметричного настроювання даної координувальної сис- теми автоматичного управління були реалізовані блоки формування значень наступних інтегральних показників якості роботи системи: 1 1 0 0 2 1 1 2 ( ( ( ) ( ) ) ( )) ( ( )) m t t mz m L m t t J L t L t u t dt fL t dt = β ⋅ − + = ∫ ∫ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 3 4 3 0 2 1 2 01 ( ) ( ) ( ) ( ) m m m m t t t t L L L L t t t t J f t dt f t dt f t dt f t dt \uf8ee \uf8f9 \uf8ee \uf8f9 = − − − \uf8ef \uf8fa \uf8ef \uf8fa \uf8ef \uf8fa \uf8ef \uf8fa \uf8f0 \uf8fb \uf8f0 \uf8fb ∫ ∫ ∫ ∫ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 1 0 0 2 2 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 2 ( ( ( ) ( ) ) ( )) ( ( )) m t t m z m m t t J t t u t dt f t dt α = β ⋅ α − α + = α ∫ ∫ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 323 Рис.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' Структурна схема моделі автоматичної системи координувального управління з контуром параметричного налаштування Block of adjusting settings Position controlsystem Lmz(t) (0) "1 PID(s) u, Outi 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='72 口 te: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3s+1 PID Controller5 Saturation3 室 In3 Out2 Denspor Transfer Fcn3 Scope Subsystem2 1 1/s Coordination control system Constant7 Integratore [ PID(s) Qutt PID Controller In2 I K, ±1/s 回 Out2 Table3PNU ubsystem4 Integrator1 Graph7 Scope11 PID(s) _ In1 1/s Constants K3 事_ In2 Constant3 中opMyBaHHA PID Controller3 Out2 Subsystem e2 PID(s Out +() 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='47 +1n2 K4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='4g+1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='αm(t) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='PID Controller8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Out2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Gain3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Saturationg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Transfer Fcng ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Scope1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Subsystem1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Control of angle KoHTyp perynroBaHH KyTa noBopoTy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='尚 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Display ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Jo1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='αmz(t) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Constant13 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Integrator1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='尚 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Graph5 k4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Constants ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='_In1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Graph3 J01 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Xin2 out2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='1/s ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Subsystem3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Constante ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Integrator4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Setpoint speed ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Display ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Ji ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='3aBAaHHAiHTeHCMWBHOCTi ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='In ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='→ 1/s ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Jo2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Out2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content='Constant14 Integrator12 ' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 0 2 3 ( ) t t J t dt = ψ ∫ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdAzT4oBgHgl3EQfGftE/content/2301.01028v1.pdf'} +page_content=' 1 3 4 3 0 2 1 2 2 2 2 2 03 ( ) ( ) ( ) ( ) t t t t t t t t J t dt t dt t dt t dt \uf8ee \uf8f9 \uf8ee \uf8f9 = ψ − ψ − ψ − ψ \uf8ef \uf8fa \uf8ef \uf8fa \uf8ef \uf8fa \uf8ef \uf8fa \uf8f0 \uf8fb \uf8f0 \uf8fb ∫ ∫ ∫ ∫ , де (t1 – t0)=(t3 – t2)=(t4 – t1)=(t5 – t3), t0 Slave Device Control bit +Data bits +Slave Device -> Master Device +Figure 2: PMBus protocol structure +The second segment is the register address to operate on. In the PMBus specification, this +segment is called the PMBus command. The segments after the second one contain the +data read from or written to the register. +Interaction between PMBus and SVID +Although the functionality of the PMBus pro- +tocol is similar to SVID, they have different specifications for the digital signal interface +and command sets. A VRM can have both SVID and PMBus interfaces, with the SVID +interface directly connected to the CPU and the PMBus interface connected to the SMBus. +Both interfaces can be used to control the voltage of the CPU, and some implementations +of the PMBus specification also have commands to override the voltages set through the +SVID interface. +2.3 +PMBus Commands +For an adversary to communicate with the VRM and e.g., configure voltage levels, they +also need to know the specific PMBus commands. As mentioned, the PMBus specification +allows manufacturers to have custom implementations of PMBus commands. The E3- +1220V6-X11SSL-CF motherboard features an Monolithic Power MP2955 voltage regulator. +To understand the PMBus implementation of this VRM, we first started looking for its +datasheet, but unfortunately, found that it is not publicly available. However, on the +Monolithic Power website1, we found the datasheet of an alternative VRM (MP2965) [Mon]. +As both chips are manufactured by the same company, we used this datasheet as a reference +and starting point to discover the available PMBus commands by analysing the PMBus +traffic on the Supermicro X11SSL-CF. +We found the relevant PMBus commands by reading and analysing the response +(ACK or NACK) of the registers, and validating found commands according to the PMBus +specification and the MP2965 datasheet : Table 1 gives the command name, command code, +and description of each commands. The first three commands in the table are implemented +according to the PMBus 1.3 specification [pmb], while the rest are manufacturer-specific. +Table 1: Discovered PMBus commands on E3-1220V6-X11SSL-CF. +Command name +Command code +Usage +CMD_PAGE +0x00 +Switch between different voltage rails +CMD_OPERATION +0x01 +PMBus override +VOUT_COMMAND +0x21 +Output voltage settings +READ_VOUT +0x8B +Voltage reading from sensor +MFR_VR_CONFIG +0xE4 +Enable overclock mode +MFR_OCP_TOTAL_SET +0xEE +Over-current protection configuration +1https://www.monolithicpower.com/ + +Zitai Chen and David Oswald +7 +With CMD_OPERATION, we can configure the operation mode of the VRM. By setting +bit 1 of this register, we can enable the PMBus override mode. In this mode, the voltage +configured in the VOUT_COMMAND register will override the voltage configuration from the +SVID bus. +Another command that is useful for PMFault is READ_VOUT, as it allows +us to read the current voltage of the CPU and establish a baseline for undervolting. +The MFR_VR_CONFIG register is manufacturer-specific. By setting bit 3 or bit 10 and +configuring CMD_OPERATION, we could enable the tracking or fixed voltage overclocking +mode, respectively. +Bit 8 VID_STEP_SEL of MFR_VR_CONFIG also allow us to use an +alternative mode of SVID. In this mode, the VRM uses 10 mV Voltage Identifier (VID) +steps instead of the default of 5 mV. This makes overvolting up to 3 V possible, which is well +beyond the operating voltage range of the E3-1220 V6 Intel CPU, with a maximum voltage +of 1.52 V [Cor18]. We also discovered that the VRM has an Over Current Protection (OCP) +circuit, which can be configured or disabled by another manufacturer-specific register +(MFR_OCP_TOTAL_SET). Some VRM also support multiple voltage output rails. CMD_PAGE +command is used to select the target rail to send the commands to. +With these discovered commands, we can now control the CPU voltage through the +PMBus. In Section 4.1, we detail how this interface is used as part of attack chains for +undervolting and overvolting attacks. +2.4 +Jumper Settings +On the Supermicro X11SSL-CF motherboard, there are several jumpers that control +different functionalities, including the connection of the VRM to other parts of the system. +We kept all jumpers in the default status as delivered by the vendor. To avoid confusion, +we still list the jumper settings in Table 2. During inspection of the jumper settings, we +discovered that the SMBDAT_VRM and SMBCLK_VRM jumpers are neither mentioned in the user +manual [Supb] nor in the quick reference guide [Supa]. Using an oscilloscope while sending +PMBus commands, we found that these two jumpers can be used for (dis)connecting +the VRM from/to the PMBus. The experiments and attacks described in this paper are +conducted under the “connected” setting of both jumpers, which according to Supermicro +is the default. +We also found server motherboard without such jumpers, e.g., Supermicro X11SPG-TF +and ASRock E3C246D4I-2T. For those, the VRM is always connected to the BMC. We +detail our finding on other motherboards in Section 6. It is worth mentioning that to the +best of our knowledge, SGX attestation does not have the functionality to include the +configuration of these (external) jumpers. +Table 2: Jumper settings on Supermicro X11SSL-CF. +Jumper name +Description +JPME2 +Manufacturer mode normal (Default) +JPB1 +BMC enabled (Default) +SMBDAT_VRM +Connect VRM data line to PMBus +SMBCLK_VRM +Connect VRM clock line to PMBus +3 +Supermicro’s BMC and Server Management Interface +Having understood the basic PMBus protocol and commands, we next look at different +ways to gain access to the PMBus and send commands to the VRM. To achieve that, an +attacker needs access to the SMBus. As described in Section 2.1, on E3-1220V6-X11SSL- +CF, one of the devices on the SMBus is the ASPEED AST2400 BMC controller. In this + +8 +PMFault: Faulting and Bricking Server CPUs through Management Interfaces +section, we introduce the functionalities and vulnerabilities in these management interfaces +that allow us to achieve our main goal—to take control of the SMBus. +During the initial investigation of the BMC, we found there are mainly three services +available: there is a web service running on port 80 (HTTP) and 443 (HTTPS), an +Intelligent Platform Management Interface (IPMI) over LAN service on port 623, and the +SSH service on port 22. Besides, we also found that the IPMI service can be accessed +through the KCS interface from the CPU. +Some of these interfaces require authentication: to use HTTP, HTTPS, SSH, and IPMI +-over-LAN, all exposed through Ethernet, one has to authenticate to the BMC. The used +credentials in this authentication process are individual for each Supermicro motherboard. +However, the IPMI-over-KCS interface does not require any authentication to the BMC. +Instead, having root privileges on the host OS running on the CPU is sufficient to access +this interface. One can also use the IPMI-over-KCS interface to add/remove/modify BMC +credentials to subsequently login to the Ethernet-exposed interfaces. +3.1 +SSH Shell +Since SSH is one of the most common interfaces that allows us to get a shell and possibly +take over the system, we first started our investigation with it. However, the SSH service +on E3-1220V6-X11SSL-CF provides a custom shell called “ATEN SMASH-CLP System +Management Shell”. It only provides limited commands that enable server monitoring +and basic management. Previously, a vulnerability was reported in [Vaz13]: the command +shell sh allows gaining root access from this shell, however, this command was not +available on our system-under-investigation. +3.2 +BMC Firmware Analysis +To further investigate the services running on the BMC and check if it is possible to +enable an SSH root shell, we dumped the firmware of the BMC with a CH341A SPI flash +programmer as shown in Figure 3. This procedure is only used once to assist our analysis, +and is not necessary to execute the actual attack. +Figure 3: Dumping BMC firmware with a flash programmer. +We found that the firmware stored in the SPI flash is neither encrypted nor signed. +There are five partitions in the firmware, where the second one contains a Linux operating +system. The SMASH shell is provided by /SMASH/msh and it is possible to change it to a +different shell by replacing this file. +The Linux operating system also has an I2C kernel module installed, which provides an +interface to communicate with the SMBus. However, during our testing in Section 4.1, we +found that the API provided by this kernel module is not compatible with the commonly + +0000 +C +C +C +O +O +SOP16 +014 +13 +12 +O +O +100 +O +C +1.27MM +O +90 +C +D +GOAET +25XX24XX +以 +二 +4683 +S9Zitai Chen and David Oswald +9 +used libi2c in i2c-tool2. As the result, in Section 4.1, we opted to write a custom +library to use the I2C interface of the BMC and communicate with the VRM. +3.3 +Firmware Upgrade +After analysing the firmware, we conclude that it is possible to enable an SSH shell by +modifying the firmware. We then started to look for software methods to re-flash the BMC +SPI flash chip. We found that the firmware upgrade functionality of the BMC provides a +way to do this. There are two interfaces for firmware upgrade: one is through the web +interface, the other through the KCS interface. +Through Web Interface +The web interface has a firmware upgrade page that can switch +the BMC into upgrade mode and allows the user to upload a BMC firmware update +package. To prevents unauthorised user from upgrading the firmware, there is a login +portal. The user is authenticated by the BMC. As the BMC is a system independent from +the OS running on the CPU, users do not need to have privileged access to the OS to be +able to use this method. Besides, this web interface can be accessed remotely through +Ethernet. The remote BMC firmware upgrade attack chain described in Section 4.3 uses +this method to upgrade the firmware. +Through IPMI-over-KCS Interface +Crucially, the BMC firmware can also be updated +through the KCS interface, using the following command: AlUpdate -f firmware.bin +-i kcs -r y. As mentioned, the KCS interface can be accessed from the OS running on +the CPU, only requiring root access to the OS, but not the BMC credentials. +Firmware Upgrade Package +After finding the firmware upgrade interface, the next step +is to produce an upgrade package that can be uploaded to the BMC. We started with the +analysis of the structure of the upgrade package. Figure 4 shows the layout of a firmware +upgrade package. Previous work by [Ecl18] founds that in the firmware upgrade package, +there is a region that contains a magic value (ATENs_FW), a half-length CRC checksum, +and the length of each section. We call this part the firmware footer. There is also a +region containing metadata of the firmware image, including the name of each region and +their length and CRC, starting with “[img]”. We refer to this region as firmware table. +In the X11 series, the firmware table, the file system header of the root file system and the +website files system header are AES-CBC encrypted. However, the files in these regions +are not encrypted, but only LZMA compressed. As a result, the key of the AES-CBC +encryption can be recovered from the ipmi.so file on the root file system. +With this information, we can modify the firmware and construct a valid firmware up- +grade package for the web interface. We discuss firmware repacking in detail in Section 4.2. +3.4 +IPMI I2C functionality +When exploring the functionalities of IPMI, we also found that the interface also allows +direct sending I2C packets with the ipmitool i2c command. This can be used either +through the Ethernet or KCS IPMI channel. The authentication requirement for using +IPMI-controlled I2C is the same as those described in Section 3.3. As shown in Section 4.3, +we can use this functionality for direct access to the SMBus/PMBus without modifying +BMC firmware. +2https://git.kernel.org/pub/scm/utils/i2c-tools/i2c-tools.git/ + +10 +PMFault: Faulting and Bricking Server CPUs through Management Interfaces +Figure 4: Layout of the BMC firmware upgrade package. +The NVRAM region stores the current +configuration of the BMC, the rootFS is a LZMA-compressed cramFS file system with only its header +encrypted. The kernel region stores a Linux kernel image, while the BMC website FS is another compressed +file system with only the file system header encrypted. The FW Footer starts with a magic value ATENs_FW +and contain information about the firmware version, checksum, etc. The FW Table is an encrypted region +and stores a table of the image layout. All encrypted region of the firmware can be decrypted with a key +extracted from ipmi.so on the rootFS. +4 +Practical Experiments +Finally, using the results from the previous sections, we explain how to construct practical +Proof-of-Concept (PoC) attacks for PMFault. Some of our experiments require physical +access to the system to understand the hardware configuration (with an overview shown +in Figure 5). Note however that physical access is not required when performing PMFault +attacks on a real-world system, as the hardware components and connections are identical +for a given motherboard model. +Oscilloscope +connected to +PMBus +Oscilloscope +to monitor +CPU voltage +BMC flash chip +soldered out +PMBus connection +for Raspberry Pi +Management +Ethernet +Connection +BMC +micro-controller +Power Button +Figure 5: Setup of the E3-1220V6-X11SSL-CF for practical experiments. These connections are for +experiments only; physical access is not required in the actual attack. +4.1 +PMBus-based Voltage Control +To understand the configuration and capabilities of using the PMBus to control the CPU +voltage, we conducted two experiments. Firstly, we used the “probe and verify” method to +find the I2C address of the VRM. Then we tried different ways of sending commands to +VRM to change the voltage. + +ipmi.so +Decompressed +Files of RootFS +C +BMC +rootFS +FW +FW +NVRAM +kernel +WebsiteFS +(Compressed) +Footer +Table +(Compressed)ROHSZitai Chen and David Oswald +11 +Discovering the VRM Address +Finding the I2C address of the VRM is the first step +of PMFault. The easiest way to explore the I2C buses is to use the interface provided +by the OS. There are two I2C buses that can be used from the OS running on the CPU: +i2c-0 is shown by default, while i2c-1 requires the i2c_i801 kernel module to be loaded. +To find all available devices on both I2C buses, we ran the i2cdetect tool on them. We +found that there are 12 devices in total connected to the I2C bus. The full list of device +addresses can be found in Appendix A. +To then determine which device is a VRM, we use the result of the standard PMBus +command, READ_VOUT, as an indicator. The Plundervolt [MOG+20] attack showed that +the normal operating voltage of the CPU should be greater than 0.55 V, thus, if the +voltage read by READ_VOUT is within this range, it may be a VRM. Of the 12 devices +detected, only one device with address 0x20 on I2C bus 1 responded with a value in this +voltage range. We hence suspect this device is the VRM. To verify the result, we also +used MFR_ADDR_PMBUS (0xE1) command found in the MP2965 datasheet [Mon] to read the +PMBus address of the device. The result is 0x20, which confirms our finding. +Changing CPU Voltage with PMBus Commands +Having identified the VRM, one can +next attempt to send commands to change the CPU voltage. +Set target voltage to +VOUT_COMMAND +Configure VOUT_OPERATION +with PMBus Override Mode +Set Bit 3 of MFR_VR_CONFIG +Figure 6: Command sequence to change the voltage via PMBus. +In the datasheet of the MP2965 [Mon], we found an “overclocking” procedure that can +be used for this purpose. There are two overclocking modes, tracking mode and fix mode. +In PMFault, we mainly use the fix mode to set a defined voltage. +In the fix overclocking mode, the VRM uses the VID configured with the PMBus +command VOUT_COMMAND and ignores the configuration from the SVID bus. Figure 6 shows +the steps of using this mode to change voltage. First, we need to configure two registers: +The first one is VOUT_OPERATION; by setting the first bit of this register, we enable PMBus +override mode. We also have to set bit 3 of MFR_VR_CONFIG to make the VRM act on +these changes. After this, the voltage supplied to the CPU will be changed according to +the configuration in VOUT_COMMAND. To send this PMBus command sequence and change +the CPU voltage, we wrote a PoC with the libi2c. This PoC can be compiled and run +under Linux. +“Stalls” caused by PMBus Commands +The experiments in Section 4.1 also show that +the VRM responds to the PMBus commands sent from the CPU. One may thus assume +that it would then be straightforward to directly send PMBus commands to change the +CPU voltage with this method. However, we found that the CPU stalls after sending the +MFR_VR_CONFIG command to actually configure the VRM to use the new voltage. This +will make the CPU voltage being kept at the changed value with no way to change it back. +This phenomenon raised two questions: Is the CPU stall caused by a crash or a recoverable +halt? If it is caused by a recoverable halt, will this protect against targeted undervolting +fault injection? +To answer this, we connected a Raspberry Pi to the PMBus to directly control the +VRM. The I2C interface to the VRM is exposed with two pins, SDA and SCL. As shown in +Figure 5, we connected the I2C interface of the Raspberry Pi to these pins. +In the first experiment, we sent a command to disable overclocking after the stall +happens. It appears that with the VRM reconfigured to normal mode, the CPU recovers +from the stall situation if the undervolting value is not too low. This shows that the stall is + +12 +PMFault: Faulting and Bricking Server CPUs through Management Interfaces +caused by a recoverable halt and not a crash. The second experiment is used to find out if +the halt will prevent the fault from happening. In this experiment, we used the CRT-RSA +PoC of the Plundervolt attack. With the CPU running this PoC, we used Raspberry Pi +to send PMBus commands to produce voltage glitches. We found that with glitches with +gradually lower voltage, an exploitable fault happens with the CRT-RSA calculation. +Hence, in summary, the “stall” phenomenon will prevent the PMBus attack from being +conducted by the CPU-VRM I2C interface, but it does not prevent the fault caused by +undervolting from having an impact on CPU calculations. +Voltage Control with BMC +Because our attempt of voltage glitching failed with the +PoC running on the CPU, we started to look into the BMC-VRM I2C interface. In the +BMC firmware dumped in Section 3.1, we found the i2c.ko kernel module, which provides +a driver for the I2C interface. However, this module does not implement a standard +ioctl() for I2C devices, which is required for using libi2c. This means that the above +PoC, which uses this standard I2C library, cannot be used to communicate with this kernel +module. +As the kernel module in the firmware did not implement the standard I2C API, we +had to find another way to utilize the BMC’s I2C interface. With the help of the I2C +driver in the latest Linux kernel [astb, asta], we found that there are 14 I2C interfaces +on the AST2400 BMC controller. Each has a set of memory-mapped registers to control +the interface. We also found the setup and message sending/receiving sequence of the +I2C interface. We then created a small library to directly write these registers and send +I2C bus commands from the BMC CPU to the address of the VRM. By monitoring +the I2C activity with an oscilloscope (this was only required for debugging and during +development), we found that the I2C bus 2 (counted from bus 0) of the BMC has the +VRM connected. +4.2 +Enabling SSH Access and Firmware Repacking +Modification of the firmware can be used to obtain a root shell on the BMC. With the +“Supermicro BMC firmware image decryptor” [Nie20] and a modified version of the “ipmi +firmware tool” [Rak15] with added support for X11 images, we were able to extract the +firmware encryption key and decrypt the file system header. With these, we can unpack +and modify the full root file system. +As described in Section 3.2, /SMASH/msh provides the shell for SSH service. To enable +full root shell access, we replaced this file with a shell script with a single line to execute +/bin/sh. +Besides, as the SSH service is running with root privileges, with the shell +redirected to sh, we could obtain a root shell once connected to the SSH. +To repack the image, we modified the “Supermicro BMC firmware image decryptor” +tool to add firmware encryption support and constructed a firmware package with a valid +footer and firmware table. We successfully tested and installed this modified firmware +package both with the web firmware upgrade interface and the IPMI firmware upgrade +interface via the AlUpdate tool. +4.3 +Attack Chains for PMBus Access +In this section, we discuss three possible attack chains to take over the PMBus with the +techniques shown in the previous sections. The attacker can use any of these attack chains +and change the CPU voltage to perform PMFault attacks, i.e., to over/undervolt the CPU. +Remote BMC Firmware Upgrade +The first attack chain assumes a malicious insider +threat model. This attack chain makes use of the web or IPMI interface through the BMC +Ethernet connection. To use this interface, the attacker needs to have access to the BMC + +Zitai Chen and David Oswald +13 +management Ethernet port or the shared management Ethernet port eth0 on the system. +Besides, the attacker needs to obtain valid credentials to login to the BMC. +In detail, the attacker can first use the method described in Section 4.2 to repack +the SMT_X11_163 firmware upgrade package from [bmc] to enable SSH root access to +the BMC. Then, they can upload the firmware with the web management interface or +the IPMI management interface over Ethernet. With the SSH interface enabled, the +attacker can cross-compile the voltage-changing PoC described in Section 4.1 for the +BMC, and then upload and execute it to send PMBus commands. We used base64 -d > +/tmp/i2c-pmbus-send to upload our exploit code due to the unavailability of the SCP +service on the BMC OS. +Local BMC Firmware Upgrade +Similar to the first, this attack chain also involves a +firmware upgrade for code execution on the BMC. However, we use the KCS interface +discussed in Section 3.3 to upgrade the firmware. The attacker does not require access to +the management Ethernet plane, instead, only root privileges on the OS running on the +CPU is required. This is e.g., relevant for data centers that host bare metal machines for +customers or for malware/ransomware that has obtained root through other exploits. +IPMI Interface +The third attack chain uses the IPMI I2C functionality. An attacker +with root access on the CPU OS or access to the management port of the BMC can use +this interface to send commands to any I2C device that is connected to the BMC. The +command used for sending the raw I2C packets is shown in Listing 1. The I2C mapping +of this interface is the same as found during the initial investigation in Section 4.1. The +VRM is at address 0x20 on bus 2. However, since the last bit of the first packet of I2C +indicates the type of operation (read or write), we need to shift the device address left by +one bit and set the last bit accordingly when using this interface to control PMBus. +ipmitool +i2c bus=2 0x40 +Listing 1: IPMI command for sending I2C packets. +5 +Undervolting and Overvolting Attacks +In this section, we show how under/overvolting through the PMBus leads to attacks on +SGX and also permanent physical damage to the CPU. The attack requires any flaw that +gives a software attacker access to the PMBus. As mentioned in Section 4.3, this can +e.g., be a malicious firmware upgrade or the use of the IPMI-to-I2C functionality. The +attack is generic in the sense that various flaws can lead to the same outcome: remote +fault injection attacks on SGX and bricking the CPU. Figure 7 shows an overview of the +attacks. +5.1 +Undervolting Attack against Intel SGX +Adversary Model +As mentioned in Section 1.2, we assume a threat model where an +attacker (including a malicious insider) has full software access to the system but no +(or limited) physical access. More precisely, the attacker has root access to the OS and +software access to the BMC via the KCS interface or Ethernet. All attack chains described +in Section 4.3 can generally be used under this threat model. It is worth mentioning that +the attack that uses ipmitool through the KCS interface does not require knowledge of +the BMC credentials. A privileged local user on a compromised host CPU can thus use +ipmitool to inject fault into SGX purely from software. + +14 +PMFault: Faulting and Bricking Server CPUs through Management Interfaces +BMC +PMBus +Overvolting +Undervolting +Brick CPU +Fault Injection to +SGX +Firmware Upgrade +to Enable SSH +IPMI I2C Command +Code Execution +in BMC +Remotely Executable Action (Management LAN) +Locally Executable Action on OS (With root) +Result of Attack +Voltage Control +Entity or Connection +Legend +Figure 7: Overview of the PMFault attack. With root access to the OS or access to the BMC via Ethernet +or KCS, the attacker can perform a malicious firmware upgrade of the BMC and then takeover the PMBus. +The attacker can also use the ipmi i2c command to directly control the PMBus via BMC. With control +over the CPU voltage, the attacker can overvolt to brick the CPU or undervolt to inject faults into SGX. +Proof of Concept +We used the same PoC code as Plundervolt/VoltPillager [MOG+20]. +Before injecting the voltage glitch, we use the attack chain described in Section 4.3 to gain +control of the PMBus. +To start with, we used the multiply operation as the first target, as it is a simple target +to fault. By gradually lowering the CPU voltage with the PMBus commands sent by +the BMC while running the Plundervolt/VoltPillager PoC on the CPU, we successfully +injected faults into the multiply operation (in our experiments at voltage 0.845 V with the +CPU running at 2 GHz. +To verify the fault injection also works for encryption operations running in SGX, we +ran the CRT-RSA signature PoC from Plundervolt/VoltPillager, with an RSA signature +computed inside an enclave using the Intel Integrated Performance Primitives (Intel IPP) +cryptography library functions [Cor]. Again, we could obtain faulty signatures as shown +in Listing 2. Furthermore, we confirmed that these faulty values could be used to factor +the RSA modulus and recover the private RSA key using the Lenstra attack [BDL97]. +// Faulty +calculation 1 +0x3f , 0xe0 , 0xb8 , 0x74 , 0x04 , 0x18 , 0x9c , 0xed , 0x91 , 0x1a , 0x02 , 0x12 , 0x2a , +0xce , 0x89 , 0xf8 , 0x32 , 0x00 , 0xdc , 0x05 , 0x15 , 0x53 , 0x72 , 0x8d , 0x84 , 0x00 , +0xd3 , 0x67 , 0xbe , 0xa1 , 0xc2 , 0x40 , 0x76 , 0xbc , 0x8c , 0xd8 , 0xfe , 0xb1 , 0x00 , +0xd7 , 0x9e , 0x0e , 0xb6 , 0xac , 0x61 , 0xc0 , 0xec , 0x9c , 0xf7 , 0x7e , 0xbc , 0x4b , +0xde , 0x18 , 0xa5 , 0xa4 , 0x1c , 0x74 , 0xc4 , 0xb5 , 0x6a , 0x8d , 0xd3 , 0xb1 , 0x35 , +0xf9 , 0xad , 0x0b , 0xe3 , 0x4a , 0x01 , 0x52 , 0xd4 , 0xc6 , 0xb2 , 0x95 , 0xbc , 0xdc , +0xad , 0x61 , 0x8e , 0x07 , 0x84 , 0x4d , 0xe3 , 0xa7 , 0xff , 0xf0 , 0xd1 , 0xa0 , 0xd4 , +0x58 , 0x9f , 0xbc , 0x37 , 0x0b , 0xa8 , 0x91 , 0x83 , 0x15 , 0x7b , 0xee , 0x28 , 0x83 , +0x12 , 0x4a , 0x89 , 0x61 , 0x1e , 0x2c , 0xe1 , 0x02 , 0x2f , 0x08 , 0x4d , 0x5b , 0x04 , +0x92 , 0x5e , 0x31 , 0xd0 , 0x7e , 0x94 , 0x85 , 0xd0 , 0xce , 0x75 , 0x4a , 0x00 , 0x00 , +0x00 , 0x00 , 0x00 , 0x00 , 0x00 , 0x00 , 0x00 , 0x00 , 0x00 , 0x00 , 0x00 , 0x00 , 0x00 , +[... +zeroes +left +out +...] +Incorrect +result! +Listing 2: Faulty CRT-RSA decryptions/signatures generated by the respective ipps functions. +Reproducibility of CRT-RSA Fault Injection +To further evaluate the reproducibility of +the attack, we setup an automated testing environment by connecting a Raspberry Pi to +an Ethernet port (eth0) and the power button of the motherboard. We ran a Python +script to repeat the following steps numerous times: +1. Upload the exploit for controlling the CPU voltage to BMC via an SSH connection. + +Zitai Chen and David Oswald +15 +2. SSH into the OS running on the host CPU and trigger CRT-RSA signing in an SGX +enclave. +3. Run the PMFault exploit on the BMC to gradually lower the CPU voltage while the +signature is computed in the SGX enclave. +4. Stop lowering the CPU voltage when a fault occurs. +5. Record the result and cleanup. +6. If no faulty result is output, the system may have crashed due to too low voltage. In +this case, we use the connection to the motherboard power button to reboot the system +and wait to allow the system to boot into a stable status. +In total, we conducted 253 tests within 545 min. Of those, faults occurred in 194 tests. +66 of these faulty results could be used to successfully recover the correct RSA private key +using the Lenstra attack, which translates to a success rate of 26%. On average, a useful +fault could be obtained within 9 minutes. +5.2 +Overvolting to Permanently Brick a CPU +Apart from the undervolting attack to extract keys from an SGX enclave, we also discovered +another attack, which is an overvolting attack that can permanently destroy the CPU. +Adversary Model +In this attack, as described in Section 1.2, we assume an attacker who +has root privilege on the host CPU. For example, this could be in the case that an attacker +has placed ransomware on a system and threatens to damage the CPU unless a ransom is +paid. Clearly, root should have full control of all software running on the CPU, but should +not be able to cause any physical damage to the system. The attack chain described in +Section 4.3 using ipmitool with KCS can be used within this threat model. +Proof of Concept +To overvolt the CPU, we firstly configure the MFR_VR_CONFIG register +of the VRM to use the 10 mV SVID table. This allows changing the CPU voltage up to +3 V. We also disabled the over-current protection by reconfiguring the MFR_OCP_TOTAL_SET +register. Then we used the voltage changing procedure to change the CPU voltage to a +value much higher than the normal operating voltage. +We found that this procedure allows changing the CPU voltage up to ∼2.84 V for +∼1 ms, which is outside the typical operating range of Intel CPUs. By increasing the +voltage beyond the specified operating voltage range (0.55 V–1.52 V) [Cor18] of a 7th Gen +Intel E3-1220V6 CPU two times, we permanently destroyed the CPU and left the system +in an unbootable state within a few seconds. We successfully repeated the experiment +with a second, identical CPU. An example of overvolting is shown in Figure 8. +For environmental and financial reasons, we were satisfied after successfully destroying +two CPUs and decided to not perform further experiments in that regard. +6 +Evaluation of other Server Motherboards +As we found the PMBus to be a common interface present on server motherboard, we +decided to investigate other manufacturers as well. To facilitate larger-scale testing of +this, we wrote a tool called PMBusDetect. With this tool, we scan the system for a +PMBus connection and try to detect the VRM address. We applied this tool to several +other systems, including an ASRock rack motherboard (ASRock E3C246D4I-2T) and a +Supermicro X12DPi-NT6 motherboard (kindly provided by Supermicro for testing). We +then conducted further analysis of these systems to check if they are vulnerable to any +PMBus-related attack. + +16 +PMFault: Faulting and Bricking Server CPUs through Management Interfaces +Figure 8: Oscillocope capture of voltage change during overvolting, VOUT_COMMAND set to 0xFF (with 10 mV +VID table). Yellow: PMBus clock, blue: Vcpu. Vcpu shoots up to 2.84 V during overvolting. +PMBusDetect Tool for VRM Detection +Based on the VRM detection process mentioned +in Section 4.1, we built the PMBusDetect tool to automatically scan all addresses of a +specified I2C bus for VRMs. During testing, we found that the implementation of PMBus +and usage of the VRM is different between motherboard, and the most stable command to +identify a VRM is READ_TEMPERATURE (0x8d). We use the response to this command as +an initial indicator to identify whether a VRM is present, and then use the VRM detection +process from Section 4.1 to verify the result. +Moreover, as the capabilities and voltage changing sequence can differ between VRM +vendor, we added an additional procedure to detect the vendor of the VRM. For this, we +use the result of reading ISL_DEVICE_ID (0xad) as an indicator for Intersil VRMs and +SVID_VENDOR_PRODUCT_ID (0xbf) for MPS, respectively. Detection based on ipmi i2c is +also implemented for detecting the connection between VRM and the BMC as mentioned +in Section 4.3. An example output of PMBusDetect with Supermicro X11SSL-CF is shown +in Appendix B, while Table 3 shows a summary of the motherboard tested and the scan +result for VRMs with PMBusDetect. We are aware that our testing—restricted by (lack +of) access to server hardware— only gives a very limited picture of the use of PMBus and +VRMs on server hardware. We hence decided to open-source PMBusDetect and build on +community efforts in the future to obtain a better view of the PMBus landscape. +Table 3: Tested motherboards and their VRM detection result. +Name +BMC +Chipset +VRM Address +PMBus Connects to +Supermicro X11SSL-CF +AST2400 +C232 +0x20 +BMC & CPU +Supermicro X12DPi-NT6 +AST2600 +C621A +0x30 & 0x34 +— +ASRock E3C246D4I-2T +AST2500 +C246 +0x60 +BMC & CPU +6.1 +ASRock Power-Down Attack +The ASRock E3C246D4I-2T motherboard uses an Intel Xeon E-2124 CPU with an +Intel C246 Chipset and ASPEED AST2500 BMC with login credentials defaulting to +ADMIN:ADMIN. We used the PMBusDetect tool together with manual probing and found +that the VRM of this motherboard is connected to both the BMC and I2C bus of the +CPU. In the following attack, we assume that the attacker is a user on a baremetal server +with root access in the OS. +The VRM used on this motherboard is an ISL69138. Because it is made by a different + +RIGOL +WAIT +H +1.00ms +250MSa/s +3.00M pts +4.00000000ms +[1 +2.68V +Horizonta +Coupling +DC +Period +BW Limit +20M +Freg +Probe +10X +Rise Time +Invert +OFF +Fall Tirme +Volts/Div +4 +Coarse ++width +Unit +[V] +width +DV#1→2=***** +tmax=-1.210ms +Max=2.84 # +Vupper=2.58 y +AW=1.25 * +2.00 v +50.0 V +. +1.00 V +:500mv日Zitai Chen and David Oswald +17 +manufacture compared to the MP2955, the voltage changing PMBus command sequence +used for the MP2955 does not work with this VRM. Due to lack of documentation of this +procedure, we at the moment could not precisely overvolt or undervolt the CPU via the +PMBus. Yet, we discovered a new attack to disable the VRM and force power-down the +CPU, leaving the system in a (temporary) inoperable state. +PMBusDetect shows that the VRM is at address 0x60 on I2C bus 2 of the host CPU. +Different to the findings for the Supermicro X11SSL-CF, this VRM uses PMBus registers +on page 0x1 instead of the default 0x0. We then issue the ON_OFF_CONFIG (0x02) and +OPERATION (0x01) commands: We configure the OPERATION to “Immediate Off” and set +the “source of enable” only to ON_OFF_CONFIG. This results in a immediate power-off of +the VRM and crashes the system. +During testing, we found the PMBus is only writable from the CPU with IPMI over +KCS interface, but not from the BMC with ipmi i2c commands. As the result, it is not +possible for the administrator of the system to remotely configure the VRM back to a +normal state. Simply issuing the ipmi powercycle command with IPMI over LAN will +leave the system in a infinite boot loop. To recover from this attack, the administrator +has to physically power-cycle the system, which might increase downtime in a Denial-of- +Service (DoS) scenario. +This shows that PMBus as an attack vector does not only affect Supermicro X11SSL- +CF, but also can have impact on servers from other manufacturers. Besides we believe that +it might also be possible to conduct CPU bricking attacks if the PMBus voltage changing +sequence of Intersil VRM is known. We leave this for future work. +6.2 +Other Supermicro X11 Motherboards +We also ran the PMBusDetect tool on X11SPG-TF and X11SSE-F Supermicro server +motherboards—in both cases, the VRM was reachable in the default configuration. To +test if they are vulnerable to PMFault, we sent PMBus commands through ipmi i2c +commands and successfully undervolted them to crash the system. This shows that the +attack chain through the IPMI interface is valid on these systems. As the systems were +provided by a third party for remote testing, we were not able to attempt overvolting and +similar, destructive experiments, but believe these motherboards to be equally affected. +6.3 +Supermicro X12 Motherboards +We disclosed the vulnerability to Supermicro in May 2022. They confirmed the issue +and also provided a X12 generation Server for further testing. This system, Supermicro +X12DPi-NT6, features a dual Intel Xeon Gold 6330 CPU, Intel C621A Chipset, and +AST2600 BMC. Our investigation shows that mitigations has already been implemented +on this motherboard to break the attack chain of PMFault before we reported the attack +to Supermicro. Firstly, the firmware upgrade package is properly signed with RSA and +verified during the firmware upgrade process, which prevents malicious firmware uploads to +the BMC via IPMI. This breaks the attack chain though firmware upgrade. Secondly, I2C +packet filtering has been implemented in the BMC, which prevents IPMI commands to +directly send packets to the PMBus. Moreover, our PMBusDetect tool shows that the VR +is not connected to the CPU, which prevents an attack directly from the operating system. +In conclusion, to the best of our knowledge, we believe that Supermicro X12DPi-NT6 +is not directly vulnerable to the attacks described in this paper. However, we note that +as-of-yet unknown vulnerabilities might remain in the firmware update process and the +complex software stack running on the BMC, which warrants further investigation. + +18 +PMFault: Faulting and Bricking Server CPUs through Management Interfaces +7 +Conclusions and Countermeasures +In this paper, we demonstrated two remote attacks that use the PMBus interface to control +the CPU voltage. An undervolting attack can be used to inject fault to the SGX enclave of +the CPU and e.g., recover a secret key used in cryptography algorithms. The overvolting +attack causes permanent damage to the CPU. +The attack affects, to our knowledge, all 11th generation Supermicro systems. It also +impacts ASRock (tested with ASRock E3C246D4I-2T), though as described the VRM +behaves differently to Supermicro. We suspect that the attack might also affect other +vendors (given that BMCs are often similar), but could not further investigate this and +thus leave it for future work. +7.1 +Server Platform Security and Embedded System Security +We first discuss the security considerations for server platforms. Previous security research +on computer platforms were mainly focused on the security of the software (either running +on the CPU or the management controller). However, each subsystem on a server platform +does not act in isolation. Instead, they may interact with each other via the physical +connections on the motherboard. In our attacks, we show that the hardware design of +the system with a correctly implemented ipmitool can lead to severe security issues and +damage to the system. +Apart from the components on the motherboard, one should also take “plugin” devices +into consideration when analysing the security of server platforms. During our investigation +of the system, we found that when a Peripheral Component Interconnect Express (PCI-E) +device is plugged onto the motherboard, it is also connected to the I2C bus of the +motherboard. However, if the firmware of a PCI-E device is compromised, it can gain +access to the PMBus to perform the same attacks described in this paper. On E3-1220V6- +X11SSL-CF, this connection can be configured with a jumper named JI2C. Although this +jumper is disconnected by default, the user may not be aware of the security implications +of connecting this jumper. +In summary, the server platform is a system that has multiple components and mi- +crocontrollers. The security of the platforms is not only down to ensuring the security of +the software running on it, but the overall design of the hardware and embedded systems +on the motherboard should also go through a thorough security review. Securing such a +system needs collaborative effort of both software developers and hardware engineers. +7.2 +SGX Security +Our attack on SGX enclaves shows that a privileged local attacker can inject a fault to the +enclave and recover secret information with the server management interface, effectively +reviving Plundervolt-like software undervolting attacks on Supermicro X11 motherboards. +We also demonstrate that a malicious service provider (e.g., cloud hoster) can use the +attack chains described in the paper to break the security guarantee provided by SGX. +Moreover, the vulnerability currently cannot be detected/mitigated by SGX attestation, +because the BMC and its firmware are not within the scope of SGX attestation. +A supply chain attack is also possible: as the firmware is not securely verified, it is +possible for a third party to implant malware into the BMC and later launch remote +attacks on SGX and/or damage the CPU. Such a firmware modification is also conceivable +while the device is being shipped to the end user. Detecting such attack would be hard, as +the firmware of the BMC is stored in a separate flash chip. The software running on the +BMC is thus usually out-of-scope of traditional malware detection methods. + +Zitai Chen and David Oswald +19 +7.3 +Countermeasures +Overvolting Attack +According to our experiments, PMBus-based overvolting can lead +to permanent damage to the CPU and thus permanent DoS of the system. +The fundamental issue that leads to this attack is the lack of a hardcoded voltage +limit of the VRM. Simply adding signature verification of the BMC firmware or using +secure boot to break the attack chain might not be sufficient to prevent overvolting, as +other, future attacks might also yield PMBus access. Besides, configuring software-based +PMBus read/write limitations of the VRM through the MFR_PWD_USER command is also +insufficient to stop the attack. This is because this features only sets a 16-bit passcode, +which is prone to brute force attack. We suggest the following mitigations be implemented +for this attack to break the attack chain: +1. In the short term, the user manual of the relevant system(s) should be updated to +describe the usage and suggested configuration of the SMBDAT_VRM and SMBCLK_VRM +jumpers, if they are present on a specific model. +2. In the long term, an alternative VRM with a hardwired voltage safety limit should be +used to replace the current VRM. +3. Another mitigation would be implementing an I2C filter to detect and block malicious +PMBus packets. MFR_VR_CONFIG, which can be used to set a 10 mV VID table, is one +of the main commands that need to be blocked. Optionally, other commands that +involved in the overclocking procedure could be blocked, however, this may affect users +who actually want to use this feature. Such a filter could be implemented in a small +microcontroller that listens to the I2C bus and “jams” malicious commands by actively +pulling the bus low once the command has been detected but before its transmission +has been completed. +PMBus-based SGX Undervolting +To the best of our knowledge, PMFault represents +the first attack that directly breaches integrity guarantees in the Intel SGX security +architecture through the PMBus interface. We believe that the fix currently deployed by +Intel against Plundervolt/V0ltPwn (CVE-2019-11157)—disabling the SVID undervolting +interface—is insufficient when a remote attacker can get access to the PMBus through +the BMC or I2C interface of the CPU, as is the case for Supermicro X11 motherboards. +We note that there might be many other devices connected to the bus, including PCI-E +devices like graphic cards. It is thus also possible for a compromised PCI-E device to send +malicious commands to control the CPU voltage. +Given the potential impact of our findings regarding fault injection into SGX enclaves, +in the short term, we recommend inserting software-based fault injection countermeasures +into cryptographic computations in enclaves (e.g., the quoting enclave). However, we note +that such fixes can only serve as mitigations, but not fully eliminate this attack vector. +We would like to highlight that in our opinion, this attack surface cannot be easily +addressed by jumpers to disconnect the VRM from the SMBus or adding signature +verification of the BMC firmware, as we believe that SGX attestation cannot independently +verify the relevant system configurations: +1. The existence of a PMBus/SMBus interface to the VRM and whether it can be controlled +through the I2C interface of the CPU; +2. The existence of an external microcontroller on the motherboard and if it has the +functionality to control the VRM (e.g., BMC or other PCI-E devices); +3. The firmware security status of the BMC and other devices on the PMBus. +This will make it impossible to give SGX assurance of the trust status of the system. +We believe that in the long term, appropriate hardware countermeasures inside the +CPU package is required: this could on the one hand include continuous monitoring +of the received supply voltage, as recently presented by Intel for critical parts of their +systems [NT22], and on the other the use of fully-integrated voltage regulators. + +20 +PMFault: Faulting and Bricking Server CPUs through Management Interfaces +Acknowledgements +This research is partially funded by the Engineering and Physical Sciences Research Council +(EPSRC) under grants EP/R012598/1, EP/R008000/1, and EP/V000454/1. The results +feed into DsbDtech. We would also like to thank Supermicro for providing a X12DPi-NT6 +server for further investigation of the issue. +A +i2cdetect Result for Supermicro X11SSL-CF +~$ sudo +i2cdetect 0 +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +a +b +c +d +e +f +[00 -20]: -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- +30: +-- -- -- -- -- -- -- 37 -- -- -- -- -- -- -- -- +40: +-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- +50: +50 -- -- -- -- -- -- -- 58 -- -- -- -- -- -- -- +60: +-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- +70: +-- -- -- -- -- -- -- -- +~$ sudo +i2cdetect 1 +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +a +b +c +d +e +f +00: +-- -- -- -- -- 08 -- -- -- -- -- -- -- +10: 10 -- -- -- -- -- -- -- -- 19 -- -- -- -- -- -- +20: 20 -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- +30: 30 -- -- -- -- 35 36 -- -- -- -- -- -- -- -- -- +40: -- -- -- -- 44 -- -- -- -- -- -- -- -- -- -- -- +50: -- 51 -- -- -- -- -- -- -- -- -- -- -- -- -- -- +60: -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- +70: -- -- -- -- -- -- -- -- +B +PMBusDetect Result for Supermicro X11SSL-CF +$ sudo +modprobe +i2c_i801 +$ sudo ./ pmbusdetect -d /dev/i2c -1 +Device 0x20 +READ_TEMPERATURE +success: 0019 +!!!!!!!!!!! +Detected! Device +addr: 20 !!!!!!!!!!! +Device 0x20 +SVID_VENDOR_PRODUCT_ID +success , data: 2555 +This +device is likely to be a MPS VRM +Device 0x20 : 00 +READ_PAGE +success +# Save the page +Page: 00 +Device 0x20 : 00 +WRITE_PAGE +success +Device 0x20 : 00 +READ_VOUT +success: 00D8 +Page: 01 +Device 0x20 : 01 +WRITE_PAGE +success +Device 0x20 : 01 +READ_VOUT +success: 0001 +Device 0x20 : 00 +WRITE_PAGE +success # Restore +the page + +Zitai Chen and David Oswald +21 +References +[asta] +Aspeed +24XX/25XX +I2C +Controller +Linux +Kernel +5.16 +Driver. +https://elixir.bootlin.com/linux/latest/source/drivers/i2c/ +busses/i2c-aspeed.c. visited on 2022-09-16. +[astb] +Linux device tree file: +aspeed-g4.dtsi. +https://github.com/torvalds/ +linux/blob/133d9c53c9dcbb1b8f317e402e79c44d9eb725c9/arch/arm/ +boot/dts/aspeed-g4.dtsi#L438. visited on 2022-09-16. +[BDL97] +Dan Boneh, Richard A. Demillo, and Richard J. Lipton. On the Importance +of Checking Computations. 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Flipping bits in memory +without accessing them: An experimental study of DRAM disturbance errors. +In ISCA, 2014. +[KFG+20] +Zijo Kenjar, Tommaso Frassetto, David Gens, Michael Franz, and Ahmad- +Reza Sadeghi. V0LTpwn: Attacking x86 Processor Integrity from Software. +In USENIX Security ’20, Boston, August 2020. USENIX Association. +[MIT17] +MITRE. CVE-2017-5689, February 2017. https://cve.mitre.org/cgi-bin/ +cvename.cgi?name=CVE-2017-5689. visited on 2022-01-06. +[MOG+20] +Kit Murdock, David Oswald, Flavio D. Garcia, Jo Van Bulck, Daniel Gruss, +and Frank Piessens. Plundervolt: Software-based Fault Injection Attacks +against Intel SGX. In Proceedings of the 41st IEEE Symposium on Security +and Privacy (S&P’20), 2020. +[Mon] +Monolithic +Power +Systems, +Inc. +MP2965 +Datasheet. +https:// +www.monolithicpower.com/en/mp2965.html. visited on 2022-09-10. +[Nie20] +Michael Niewöhner. Supermicro BMC firmware image decryptor, 2020. https: +//github.com/c0d3z3r0/smcbmc. visited on 2022-09-08. +[NT22] +Daniel Nemiroff and Carlos Tokunaga. Whitepaper: Fault Injection Counter- +measures, Deployed at Scale. Technical report, 2022. +[PGC18] +Fabien Périgaud, Alexandre Gazet, and Joffrey Czarny. Subverting your +server through its BMC: the HPE iLO4 case. In Recon Brussels ’18, 2018. +[pmb] +PMBus Power System Management Protocol Specification, Part II – Com- +mand Language. https://470q2hhkn9g15l4bc2btbal1-wpengine.netdna- +ssl.com/wp-content/uploads/2022/01/PMBus-Specification-Rev-1-3- +1-Part-II-20150313.pdf. visited on 2022-09-11. +[QWLQ19] +P. Qiu, D. Wang, Y. Lyu, and G. Qu. VoltJockey: Breaking SGX by Software- +Controlled Voltage-Induced Hardware Faults. In AsianHOST ’19, pages 1–6, +2019. +[Rak15] +Brian Rak. Github repo: ipmi_firmware_tools, 2015. https://github.com/ +devicenull/ipmi_firmware_tools. visited on 2022-09-15. +[RR18] +Jordan Robertson and Michael Riley. The Big Hack: How China Used a Tiny +Chip to Infiltrate U.S. Companies, Oct 2018. https://www.bloomberg.com/ +news/features/2018-10-04/the-big-hack-how-china-used-a-tiny- +chip-to-infiltrate-america-s-top-companies#xj4y7vzkg. visited on +2022-09-19. +[Supa] +Supermicro. +X11SSL-CF(-nF) +Quick +Reference +Guide. +https:// +www.supermicro.com/QuickRefs/motherboard/C232/QRG-1782.pdf. visited +on 2022-09-13. +[Supb] +Supermicro. X11SSL-CF X11SSL-nF USER MANUAL Revision 1.1. https: +//www.supermicro.com/manuals/motherboard/C232/MNL-1782.pdf. visited +on 2022-09-10. +[TSS17] +Adrian Tang, Simha Sethumadhavan, and Salvatore Stolfo. CLKSCREW: +Exposing the perils of security-oblivious energy management. In USENIX +Security ’17, pages 1057–1074, Vancouver, BC, August 2017. USENIX Associ- +ation. + +Zitai Chen and David Oswald +23 +[TW09] +Alexander Tereshkin and Rafal Wojtczuk. +Introducing ring -3 rootkits, +2009. Black Hat USA, https://www.blackhat.com/presentations/bh-usa- +09/TERESHKIN/BHUSA09-Tereshkin-Ring3Rootkit-SLIDES.pdf. visited on +2023-01-06. +[Vaz13] +Juan Vazquez. Exploiting the Supermicro Onboard IPMI Controller, Nov +2013. https://www.rapid7.com/blog/post/2013/11/15/exploiting-the- +supermicro-onboard-ipmi-controller/. visited on 2022-09-12. +[WS18] +Nico Waisman and Matias Sebastian Soler. The Unbearable Lightness of +BMC’s. In BlackHat ’18, 2018. + diff --git a/CdE5T4oBgHgl3EQfTw8s/content/tmp_files/load_file.txt b/CdE5T4oBgHgl3EQfTw8s/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..3f054e2df7e036a67cd95a985c64e9ed26f3642f --- /dev/null +++ b/CdE5T4oBgHgl3EQfTw8s/content/tmp_files/load_file.txt @@ -0,0 +1,996 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf,len=995 +page_content='PMFault: Faulting and Bricking Server CPUs through Management Interfaces Or: A Modern Example of Halt and Catch Fire Zitai Chen1 and David Oswald2 1 University of Birmingham, Birmingham, UK, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='Chen@pgr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='bham.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='uk 2 University of Birmingham, Birmingham, UK, d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='oswald@bham.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='uk Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Apart from the actual CPU, modern server motherboards contain other auxiliary components, for example voltage regulators for power management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Those are connected to the CPU and the separate Baseboard Management Controller (BMC) via the I2C-based PMBus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In this paper, using the case study of the widely used Supermicro X11SSL motherboard, we show how remotely exploitable software weaknesses in the BMC (or other processors with PMBus access) can be used to access the PMBus and then perform hardware-based fault injection attacks on the main CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The underlying weaknesses include insecure firmware encryption and signing mechanisms, a lack of authentication for the firmware upgrade process and the IPMI KCS control interface, as well as the motherboard design (with the PMBus connected to the BMC and SMBus by default).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' First, we show that undervolting through the PMBus allows breaking the integrity guarantees of SGX enclaves, bypassing Intel’s countermeasures against previous undervolting attacks like Plundervolt/V0ltPwn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Second, we experimentally show that overvolting outside the specified range has the potential of permanently damaging Intel Xeon CPUs, rendering the server inoperable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We assess the impact of our findings on other server motherboards made by Supermicro and ASRock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Our attacks, dubbed PMFault, can be carried out by a privileged software adversary and do not require physical access to the server motherboard or knowledge of the BMC login credentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We responsibly disclosed the issues reported in this paper to Supermicro and discuss possible countermeasures at different levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' To the best of our knowledge, the 12th generation of Supermicro motherboards, which was designed before we reported PMFault to Supermicro, is not vulnerable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Keywords: fault injection · software-based faults · Intel SGX · under/overvolting 1 Introduction In recent years, the security implications of software-exposed power and clock manage- ment features have received substantial attention by the research community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Several attacks including CLKSCREW [TSS17], Plundervolt [MOG+20], V0ltPwn [KFG+20], and VoltJockey [QWLQ19] showed that undervolting or overclocking from software can be used to inject faults (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=', bitflips) into computations and break Trusted Execution Environments (TEEs) like Intel Software Guard Extensions (SGX) and ARM TrustZone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Subsequent attacks like VoltPillager [CVM+21] and the work by Buhren et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' [BJKS21] showed that similar attacks can be mounted with direct access to the computer hardware, physically connecting to the control interface of the Voltage Regulator (VR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In particular, Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' targeted the Serial Voltage Identification (SVID) interface used by Intel CPUs to set the desired supply voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' However, apart from SVID, many systems, in particular servers, support a second interface, the so-called Power Management Bus (PMBus), to control the Voltage Regulator Module (VRM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' PMBus is an open arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='05538v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='CR] 13 Jan 2023 2 PMFault: Faulting and Bricking Server CPUs through Management Interfaces standard for digital power management [pmb] and has been adopted by more than 40 companies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' It is based on the Inter-Integrated Circuit (I2C) bus and offers monitoring features apart from voltage and current control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Another component usually presents on server motherboards is the Baseboard Manage- ment Controller (BMC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This chip, intended to remotely manage the server even if e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=', the main CPU has crashed or is powered down, has connections to several buses and chips on the motherboard, including the I2C bus on which the VRM resides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Previous research on x86 platforms has focused on the software-hardware interface provided by the Central Processing Unit (CPU) itself and on the security within the perimeter of each individual component, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=', the BMC [PGC18] or Intel Management Engine (Intel ME) [TW09, MIT17, GE17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' There is a lack of board-level security analysis that reviews the system and motherboard design and interactions between the different components: even if an individual part of the system is secure within its individual threat model, the combination of it with other parts can cause security risks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In our PMFault attacks, the privileged position of the BMC, combined with its large attack surface, makes it interesting from an adversary’s perspective to exploit vulnerabilities of the system via power management features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='1 Our Contribution Our main contributions in this paper are: PMBus-based under/overvolting against server platforms: We first analyse the VRM management interface at the hardware level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We discovered that the semi-standardised PMBus can be used to control the CPU voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Using the case study of a widely-used server motherboard, the Supermicro X11SSL-CF, we explore this attack surface and show that software vulnerabilities in the BMC (or another programmable chip connected to the PMBus) can have severe consequences for the security and safety of the server platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' To determine if the vulnerabilities can affect other server motherboards, we also investigated the PMBus connections and usage on an ASRock E3C246D4I-2T and a Supermicro X12DPi-NT6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' PMBus access through BMC exploits: We then study the BMC firmware and—based on prior work in [Ecl18, Rak15, Nie20]—found that it can indeed be exploited to send arbitrary PMBus commands to control the voltage of the CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' More precisely, several software vulnerabilities in the BMC, including incorrect firmware encryption and signing mechanisms, a lack of authentication for firmware upgrades and control interfaces, an attacker can manipulate the CPU voltage remotely because the PMBus is connected to the BMC and the System Management Bus (SMBus) by default.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' PMBus-based undervolting against SGX enclaves: With this, we observed the same faults as with Plundervolt/V0ltPwn (CVE-2019-11157), including for code running inside an SGX enclave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' As the BMC has an independent, external flash chip for its firmware, SGX attestation currently does not have the ability to verify its status.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Crucially, because the software voltage-control interface in Model Specific Register (MSR) 0x150 is not used, Intel’s fix for CVE-2019-11157 does not address this attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Permanent denial-of-service through overvolting: We also discovered a novel overvolting attack: by sending a certain sequence of PMBus commands, we can set the CPU voltage outside the specification (as high as 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='84 V) and permanently brick the Xeon CPU used in our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Countermeasures and mitigations: Finally, we develop the PMBusDetect tool for detecting if the VRM is connected to the PMBus, and then discuss countermeasures and challenges in securing server platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Importantly, we point out that TEEs like SGX must not only rely on the security of the CPU itself, but also of that of management components the hardware design of the platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Zitai Chen and David Oswald 3 The details of our experiments and source code can be found at: https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='com/ zt-chen/PMFault.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' CVE number CVE-2022-43309 has been reserved for PMFault.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='2 Adversary Model In this paper, we assume a privileged software attacker, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=', who has obtained root on the host CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This is the standard adversary model in the case of TEEs like SGX, and is also realistic in the case of overvolting to permanently destroy the CPU, which could be e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=', exploited by ransomware with root rights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Notably, our attacks do not require physical access (for additional hardware to be added to the system) and can thus be conducted remotely e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=', over SSH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='3 Responsible Disclosure We have responsibly disclosed our findings to Intel and Supermicro in April 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We discussed the details of our methods in several calls with Supermicro, and they acknowledge the existence of the issue and are looking into deploying fixes for their 11th generation products like the Supermicro X11SSL-CF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Supermicro highlighted that the attacks do not replicate on their 12th generation, which e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=', include secure boot and update for the BMC and filtering on PMBus commands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Both of these features break the attack chains described in the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Intel considered the issue in the context of their own server motherboards and did not find them vulnerable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Intel did not comment on the impact on SGX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='4 Related Work Since Boneh et al.’s seminal work on fault injection [BDL97], the research community has devoted substantial efforts to investigating fault attacks and developing according countermeasures (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=', [BECN+06] for an overview).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Software-based Fault Injection Often, fault injection was considered a technique limited to attacks with physical access to the target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' However, with the discovery of the Rowhammer effect [KDK+14], it was shown that faults can also be injected from software (through specific memory access patterns in the case of Rowhammer).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Then, in 2017, Tang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' showed that the clock management features of ARM processors can be exploited to inject faults into computations shielded inside a TEE like ARM TrustZone [TSS17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Similarly, Plundervolt, V0ltPwn, and VoltJockey [MOG+20, KFG+20, QWLQ19] (all tracked via CVE-2019-11157) use the software-exposed voltage control MSR in Intel processors to break the integrity guarantees of SGX enclaves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In response, Intel deployed a microcode update that disables the undervolting interface in MSR 0x150 and allows remote parties to verify correct configuration through SGX’s remote attestation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Thus, purely software-based undervolting attacks against Intel processors were considered no longer possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Hardware-based Fault Injection on TEEs The second generation of undervolting attacks on TEEs like SGX and AMD Secure Encrypted Virtualization (SEV) require physical access to the target motherboard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In the case of VoltPillager [CVM+21], the adversary attaches two wires to the data and clock lines of the SVID bus and can then control the VRM external to the CPU, enabling undervolting even if Intel’s microcode fixes for CVE- 2019-11157 are installed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' For AMD SEV, the adversary does not glitch the actual CPU, but the separate security co-processor, the AMD Secure Processor (SP) [BJKS21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The adversary then proceeds to upload custom firmware to the SP to leak memory encryption keys and also endorsement secrets, which ultimately enable attacks without permanent physical access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 4 PMFault: Faulting and Bricking Server CPUs through Management Interfaces Security of servers and BMCs Independent of hardware-based attacks, the security of server platforms has received attention in the research community and wider society.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In 2018, Bloomberg published a—since widely disproven—article that incorrectly claimed the inclusion of small backdoor chips on Supermicro motherboards [RR18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' However, at the same time, researchers at Eclypsium showed that it is indeed possible to maliciously manipulate the BMC firmware of Supermicro motherboards from 8th to 11th genera- tion [Ecl18], without the need to add a hardware implant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' They also demonstrated how flashing corrupted BMC firmware can “brick” the server system by preventing it to boot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Niewöhner [Nie20] subsequently published a tool to exploit the (weak) firmware en- cryption of Supermicro BMCs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Other work, for example by Waisman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' [WS18] and Périgaud et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' [PGC18], has shown that software weaknesses in BMCs are not limited to Supermicro motherboards, but also applied to Dell, HP, and Lenovo systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' However, the implications of direct access to the PMBus from a compromised BMC have not been deeply studied to our knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='5 Paper Outline The remainder of this paper is structured as follows: in Section 2, we review the PMBus protocol and analyse its specific implementation and usage on Supermicro motherboards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Then, in Section 3, we describe Supermicro’s BMC implementation and methods to modify the firmware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In Section 4, we experimentally investigate how a compromised BMC can interact with the VRM through the PMBus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We then use this to develop over/undervolting attacks in Section 5, before concluding in Section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 2 Analysis of Power Management Bus We started our work by analysing how the PMBus is used on practical server mother- boards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' PMBus is an interface that is used to control the VRM, supplying the power to the CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The most recent public available specification is version 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='3 [pmb].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This specification standardises the physical interface, packet structure, and command set of the PMBus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' However, some commands are left as “manufacturer specified”, so that each VRM manufacturer can have a slightly different implementation of the command set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This matches what we found during our investigation of the MP2955 VRM on the Supermicro X11SSL-CF platform described in the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='1 Experimental Setup We carried out initial experiments with an Intel Xeon E3-1220 v6 (CPU family: 6, model: 158, microcode version: 0xea) on a Supermicro X11SSL-CF Rev 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='01 motherboard (BMC microcontroller ASPEED AST2400, firmware revision 01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='63, BIOS version: 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='We used 64- bit Ubuntu 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='3 LTS with a stock 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='0-107-generic kernel, Intel SGX driver V2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='0, and Intel SGX-SDK V2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We refer to this system as E3-1220V6-X11SSL-CF throughout the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' An overview of the server motherboard representative for Supermicro’s 11th generation products is shown in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The target of the PMFault attack is an Intel CPU with SGX technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' As mentioned, our actual attacks do not require additional hardware or physical access to the system, though we soldered some wires to the motherboard during the analysis phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' On Intel platforms, the voltage of the CPU is controlled by an external VRM Integrated Circuit (IC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The CPU connects to the VRM via the SVID bus to control the voltage supplied by it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This interface for CPU voltage control is present on all desktop and server motherboards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Zitai Chen and David Oswald 5 CPU Voltage Regulator (VRM) Board Management Controller (BMC) SVID Other I2C Devices SMBus/I2C Bus Ethernet 0 KCS PMBus Management Ethernet BMC Flash Chip Figure 1: Overview of the connections on the server motherboard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' However, server VRMs—including the Supermicro X11SSL-CF—often have an ad- ditional I2C-based communication interface called PMBus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This interface allows e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=', overclocking or fine-tuning of the CPU voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' One of the crucial steps in the PMFault is to get access to this interface and understand the communication protocol, so that we gain full control of the CPU voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' One of the design issues we found on our server motherboard is that the PMBus can be directly connected to the more general SMBus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' There are various components on the system on that bus, including the CPU, BMC, and other I2C devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' A compromise of any of these components leads to the takeover of PMBus and thus control of the CPU voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In this paper, we use the BMC as the starting point of the attack, as it commonly exists on server platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In order to analyse the attack surface of the BMC, we further investigated its connection and hardware design on the Supermicro X11SSL-CF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' First, we found that its firmware is stored in a Serial Peripheral Interface (SPI) flash chip, separate from the BIOS flash.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We also found there are two Ethernet ports on the system for communication with the BMC: one is called “Management Ethernet” and is dedicated for server management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The other port can be shared between CPU and BMC so that devices on this Ethernet port can communicate with both CPU and BMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Finally, the BMC also has a Keyboard Controller Style (KCS) interface that enables direct access from the Operating System (OS) running on the CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' These management interfaces open a large attack surface on the BMC, and make remote attacks possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='2 Protocol Structure To be able to eavesdrop and forge PMBus commands, knowledge of the protocol structure shown in Figure 2 is necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The PMBus is an I2C-based protocol (with clock speed of 100 kHz–1 MHz and an open-drain data pin) and uses a master-slave communication mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The master device can query or change the setting of the slave device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Each slave device is assigned a unique 7-bit device address.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The master device first sends a starting bit to initiate a transmission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' During transmis- sion, every group of 9 bits forms a segment, with the 9th bit indicating ACK (0) or NACK (1) for every 8 bits received.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The starting bit and the (N)ACK mechanism are handled at hardware level and do not need to be handled manually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The first segment is always sent by the master.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The first 7 bits are the address of the target slave, and the 8th bit indicates whether this transmission is a read (1) or write (0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 6 PMFault: Faulting and Bricking Server CPUs through Management Interfaces S R / W A C K A C K A C K Device Address Command or Register Addr Data A C K .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 0 1 8 9 10 18 19 27 28 Master Device -> Slave Device Control bit Data bits Slave Device -> Master Device Figure 2: PMBus protocol structure The second segment is the register address to operate on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In the PMBus specification, this segment is called the PMBus command.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The segments after the second one contain the data read from or written to the register.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Interaction between PMBus and SVID Although the functionality of the PMBus pro- tocol is similar to SVID, they have different specifications for the digital signal interface and command sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' A VRM can have both SVID and PMBus interfaces, with the SVID interface directly connected to the CPU and the PMBus interface connected to the SMBus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Both interfaces can be used to control the voltage of the CPU, and some implementations of the PMBus specification also have commands to override the voltages set through the SVID interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='3 PMBus Commands For an adversary to communicate with the VRM and e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=', configure voltage levels, they also need to know the specific PMBus commands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' As mentioned, the PMBus specification allows manufacturers to have custom implementations of PMBus commands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The E3- 1220V6-X11SSL-CF motherboard features an Monolithic Power MP2955 voltage regulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' To understand the PMBus implementation of this VRM, we first started looking for its datasheet, but unfortunately, found that it is not publicly available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' However, on the Monolithic Power website1, we found the datasheet of an alternative VRM (MP2965) [Mon].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' As both chips are manufactured by the same company, we used this datasheet as a reference and starting point to discover the available PMBus commands by analysing the PMBus traffic on the Supermicro X11SSL-CF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We found the relevant PMBus commands by reading and analysing the response (ACK or NACK) of the registers, and validating found commands according to the PMBus specification and the MP2965 datasheet : Table 1 gives the command name, command code, and description of each commands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The first three commands in the table are implemented according to the PMBus 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='3 specification [pmb], while the rest are manufacturer-specific.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Table 1: Discovered PMBus commands on E3-1220V6-X11SSL-CF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Command name Command code Usage CMD_PAGE 0x00 Switch between different voltage rails CMD_OPERATION 0x01 PMBus override VOUT_COMMAND 0x21 Output voltage settings READ_VOUT 0x8B Voltage reading from sensor MFR_VR_CONFIG 0xE4 Enable overclock mode MFR_OCP_TOTAL_SET 0xEE Over-current protection configuration 1https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='monolithicpower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='com/ Zitai Chen and David Oswald 7 With CMD_OPERATION, we can configure the operation mode of the VRM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' By setting bit 1 of this register, we can enable the PMBus override mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In this mode, the voltage configured in the VOUT_COMMAND register will override the voltage configuration from the SVID bus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Another command that is useful for PMFault is READ_VOUT, as it allows us to read the current voltage of the CPU and establish a baseline for undervolting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The MFR_VR_CONFIG register is manufacturer-specific.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' By setting bit 3 or bit 10 and configuring CMD_OPERATION, we could enable the tracking or fixed voltage overclocking mode, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Bit 8 VID_STEP_SEL of MFR_VR_CONFIG also allow us to use an alternative mode of SVID.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In this mode, the VRM uses 10 mV Voltage Identifier (VID) steps instead of the default of 5 mV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This makes overvolting up to 3 V possible, which is well beyond the operating voltage range of the E3-1220 V6 Intel CPU, with a maximum voltage of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='52 V [Cor18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We also discovered that the VRM has an Over Current Protection (OCP) circuit, which can be configured or disabled by another manufacturer-specific register (MFR_OCP_TOTAL_SET).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Some VRM also support multiple voltage output rails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' CMD_PAGE command is used to select the target rail to send the commands to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' With these discovered commands, we can now control the CPU voltage through the PMBus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='1, we detail how this interface is used as part of attack chains for undervolting and overvolting attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='4 Jumper Settings On the Supermicro X11SSL-CF motherboard, there are several jumpers that control different functionalities, including the connection of the VRM to other parts of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We kept all jumpers in the default status as delivered by the vendor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' To avoid confusion, we still list the jumper settings in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' During inspection of the jumper settings, we discovered that the SMBDAT_VRM and SMBCLK_VRM jumpers are neither mentioned in the user manual [Supb] nor in the quick reference guide [Supa].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Using an oscilloscope while sending PMBus commands, we found that these two jumpers can be used for (dis)connecting the VRM from/to the PMBus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The experiments and attacks described in this paper are conducted under the “connected” setting of both jumpers, which according to Supermicro is the default.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We also found server motherboard without such jumpers, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=', Supermicro X11SPG-TF and ASRock E3C246D4I-2T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' For those, the VRM is always connected to the BMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We detail our finding on other motherboards in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' It is worth mentioning that to the best of our knowledge, SGX attestation does not have the functionality to include the configuration of these (external) jumpers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Table 2: Jumper settings on Supermicro X11SSL-CF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Jumper name Description JPME2 Manufacturer mode normal (Default) JPB1 BMC enabled (Default) SMBDAT_VRM Connect VRM data line to PMBus SMBCLK_VRM Connect VRM clock line to PMBus 3 Supermicro’s BMC and Server Management Interface Having understood the basic PMBus protocol and commands, we next look at different ways to gain access to the PMBus and send commands to the VRM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' To achieve that, an attacker needs access to the SMBus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' As described in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='1, on E3-1220V6-X11SSL- CF, one of the devices on the SMBus is the ASPEED AST2400 BMC controller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In this 8 PMFault: Faulting and Bricking Server CPUs through Management Interfaces section, we introduce the functionalities and vulnerabilities in these management interfaces that allow us to achieve our main goal—to take control of the SMBus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' During the initial investigation of the BMC, we found there are mainly three services available: there is a web service running on port 80 (HTTP) and 443 (HTTPS), an Intelligent Platform Management Interface (IPMI) over LAN service on port 623, and the SSH service on port 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Besides, we also found that the IPMI service can be accessed through the KCS interface from the CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Some of these interfaces require authentication: to use HTTP, HTTPS, SSH, and IPMI over-LAN, all exposed through Ethernet, one has to authenticate to the BMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The used credentials in this authentication process are individual for each Supermicro motherboard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' However, the IPMI-over-KCS interface does not require any authentication to the BMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Instead, having root privileges on the host OS running on the CPU is sufficient to access this interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' One can also use the IPMI-over-KCS interface to add/remove/modify BMC credentials to subsequently login to the Ethernet-exposed interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='1 SSH Shell Since SSH is one of the most common interfaces that allows us to get a shell and possibly take over the system, we first started our investigation with it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' However, the SSH service on E3-1220V6-X11SSL-CF provides a custom shell called “ATEN SMASH-CLP System Management Shell”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' It only provides limited commands that enable server monitoring and basic management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Previously, a vulnerability was reported in [Vaz13]: the command shell sh allows gaining root access from this shell, however, this command was not available on our system-under-investigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='2 BMC Firmware Analysis To further investigate the services running on the BMC and check if it is possible to enable an SSH root shell, we dumped the firmware of the BMC with a CH341A SPI flash programmer as shown in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This procedure is only used once to assist our analysis, and is not necessary to execute the actual attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Figure 3: Dumping BMC firmware with a flash programmer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We found that the firmware stored in the SPI flash is neither encrypted nor signed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' There are five partitions in the firmware, where the second one contains a Linux operating system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The SMASH shell is provided by /SMASH/msh and it is possible to change it to a different shell by replacing this file.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The Linux operating system also has an I2C kernel module installed, which provides an interface to communicate with the SMBus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' However, during our testing in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='1, we found that the API provided by this kernel module is not compatible with the commonly 0000 C C C O O SOP16 014 13 12 O O 100 O C 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='27MM O 90 C D GOAET 25XX24XX 以 二 4683 S9Zitai Chen and David Oswald 9 used libi2c in i2c-tool2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' As the result, in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='1, we opted to write a custom library to use the I2C interface of the BMC and communicate with the VRM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='3 Firmware Upgrade After analysing the firmware, we conclude that it is possible to enable an SSH shell by modifying the firmware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We then started to look for software methods to re-flash the BMC SPI flash chip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We found that the firmware upgrade functionality of the BMC provides a way to do this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' There are two interfaces for firmware upgrade: one is through the web interface, the other through the KCS interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Through Web Interface The web interface has a firmware upgrade page that can switch the BMC into upgrade mode and allows the user to upload a BMC firmware update package.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' To prevents unauthorised user from upgrading the firmware, there is a login portal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The user is authenticated by the BMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' As the BMC is a system independent from the OS running on the CPU, users do not need to have privileged access to the OS to be able to use this method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Besides, this web interface can be accessed remotely through Ethernet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The remote BMC firmware upgrade attack chain described in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='3 uses this method to upgrade the firmware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Through IPMI-over-KCS Interface Crucially, the BMC firmware can also be updated through the KCS interface, using the following command: AlUpdate -f firmware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='bin i kcs -r y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' As mentioned, the KCS interface can be accessed from the OS running on the CPU, only requiring root access to the OS, but not the BMC credentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Firmware Upgrade Package After finding the firmware upgrade interface, the next step is to produce an upgrade package that can be uploaded to the BMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We started with the analysis of the structure of the upgrade package.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Figure 4 shows the layout of a firmware upgrade package.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Previous work by [Ecl18] founds that in the firmware upgrade package, there is a region that contains a magic value (ATENs_FW), a half-length CRC checksum, and the length of each section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We call this part the firmware footer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' There is also a region containing metadata of the firmware image, including the name of each region and their length and CRC, starting with “[img]”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We refer to this region as firmware table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In the X11 series, the firmware table, the file system header of the root file system and the website files system header are AES-CBC encrypted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' However, the files in these regions are not encrypted, but only LZMA compressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' As a result, the key of the AES-CBC encryption can be recovered from the ipmi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='so file on the root file system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' With this information, we can modify the firmware and construct a valid firmware up- grade package for the web interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We discuss firmware repacking in detail in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='4 IPMI I2C functionality When exploring the functionalities of IPMI, we also found that the interface also allows direct sending I2C packets with the ipmitool i2c command.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This can be used either through the Ethernet or KCS IPMI channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The authentication requirement for using IPMI-controlled I2C is the same as those described in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' As shown in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='3, we can use this functionality for direct access to the SMBus/PMBus without modifying BMC firmware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 2https://git.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='org/pub/scm/utils/i2c-tools/i2c-tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='git/ 10 PMFault: Faulting and Bricking Server CPUs through Management Interfaces Figure 4: Layout of the BMC firmware upgrade package.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The NVRAM region stores the current configuration of the BMC, the rootFS is a LZMA-compressed cramFS file system with only its header encrypted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The kernel region stores a Linux kernel image, while the BMC website FS is another compressed file system with only the file system header encrypted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The FW Footer starts with a magic value ATENs_FW and contain information about the firmware version, checksum, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The FW Table is an encrypted region and stores a table of the image layout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' All encrypted region of the firmware can be decrypted with a key extracted from ipmi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='so on the rootFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 4 Practical Experiments Finally, using the results from the previous sections, we explain how to construct practical Proof-of-Concept (PoC) attacks for PMFault.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Some of our experiments require physical access to the system to understand the hardware configuration (with an overview shown in Figure 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Note however that physical access is not required when performing PMFault attacks on a real-world system, as the hardware components and connections are identical for a given motherboard model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Oscilloscope connected to PMBus Oscilloscope to monitor CPU voltage BMC flash chip soldered out PMBus connection for Raspberry Pi Management Ethernet Connection BMC micro-controller Power Button Figure 5: Setup of the E3-1220V6-X11SSL-CF for practical experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' These connections are for experiments only;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' physical access is not required in the actual attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='1 PMBus-based Voltage Control To understand the configuration and capabilities of using the PMBus to control the CPU voltage, we conducted two experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Firstly, we used the “probe and verify” method to find the I2C address of the VRM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Then we tried different ways of sending commands to VRM to change the voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' ipmi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='so Decompressed Files of RootFS C BMC rootFS FW FW NVRAM kernel WebsiteFS (Compressed) Footer Table (Compressed)ROHSZitai Chen and David Oswald 11 Discovering the VRM Address Finding the I2C address of the VRM is the first step of PMFault.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The easiest way to explore the I2C buses is to use the interface provided by the OS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' There are two I2C buses that can be used from the OS running on the CPU: i2c-0 is shown by default, while i2c-1 requires the i2c_i801 kernel module to be loaded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' To find all available devices on both I2C buses, we ran the i2cdetect tool on them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We found that there are 12 devices in total connected to the I2C bus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The full list of device addresses can be found in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' To then determine which device is a VRM, we use the result of the standard PMBus command, READ_VOUT, as an indicator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The Plundervolt [MOG+20] attack showed that the normal operating voltage of the CPU should be greater than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='55 V, thus, if the voltage read by READ_VOUT is within this range, it may be a VRM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Of the 12 devices detected, only one device with address 0x20 on I2C bus 1 responded with a value in this voltage range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We hence suspect this device is the VRM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' To verify the result, we also used MFR_ADDR_PMBUS (0xE1) command found in the MP2965 datasheet [Mon] to read the PMBus address of the device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The result is 0x20, which confirms our finding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Changing CPU Voltage with PMBus Commands Having identified the VRM, one can next attempt to send commands to change the CPU voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Set target voltage to VOUT_COMMAND Configure VOUT_OPERATION with PMBus Override Mode Set Bit 3 of MFR_VR_CONFIG Figure 6: Command sequence to change the voltage via PMBus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In the datasheet of the MP2965 [Mon], we found an “overclocking” procedure that can be used for this purpose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' There are two overclocking modes, tracking mode and fix mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In PMFault, we mainly use the fix mode to set a defined voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In the fix overclocking mode, the VRM uses the VID configured with the PMBus command VOUT_COMMAND and ignores the configuration from the SVID bus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Figure 6 shows the steps of using this mode to change voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' First, we need to configure two registers: The first one is VOUT_OPERATION;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' by setting the first bit of this register, we enable PMBus override mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We also have to set bit 3 of MFR_VR_CONFIG to make the VRM act on these changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' After this, the voltage supplied to the CPU will be changed according to the configuration in VOUT_COMMAND.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' To send this PMBus command sequence and change the CPU voltage, we wrote a PoC with the libi2c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This PoC can be compiled and run under Linux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' “Stalls” caused by PMBus Commands The experiments in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='1 also show that the VRM responds to the PMBus commands sent from the CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' One may thus assume that it would then be straightforward to directly send PMBus commands to change the CPU voltage with this method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' However, we found that the CPU stalls after sending the MFR_VR_CONFIG command to actually configure the VRM to use the new voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This will make the CPU voltage being kept at the changed value with no way to change it back.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This phenomenon raised two questions: Is the CPU stall caused by a crash or a recoverable halt?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' If it is caused by a recoverable halt, will this protect against targeted undervolting fault injection?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' To answer this, we connected a Raspberry Pi to the PMBus to directly control the VRM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The I2C interface to the VRM is exposed with two pins, SDA and SCL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' As shown in Figure 5, we connected the I2C interface of the Raspberry Pi to these pins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In the first experiment, we sent a command to disable overclocking after the stall happens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' It appears that with the VRM reconfigured to normal mode, the CPU recovers from the stall situation if the undervolting value is not too low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This shows that the stall is 12 PMFault: Faulting and Bricking Server CPUs through Management Interfaces caused by a recoverable halt and not a crash.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The second experiment is used to find out if the halt will prevent the fault from happening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In this experiment, we used the CRT-RSA PoC of the Plundervolt attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' With the CPU running this PoC, we used Raspberry Pi to send PMBus commands to produce voltage glitches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We found that with glitches with gradually lower voltage, an exploitable fault happens with the CRT-RSA calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Hence, in summary, the “stall” phenomenon will prevent the PMBus attack from being conducted by the CPU-VRM I2C interface, but it does not prevent the fault caused by undervolting from having an impact on CPU calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Voltage Control with BMC Because our attempt of voltage glitching failed with the PoC running on the CPU, we started to look into the BMC-VRM I2C interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In the BMC firmware dumped in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='1, we found the i2c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='ko kernel module, which provides a driver for the I2C interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' However, this module does not implement a standard ioctl() for I2C devices, which is required for using libi2c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This means that the above PoC, which uses this standard I2C library, cannot be used to communicate with this kernel module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' As the kernel module in the firmware did not implement the standard I2C API, we had to find another way to utilize the BMC’s I2C interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' With the help of the I2C driver in the latest Linux kernel [astb, asta], we found that there are 14 I2C interfaces on the AST2400 BMC controller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Each has a set of memory-mapped registers to control the interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We also found the setup and message sending/receiving sequence of the I2C interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We then created a small library to directly write these registers and send I2C bus commands from the BMC CPU to the address of the VRM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' By monitoring the I2C activity with an oscilloscope (this was only required for debugging and during development), we found that the I2C bus 2 (counted from bus 0) of the BMC has the VRM connected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='2 Enabling SSH Access and Firmware Repacking Modification of the firmware can be used to obtain a root shell on the BMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' With the “Supermicro BMC firmware image decryptor” [Nie20] and a modified version of the “ipmi firmware tool” [Rak15] with added support for X11 images, we were able to extract the firmware encryption key and decrypt the file system header.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' With these, we can unpack and modify the full root file system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' As described in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='2, /SMASH/msh provides the shell for SSH service.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' To enable full root shell access, we replaced this file with a shell script with a single line to execute /bin/sh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Besides, as the SSH service is running with root privileges, with the shell redirected to sh, we could obtain a root shell once connected to the SSH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' To repack the image, we modified the “Supermicro BMC firmware image decryptor” tool to add firmware encryption support and constructed a firmware package with a valid footer and firmware table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We successfully tested and installed this modified firmware package both with the web firmware upgrade interface and the IPMI firmware upgrade interface via the AlUpdate tool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='3 Attack Chains for PMBus Access In this section, we discuss three possible attack chains to take over the PMBus with the techniques shown in the previous sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The attacker can use any of these attack chains and change the CPU voltage to perform PMFault attacks, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=', to over/undervolt the CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Remote BMC Firmware Upgrade The first attack chain assumes a malicious insider threat model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This attack chain makes use of the web or IPMI interface through the BMC Ethernet connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' To use this interface, the attacker needs to have access to the BMC Zitai Chen and David Oswald 13 management Ethernet port or the shared management Ethernet port eth0 on the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Besides, the attacker needs to obtain valid credentials to login to the BMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In detail, the attacker can first use the method described in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='2 to repack the SMT_X11_163 firmware upgrade package from [bmc] to enable SSH root access to the BMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Then, they can upload the firmware with the web management interface or the IPMI management interface over Ethernet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' With the SSH interface enabled, the attacker can cross-compile the voltage-changing PoC described in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='1 for the BMC, and then upload and execute it to send PMBus commands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We used base64 -d > /tmp/i2c-pmbus-send to upload our exploit code due to the unavailability of the SCP service on the BMC OS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Local BMC Firmware Upgrade Similar to the first, this attack chain also involves a firmware upgrade for code execution on the BMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' However, we use the KCS interface discussed in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='3 to upgrade the firmware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The attacker does not require access to the management Ethernet plane, instead, only root privileges on the OS running on the CPU is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This is e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=', relevant for data centers that host bare metal machines for customers or for malware/ransomware that has obtained root through other exploits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' IPMI Interface The third attack chain uses the IPMI I2C functionality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' An attacker with root access on the CPU OS or access to the management port of the BMC can use this interface to send commands to any I2C device that is connected to the BMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The command used for sending the raw I2C packets is shown in Listing 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The I2C mapping of this interface is the same as found during the initial investigation in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The VRM is at address 0x20 on bus 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' However, since the last bit of the first packet of I2C indicates the type of operation (read or write), we need to shift the device address left by one bit and set the last bit accordingly when using this interface to control PMBus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' ipmitool i2c bus=2 0x40 Listing 1: IPMI command for sending I2C packets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 5 Undervolting and Overvolting Attacks In this section, we show how under/overvolting through the PMBus leads to attacks on SGX and also permanent physical damage to the CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The attack requires any flaw that gives a software attacker access to the PMBus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' As mentioned in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='3, this can e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=', be a malicious firmware upgrade or the use of the IPMI-to-I2C functionality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The attack is generic in the sense that various flaws can lead to the same outcome: remote fault injection attacks on SGX and bricking the CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Figure 7 shows an overview of the attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='1 Undervolting Attack against Intel SGX Adversary Model As mentioned in Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='2, we assume a threat model where an attacker (including a malicious insider) has full software access to the system but no (or limited) physical access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' More precisely, the attacker has root access to the OS and software access to the BMC via the KCS interface or Ethernet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' All attack chains described in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='3 can generally be used under this threat model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' It is worth mentioning that the attack that uses ipmitool through the KCS interface does not require knowledge of the BMC credentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' A privileged local user on a compromised host CPU can thus use ipmitool to inject fault into SGX purely from software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 14 PMFault: Faulting and Bricking Server CPUs through Management Interfaces BMC PMBus Overvolting Undervolting Brick CPU Fault Injection to SGX Firmware Upgrade to Enable SSH IPMI I2C Command Code Execution in BMC Remotely Executable Action (Management LAN) Locally Executable Action on OS (With root) Result of Attack Voltage Control Entity or Connection Legend Figure 7: Overview of the PMFault attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' With root access to the OS or access to the BMC via Ethernet or KCS, the attacker can perform a malicious firmware upgrade of the BMC and then takeover the PMBus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The attacker can also use the ipmi i2c command to directly control the PMBus via BMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' With control over the CPU voltage, the attacker can overvolt to brick the CPU or undervolt to inject faults into SGX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Proof of Concept We used the same PoC code as Plundervolt/VoltPillager [MOG+20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Before injecting the voltage glitch, we use the attack chain described in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='3 to gain control of the PMBus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' To start with, we used the multiply operation as the first target, as it is a simple target to fault.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' By gradually lowering the CPU voltage with the PMBus commands sent by the BMC while running the Plundervolt/VoltPillager PoC on the CPU, we successfully injected faults into the multiply operation (in our experiments at voltage 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='845 V with the CPU running at 2 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' To verify the fault injection also works for encryption operations running in SGX, we ran the CRT-RSA signature PoC from Plundervolt/VoltPillager, with an RSA signature computed inside an enclave using the Intel Integrated Performance Primitives (Intel IPP) cryptography library functions [Cor].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Again, we could obtain faulty signatures as shown in Listing 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Furthermore, we confirmed that these faulty values could be used to factor the RSA modulus and recover the private RSA key using the Lenstra attack [BDL97].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' // Faulty calculation 1 0x3f ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 0xe0 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 0xb8 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 0x74 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 0x04 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 0x18 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 0x9c ,' 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 0x00 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 0x00 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 0x00 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' [.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' zeroes left out .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='] Incorrect result!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Listing 2: Faulty CRT-RSA decryptions/signatures generated by the respective ipps functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Reproducibility of CRT-RSA Fault Injection To further evaluate the reproducibility of the attack, we setup an automated testing environment by connecting a Raspberry Pi to an Ethernet port (eth0) and the power button of the motherboard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We ran a Python script to repeat the following steps numerous times: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Upload the exploit for controlling the CPU voltage to BMC via an SSH connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Zitai Chen and David Oswald 15 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' SSH into the OS running on the host CPU and trigger CRT-RSA signing in an SGX enclave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Run the PMFault exploit on the BMC to gradually lower the CPU voltage while the signature is computed in the SGX enclave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Stop lowering the CPU voltage when a fault occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Record the result and cleanup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' If no faulty result is output, the system may have crashed due to too low voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In this case, we use the connection to the motherboard power button to reboot the system and wait to allow the system to boot into a stable status.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In total, we conducted 253 tests within 545 min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Of those, faults occurred in 194 tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 66 of these faulty results could be used to successfully recover the correct RSA private key using the Lenstra attack, which translates to a success rate of 26%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' On average, a useful fault could be obtained within 9 minutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='2 Overvolting to Permanently Brick a CPU Apart from the undervolting attack to extract keys from an SGX enclave, we also discovered another attack, which is an overvolting attack that can permanently destroy the CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Adversary Model In this attack, as described in Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='2, we assume an attacker who has root privilege on the host CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' For example, this could be in the case that an attacker has placed ransomware on a system and threatens to damage the CPU unless a ransom is paid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Clearly, root should have full control of all software running on the CPU, but should not be able to cause any physical damage to the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The attack chain described in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='3 using ipmitool with KCS can be used within this threat model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Proof of Concept To overvolt the CPU, we firstly configure the MFR_VR_CONFIG register of the VRM to use the 10 mV SVID table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This allows changing the CPU voltage up to 3 V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We also disabled the over-current protection by reconfiguring the MFR_OCP_TOTAL_SET register.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Then we used the voltage changing procedure to change the CPU voltage to a value much higher than the normal operating voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We found that this procedure allows changing the CPU voltage up to ∼2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='84 V for ∼1 ms, which is outside the typical operating range of Intel CPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' By increasing the voltage beyond the specified operating voltage range (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='55 V–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='52 V) [Cor18] of a 7th Gen Intel E3-1220V6 CPU two times, we permanently destroyed the CPU and left the system in an unbootable state within a few seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We successfully repeated the experiment with a second, identical CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' An example of overvolting is shown in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' For environmental and financial reasons, we were satisfied after successfully destroying two CPUs and decided to not perform further experiments in that regard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 6 Evaluation of other Server Motherboards As we found the PMBus to be a common interface present on server motherboard, we decided to investigate other manufacturers as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' To facilitate larger-scale testing of this, we wrote a tool called PMBusDetect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' With this tool, we scan the system for a PMBus connection and try to detect the VRM address.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We applied this tool to several other systems, including an ASRock rack motherboard (ASRock E3C246D4I-2T) and a Supermicro X12DPi-NT6 motherboard (kindly provided by Supermicro for testing).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We then conducted further analysis of these systems to check if they are vulnerable to any PMBus-related attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 16 PMFault: Faulting and Bricking Server CPUs through Management Interfaces Figure 8: Oscillocope capture of voltage change during overvolting, VOUT_COMMAND set to 0xFF (with 10 mV VID table).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Yellow: PMBus clock, blue: Vcpu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Vcpu shoots up to 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='84 V during overvolting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' PMBusDetect Tool for VRM Detection Based on the VRM detection process mentioned in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='1, we built the PMBusDetect tool to automatically scan all addresses of a specified I2C bus for VRMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' During testing, we found that the implementation of PMBus and usage of the VRM is different between motherboard, and the most stable command to identify a VRM is READ_TEMPERATURE (0x8d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We use the response to this command as an initial indicator to identify whether a VRM is present, and then use the VRM detection process from Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='1 to verify the result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Moreover, as the capabilities and voltage changing sequence can differ between VRM vendor, we added an additional procedure to detect the vendor of the VRM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' For this, we use the result of reading ISL_DEVICE_ID (0xad) as an indicator for Intersil VRMs and SVID_VENDOR_PRODUCT_ID (0xbf) for MPS, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Detection based on ipmi i2c is also implemented for detecting the connection between VRM and the BMC as mentioned in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' An example output of PMBusDetect with Supermicro X11SSL-CF is shown in Appendix B, while Table 3 shows a summary of the motherboard tested and the scan result for VRMs with PMBusDetect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We are aware that our testing—restricted by (lack of) access to server hardware— only gives a very limited picture of the use of PMBus and VRMs on server hardware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We hence decided to open-source PMBusDetect and build on community efforts in the future to obtain a better view of the PMBus landscape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Table 3: Tested motherboards and their VRM detection result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Name BMC Chipset VRM Address PMBus Connects to Supermicro X11SSL-CF AST2400 C232 0x20 BMC & CPU Supermicro X12DPi-NT6 AST2600 C621A 0x30 & 0x34 — ASRock E3C246D4I-2T AST2500 C246 0x60 BMC & CPU 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='1 ASRock Power-Down Attack The ASRock E3C246D4I-2T motherboard uses an Intel Xeon E-2124 CPU with an Intel C246 Chipset and ASPEED AST2500 BMC with login credentials defaulting to ADMIN:ADMIN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We used the PMBusDetect tool together with manual probing and found that the VRM of this motherboard is connected to both the BMC and I2C bus of the CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In the following attack, we assume that the attacker is a user on a baremetal server with root access in the OS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The VRM used on this motherboard is an ISL69138.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Because it is made by a different RIGOL WAIT H 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='00ms 250MSa/s 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='00M pts 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='00000000ms [1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='68V Horizonta Coupling DC Period BW Limit 20M Freg Probe 10X Rise Time Invert OFF Fall Tirme Volts/Div 4 Coarse +width Unit [V] width DV#1→2=***** tmax=-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='210ms Max=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='84 # Vupper=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='58 y AW=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='25 * 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='00 v 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='0 V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='00 V :500mv日Zitai Chen and David Oswald 17 manufacture compared to the MP2955, the voltage changing PMBus command sequence used for the MP2955 does not work with this VRM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Due to lack of documentation of this procedure, we at the moment could not precisely overvolt or undervolt the CPU via the PMBus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Yet, we discovered a new attack to disable the VRM and force power-down the CPU, leaving the system in a (temporary) inoperable state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' PMBusDetect shows that the VRM is at address 0x60 on I2C bus 2 of the host CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Different to the findings for the Supermicro X11SSL-CF, this VRM uses PMBus registers on page 0x1 instead of the default 0x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We then issue the ON_OFF_CONFIG (0x02) and OPERATION (0x01) commands: We configure the OPERATION to “Immediate Off” and set the “source of enable” only to ON_OFF_CONFIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This results in a immediate power-off of the VRM and crashes the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' During testing, we found the PMBus is only writable from the CPU with IPMI over KCS interface, but not from the BMC with ipmi i2c commands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' As the result, it is not possible for the administrator of the system to remotely configure the VRM back to a normal state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Simply issuing the ipmi powercycle command with IPMI over LAN will leave the system in a infinite boot loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' To recover from this attack, the administrator has to physically power-cycle the system, which might increase downtime in a Denial-of- Service (DoS) scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This shows that PMBus as an attack vector does not only affect Supermicro X11SSL- CF, but also can have impact on servers from other manufacturers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Besides we believe that it might also be possible to conduct CPU bricking attacks if the PMBus voltage changing sequence of Intersil VRM is known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We leave this for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='2 Other Supermicro X11 Motherboards We also ran the PMBusDetect tool on X11SPG-TF and X11SSE-F Supermicro server motherboards—in both cases, the VRM was reachable in the default configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' To test if they are vulnerable to PMFault, we sent PMBus commands through ipmi i2c commands and successfully undervolted them to crash the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This shows that the attack chain through the IPMI interface is valid on these systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' As the systems were provided by a third party for remote testing, we were not able to attempt overvolting and similar, destructive experiments, but believe these motherboards to be equally affected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='3 Supermicro X12 Motherboards We disclosed the vulnerability to Supermicro in May 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' They confirmed the issue and also provided a X12 generation Server for further testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This system, Supermicro X12DPi-NT6, features a dual Intel Xeon Gold 6330 CPU, Intel C621A Chipset, and AST2600 BMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Our investigation shows that mitigations has already been implemented on this motherboard to break the attack chain of PMFault before we reported the attack to Supermicro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Firstly, the firmware upgrade package is properly signed with RSA and verified during the firmware upgrade process, which prevents malicious firmware uploads to the BMC via IPMI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This breaks the attack chain though firmware upgrade.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Secondly, I2C packet filtering has been implemented in the BMC, which prevents IPMI commands to directly send packets to the PMBus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Moreover, our PMBusDetect tool shows that the VR is not connected to the CPU, which prevents an attack directly from the operating system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In conclusion, to the best of our knowledge, we believe that Supermicro X12DPi-NT6 is not directly vulnerable to the attacks described in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' However, we note that as-of-yet unknown vulnerabilities might remain in the firmware update process and the complex software stack running on the BMC, which warrants further investigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 18 PMFault: Faulting and Bricking Server CPUs through Management Interfaces 7 Conclusions and Countermeasures In this paper, we demonstrated two remote attacks that use the PMBus interface to control the CPU voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' An undervolting attack can be used to inject fault to the SGX enclave of the CPU and e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=', recover a secret key used in cryptography algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The overvolting attack causes permanent damage to the CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The attack affects, to our knowledge, all 11th generation Supermicro systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' It also impacts ASRock (tested with ASRock E3C246D4I-2T), though as described the VRM behaves differently to Supermicro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We suspect that the attack might also affect other vendors (given that BMCs are often similar), but could not further investigate this and thus leave it for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='1 Server Platform Security and Embedded System Security We first discuss the security considerations for server platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Previous security research on computer platforms were mainly focused on the security of the software (either running on the CPU or the management controller).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' However, each subsystem on a server platform does not act in isolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Instead, they may interact with each other via the physical connections on the motherboard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In our attacks, we show that the hardware design of the system with a correctly implemented ipmitool can lead to severe security issues and damage to the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Apart from the components on the motherboard, one should also take “plugin” devices into consideration when analysing the security of server platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' During our investigation of the system, we found that when a Peripheral Component Interconnect Express (PCI-E) device is plugged onto the motherboard, it is also connected to the I2C bus of the motherboard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' However, if the firmware of a PCI-E device is compromised, it can gain access to the PMBus to perform the same attacks described in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' On E3-1220V6- X11SSL-CF, this connection can be configured with a jumper named JI2C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Although this jumper is disconnected by default, the user may not be aware of the security implications of connecting this jumper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In summary, the server platform is a system that has multiple components and mi- crocontrollers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The security of the platforms is not only down to ensuring the security of the software running on it, but the overall design of the hardware and embedded systems on the motherboard should also go through a thorough security review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Securing such a system needs collaborative effort of both software developers and hardware engineers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='2 SGX Security Our attack on SGX enclaves shows that a privileged local attacker can inject a fault to the enclave and recover secret information with the server management interface, effectively reviving Plundervolt-like software undervolting attacks on Supermicro X11 motherboards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We also demonstrate that a malicious service provider (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=', cloud hoster) can use the attack chains described in the paper to break the security guarantee provided by SGX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Moreover, the vulnerability currently cannot be detected/mitigated by SGX attestation, because the BMC and its firmware are not within the scope of SGX attestation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' A supply chain attack is also possible: as the firmware is not securely verified, it is possible for a third party to implant malware into the BMC and later launch remote attacks on SGX and/or damage the CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Such a firmware modification is also conceivable while the device is being shipped to the end user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Detecting such attack would be hard, as the firmware of the BMC is stored in a separate flash chip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The software running on the BMC is thus usually out-of-scope of traditional malware detection methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Zitai Chen and David Oswald 19 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='3 Countermeasures Overvolting Attack According to our experiments, PMBus-based overvolting can lead to permanent damage to the CPU and thus permanent DoS of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The fundamental issue that leads to this attack is the lack of a hardcoded voltage limit of the VRM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Simply adding signature verification of the BMC firmware or using secure boot to break the attack chain might not be sufficient to prevent overvolting, as other, future attacks might also yield PMBus access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Besides, configuring software-based PMBus read/write limitations of the VRM through the MFR_PWD_USER command is also insufficient to stop the attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This is because this features only sets a 16-bit passcode, which is prone to brute force attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We suggest the following mitigations be implemented for this attack to break the attack chain: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In the short term, the user manual of the relevant system(s) should be updated to describe the usage and suggested configuration of the SMBDAT_VRM and SMBCLK_VRM jumpers, if they are present on a specific model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In the long term, an alternative VRM with a hardwired voltage safety limit should be used to replace the current VRM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Another mitigation would be implementing an I2C filter to detect and block malicious PMBus packets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' MFR_VR_CONFIG, which can be used to set a 10 mV VID table, is one of the main commands that need to be blocked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Optionally, other commands that involved in the overclocking procedure could be blocked, however, this may affect users who actually want to use this feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Such a filter could be implemented in a small microcontroller that listens to the I2C bus and “jams” malicious commands by actively pulling the bus low once the command has been detected but before its transmission has been completed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' PMBus-based SGX Undervolting To the best of our knowledge, PMFault represents the first attack that directly breaches integrity guarantees in the Intel SGX security architecture through the PMBus interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We believe that the fix currently deployed by Intel against Plundervolt/V0ltPwn (CVE-2019-11157)—disabling the SVID undervolting interface—is insufficient when a remote attacker can get access to the PMBus through the BMC or I2C interface of the CPU, as is the case for Supermicro X11 motherboards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We note that there might be many other devices connected to the bus, including PCI-E devices like graphic cards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' It is thus also possible for a compromised PCI-E device to send malicious commands to control the CPU voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Given the potential impact of our findings regarding fault injection into SGX enclaves, in the short term, we recommend inserting software-based fault injection countermeasures into cryptographic computations in enclaves (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=', the quoting enclave).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' However, we note that such fixes can only serve as mitigations, but not fully eliminate this attack vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We would like to highlight that in our opinion, this attack surface cannot be easily addressed by jumpers to disconnect the VRM from the SMBus or adding signature verification of the BMC firmware, as we believe that SGX attestation cannot independently verify the relevant system configurations: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The existence of a PMBus/SMBus interface to the VRM and whether it can be controlled through the I2C interface of the CPU;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The existence of an external microcontroller on the motherboard and if it has the functionality to control the VRM (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=', BMC or other PCI-E devices);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The firmware security status of the BMC and other devices on the PMBus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' This will make it impossible to give SGX assurance of the trust status of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We believe that in the long term, appropriate hardware countermeasures inside the CPU package is required: this could on the one hand include continuous monitoring of the received supply voltage, as recently presented by Intel for critical parts of their systems [NT22], and on the other the use of fully-integrated voltage regulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' 20 PMFault: Faulting and Bricking Server CPUs through Management Interfaces Acknowledgements This research is partially funded by the Engineering and Physical Sciences Research Council (EPSRC) under grants EP/R012598/1, EP/R008000/1, and EP/V000454/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The results feed into DsbDtech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' We would also like to thank Supermicro for providing a X12DPi-NT6 server for further investigation of the issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='A ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='i2cdetect Result for Supermicro X11SSL-CF ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='~$ sudo ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='i2cdetect 0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='7 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='9 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='a ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='b ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='c ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='d ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='e ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='f ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='[00 -20]: -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='30: ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='-- -- -- -- -- -- -- 37 -- -- -- -- -- -- -- -- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='40: ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='50: ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='50 -- -- -- -- -- -- -- 58 -- -- -- -- -- -- -- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='60: ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='70: ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='-- -- -- -- -- -- -- -- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='~$ sudo ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='i2cdetect 1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='7 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='9 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='a ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='b ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='c ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='d ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='e ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='f ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='00: ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='-- -- -- -- -- 08 -- -- -- -- -- -- -- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='10: 10 -- -- -- -- -- -- -- -- 19 -- -- -- -- -- -- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='20: 20 -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='30: 30 -- -- -- -- 35 36 -- -- -- -- -- -- -- -- -- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='40: -- -- -- -- 44 -- -- -- -- -- -- -- -- -- -- -- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='50: -- 51 -- -- -- -- -- -- -- -- -- -- -- -- -- -- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='60: -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='70: -- -- -- -- -- -- -- -- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='B ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='PMBusDetect Result for Supermicro X11SSL-CF ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='$ sudo ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='modprobe ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='i2c_i801 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='$ sudo .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='/ pmbusdetect -d /dev/i2c -1 Device 0x20 READ_TEMPERATURE success: 0019 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='!!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='!!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='!!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='!!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Detected!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Device addr: 20 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='!!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='!!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='!!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='!!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Device 0x20 SVID_VENDOR_PRODUCT_ID success ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' data: 2555 This device is likely to be a MPS VRM Device 0x20 : 00 READ_PAGE success # Save the page Page: 00 Device 0x20 : 00 WRITE_PAGE success Device 0x20 : 00 READ_VOUT success: 00D8 Page: 01 Device 0x20 : 01 WRITE_PAGE success Device 0x20 : 01 READ_VOUT success: 0001 Device 0x20 : 00 WRITE_PAGE success # Restore the page Zitai Chen and David Oswald 21 References [asta] Aspeed 24XX/25XX I2C Controller Linux Kernel 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='16 Driver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' https://elixir.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='bootlin.' metadata={'source': 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Corporation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Intel Xeon Processor E3-1200 v6 Product Family for S Platforms, 01 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='intel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='co.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='uk/content/dam/www/public/ us/en/documents/datasheets/xeon-e3-1200v6-vol-1-datasheet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} 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699–716.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' USENIX Association, August 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' [Ecl18] Eclypsium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Insecure firmware updates in server management systems, Sep 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' https://eclypsium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='com/2018/09/06/insecure-firmware-updates- in-server-management-systems/.' metadata={'source': 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disturbance errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In ISCA, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' [KFG+20] Zijo Kenjar, Tommaso Frassetto, David Gens, Michael Franz, and Ahmad- Reza Sadeghi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' V0LTpwn: Attacking x86 Processor Integrity from Software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In USENIX Security ’20, Boston, August 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' USENIX Association.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' [NT22] Daniel Nemiroff and Carlos Tokunaga.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Whitepaper: Fault Injection Counter- measures, Deployed at Scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Technical report, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' [PGC18] Fabien Périgaud, Alexandre Gazet, and Joffrey Czarny.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Subverting your server through its BMC: the HPE iLO4 case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In Recon Brussels ’18, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' [pmb] PMBus Power System Management Protocol Specification, Part II – Com- mand Language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' https://470q2hhkn9g15l4bc2btbal1-wpengine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='netdna- ssl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='com/wp-content/uploads/2022/01/PMBus-Specification-Rev-1-3- 1-Part-II-20150313.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' VoltJockey: Breaking SGX by Software- Controlled Voltage-Induced Hardware Faults.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In AsianHOST ’19, pages 1–6, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' [Rak15] Brian Rak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Github repo: ipmi_firmware_tools, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='com/ 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+page_content=' https:// www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='supermicro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='com/QuickRefs/motherboard/C232/QRG-1782.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' visited on 2022-09-13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' [Supb] Supermicro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' X11SSL-CF X11SSL-nF USER MANUAL Revision 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' https: //www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='supermicro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='com/manuals/motherboard/C232/MNL-1782.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' visited on 2022-09-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' [TSS17] Adrian Tang, Simha Sethumadhavan, and Salvatore Stolfo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' CLKSCREW: Exposing the perils of security-oblivious energy management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In USENIX Security ’17, pages 1057–1074, Vancouver, BC, August 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' USENIX Associ- ation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Zitai Chen and David Oswald 23 [TW09] Alexander Tereshkin and Rafal Wojtczuk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Introducing ring -3 rootkits, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Black Hat USA, https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='blackhat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='com/presentations/bh-usa- 09/TERESHKIN/BHUSA09-Tereshkin-Ring3Rootkit-SLIDES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' visited on 2023-01-06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' [Vaz13] Juan Vazquez.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' Exploiting the Supermicro Onboard IPMI Controller, Nov 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='rapid7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content='com/blog/post/2013/11/15/exploiting-the- supermicro-onboard-ipmi-controller/.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' visited on 2022-09-12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' [WS18] Nico Waisman and Matias Sebastian Soler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' The Unbearable Lightness of BMC’s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} +page_content=' In BlackHat ’18, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE5T4oBgHgl3EQfTw8s/content/2301.05538v1.pdf'} diff --git a/CdFQT4oBgHgl3EQf_DcV/content/2301.13456v1.pdf b/CdFQT4oBgHgl3EQf_DcV/content/2301.13456v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b701c5e96dbea072401074e1b80b72561906e8f6 --- /dev/null +++ b/CdFQT4oBgHgl3EQf_DcV/content/2301.13456v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c0e160df3d9557bc921cd6fe8084667a793b479406ad1a1fd55181e8d0e7db9e +size 468879 diff --git a/CdFQT4oBgHgl3EQf_DcV/vector_store/index.pkl 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CNRS/Thales, Université Paris-Saclay, 91767 Palaiseau, France + + +Spintronic nano-oscillators with reduced non-linearity could offer key benefits for +realizing neuromorphic applications such as spike-based neurons and frequency multiplexing +in neural networks. Here, we experimentally demonstrate the reduction in non-linearity of a +spin-Hall nano-oscillator (SHNO) by compensation of its effective magnetic anisotropy. The +study involves optimization of Co/Ni multilayer growth to achieve the compensation, followed +by spin diode measurements on patterned microstrips to quantify their anisotropy. The relation +between the second (Hk2 = 0.47 mT) and the first order (Hk1eff = ̶ 0.8 mT) anisotropy fields +reveals the existence of an easy cone, thereby validating the presence of compensation. +Furthermore, we demonstrate a synapse based on the compensated spin diode which has a fixed +frequency when the input power is varied. We then study the current-induced auto-oscillation +properties of SHNOs on compensated films by patterning nano-constrictions of widths 200 and +100 nm. The invariance of the resonance frequency and linewidth of the compensated SHNO +with applied dc current indicates the absence of non-linearity. This independence is maintained +irrespective of the applied external fields and its orientations. The compensated SHNO obtained +has a linewidth of 1.1 MHz and a peak output power of up to 1 pW/MHz emulating a nano- +neuron with a low linewidth and a fixed frequency. + +a) Present address: Department of Physics and Center for Advanced Nanoscience, University of +California, San Diego, La Jolla, CA, 92093, USA +*Corresponding author: pankaj.sethi@cnrs-thales.fr, pankaj8684@gmail.com + + + + + + +2 + +I. INTRODUCTION +Spintronic nano-oscillators with their low device footprint, rich dynamics and +multifunctionality can provide an energy efficient solution to realize neuromorphic +applications [1–4]. Non-linearity is prevalent in the magnetization dynamics of such nano- +oscillators. In a non-linear auto-oscillator, the frequency, f, has a component which depends on +the precession amplitude or the effective magnetization given by, + + + + + + + +f = fFMR + Np, +(1) + +where fFMR is the frequency at ferromagnetic resonance, N is the non-linear frequency shift +coefficient and p is the term related to the amplitude of precession [5]. This non-linearity +emerges from an effective anisotropy in the system, which results in non-circular trajectory of +the precessing magnetization. It leads to a large frequency tunability with current which +provides multifunctionality to these nano-oscillators such as the possibility to be modulated or +synchronized. This has been exploited in realizing numerous applications relevant to data +communication [6–10] and neuromorphic computing [3,4,11,12]. However, there are certain +systems where it is possible to reduce the effective anisotropy and, as a result, the non-linearity. +In such compensated systems, the anisotropy field is counterbalanced by the demagnetization +field, resulting in circular trajectories of the precessing magnetization. The absence of +nonlinearity, which results in a constant frequency with respect to the injected input power or +current, also offers key benefits for realizing neuromorphic applications. For instance, multiply- +and-accumulate (MAC) operations using spintronic resonators employ frequency multiplexing +to uniquely address input radio frequency (RF) signals from neurons to the corresponding +resonators [13,14]. This requires the neurons and the corresponding spin diode-based synapses +to resonate at a relatively fixed frequency independent of the injected RF power, which can be +accomplished by compensating anisotropy in spintronic nano-oscillators and spin diodes, +respectively. Secondly, an absence of non-linearity can reduce the phase noise of the nano- +oscillator by removing the effect of amplitude noise on it. The phase noise, Δf, of an auto- +oscillator is given by, + + +Δf = Δfthermal (1+ N2/Γeff2), +(2) + + + + + + + +3 + +where Δfthermal is the contribution from the thermal generation linewidth and Γeff is the effective +damping [5]. The second term, which is the contribution from the amplitude noise, can be +neglected if N is very small. Thus, a neuron with low linewidth and a relatively fixed frequency +can be realized using anisotropy compensation. A third application is the realization of spike- +based neurons which was recently demonstrated via macro-spin approach and micromagnetic +simulations [15]. It was shown that anisotropy compensation in a spin Hall geometry results in +circular trajectories of the precessing magnetization and the resulting output is a chain of spikes +emulating the biological neurons. Thus, it is important to study systems with compensated +anisotropy. +Recently, Jiang et al. have demonstrated a linewidth reduction of spin-valve based spin- +torque nano-oscillators (STNOs) by controlling the perpendicular magnetic anisotropy (PMA) +of their films using He-ion irradiation [16]. An alternate planar geometry based on heavy metal +and ferromagnetic layers, which utilizes spin current injected from the heavy metal by spin Hall +effect to sustain precession in the ferromagnet, benefits from ease of fabrication [17–19]. +Moreover, spin Hall nano-oscillators (SHNOs), in the form of a nano-constriction geometry of +these layers, exhibit auto-oscillations by way of mode confinement in a potential well formed +by non-uniform magnetic field [20–22]. Divinskiy et al. demonstrated the suppression of +nonlinear damping by compensation of in-plane dipolar anisotropy with PMA in Co/Ni based +disks patterned on Pt heavy metal [23]. However, the detection of auto-oscillations was +performed by optical methods which are less suitable for on chip applications. +Here, we experimentally demonstrate, by all-electrical measurements, a reduction of non- +linearity and linewidth of an SHNO, based on Co/Ni multilayers with compensated anisotropy +and a Pt heavy metal layer. Compensation is achieved by tuning the thicknesses of the Co/Ni +multilayers. The effective anisotropy is estimated using spin diode measurements performed on +microstrip waveguides. The relation between the second and the first order anisotropy terms +indicate the presence of an easy cone state [24–26] which validates the existence of +compensation. The compensated spin diode thus obtained, does not show variation of its +frequency with the injected RF power and can function as a synapse. Nano-constriction based +SHNOs with different widths are then patterned on the compensated stacks and the output +microwave spectra are analysed. The frequency is found to remain nearly constant as a function +of dc current for a wide range of magnetic field strengths and orientations. Moreover, an +extremely low linewidth close to 1 MHz (quality factor = 7500) is obtained, which does not +increase significantly at large applied dc currents. Control SHNO fabricated with an in-plane +anisotropy Ni81Fe19/Pt stack exhibits significant shift of frequency and linewidth with the + + + + + +4 + +applied dc current. The compensated SHNOs can thus operates as a neuron with a fixed +frequency and a low linewidth. + +II. COMPENSATION OF ANISOTROPY IN SPIN HALL DEVICES +A. Sample preparation +The stacks consisting of Ta (5) /Pt (6) /[Co (x) /Ni (y)]5 /Co (x) /Al (2) (thicknesses are in +nm) are deposited on high resistivity Silicon (001) substrates (resistivity > 10000 Ω-cm) by dc- +magnetron sputtering at room temperature. Ta is used as a seed layer to promote adhesion +between silicon and the subsequent layer and Pt serves as the heavy metal layer. Co/Ni +multilayers are chosen for their large PMA and spin polarization which can be tuned by varying +layer thicknesses [27], as demonstrated previously for domain-wall based devices [28,29]. A +Co/Ni multilayer repetition of five was chosen to obtain a sizeable absolute magnetization [30]. +FIG. 1. Alternating gradient magnetometry measurements for Ta (5) /Pt (6)/ [Co (x) / Ni (y)]5/ +Co (x)/ Al (2) (thicknesses are in nm) films with (a) in-plane anisotropy (x = 0.5, y = 0.8), (b) +compensated anisotropy (x = 0.4, y = 0.9) and (c) perpendicular anisotropy (x = 0.4, y = 0.8). + +(a) +Co 0.5/Ni 0.8 +1.0 +0.5 +0.0 +Norm. +-0.5 +OOP +-1.0 +IP +(b) +LCo 0.4/Ni 0.9 +0.5 +0.0 +-0.5 +OOP +-1.0 +IP +(c +Co 0.4/Ni 0.8 +0.5 +0.0 +Norm.I +-0.5 +OOP +-1.0 +IP +-500 +-250 +0 +250 +500 +Hext (mT) + + + +5 + +Thicknesses of Co (x) and Ni (y) are varied to tune the anisotropy and the corresponding M-H +loops are measured for in-plane (IP) and out-of-plane (OOP) field orientations using alternating +gradient force magnetometry (AGFM). Starting with in-plane anisotropy (IPA) for Co (0.5 nm) +and Ni (0.8 nm) [Fig. 1(a)], the thickness of Co is reduced to 0.4 nm and PMA is obtained [Fig. +1(c)] due to interfacial anisotropy overcoming the demagnetization field. Henceforth, in this +article, Co (0.5 nm) /Ni (0.8 nm) and Co (0.4 nm) /Ni (0.8 nm) multilayers are referred to as +IPA and PMA stacks, respectively. Further, when the thickness of Ni is increased to 0.9 nm, +the PMA reduces but the anisotropy is neither fully in-plane nor out-of-plane [Fig. 1(b)]. As +will be described in what follows, the intermediate anisotropy obtained with Co (0.4 nm) and +Ni (0.9 nm) has been compensated and this film is referred to as the compensated stack. The +anisotropy fields were extracted using spin diode measurements [18,31]. To carry out the +measurements, the multilayers were patterned into microstrip waveguides of width 10 µm and +length 25 µm using optical lithography and Ar ion beam etching techniques. Ti (15 nm)/Au +(150 nm) metal stacks are deposited as electrodes and patterned into coplanar waveguides +overlaying the microstrips using optical lithography and lift-off techniques. The resulting +samples are henceforth referred as IPA, PMA and compensated devices, respectively. + +B. Spin-diode measurements and estimation of effective anisotropy +Figure 2 shows the spin-diode measurement set-up. A microwave current with a power of +8 mW (9 dBm) is injected into the microstrip device to generate microwave frequency spin- +orbit torque (SOT) on the ferromagnetic layers due to the heavy metal Pt [18]. The mixing +between the oscillating magneto-resistance and the microwave current produces a dc rectified +voltage, Vdc, at the ferromagnetic resonance, which is detected by using a lock-in amplifier. +The external field is swept close to the OOP direction for the PMA device (θ = 5 deg) and is +swept in-plane (φ = 45 deg) for the compensated and IPA devices. By keeping the field +FIG. 2. Schematic illustration of spin-diode measurement set-up + +sΦ x + + + +6 + +orientation close to the anisotropy of the devices we can eliminate the artefacts due to geometry +induced local anisotropy variation and simplify the analysis [32]. All measurements are +performed at room temperature. Resonance plots obtained for the PMA, the compensated and +the IPA devices are shown in Figures 3 (a), (b) and (c), respectively. The amplitudes observed +in the resonance plots are not corrected for the non-flat frequency response of the wire bonds +and the cabling in the set-up. However, in our analysis we are only interested in the estimation +of the resonance fields which are independent of amplitude losses. The plots can be well fit by +FIG. 3. Spin diode resonance plots at different injected microwave frequencies for (a) PMA, +(b) compensated and (c) IPA stacks based microstrip waveguides. Resonance frequency as a +function of the resonance field for (d) PMA, (e) compensated and (f) IPA stacks based +microstrip waveguides. Solid red lines are Kittel fits and dotted blue lines, plotted for +guidance, corresponds to Meff = 0. + +a) +60 +(d) +ExtractedPeaks +4 GHz +50 +(GHz) +Kittel Fit +5 GHz + - Meft = 0 +6 GHz +40 +7 GHz +Meff=-35mT +30 +8 GHz +6 +Meff +& +20 +5 +10 +0 +100 +200 +300 +400 +120 +160 +200 +240 +280 +Hext (mT) +Hext (mT) +(b) +50 +(e) 8 +ExtractedPeaks +(GHz) +Kittel Fit ++ -Mer= 0 +(Λr) +-50 +Frequency +6 +3 GHz +4 GHz +5 +Meff +>-100 +5 GHz +Meff=0.5mT +6GHz +-150 +7 GHz +4 +8GHz +3 +-200 +100 +200 +300 +400 +80 +120 +160200240280 +Hext (mT) +Hext (mT) +(c) 100 +(f) +.. +Extractedpeaks +(GHz) +Fit +0 +- Mef = 0 +3 GHz +Frequency +6 +Mof=86.6mT +4 GHz +5 GHz +5 +-200 +6 GHz +7 GHz +4 +-300 +8 GHz +3 +100 +200 +300 +400 +80 +120 +160 +200 +240 +Hext (mT) +Hext (mT) + + + +7 + +the sum of symmetric and antisymmetric Lorentzian curves [18]. The resonance field, Hr is +extracted for each of the injected microwave frequency (fres) and the Kittel functions (fres vs Hr) +are plotted for each of the three configurations. The linear relation obtained in Figure 3 (d) for +the PMA device is well explained by the Kittel formula, fres = γ/2π(Hr ̶ µ0Meff ) [33], where +µ0Meff = µ0Ms – Hk, is the effective anisotropy field. The fit of the equation yields an Meff = ̶ +35 mT. The negative sign of Meff confirms the existence of PMA. Figures 3 (e) and (f) depict +the fres vs Hr plots for the compensated and the IPA devices, respectively which are well fit with +the equation, fres= γ/2π[Hr(Hr + µ0Meff)]1/2 [18]. The extracted values of Meff are 0.5 mT and ++86.6 mT for the compensated and the IPA devices, respectively. As a comparison, the Kittel +function corresponding to Meff = 0 is also plotted together with the as obtained fits for each of +the three devices. Clearly, the compensated stack-based device is closest to the near zero +effective anisotropy. +Given that the first order anisotropy is close to zero in the compensated device, the possible +influence of the second order anisotropy needs to be taken into consideration. The following +equations are the more generalized forms which take the second order anisotropy into +consideration, + + + + +f = γ/2π(H1H2)1/2 +(3) +with +H1 = Hr cos(θH ̶ θM) + Hk1eff cos2θM ̶ Hk2cos4θM, + +H2 = Hr cos(θH ̶ θM) + Hk1effcos 2θM ̶ Hk2/2(cos 2θM + cos 4θM), +(4) + +where θH, θM correspond to the angle of the external magnetic field and the magnetization angle +measured from the sample normal, respectively. Hk1eff and Hk2 correspond to the first and the +second order effective anisotropy fields, respectively [34]. By adopting Hk1eff, Hk2 and γ as +adjustable parameters, the θH dependence of Hr yields the first and the second order anisotropy +fields. The energy minimum conditions ∂F/∂θM = 0 and ∂2F/∂θM2 > 0 are used to extract the +value for θM, where F is the magnetic energy density [34]. + + + + + + + +8 + + + +Spin-diode measurements are performed by sweeping the magnetic field at different out- +of-plane angles, θH, in the y-z plane as shown in the schematic of Figure 4. In this geometry, +the signal strength of the output voltage is larger due to the spin pumping contributions [35]. +The resonance fields, Hr, are extracted from the sum of symmetric and antisymmetric +Lorentzians for each of the angles. The measurements are first performed for the IPA and the +PMA devices. The extracted Hr as a function of θH are shown in Figures 5 (a) and (b), with +input microwave frequencies fixed at 3 GHz and 4 GHz for the IPA and the PMA devices, +respectively. The curves display a monotonic behaviour, where the Hr is minimum close to the +in-plane angle (θH = ±90 deg) for the IPA device and close to the out-of-plane angle (θH = 0 +deg) for the PMA device. The nature of the curves is independent of the input microwave +frequency, different values are selected for the two devices based on the signal quality. The +measurements have been performed for the compensated device at a frequency of 5 GHz and +the corresponding Hr vs θH plots are shown in Figure 5 (c). The curves display a non-monotonic +FIG. 4. Schematic illustration of spin-diode measurement set-up when external field is rotated +out-of-plane. +FIG. 5. Resonance field vs field angle for the microstrip waveguide with (a) IPA stack, +microwave frequency fixed at 3 GHz (b) PMA stack, microwave frequency fixed at 4 GHz and +(c) compensated stack, microwave frequency fixed at 5 GHz. + +Bias-tee +Input +Lod: +am:(a) +(b) +(c) +In-Plane +PMA +Compensated +240 +240 +Exp. +240 +Fit +200 +E +200 +220 +160 +H +160 + 200 +120 +80 +3 GHz +120 +4 GHz +180 +5 GHz +-90 +-60-30 +0 +30 +60 +90 +-90 +-60 +-30 +0 +30 +60 +90 +-90-60-30 +0 +30 +60 +90 +Angle (deg) +Angle (deg) +Angle Qμ (deg) + + + +9 + +behaviour, where the Hr is minimum at an intermediate angle close to 50 deg. This is referred +to as the cone angle and its existence is an indication of compensation of the anisotropy [24,36]. +The curves are well fit with (4) and are used to extract Hk1eff = ̶ 0.8 mT and Hk2 = 0.47 mT. +The obtained parameters also satisfy the following conditions for the existence of an easy cone: +Hk1eff < 0; Hk2 >0 and Hk2 > ̶ Hk1eff/2 [24].These measurements thus demonstrate that a device +with compensated anisotropy has been fabricated that can be employed to realize a synapse +with a fixed frequency. + + + +FIG. 6. (a) Comparison of shift in resonance field as a function of input rf power for a spin +diode in IPA, compensated and PMA configuration. (b) Resonance curves as a function of input +rf power for (b) IPA and (c) compensated (synapse) spin diodes + +(a)1.5 +In-Piane +Comp. +1.0 +PMA +0.5 +res +0.0 +-0.5 +-1.0 +-1.5 +2345678910 +RFpower(mW) +(b) +40 +UncompensatedDevice(IPA) +0 +0 +(μV) +-40 +-4 +-80 +> +-8 +RFpower +-120 +-12 +1mW +-160 +10mW +-16 +45 +60 +75 +90 +(c) 80 +Hext (mT) +8 +40 +CompensatedDevice +0 +0 +-40 +-4 +-80 +-8 +%-120 +-12 +-160 +FRFpower +-16 +-200 +1mW +-20 +-240 +10mW +-24 +75 +90 +105 +120 +Hext (mT) + + + +10 + +C. Input independent spin-Hall synapse with fixed frequency +A synapse can be realized using spin-diodes. Leroux et al. demonstrated a MAC operation +using magnetic tunnel junctions as spin diodes [14]. In a MAC operation, the output voltage Uj +can be represented by a weighted sum of the input power, Uj = ΣPiWji. The above equation can +be mapped to a spin-diode equation in the linear zone close to resonance, where the weights are +represented by the resonator frequencies. During the frequency multiplexing in a MAC +operation, each injected input power Pi, should be able to uniquely address the corresponding +synapse by its frequency. This imposes a constraint on the frequency of the synapse which +should not change with the injected rf power. In a spintronic resonator, this criterion is usually +not satisfied on account of the inherent non-linearity. However, the compensated spin diode can +be operated as an input independent synapse with a fixed frequency. Figure 6 (a) shows the +shift in Hr as a function of the injected input rf power for the IPA, the compensated and the +PMA spin diodes. Starting at the minimum input power ( = 1 mW), the shift is normalized to 0 +for all the three devices. As the input power is increased, the IPA and the PMA devices exhibit +an increase in the shift of Hr, whereas, the compensated device shows a negligible shift in Hr. +Figure 6 (b) and (c) show the comparison of the resonance plots for the IPA and the +compensated devices, respectively, as a function of the input power. Clearly, there is no visible +shift in the resonance field and the equivalent frequency with the injected rf power for the +compensated device as compared to the IPA device. Thus, the compensated spin diode can +function as an input independent spin-Hall synapse. + +III. AUTO-OSCILLATIONS IN COMPENSATED SPIN HALL DEVICES – +NEURON OPERATION +A. Device fabrication and measurement set-up +Nano-constrictions with widths of 100 nm and 200 nm are fabricated on the compensated +Co/Ni stacks using electron-beam lithography and Ar ion beam etching. Ti (15 nm)/Au (150 +nm) metal stacks are deposited as electrodes and patterned into coplanar waveguides overlaying +the nano-constrictions using optical lithography and lift-off. The device geometry is similar to +the one used in previous reports for realizing an SHNO [21,22]. As a comparison, in-plane +SHNO based on Py/Pt stacks are also patterned into nano-constrictions (Py = Permalloy = +Ni81Fe19). +The scanning electron microscopy image of a 200 nm nano-constriction along with the +measurement set-up to detect the auto-oscillations is shown in Figure 7 (a). A dc current, Idc, is + + + + + + +11 + + + + +FIG. 7. (a) SEM image of 200 nm nano-constriction and a schematic to study the microwave +emission from the SHNO. (b) Auto-oscillation spectra for the compensated Co/Ni SHNO obtained +at Idc = + 2.8 mA, Hext = 300 mT (θH = 15 deg, ϕH = 50 deg). (c) Auto-oscillation spectra for the in- +plane Py/Pt SHNO obtained at Idc = ̶ 3.5 mA, Hext = 50 mT (θH = 85 deg, ϕH = 42 deg). Linewidth +as a function of Idc sweep for (d) compensated Co/Ni SHNO and (e) in-plane Py/Pt SHNO. Power +spectral density plots showing frequency vs Idc sweep for (f) compensated Co/Ni SHNO and (g) in- +plane Py/Pt SHNO. + + +300 nm +t,xy +8.0 +20 +1.0 +ee +200 +9150 +Frequency (GHz) +7.8 +(zHW/Md) +0.8 +Af=1.1MHz +6 +10 +0.6 +Compensated +(zHW) +5 +7.6 +-3.0 -3.5 +Pt/(Co/Ni)5 +0 +alove +0.4 +7.4 +PSD +-10 +0.2 +7.2 +Ise +0.0 +20 +7.00 +7.25 +7.50 +7.75 +8.00 +-3.0 +-3.5 +-4.0 +-4.5 +-5.0 +2.5-3.0-3.5-4.0-4.5-5.0 +Frequency (GHz) +Idc (mA) +(c) +(e) +'dc (mA) +0.5 +300 +Emitted +20 +0.4 +250 +(GHz) +6.0 +(zHW/Md) +Af=7.85MHz +10 +In-plane +200 +0.3 +(zHW) +Frequency +5.8 +150 +Py 5/Pt 5 +5.6 +0 +0.2 +PSD +100 +-10 +0.1 +5.4 +noise +50 +0.0 +0 +5.2 +20° +B +5.00 +5.25 +5.50 +5.75 +6.00 +2.5 +3.0 +3.5 +4.0 +4.5 +5.0 +2.5 +3.0 +3.54.0 +4.5 +5.0 +Frequency (GHz) +Idc (mA) +Idc (mA) + + + +12 + +injected into the nano-constriction via the dc port of a bias-tee. An external magnetic field is +applied at an in-plane angle, ϕH and an out-of-plane angle, θH. The SHNO emits microwave +power which is extracted from the rf port of the bias-tee and amplified by 38 dB using a low +noise wide-band amplifier. The output spectra are sampled using a spectrum analyzer. All +measurements are performed at room temperature. + +B. Electrical microwave measurements for compensated and in-plane devices +Figure 7 (b) shows the emission spectra for the 200 nm SHNO realized using the +compensated Co/Ni stack at Idc = ̶ 2.8 mA (+ x-direction) and Hext = 300 mT (θH = 15 deg, ϕH += 50 deg). The linewidth (Δf) obtained from the Lorentz fit is 1.1 MHz with the peak power +spectral density (PSD), after subtracting the amplifier gain, as high as 1 pW/MHz. To the best +of our knowledge, the quality factor (Q ≈ 7500) obtained is more than the highest reported +using a single constriction based SHNO [3,37]. As a comparison, the above measurements are +also performed on Py/Pt based SHNO devices. Figure 7 (c) shows the corresponding spectra +obtained at Idc = +3.5 mA and Hext = 50 mT (θH = 85 deg, ϕH = 42 deg). It is worth noting that +the field orientation is maintained close to the in-plane direction for this device to excite the in- +plane modes and the sign of Idc is positive as the SOT is from the top interface. The minimum +linewidth obtained from the Lorentz fit is 7.85 MHz and is much larger than that achieved using +the compensated Co/Ni SHNO. The above observations can be explained from (2), which +indicate a reduction of Δf if N reduces. To further validate this claim, we sweep the injected Idc +and record the variation of the frequency and Δf for the two SHNOs at the above-mentioned +external fields and orientations, respectively. Figures 7 (d) and (e) show Δf as a function of Idc +for the compensated Co/Ni and the in-plane Py/Pt SHNOs, respectively. Figure 7 (d) is plotted +for Idc larger than the critical current of auto-oscillations (Ic = ̶ 2.7 mA), which is the region of +interest, and the inset shows the data for I < Ic as well. When Idc < Ic, Δf increases with the +reduction in current for both the devices, as expected. At large Idc, the Py/Pt SHNO shows an +increase in Δf due to the inherent non-linearity, which is not the case with the compensated +Co/Ni SHNO which shows a near constant Δf. The evidence for the absence of non-linearity in +the compensated Co/Ni SHNO becomes stronger when we compare its frequency vs Idc shown +in the power spectral density plots in Figure 7 (f) to that obtained for Py/Pt SHNO in Figure 7 +(g). Clearly, the rate of change of frequency with the current (df/dI) is minimal for the +compensated Co/Ni SHNO (= 10 MHz/ mA) and significant for the in-plane Py/Pt SHNO (= +500 MHz/mA). However, for Idc > ̶ 4.5 mA, some non-linearity can be observed in Figure 7 + + + + + + +13 + + +(f), which could be ascribed to the device heating or frequency shift due to the Oersted field or +the field-like torque [30]. The above observations are a direct validation of a reduction in the +non-linearity as indicated in (1). The measurements are repeated at different applied external +magnetic fields to the compensated Co/Ni SHNO and are shown in Figure 8. As is the case, the +FIG. 8. Auto-oscillation frequency as a function of Idc sweep for compensated Co/Ni SHNO +performed at external fields of 165 mT, 300 mT and 500 mT. +FIG. 9. (a) Linewidth as a function of Idc sweep at Hext = 180 mT (θH = 15 deg, ϕH = 50 deg) for +the compensated Co/Ni SHNO with 100 nm width. (b) Comparison of frequency vs Idc sweep +when Hext = 180 mT is applied along out-of-plane angles of 22, 30 and 46 deg to the 100 nm +compensated Co/Ni SHNO + + +11 +10 +9 +8 +7 +6 +165mT +5 +300mT +500 mT +4 +3 +-2.5 +-3.0 +-3.5 +-4.0 +-4.5 +Idc (mA)a) +35 +250 +30 +150 +25 +15 +10 +5 +0 +-2.0 +-2.4 +-2.8 +-3.2 +-3.6 +Idc (mA) +(b) +6.4 +6.2 +6.0 +Out-of-plane angle +22deg +5.8 +30deg +46deg +5.6 +5.4 +-1.5 +-2.0 +-2.5 +-3.0 +-3.5 +Idc (mA) + + + +14 + +external fields only change the frequency of the ferromagnetic resonance and not the slope +which are nearly zero for the compensated Co/Ni SHNO. +To further validate the existence of compensation across different devices, the +measurements are repeated on a 100 nm constriction. Figure 9 (a) shows the variation of ∆f vs +Idc for this device, performed at Hext = 180 mT (θH = 15 deg, ϕH = 50 deg). The plot indicates a +high ∆f for Idc < Ic (= ̶ 1.8 mA), as shown in the inset, upon which it does not increase +significantly at higher currents. A larger ∆f in excess of 5 MHz as opposed to 1.1 MHz is +obtained when the width of the constriction is reduced from 200 to 100 nm, which is expected +due to a smaller mode volume. We also performed frequency vs Idc for this device at different +orientations of the external magnetic field (Hext = 180 mT). The measurements are performed +for three different angles, θH = 22, 30 and 46 degrees, respectively keeping ϕH fixed at 90 deg. +Figure 9 (b) shows the results of frequency vs Idc at different out-of-plane angles of the external +field. At each angle, the frequency is different as expected, and is minimum at 46 deg which is +close to the cone angle of precession. However, the frequency remains nearly constant with +respect to Idc, even at different angles, thus providing a strong evidence for the absence of non- +linearity in the compensated SHNO device. + + +IV. CONCLUSION +In summary, we experimentally demonstrate a strong reduction of non-linearity in the +magnetization dynamics of an SHNO by compensation of its effective magnetic anisotropy. +Co/Ni multilayers with a Pt heavy metal form the system for the study. The thicknesses of Co +and Ni are tuned to change the magnetization anisotropy, which is estimated using spin-diode +measurements. An easy cone anisotropy is obtained for the compensated stack when the PMA +is counterbalanced by the demagnetization field. The relation between the second and the first +order anisotropy fields thus obtained, satisfies the condition for the existence of an easy cone. +The spin-diode signal is shown to be independent of the input power as required to operate as +a synapse in neuromorphic computing applications. Auto-oscillations in the SHNO are +examined using nano-constrictions fabricated from the compensated stacks and are compared +with the emission spectra of Py/Pt based SHNO with an in-plane anisotropy. The frequency and +the linewidth are found to be independent of the applied dc current for the compensated SHNO +even at different external fields and orientations. The linewidth obtained is as low as 1.1 MHz +and the peak emission power is as high as 1 pW/MHz. Thus, the compensated SHNO can +operate as an artificial neuron with a fixed frequency and a low linewidth. 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Park, +Voltage-Driven Gigahertz Frequency Tuning of Spin Hall Nano-Oscillators, Nat +Commun 13, (2022). +[33] J.-M. Beaujour, D. Ravelosona, I. Tudosa, E. E. Fullerton, and A. D. Kent, +Ferromagnetic Resonance Linewidth in Ultrathin Films with Perpendicular Magnetic +Anisotropy, Phys Rev B 80, 180415 (2009). +[34] A. Okada, S. Kanai, M. Yamanouchi, S. Ikeda, F. Matsukura, and H. Ohno, Electric- +Field Effects on Magnetic Anisotropy and Damping Constant in Ta/CoFeB/MgO +Investigated by Ferromagnetic Resonance, Appl Phys Lett 105, (2014). +[35] A. Okada, Y. Takeuchi, K. Furuya, C. Zhang, H. Sato, S. Fukami, and H. Ohno, Spin- +Pumping-Free Determination of Spin-Orbit Torque Efficiency from Spin-Torque +Ferromagnetic Resonance, Phys Rev Appl 12, (2019). +[36] Y. Fu, I. Barsukov, J. Li, A. M. Gonçalves, C. C. Kuo, M. Farle, and I. N. Krivorotov, +Temperature Dependence of Perpendicular Magnetic Anisotropy in CoFeB Thin Films, +Appl Phys Lett 108, (2016). +[37] T. Chen, R. K. Dumas, A. Eklund, P. K. Muduli, A. Houshang, A. A. Awad, P. +Dürrenfeld, B. G. Malm, A. Rusu, and J. Åkerman, Spin-Torque and Spin-Hall Nano- +Oscillators, Proceedings of the IEEE 104, 1919 (2016). + + + diff --git a/EdE2T4oBgHgl3EQfSgfT/content/tmp_files/load_file.txt b/EdE2T4oBgHgl3EQfSgfT/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..71594749d9abbdc8050f95063c66ee8620b4a11f --- /dev/null +++ b/EdE2T4oBgHgl3EQfSgfT/content/tmp_files/load_file.txt @@ -0,0 +1,682 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf,len=681 +page_content='1 Compensation of anisotropy in spin-Hall devices for neuromorphic applications Pankaj Sethi*,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Dédalo Sanz-Hernández,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Florian Godel,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Sachin Krishnia,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Fernando Ajejasa),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Alice Mizrahi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Vincent Cros,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Danijela Marković and Julie Grollier Unité Mixte de Physique CNRS/Thales,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Université Paris-Saclay,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' 91767 Palaiseau,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' France Spintronic nano-oscillators with reduced non-linearity could offer key benefits for realizing neuromorphic applications such as spike-based neurons and frequency multiplexing in neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Here, we experimentally demonstrate the reduction in non-linearity of a spin-Hall nano-oscillator (SHNO) by compensation of its effective magnetic anisotropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The study involves optimization of Co/Ni multilayer growth to achieve the compensation, followed by spin diode measurements on patterned microstrips to quantify their anisotropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The relation between the second (Hk2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='47 mT) and the first order (Hk1eff = ̶ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='8 mT) anisotropy fields reveals the existence of an easy cone, thereby validating the presence of compensation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Furthermore, we demonstrate a synapse based on the compensated spin diode which has a fixed frequency when the input power is varied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' We then study the current-induced auto-oscillation properties of SHNOs on compensated films by patterning nano-constrictions of widths 200 and 100 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The invariance of the resonance frequency and linewidth of the compensated SHNO with applied dc current indicates the absence of non-linearity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' This independence is maintained irrespective of the applied external fields and its orientations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The compensated SHNO obtained has a linewidth of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='1 MHz and a peak output power of up to 1 pW/MHz emulating a nano- neuron with a low linewidth and a fixed frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' a) Present address: Department of Physics and Center for Advanced Nanoscience, University of California, San Diego, La Jolla, CA, 92093, USA *Corresponding author: pankaj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='sethi@cnrs-thales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='fr, pankaj8684@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='com 2 I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' INTRODUCTION Spintronic nano-oscillators with their low device footprint, rich dynamics and multifunctionality can provide an energy efficient solution to realize neuromorphic applications [1–4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Non-linearity is prevalent in the magnetization dynamics of such nano- oscillators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' In a non-linear auto-oscillator, the frequency, f, has a component which depends on the precession amplitude or the effective magnetization given by, f = fFMR + Np, (1) where fFMR is the frequency at ferromagnetic resonance, N is the non-linear frequency shift coefficient and p is the term related to the amplitude of precession [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' This non-linearity emerges from an effective anisotropy in the system, which results in non-circular trajectory of the precessing magnetization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' It leads to a large frequency tunability with current which provides multifunctionality to these nano-oscillators such as the possibility to be modulated or synchronized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' This has been exploited in realizing numerous applications relevant to data communication [6–10] and neuromorphic computing [3,4,11,12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' However, there are certain systems where it is possible to reduce the effective anisotropy and, as a result, the non-linearity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' In such compensated systems, the anisotropy field is counterbalanced by the demagnetization field, resulting in circular trajectories of the precessing magnetization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The absence of nonlinearity, which results in a constant frequency with respect to the injected input power or current, also offers key benefits for realizing neuromorphic applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' For instance, multiply- and-accumulate (MAC) operations using spintronic resonators employ frequency multiplexing to uniquely address input radio frequency (RF) signals from neurons to the corresponding resonators [13,14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' This requires the neurons and the corresponding spin diode-based synapses to resonate at a relatively fixed frequency independent of the injected RF power, which can be accomplished by compensating anisotropy in spintronic nano-oscillators and spin diodes, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Secondly, an absence of non-linearity can reduce the phase noise of the nano- oscillator by removing the effect of amplitude noise on it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The phase noise, Δf, of an auto- oscillator is given by, Δf = Δfthermal (1+ N2/Γeff2), (2) 3 where Δfthermal is the contribution from the thermal generation linewidth and Γeff is the effective damping [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The second term, which is the contribution from the amplitude noise, can be neglected if N is very small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Thus, a neuron with low linewidth and a relatively fixed frequency can be realized using anisotropy compensation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' A third application is the realization of spike- based neurons which was recently demonstrated via macro-spin approach and micromagnetic simulations [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' It was shown that anisotropy compensation in a spin Hall geometry results in circular trajectories of the precessing magnetization and the resulting output is a chain of spikes emulating the biological neurons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Thus, it is important to study systems with compensated anisotropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Recently, Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' have demonstrated a linewidth reduction of spin-valve based spin- torque nano-oscillators (STNOs) by controlling the perpendicular magnetic anisotropy (PMA) of their films using He-ion irradiation [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' An alternate planar geometry based on heavy metal and ferromagnetic layers, which utilizes spin current injected from the heavy metal by spin Hall effect to sustain precession in the ferromagnet, benefits from ease of fabrication [17–19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Moreover, spin Hall nano-oscillators (SHNOs), in the form of a nano-constriction geometry of these layers, exhibit auto-oscillations by way of mode confinement in a potential well formed by non-uniform magnetic field [20–22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Divinskiy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' demonstrated the suppression of nonlinear damping by compensation of in-plane dipolar anisotropy with PMA in Co/Ni based disks patterned on Pt heavy metal [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' However, the detection of auto-oscillations was performed by optical methods which are less suitable for on chip applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Here, we experimentally demonstrate, by all-electrical measurements, a reduction of non- linearity and linewidth of an SHNO, based on Co/Ni multilayers with compensated anisotropy and a Pt heavy metal layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Compensation is achieved by tuning the thicknesses of the Co/Ni multilayers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The effective anisotropy is estimated using spin diode measurements performed on microstrip waveguides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The relation between the second and the first order anisotropy terms indicate the presence of an easy cone state [24–26] which validates the existence of compensation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The compensated spin diode thus obtained, does not show variation of its frequency with the injected RF power and can function as a synapse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Nano-constriction based SHNOs with different widths are then patterned on the compensated stacks and the output microwave spectra are analysed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The frequency is found to remain nearly constant as a function of dc current for a wide range of magnetic field strengths and orientations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Moreover, an extremely low linewidth close to 1 MHz (quality factor = 7500) is obtained, which does not increase significantly at large applied dc currents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Control SHNO fabricated with an in-plane anisotropy Ni81Fe19/Pt stack exhibits significant shift of frequency and linewidth with the 4 applied dc current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The compensated SHNOs can thus operates as a neuron with a fixed frequency and a low linewidth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' COMPENSATION OF ANISOTROPY IN SPIN HALL DEVICES A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Sample preparation The stacks consisting of Ta (5) /Pt (6) /[Co (x) /Ni (y)]5 /Co (x) /Al (2) (thicknesses are in nm) are deposited on high resistivity Silicon (001) substrates (resistivity > 10000 Ω-cm) by dc- magnetron sputtering at room temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Ta is used as a seed layer to promote adhesion between silicon and the subsequent layer and Pt serves as the heavy metal layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Co/Ni multilayers are chosen for their large PMA and spin polarization which can be tuned by varying layer thicknesses [27], as demonstrated previously for domain-wall based devices [28,29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' A Co/Ni multilayer repetition of five was chosen to obtain a sizeable absolute magnetization [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Alternating gradient magnetometry measurements for Ta (5) /Pt (6)/ [Co (x) / Ni (y)]5/ Co (x)/ Al (2) (thicknesses are in nm) films with (a) in-plane anisotropy (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5, y = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='8), (b) compensated anisotropy (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='4, y = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='9) and (c) perpendicular anisotropy (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='4, y = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' (a) Co 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5/Ni 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 OOP 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 IP (b) LCo 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='4/Ni 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 OOP 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 IP (c Co 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='4/Ni 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='I 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 OOP 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 IP 500 250 0 250 500 Hext (mT) 5 Thicknesses of Co (x) and Ni (y) are varied to tune the anisotropy and the corresponding M-H loops are measured for in-plane (IP) and out-of-plane (OOP) field orientations using alternating gradient force magnetometry (AGFM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Starting with in-plane anisotropy (IPA) for Co (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 nm) and Ni (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='8 nm) [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' 1(a)], the thickness of Co is reduced to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='4 nm and PMA is obtained [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' 1(c)] due to interfacial anisotropy overcoming the demagnetization field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Henceforth, in this article, Co (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 nm) /Ni (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='8 nm) and Co (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='4 nm) /Ni (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='8 nm) multilayers are referred to as IPA and PMA stacks, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Further, when the thickness of Ni is increased to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='9 nm, the PMA reduces but the anisotropy is neither fully in-plane nor out-of-plane [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' 1(b)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' As will be described in what follows, the intermediate anisotropy obtained with Co (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='4 nm) and Ni (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='9 nm) has been compensated and this film is referred to as the compensated stack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The anisotropy fields were extracted using spin diode measurements [18,31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' To carry out the measurements, the multilayers were patterned into microstrip waveguides of width 10 µm and length 25 µm using optical lithography and Ar ion beam etching techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Ti (15 nm)/Au (150 nm) metal stacks are deposited as electrodes and patterned into coplanar waveguides overlaying the microstrips using optical lithography and lift-off techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The resulting samples are henceforth referred as IPA, PMA and compensated devices, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Spin-diode measurements and estimation of effective anisotropy Figure 2 shows the spin-diode measurement set-up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' A microwave current with a power of 8 mW (9 dBm) is injected into the microstrip device to generate microwave frequency spin- orbit torque (SOT) on the ferromagnetic layers due to the heavy metal Pt [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The mixing between the oscillating magneto-resistance and the microwave current produces a dc rectified voltage, Vdc, at the ferromagnetic resonance, which is detected by using a lock-in amplifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The external field is swept close to the OOP direction for the PMA device (θ = 5 deg) and is swept in-plane (φ = 45 deg) for the compensated and IPA devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' By keeping the field FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Schematic illustration of spin-diode measurement set-up sΦ x 6 orientation close to the anisotropy of the devices we can eliminate the artefacts due to geometry induced local anisotropy variation and simplify the analysis [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' All measurements are performed at room temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Resonance plots obtained for the PMA, the compensated and the IPA devices are shown in Figures 3 (a), (b) and (c), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The amplitudes observed in the resonance plots are not corrected for the non-flat frequency response of the wire bonds and the cabling in the set-up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' However, in our analysis we are only interested in the estimation of the resonance fields which are independent of amplitude losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The plots can be well fit by FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Spin diode resonance plots at different injected microwave frequencies for (a) PMA, (b) compensated and (c) IPA stacks based microstrip waveguides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Resonance frequency as a function of the resonance field for (d) PMA, (e) compensated and (f) IPA stacks based microstrip waveguides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Solid red lines are Kittel fits and dotted blue lines, plotted for guidance, corresponds to Meff = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' a) 60 (d) ExtractedPeaks 4 GHz 50 (GHz) Kittel Fit 5 GHz Meft = 0 6 GHz 40 7 GHz Meff= 35mT 30 8 GHz 6 Meff & 20 5 10 0 100 200 300 400 120 160 200 240 280 Hext (mT) Hext (mT) (b) 50 (e) 8 ExtractedPeaks (GHz) Kittel Fit + Mer= 0 (Λr) 50 Frequency 6 3 GHz 4 GHz 5 Meff > 100 5 GHz Meff=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5mT 6GHz 150 7 GHz 4 8GHz 3 200 100 200 300 400 80 120 160200240280 Hext (mT) Hext (mT) (c) 100 (f) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='. Extractedpeaks (GHz) Fit 0 Mef = 0 3 GHz Frequency 6 Mof=86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='6mT 4 GHz 5 GHz 5 200 6 GHz 7 GHz 4 300 8 GHz 3 100 200 300 400 80 120 160 200 240 Hext (mT) Hext (mT) 7 the sum of symmetric and antisymmetric Lorentzian curves [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The resonance field, Hr is extracted for each of the injected microwave frequency (fres) and the Kittel functions (fres vs Hr) are plotted for each of the three configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The linear relation obtained in Figure 3 (d) for the PMA device is well explained by the Kittel formula, fres = γ/2π(Hr ̶ µ0Meff ) [33], where µ0Meff = µ0Ms – Hk, is the effective anisotropy field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The fit of the equation yields an Meff = ̶ 35 mT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The negative sign of Meff confirms the existence of PMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Figures 3 (e) and (f) depict the fres vs Hr plots for the compensated and the IPA devices, respectively which are well fit with the equation, fres= γ/2π[Hr(Hr + µ0Meff)]1/2 [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The extracted values of Meff are 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 mT and +86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='6 mT for the compensated and the IPA devices, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' As a comparison, the Kittel function corresponding to Meff = 0 is also plotted together with the as obtained fits for each of the three devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Clearly, the compensated stack-based device is closest to the near zero effective anisotropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Given that the first order anisotropy is close to zero in the compensated device, the possible influence of the second order anisotropy needs to be taken into consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The following equations are the more generalized forms which take the second order anisotropy into consideration, f = γ/2π(H1H2)1/2 (3) with H1 = Hr cos(θH ̶ θM) + Hk1eff cos2θM ̶ Hk2cos4θM, H2 = Hr cos(θH ̶ θM) + Hk1effcos 2θM ̶ Hk2/2(cos 2θM + cos 4θM), (4) where θH, θM correspond to the angle of the external magnetic field and the magnetization angle measured from the sample normal, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Hk1eff and Hk2 correspond to the first and the second order effective anisotropy fields, respectively [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' By adopting Hk1eff, Hk2 and γ as adjustable parameters, the θH dependence of Hr yields the first and the second order anisotropy fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The energy minimum conditions ∂F/∂θM = 0 and ∂2F/∂θM2 > 0 are used to extract the value for θM, where F is the magnetic energy density [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' 8 Spin-diode measurements are performed by sweeping the magnetic field at different out- of-plane angles, θH, in the y-z plane as shown in the schematic of Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' In this geometry, the signal strength of the output voltage is larger due to the spin pumping contributions [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The resonance fields, Hr, are extracted from the sum of symmetric and antisymmetric Lorentzians for each of the angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The measurements are first performed for the IPA and the PMA devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The extracted Hr as a function of θH are shown in Figures 5 (a) and (b), with input microwave frequencies fixed at 3 GHz and 4 GHz for the IPA and the PMA devices, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The curves display a monotonic behaviour, where the Hr is minimum close to the in-plane angle (θH = ±90 deg) for the IPA device and close to the out-of-plane angle (θH = 0 deg) for the PMA device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The nature of the curves is independent of the input microwave frequency, different values are selected for the two devices based on the signal quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The measurements have been performed for the compensated device at a frequency of 5 GHz and the corresponding Hr vs θH plots are shown in Figure 5 (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The curves display a non-monotonic FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Schematic illustration of spin-diode measurement set-up when external field is rotated out-of-plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Resonance field vs field angle for the microstrip waveguide with (a) IPA stack, microwave frequency fixed at 3 GHz (b) PMA stack, microwave frequency fixed at 4 GHz and (c) compensated stack, microwave frequency fixed at 5 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Bias tee Input Lod: am:(a) (b) (c) In Plane PMA Compensated 240 240 Exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' 240 Fit 200 E 200 220 160 H 160 200 120 80 3 GHz 120 4 GHz 180 5 GHz 90 60 30 0 30 60 90 90 60 30 0 30 60 90 90 60 30 0 30 60 90 Angle (deg) Angle (deg) Angle Qμ (deg) 9 behaviour, where the Hr is minimum at an intermediate angle close to 50 deg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' This is referred to as the cone angle and its existence is an indication of compensation of the anisotropy [24,36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The curves are well fit with (4) and are used to extract Hk1eff = ̶ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='8 mT and Hk2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='47 mT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The obtained parameters also satisfy the following conditions for the existence of an easy cone: Hk1eff < 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Hk2 >0 and Hk2 > ̶ Hk1eff/2 [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='These measurements thus demonstrate that a device with compensated anisotropy has been fabricated that can be employed to realize a synapse with a fixed frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' (a) Comparison of shift in resonance field as a function of input rf power for a spin diode in IPA, compensated and PMA configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' (b) Resonance curves as a function of input rf power for (b) IPA and (c) compensated (synapse) spin diodes (a)1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 In Piane Comp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 PMA 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 res 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 2345678910 RFpower(mW) (b) 40 UncompensatedDevice(IPA) 0 0 (μV) 40 4 80 > 8 RFpower 120 12 1mW 160 10mW 16 45 60 75 90 (c) 80 Hext (mT) 8 40 CompensatedDevice 0 0 40 4 80 8 % 120 12 160 FRFpower 16 200 1mW 20 240 10mW 24 75 90 105 120 Hext (mT) 10 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Input independent spin-Hall synapse with fixed frequency A synapse can be realized using spin-diodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Leroux et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' demonstrated a MAC operation using magnetic tunnel junctions as spin diodes [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' In a MAC operation, the output voltage Uj can be represented by a weighted sum of the input power, Uj = ΣPiWji.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The above equation can be mapped to a spin-diode equation in the linear zone close to resonance, where the weights are represented by the resonator frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' During the frequency multiplexing in a MAC operation, each injected input power Pi, should be able to uniquely address the corresponding synapse by its frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' This imposes a constraint on the frequency of the synapse which should not change with the injected rf power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' In a spintronic resonator, this criterion is usually not satisfied on account of the inherent non-linearity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' However, the compensated spin diode can be operated as an input independent synapse with a fixed frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Figure 6 (a) shows the shift in Hr as a function of the injected input rf power for the IPA, the compensated and the PMA spin diodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Starting at the minimum input power ( = 1 mW), the shift is normalized to 0 for all the three devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' As the input power is increased, the IPA and the PMA devices exhibit an increase in the shift of Hr, whereas, the compensated device shows a negligible shift in Hr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Figure 6 (b) and (c) show the comparison of the resonance plots for the IPA and the compensated devices, respectively, as a function of the input power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Clearly, there is no visible shift in the resonance field and the equivalent frequency with the injected rf power for the compensated device as compared to the IPA device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Thus, the compensated spin diode can function as an input independent spin-Hall synapse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' AUTO-OSCILLATIONS IN COMPENSATED SPIN HALL DEVICES – NEURON OPERATION A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Device fabrication and measurement set-up Nano-constrictions with widths of 100 nm and 200 nm are fabricated on the compensated Co/Ni stacks using electron-beam lithography and Ar ion beam etching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Ti (15 nm)/Au (150 nm) metal stacks are deposited as electrodes and patterned into coplanar waveguides overlaying the nano-constrictions using optical lithography and lift-off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The device geometry is similar to the one used in previous reports for realizing an SHNO [21,22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' As a comparison, in-plane SHNO based on Py/Pt stacks are also patterned into nano-constrictions (Py = Permalloy = Ni81Fe19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The scanning electron microscopy image of a 200 nm nano-constriction along with the measurement set-up to detect the auto-oscillations is shown in Figure 7 (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' A dc current, Idc, is 11 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' (a) SEM image of 200 nm nano-constriction and a schematic to study the microwave emission from the SHNO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' (b) Auto-oscillation spectra for the compensated Co/Ni SHNO obtained at Idc = + 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='8 mA, Hext = 300 mT (θH = 15 deg, ϕH = 50 deg).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' (c) Auto-oscillation spectra for the in- plane Py/Pt SHNO obtained at Idc = ̶ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 mA, Hext = 50 mT (θH = 85 deg, ϕH = 42 deg).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Linewidth as a function of Idc sweep for (d) compensated Co/Ni SHNO and (e) in-plane Py/Pt SHNO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Power spectral density plots showing frequency vs Idc sweep for (f) compensated Co/Ni SHNO and (g) in- plane Py/Pt SHNO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' 300 nm t,xy 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 20 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 ee 200 9150 Frequency (GHz) 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='8 (zHW/Md) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='8 Af=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='1MHz 6 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='6 Compensated (zHW) 5 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='6 3.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='3 (zHW) Frequency 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='8 150 Py 5/Pt 5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='6 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='2 PSD 100 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='1 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='4 noise 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 0 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='2 20° B 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='00 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='25 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='50 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='75 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='00 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 Frequency (GHz) Idc (mA) Idc (mA) 12 injected into the nano-constriction via the dc port of a bias-tee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' An external magnetic field is applied at an in-plane angle, ϕH and an out-of-plane angle, θH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The SHNO emits microwave power which is extracted from the rf port of the bias-tee and amplified by 38 dB using a low noise wide-band amplifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The output spectra are sampled using a spectrum analyzer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' All measurements are performed at room temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Electrical microwave measurements for compensated and in-plane devices Figure 7 (b) shows the emission spectra for the 200 nm SHNO realized using the compensated Co/Ni stack at Idc = ̶ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='8 mA (+ x-direction) and Hext = 300 mT (θH = 15 deg, ϕH = 50 deg).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The linewidth (Δf) obtained from the Lorentz fit is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='1 MHz with the peak power spectral density (PSD), after subtracting the amplifier gain, as high as 1 pW/MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' To the best of our knowledge, the quality factor (Q ≈ 7500) obtained is more than the highest reported using a single constriction based SHNO [3,37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' As a comparison, the above measurements are also performed on Py/Pt based SHNO devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Figure 7 (c) shows the corresponding spectra obtained at Idc = +3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 mA and Hext = 50 mT (θH = 85 deg, ϕH = 42 deg).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' It is worth noting that the field orientation is maintained close to the in-plane direction for this device to excite the in- plane modes and the sign of Idc is positive as the SOT is from the top interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The minimum linewidth obtained from the Lorentz fit is 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='85 MHz and is much larger than that achieved using the compensated Co/Ni SHNO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The above observations can be explained from (2), which indicate a reduction of Δf if N reduces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' To further validate this claim, we sweep the injected Idc and record the variation of the frequency and Δf for the two SHNOs at the above-mentioned external fields and orientations, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Figures 7 (d) and (e) show Δf as a function of Idc for the compensated Co/Ni and the in-plane Py/Pt SHNOs, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Figure 7 (d) is plotted for Idc larger than the critical current of auto-oscillations (Ic = ̶ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='7 mA), which is the region of interest, and the inset shows the data for I < Ic as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' When Idc < Ic, Δf increases with the reduction in current for both the devices, as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' At large Idc, the Py/Pt SHNO shows an increase in Δf due to the inherent non-linearity, which is not the case with the compensated Co/Ni SHNO which shows a near constant Δf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The evidence for the absence of non-linearity in the compensated Co/Ni SHNO becomes stronger when we compare its frequency vs Idc shown in the power spectral density plots in Figure 7 (f) to that obtained for Py/Pt SHNO in Figure 7 (g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Clearly, the rate of change of frequency with the current (df/dI) is minimal for the compensated Co/Ni SHNO (= 10 MHz/ mA) and significant for the in-plane Py/Pt SHNO (= 500 MHz/mA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' However, for Idc > ̶ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 mA, some non-linearity can be observed in Figure 7 13 (f), which could be ascribed to the device heating or frequency shift due to the Oersted field or the field-like torque [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The above observations are a direct validation of a reduction in the non-linearity as indicated in (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The measurements are repeated at different applied external magnetic fields to the compensated Co/Ni SHNO and are shown in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' As is the case, the FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Auto-oscillation frequency as a function of Idc sweep for compensated Co/Ni SHNO performed at external fields of 165 mT, 300 mT and 500 mT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' (a) Linewidth as a function of Idc sweep at Hext = 180 mT (θH = 15 deg, ϕH = 50 deg) for the compensated Co/Ni SHNO with 100 nm width.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' (b) Comparison of frequency vs Idc sweep when Hext = 180 mT is applied along out-of-plane angles of 22, 30 and 46 deg to the 100 nm compensated Co/Ni SHNO 11 10 9 8 7 6 165mT 5 300mT 500 mT 4 3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 Idc (mA)a) 35 250 30 150 25 15 10 5 0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='8 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='2 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='6 Idc (mA) (b) 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='4 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='2 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 Out of plane angle 22deg 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='8 30deg 46deg 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='6 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='5 Idc (mA) 14 external fields only change the frequency of the ferromagnetic resonance and not the slope which are nearly zero for the compensated Co/Ni SHNO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' To further validate the existence of compensation across different devices, the measurements are repeated on a 100 nm constriction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Figure 9 (a) shows the variation of ∆f vs Idc for this device, performed at Hext = 180 mT (θH = 15 deg, ϕH = 50 deg).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The plot indicates a high ∆f for Idc < Ic (= ̶ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='8 mA), as shown in the inset, upon which it does not increase significantly at higher currents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' A larger ∆f in excess of 5 MHz as opposed to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='1 MHz is obtained when the width of the constriction is reduced from 200 to 100 nm, which is expected due to a smaller mode volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' We also performed frequency vs Idc for this device at different orientations of the external magnetic field (Hext = 180 mT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The measurements are performed for three different angles, θH = 22, 30 and 46 degrees, respectively keeping ϕH fixed at 90 deg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Figure 9 (b) shows the results of frequency vs Idc at different out-of-plane angles of the external field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' At each angle, the frequency is different as expected, and is minimum at 46 deg which is close to the cone angle of precession.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' However, the frequency remains nearly constant with respect to Idc, even at different angles, thus providing a strong evidence for the absence of non- linearity in the compensated SHNO device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' CONCLUSION In summary, we experimentally demonstrate a strong reduction of non-linearity in the magnetization dynamics of an SHNO by compensation of its effective magnetic anisotropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Co/Ni multilayers with a Pt heavy metal form the system for the study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The thicknesses of Co and Ni are tuned to change the magnetization anisotropy, which is estimated using spin-diode measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' An easy cone anisotropy is obtained for the compensated stack when the PMA is counterbalanced by the demagnetization field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The relation between the second and the first order anisotropy fields thus obtained, satisfies the condition for the existence of an easy cone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The spin-diode signal is shown to be independent of the input power as required to operate as a synapse in neuromorphic computing applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Auto-oscillations in the SHNO are examined using nano-constrictions fabricated from the compensated stacks and are compared with the emission spectra of Py/Pt based SHNO with an in-plane anisotropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The frequency and the linewidth are found to be independent of the applied dc current for the compensated SHNO even at different external fields and orientations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' The linewidth obtained is as low as 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content='1 MHz and the peak emission power is as high as 1 pW/MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' Thus, the compensated SHNO can operate as an artificial neuron with a fixed frequency and a low linewidth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' This study opens up 15 a possibility of realizing neuromorphic applications such as frequency multiplexing in a multiply-and-accumulate (MAC) operation, and spike-based neurons exploiting easy-plane oscillations in a compensated SHNO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} +page_content=' ACKNOWLEDGMENTS This work is supported by the Agence Nationale de la Recherche Project ANR-20-CE24-0002 (SpinSpike).' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdE2T4oBgHgl3EQfSgfT/content/2301.03794v1.pdf'} diff --git a/HtA0T4oBgHgl3EQfB_9Y/content/tmp_files/2301.01983v1.pdf.txt b/HtA0T4oBgHgl3EQfB_9Y/content/tmp_files/2301.01983v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..cbea396c6113867dffc715de06b8dec007e0aec8 --- /dev/null +++ b/HtA0T4oBgHgl3EQfB_9Y/content/tmp_files/2301.01983v1.pdf.txt @@ -0,0 +1,1041 @@ +Characterization of a half-wave plate for CMB circular polarization measurement +with POLARBEAR +T. Fujino,1, a) S. Takakura,2 Y. Chinone,3, 4 M. Hasegawa,5, 3, 6 M. Hazumi,3, 4, 5, 7, 6 N. +Katayama,4 A. T. Lee,8, 9, 3 T. Matsumura,4 Y. Minami,10 and H. Nishino11 +1)Graduate School of Engineering Science, Yokohama National University, +Yokohama, 240-8501, Japan +2)Department of Astrophysical and Planetary Sciences, University of Colorado +Boulder, Boulder, CO 80309, USA +3)International Center for Quantum-field Measurement Systems +for Studies of the Universe and Particles (QUP), High Energy +Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, +Japan +4)Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU, +WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, +Japan +5)Institute of Particle and Nuclear Studies (IPNS), High Energy +Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, +Japan +6)The Graduate University for Advanced Studies (SOKENDAI), Miura District, +Kanagawa 240-0115, Hayama, Japan +7)Japan Aerospace Exploration Agency (JAXA), Institute of Space +and Astronautical Science (ISAS), Sagamihara, Kanagawa 252-5210, +Japan +8)Department of Physics, University of California, Berkeley, Berkeley, CA 94720, +USA +9)Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, +USA +10)Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka, +567-0047, Japan +11)The University of Tokyo, Tokyo, Research Center for the Early Universe, +School of Science, 113-0033, Japan +1 +arXiv:2301.01983v1 [astro-ph.CO] 5 Jan 2023 + +(Dated: 6 January 2023) +A half-wave plate (HWP) is often used as a modulator to suppress systematic error in +the measurements of cosmic microwave background (CMB) polarization. An HWP +can also be used to measure circular polarization (CP) through its optical leakage +from CP to linear polarization. The CP of the CMB is predicted to be produced by +interactions in the Universe, such as interactions with supernova remnants of popu- +lation III stars. Thus, the observation of the CP of CMB is a new tool for searching +for population III stars. In this paper, we demonstrate the improved measurement +of the leakage coefficient using the transmission spectrum measurement of an actual +HWP in the laboratory. We measured the transmittance of linearly polarized light +through the HWP used in the Polarbear experiment in the frequency range of +120 GHz to 160 GHz. We evaluate properties of the HWP by fitting the data with +a physical model using the Markov Chain Monte Carlo method. We then estimate +the band-averaged CP leakage coefficient using the physical model. We find that the +leakage coefficient strongly depends on the spectra of CP sources. We thus calculate +the maximum rate of leakage from CP to linear polarization as 0.133 ± 0.009 in the +Rayleigh–Jeans spectrum. The nonzero value shows that Polarbear would have +sensitivity to the CP. Additionally, because we use the bandpass of detectors installed +in the telescope to calculate the band-averaged values, we also consider systematic +effects in the experiment. +a)Electronic mail: fugino-takuro-yk@ynu.jp +2 + +I. +INTRODUCTION +Measuring the polarization of the cosmic microwave background (CMB) is a powerful +method of probing the physics of the early universe. The linear polarization of the CMB +comes from the quadrupole anisotropy at the last scattering of CMB photons. There are +two sources of quadrupole anisotropy, namely the density perturbation and primordial grav- +itational wave. The density perturbation makes an even-parity linear polarization pattern +called the E-mode in the CMB polarization whereas the primordial gravitational wave gen- +erated by cosmic inflation in the early universe makes an odd-parity linear polarization +pattern called the B-mode as well as the E-mode. The primordial B-mode polarization +can be considered a smoking gun for the inflation. The scientific goal of many ongoing and +future planed CMB experiments is finding the signal in the linear polarization. +CMB photons can also have circular polarization (CP). Although the CP of the CMB +is not predicted by the standard models of cosmology, the so-called Λ Cold Dark Matter +(ΛCDM) model, there are mechanisms that can generate the CP of the CMB photons dur- +ing their propagation from the last scattering to an observer today. Examples are Faraday +conversion (FC) by the magnetic fields of galaxy clusters1, FC by relativistic plasma rem- +nants of Population III stars2, scattering from the cosmic neutrino background (CνB)3, and +photon-photon-scattering4. +Some CMB polarization experiments have set an experimental constraint on the angular +power spectrum of CP. The optics of the Cosmology Large Angular Scale Surveyor (CLASS) +have sensitivity to CP because of the use of a variable-delay polarization modulator5. SPI- +DER, a balloon-borne telescope designed to search for the B-mode linear polarization of +the CMB, placed a limit on the CP power spectrum even though the telescope was not +designed to be sensitive to the CP. The SPIDER project utilized the imperfection of the +half-wave plate (HWP) modulator6. An ideal HWP works as a retarder of phase π, inverting +the electric field of one axis of the incident linearly polarized light. The outgoing light is +thus linearly polarized at a different angle from the incoming light. In practice, however, an +HWP comprising single-layer birefringent material only satisfies this condition at a target +frequency. Outside the target frequency range within the observational frequency band, the +retardance is no longer π, and a coupling between linear polarization and CP is thus created. +In this case, a part of the incident CP leaks to linear polarization. Thus, a CMB telescope, +3 + +which is designed to detect a linearly polarized signal, gains sensitivity to CP as long as the +properties of its HWP are well characterized. +To utilize this infinitesimal leakage, we need to know the amount of leakage precisely +by calibration with known CP light or characterization from measured optical parameters. +Because we do not have a calibrator for CP in Polarbear, in this paper, we choose to +characterize the leakage of the HWP. Although there have been papers on CMB experiments +using an HWP as a polarization modulator7–9, they mainly reported only the efficiency of +the linear polarization and did not include the leakage between CP and linear polarization +because they aimed to measure the linear polarization of the CMB. Some papers10,11 reported +the leakage between the CP and linear polarization using Mueller matrix formalism; however, +these were simulation-only results or proto-type results, not evaluation results of an HWP +for actual CMB observation. A study on CP by SPIDER6 used the leakage estimated from +the design values of the HWP and calculated an upper limit on the angular power spectrum +of the CMB CP. +In the present paper, we report the characterization of an HWP installed in the Polar- +bear telescope. Polarbear is a CMB experiment that began in January 2012. From May +2014 to December 2016, Polarbear performed large-angular-scale observations using the +HWP, which was continuously rotated at 2 Hz. With these data, we measured the CMB +B-mode power spectrum over a multipole range of 50 < ℓ < 600 and put a limit on the +tensor-to-scalar ratio, r < 0.3312. We evaluate the HWP using transmission spectrum taken +in the laboratory in 2014 before its installation in the Polarbear telescope. We determine +physical parameters of the HWP by fitting the data with a theoretical transmission model +and then estimate the leakage between the CP and linear polarization using this model. +Through measurement of the fringe, we determine the thickness and the difference in the +refractive index between the ordinary and extra-ordinary axes of sapphire precisely. +Section II presents an overview of the CMB polarization observation with the continuously +rotating HWP. Section III explains the Polarbear experiment. Section IV details the +characterization of the Polarbear HWP in the laboratory. We also present the results of +the transmittance of the HWP for linearly polarized light. In section V, we explain a method +of estimating the HWP leakage between CP and linear polarization and present estimation +results. We discuss systematic uncertainty of the leakage in section VI. We also discuss the +prospects of CP measurements using Polarbear. +4 + +TABLE I. Design values of the HWP used in the Polarbear experiment. The first and second rows +give values for the ordinary and extra-ordinary axes of the sapphire, respectively. The refractive +indices and loss tangents of the components come from V. Parshin (1994)13, RT/duroid (2020)14, +and J. W. Lamb (1996)15. +thickness +refractive index loss tangent +Sapphire (o-axis) (3.1 ± 0.1) mm +3.068 ± 0.003 +2.30 × 10−4 +Sapphire (e-axis) (3.1 ± 0.1) mm +3.402 ± 0.003 +1.25 × 10−4 +Duroid +0.254 mm +1.715 ± 0.012 +12.0 × 10−4 +LDPE +0.038 mm +1.514 ± 0.010 +∼5.0 × 10−4 +II. +POLARIZATION OBSERVATION WITH AN HWP +An HWP is an optical device that creates an optical path difference of half of the wave- +length. CMB experiments widely use HWPs made from birefringent materials. An HWP +converts linearly polarized incident light with angle αin to linearly polarized light with angle +2θh − αin, where θh is the angle of the fast axis of the HWP. In Polarbear, we rotate the +HWP continuously to separate the linear polarization signal from the unpolarized signal in +the frequency domain for the reduction of the systematic uncertainties, which are generated +in the instruments after the HWP and by the detector pair difference, and low-frequency +noise. In this section, we explain the optical model of the HWP and how the HWP modulates +polarization signals. +A. +HWP modeling +The HWP used in Polarbear comprises a 28 cm diameter 3.1 mm thick single sapphire +as birefringent material, which is sandwiched between two anti-reflection coating layers of +0.254 mm thick Duroid 6002. They are attached with a glue layer comprising 0.038 mm-thick +polyethylene (LDPE). The thickness of the birefringent material is determined so that the +optical path difference between the slow axis and fast axis is half of the wavelength. The +HWP is shown in Figure 1 and the design values of the HWP are given in Table I. +5 + +FIG. 1. Photograph of the HWP in the Polarbear experiment. +To express the polarization state of light, we introduce the Stokes vector as +P = ⟨EE†⟩ = Iσ0 + Qσ3 + Uσ1 + V σ2, +(1) +where E, E†, σx, and the angled brackets denote the vector of complex electric fields, its +complex conjugate transposition, Pauli matrices, and time averaging, respectively. The ele- +ments of the Stokes vector, I, Q, U, and V , are respectively the intensity, linear polarization +amplitude on the axes, amplitude of 45-degree-tilted linear polarization, and amplitude of +CP. +We also introduce the Mueller matrix, which represents the conversion of the Stokes +parameter by each optical element. +A Mueller matrix M is expressed using the Jones +matrix J as +Mij = 1 +2Tr(σiJσjJ†), +(2) +where i, j are indices of the matrix. The Jones matrix is a 2 × 2 matrix expressing the +complex transmission of the electric field of each axis, +J = +� +�a(ν) +ϵ1(ν) +ϵ2(ν) b(ν)eiδ(ν) +� +� , +(3) +where a(ν) and b(ν) represent the transmittance of each axis, ϵ1(ν) and ϵ2(ν) represent the +coupling of axes, and δ is the retardance. +6 + +Because the HWP of Polarbear is made from a single-layer birefringent material in +which the coupling of ϵ1(ν) and ϵ2(ν) vanishes, we neglect ϵ1(ν) and ϵ2(ν) hereafter. There- +fore, the Mueller matrix of the Polarbear HWP is expressed as +MHWP = +� +� +� +� +� +� +� +T ρ 0 +0 +ρ T 0 +0 +0 0 c −s +0 0 s +c +� +� +� +� +� +� +� += +� +� +� +� +� +� +� +a2 + b2 a2 − b2 +0 +0 +a2 − b2 a2 + b2 +0 +0 +0 +0 +ab cos δ −ab sin δ +0 +0 +ab sin δ +ab cos δ +� +� +� +� +� +� +� +. +(4) +In this matrix, T, ρ, c, and s, denote the transmittance, differential transmittance between +the two HWP axes, polarization efficiency, and coupling between linear polarization and +CP states, respectively. The retardance δ is the phase difference caused by this HWP as +δ = 2π(ns − nf)dν/vc, where nf and ns are the indices of the fast and slow axes, d is the +thickness of the birefringent material, ν is the electromagnetic frequency of the incoming +radiation, and vc is the speed of light. +In the case of an ideal HWP, these values are +T = 1, c = −1, and ρ = s = 0. +We follow T. Essinger-Hileman (2013)16 in calculating the Mueller matrix of the HWP. +In this method, the Mueller matrix of a stack of isotropic and birefringent material layers +is calculated using a generalized transfer matrix, which solves the boundary conditions of +the electric and magnetic fields of the transmitted, reflected, and absorbed waves. In this +paper, we consider that the HWP comprises a sapphire and an anti-reflective (AR) coating +(Duroid) with glue (LDPE) on both sides of the sapphire. We use the thickness, refractive +index, and loss tangent of each layer of the HWP to calculate the Mueller matrix of the +HWP. In this calculation, we assume that the thickness of the AR coating is the same on +the two sides of the sapphire. We also assume that the HWP is in air with a refractive index +of 1 and that light enters the HWP vertically. +B. +Polarization measurement with the HWP +When a detector sensitive to a single linear polarization observes the sky through an HWP +continuously rotating at an angular velocity of ωh, the observed quantity is the integral of +the signal spectrum over the observational bandwidth: +¯d = +� ∞ +0 +W(ν)d(ν)dν, +(5) +7 + +where d(ν) is the detector signal at each frequency and W(ν) is the window function for the +spectral band-shape. For the incident signal with a Stokes vector of (I(ν), Q(ν), U(ν), V (ν)), +the signal is derived as +d(ν) = VdetMrot(−2ωht)MHWP(ν)Mrot(2ωht) (I(ν), Q(ν), U(ν), V (ν))T += d0(ν) + d2(ν) + d4(ν). +(6) +Here, Vdet = (1, cos(2θdet), sin(2θdet), 0) is the vector of the detector, θdet is the angle of +the detector, and Mrot is the Mueller matrix of the coordinate rotation: +Mrot(θ) = +� +� +� +� +� +� +� +1 +0 +0 +0 +0 +cos(θ) +sin(θ) 0 +0 − sin(θ) cos(θ) 0 +0 +0 +0 +1 +� +� +� +� +� +� +� +. +(7) +d0(ν), d2(ν), and d4(ν) are respectively the zeroth, second, and fourth harmonics signals of +the HWP rotation frequency, +d0(ν) =I(ν)T(ν) + Q(ν)T(ν) + c(ν) +2 +cos(2θdet) − U(ν)T(ν) + c(ν) +2 +sin(2θdet), +(8) +d2(ν) =I(ν)ρ(ν) cos(2ωht − 2θdet) + Q(ν)ρ(ν) cos(2ωht) − U(ν)ρ(ν) sin(2ωht) ++ V (ν)s(ν) sin(2ωht − 2θdet), +(9) +d4(ν) =Q(ν)T(ν) − c(ν) +2 +cos(4ωht − 2θdet) − U(ν)T(ν) − c(ν) +2 +sin(4ωht − 2θdet). +(10) +Equation (10) shows that the Q and U signals are modulated into the fourth harmonics sig- +nal. In a previous linear polarization observation17, we evaluated the polarization efficiency, +which is shown as (T − c)/2 in Eq (10), by observation of the Crab Nebula and physical +optics simulation. Equation (9) shows that the CP component V is in the second harmonics +signal. +Unlike T(ν) and (T(ν) − c(ν))/2, which are ∼ 1 over the observational bandwidth, the +other leakage coefficients, (T(ν)+c(ν))/2, ρ(ν), and s(ν), vary within the band. We therefore +use the band average of the leakage coefficient for the effective leakage coefficient: +¯s ≡ +� +s(ν)V (ν)W(ν)dν +� +V (ν)W(ν)dν +, +(11) +where V (ν) is the source spectra. If this ¯s is nonzero, the detector has sensitivity to the +incident CP signal. +8 + +From the modulated detector timestream, we extract each harmonics signal through +demodulation using the recorded angle of the HWP.18 However, unlike the fourth harmonics +signal, the second harmonics signal contains not only the CP signal but also the intensity +and linear polarization signals. We thus need to eliminate these contaminations. We can +subtract the linear polarization component considering the correlation with the second and +fourth harmonic signals because the linear polarization signal is simultaneously present in the +second and fourth harmonics signals. The zeroth harmonics signal is available for the removal +of intensity. The coefficient of the linear polarization in the zeroth signal T(ν) + c(ν) ≪ 1, +and the intensity signal is thus dominant in the zeroth harmonics. We thus subtract the +intensity component from the correlation between the zeroth and second harmonic signals. +III. +POLARBEAR EXPERIMENT +Polarbear is a CMB experiment conducted at the James Ax Observatory, which is +at an altitude of 5190 m in the Atacama Desert, Chile. +Polarbear searched for both +degree-scale and sub-degree-scale B-mode polarization signals originating from inflationary +gravitational waves and the weak gravitational lensing effect, respectively. The Huan Tran +Telescope, which is equipped with the Polarbear receiver, has an off-axis Gregorian optics +configuration with a 2.5 m-diameter primary mirror and secondary mirror. The Polarbear +receiver has seven wafers on the focal plane (see Figure 2). Each wafer is mounted with 182 +detectors, and there is thus a total of 1274 detectors on the focal plane. The detector is +sensitive to the frequency band centered at 150 GHz with a fractional band width of ap- +proximately 30 %. We measured the band-pass window function at the site with a Fourier +transform spectrometer (FTS). In this paper, we use the wafer-averaged values of this mea- +surement. See F. Matsuda et al. (2019)19 for details. Polarbear began observations in +January 2012. We placed a continuously rotating HWP between the primary and secondary +mirrors to measure the degree-scale B-mode polarization from May 201418. Note that the +HWP was not installed during the FTS measurement. +9 + +FIG. 2. Layout of detector wafers on the focal plane of Polarbear +19. There are seven wafers on the Polarbear focal plane. Six wafers have silicon lenslets, and +one wafer, which is labeled 8.2.0, has alumina lenslets. +IV. +LABORATORY MEASUREMENT +We characterized the optical properties of the HWP installed in the Polarbear tele- +scope. The characterization was conducted in a laboratory environment prior to the deploy- +ment of the HWP to the Polarbear telescope. +A. +Measurement System +Figure 3 shows the measurement setup for characterizing the Polarbear HWP. A +millimeter-wave source signal is generated by a continuous wave generator (12 to 18 GHz) +with a multiplier (× 9) covering a frequency range from 108 to 162 GHz. The source signal +is emitted through the waveguide with a pyramidal feed horn. After the feed horn, we place +an optical chopper to chop the signal. We insert a wire grid along the optical path to define +the polarization angle. The polarized signal is collimated by a lens before the aperture. The +lens is composed of Rexolite with a sub-wave grading AR coating. The HWP is mounted +on a holder that rotates about the z-axis. The HWP is placed normal to the incident radi- +ation. This rotational mechanism is controlled by a stepping motor. In our measurement, +the HWP is rotationally stepped in intervals of 6 degrees. The angle of the fast axis of the +10 + +10.4 +10.3 +8.2.0 +10.2 +19 cm +10.5 +10.1 +9.4Multipliers +Signal +Generator +z +x +Source horn +Wire grid +Lens +Aperture +HWP +Wire grid +Detector horn +Chopper +Lock-in +Amplifier +FIG. 3. Setup of the transmission measurement of the HWP. +HWP is originally unknown, and we thus calculate this angle in the data analysis. Behind +the HWP, another wire grid is inserted to determine the outgoing polarized signal. The +detector is a diode detector that is sensitive to the input millimeter wave. The detector is +set on a linear stage to calibrate the effect of standing waves and moves 1.9 mm along the +z-axis. The detected signal is read by a lock-in amplifier with a reference signal from the +chopper. +B. +Methods +The following measurement method was adopted using the setup in Figure 3. We start +the measurement by setting the frequency of the signal generator to 12 GHz and the rotation +angle of the HWP to 0 degrees. In this measurement, we take data by changing the detector +position along the z-axis from 0 to 1.9 mm. After the measurement at 0 degrees and 12 GHz, +we step the rotation angle of the stepping motor to 6 degrees and repeat the measurement. +After making measurements from 0 to 354 degrees, we step the frequency of the signal +generator by 0.1 GHz. We repeat the measurements until making measurements at 18 GHz. +We also measure the transmittance of the linear polarization by taking the ratio of the +output signal when the HWP is inserted into the optical system and the output signal when +the HWP is not inserted. These measurements are performed after the angle of the fast axis +of the HWP is determined by the previous measurement. +11 + +C. +Analysis +In the analysis, we firstly remove the effect of the standing wave from the signal. For each +frequency and rotation angle, we plot the signal as a function of the linear stage position. +We then fit the signal with a sinusoidal wave plus a constant component and extract the +constant component as the signal for this frequency and rotation angle. +Then, given the above setup and the measurement procedure, the data are modeled as +dm(ν, θh) =G(ν) (1, 1, 0, 0) Mrot(−2θh)MHWP(ν)Mrot(2θh) (1, 1, 0, 0)T + doffset +=G(ν)3T(ν) + c(ν) +2 ++ 2G(ν)ρ(ν) cos(2θh) ++ G(ν)T(ν) − c(ν) +2 +cos(4θh) + doffset, +(12) +where θh is the rotation angle of the HWP, G(ν) is the gain of the system, and doffset is the +offset of the lock-in amplifier. We find that some measurements are negative and assume +that this is due to the offset of the lock-in amplifier. We thus include doffset as a parameter. +Given this model, we fit the data using the equation +d = A0 + A2 cos (2θh + 2φ2) + A4 cos (4θh + 4φ4). +(13) +Figure 4 shows a typical modulated response curve when the HWP rotates about the z-axis. +The top panel shows the modulated power as a function of the HWP angle at 143 GHz. The +points are the measurement data, and the curve is the fit using Eq. (13). The middle panel +shows the second harmonic component obtained by computing d−(A0 +A4 cos (4θh + 4φ4)) +in Eq. (13). The bottom panel shows the residual of the fit. Here, the peaks of the top +panel correspond to the angles where the fast or slow axis of the HWP becomes parallel to +the incident polarization. There is a small difference in the transmission between the fast +and slow axes owing to the difference in the refractive index, which is seen as the second +harmonics component in the middle panel. The signal becomes almost zero at the middle +of the peaks. This means that the input polarization is efficiently rotated to the orthogonal +polarization, and the leakage to the CP is small. +We then relate the obtained amplitudes, A0, A2, and A4, to the components of the Mueller +matrix of the HWP. By comparing Eqs (12) and (13), we obtain +ρ(ν) +T(ν) + δ1(ν) = +A2(ν) +A0(ν) + A4(ν), +c(ν) +T(ν) + δ2(ν) = A0(ν) − 3A4(ν) +A0(ν) + A4(ν) , +(14) +12 + +0.0 +0.5 +1.0 +1.5 +Output [V] +fit +data +0.01 +0.00 +0.01 +A2 [V] +0.0 +90.0 +180.0 +270.0 +360.0 +rotation angle [degree] +0.005 +0.000 +0.005 +Residual [V] +FIG. 4. (Top) Example of the output signal for each rotation angle at an incident frequency of +143.1 GHz. The blue points are the data, and the orange line shows the fit with Eq. (13). (Middle) +The second harmonics component of the same data obtained by subtracting A0 +A4 cos(4θh +4φ4) +of Eq. (13). (Bottom) Residual of the fit. +where δ1(ν) and δ2(ν) denote the effect of the offset of the lock-in amplifier. These values +are calculated using doffset: +δ1(ν) = +−A2(ν)doffset +((A0(ν) + A4(ν))(A0(ν) − doffset + A4(ν)), +(15) +δ2(ν) = +4A0(ν)doffset +((A0(ν) + A4(ν))(A0(ν) − doffset + A4(ν)). +(16) +We also calculate the transmittance of the linear polarization T + ρ from the ratio of the +observations made with an HWP rotation angle θh = 0 and observations made without the +HWP as +T(ν) + ρ(ν) = dm(θh = 0)(ν) +dnoHWP +(ν). +(17) +Finally, we fit the spectra obtained from Eqs. (14) and (17) with the model of the Mueller +matrix of the HWP described in section II A using the Markov Chain Monte Carlo (MCMC) +method with the thickness, refractive index, and loss tangent of each layer of the HWP as +13 + +120 +140 +160 +Frequency [GHz] +0.90 +0.95 +1.00 +1.05 +T + +120 +140 +160 +Frequency [GHz] +0.04 +0.02 +0.00 +0.02 +0.04 +/T +120 +140 +160 +Frequency [GHz] +1.00 +0.95 +0.90 +0.85 +c/T +FIG. 5. Calculated spectra of the Mueller matrix components and results of MCMC fitting. Blue +points are measured points with error explained in section IV A. The red dashed line and green +band are the estimated mean value and one-sigma distribution respectively. Note that these data +points and fitting lines include the effect of the offset of the lock-in amplifier. +input parameters. As the prior distribution of the HWP model, we use the design values +given in Table I. To avoid negative values, we assume the exponential distribution as the prior +distribution of loss tangents. We assume Gaussian distributions for the prior distributions +of other parameters. Additionally, we include doffset as the input parameter of the MCMC +fitting. The prior distribution of doffset is a uniform distribution because we do not know the +detail of doffset. We take the following steps before performing the MCMC fitting. +• The statistical uncertainties in the observations are smaller than the actual deviations +from the model, and we thus introduce the contribution of systematic uncertainties +possibly due to gain fluctuations, standing waves, and stray light. We use the MCMC +method only with the detector offset as an input parameter and the design values for +other parameters and determine an additional error so that the reduced chi-squared +becomes 1. +• We use only data in the frequency range above 120.6 GHz for two reasons. One reason +is that these points are away from the observation frequency. The other reason is that +the value of c/T drops off unreasonably around 119 GHz. +14 + +TABLE II. Parameters of the HWP model obtained by MCMC fitting. These values are calculated +from the mean values of the posterior distributions and the uncertainties come from the samples’ +standard deviation. A comparison with Table I shows that all parameters are consistent within the +uncertainty given in the table. The uncertainty in the sapphire thickness and the uncertainty in +the refractive index difference of the sapphire become smaller than the uncertainties in the design +values. +thickness +refractive index +loss tangent +Sapphire (o-axis) 3.086 ± 0.005 mm +3.065 ± 0.002 +(1.11 ± 0.89) × 10−4 +Sapphire (e-axis) 3.086 ± 0.005 mm +3.404 ± 0.002 +(0.51 ± 0.50) × 10−4 +Duroid +0.255 ± 0.002 mm +1.710 ± 0.008 +(5.4 ± 0.53) × 10−4 +LDPE +0.039 ± 0.002 mm +1.514 ± 0.010 +(4.3 ± 4.7) × 10−4 +D. +Results +The blue points in Figure 5 show measured spectra of T + ρ, ρ/T, and c/T. Figure 5 +also shows the spectra calculated with the HWP model with parameters from the MCMC. +The red dashed lines and green band indicate the converged average value and one-sigma +band. Note that these data points and fitting lines include the effect of the offset of the +lock-in amplifier. Table II gives the parameters of the HWP model after the MCMC fitting. +In this table, we give the mean values of the posterior distribution. A comparison with +Table I shows that the results are consistent with the fiducial values. We also find that the +uncertainty in the sapphire thickness becomes 1/20 and the uncertainty in the refractive +index difference of the sapphire becomes 1/3. The accuracy of the model is improved. +In this measurement, the uncertainties in the measured spectra are limited by the un- +known systematic error. The cause of this systematic error must be understood to improve +the accuracy. Additionally, the offset of the lock-in amplifier doffset is estimated from the +fitting as a nuisance parameter. In future measurements, it would beneficial to measure the +background signal to determine the offset. +Ideally, a vector network analyzer (VNA) would be used for the HWP characterization. +A VNA can measure the amplitude and phase of the electric field, allowing the calculation +of the Mueller matrix directly from Eq. (2). +15 + +120 +130 +140 +150 +160 +0.4 +0.2 +0.0 +0.2 +0.4 +s +120 +130 +140 +150 +160 +Frequency [GHz] +0.01 +0.00 +0.01 +68% C.L. of s +FIG. 6. Spectra of the estimated s parameter. The top panel shows the spectra of the mean s value +(red dash line) and the range of one sigma (green band). The bottom panel shows the one-sigma +uncertainty of the s parameter. +V. +LEAKAGE ESTIMATION +We calculate the coupling between the CP and linear polarization, s, using the HWP +model (see section II A) and the parameters obtained from the samples of the MCMC fitting +in section IV. Figure 6 shows the spectra of s. The s spectrum is close to zero at the obser- +vation frequency, which is given in Table III, and decreases at high frequency as expected +from Eq. (4). The frequency at which s is zero is approximately 143 GHz. This frequency +is close to the central frequency of the Polarbear telescope (see Table III). We show the +uncertainty in this spectrum in the bottom panel. The uncertainty is almost constant within +the observation frequency range. +We calculate the band-averaged value, ¯s, using Eq. (11). +We give the details of the +bandpass of each wafer in Table III. For the detector band-pass window function, W(ν), we +use the wafer-averaged spectrum of the FTS measurement at the site (see section III). The +detector bandpass properties are summarized in Table III for each wafer. We calculate ¯s for +each wafer because ¯s is sensitive to the wafer-by-wafer variation of the band center. The +16 + +TABLE III. Detector bandpass of each wafer. The average (AVG) and standard deviation (STD) +of the band center and bandwidth are shown. We also show the uncertainty in the bandpass of +each wafer. These values are obtained from FTS measurement at the site19. +Band Center (GHz) +BandWidth (GHz) +Uncertainty +Wafer +AVG +STD +AVG +STD +8.2.0 +136.9 +0.7 +30.4 +1.8 +0.007 +9.4 +146.9 +0.5 +32.8 +1.6 +0.007 +10.1 +142.1 +2.5 +31.8 +1.8 +0.010 +10.2 +143.5 +0.5 +32.6 +1.1 +0.005 +10.3 +148.7 +0.6 +31.0 +1.9 +0.007 +10.4 +144.0 +0.5 +32.2 +1.2 +0.005 +10.5 +145.5 +0.4 +31.8 +1.3 +0.006 +statistical uncertainty in ¯s is calculated from the standard deviation of the samples of ¯s. +Unlike the case for the linear polarization of the CMB, there is a variation in the frequency +dependence of the CMB CP. Here, we consider four spectra of the CP of the CMB, namely +the Rayleigh–Jeans (RJ) spectrum, CMB spectrum, the frequency dependence of the FC20, +and the frequency dependence of the CP caused by CνB3: +SRJ(ν) = S(ν0) +� ν +ν0 +�2 +, +(18) +SCMB(ν) = S(ν0) +� ν +ν0 +�4 +exp(hν/kBT)/ exp(hν0/kBT) +(exp(hν/kBT) − 1)2/(exp(hν0/kBT) − 1)2, +(19) +SFC(ν) = SCMB(ν) +�ν0 +ν +�3 +, +(20) +SCνB(ν) = SCMB(ν)ν0 +ν , +(21) +where S(ν0) is the amplitude of the signal at the pivot frequency ν0, and h, kB, T are the +Planck constant, Boltzmann constant, and temperature of the CMB (2.725 K)21. We also +consider the spectrum of CP due to the atmospheric Zeeman emission22,23. The Zeeman +emission is a signal produced by the splitting of the energy levels of the oxygen molecules +in the atmosphere by the Earth’s magnetic field. This signal is expected in that the low- +frequency side of the split level at 118.75 GHz is circularly polarized clockwise and the +high-frequency side is circularly polarized counterclockwise. +17 + +Table IV presents the band- and spectral-dependence of the band-averaged s value. The +values of wafer 8.2.0 are larger than those of other wafers because the central frequency +of wafer 8.2.0 is lower than that of the other wafers. This relation of ¯s among wafers is +independent of the source spectrum. +Regarding the source spectrum dependence, the values of the CMB spectrum are ap- +proximately 0.02 larger than those of the RJ spectrum. The maximum absolute value of +our estimates is almost the same as that of the SPIDER HWP s parameters6 (0.149 in +this paper versus 0.154 in SPIDER), which are also band-averaged using the CMB source +spectrum and their bandpass. However, the minimum value in this paper is larger than +that in SPIDER (0.007 versus 0.003). We also compare the uncertainty in the s parameter. +The uncertainty in the s parameter of the SPIDER HWP is approximately 0.041 whereas +the uncertainty in the s parameter obtained from the design values of Polarbear HWP +(Table I) is approximately 0.1. In contrast to these results, the uncertainty in our estimated +s parameter is approximately 0.009. The method described in this paper thus reduces the +uncertainty in the HWP model. +Meanwhile, the values of the FC spectrum, CνB spectrum, and Zeeman spectrum are +different. Although some signs of band-integrated s values are reversed, the set of absolute +values of the FC spectrum and CνB spectrum are almost the same as those of the RJ +spectrum and CMB spectrum. +The band-integrated s values are larger for the Zeeman +spectrum than for the other spectra. The CP signal of the Zeeman emission is expected to +be approximately 61 µK in the Polarbear frequency band. Even with the suppression by +¯s, the apparent signal is approximately 31 µK, which is above the noise level of Polarbear +(NETarray = 23 µK√s )17. +VI. +DISCUSSION +A. +Systematic Uncertainty +We estimate the systematic uncertainties in the band-averaged s parameter of the HWP +under the conditions of actual operation in the telescope. We consider the uncertainty in +the bandpass dependence and the non-vertical incident light. +We first consider the uncertainty in the bandpass dependence. There is uncertainty in the +18 + +TABLE IV. Band-averaged s values for various spectra of sources. +In this paper, we assume +Rayleigh–Jeans spectrum (RJ), CMB spectrum (CMB), spectrum of the CP due to Faraday Con- +version (FC), spectrum of the CP due to the cosmic neutrino background (CνB), and atmospheric +Zeeman emission (Zeeman). The difference in the values between the RJ and CMB is smaller than +the differences between other spectra. Meanwhile, the values of FC and CνB differ largely from +those of RJ. Moreover, the values of the atmospheric Zeeman emission are larger than those of the +other spectra. +Wafer +RJ +CMB +FC +CνB +Zeeman +8.2.0 0.133 ± 0.009 0.149 ± 0.009 0.207 ± 0.008 0.168 ± 0.009 0.437 ± 0.011 +9.4 +-0.075 ± 0.009 -0.055 ± 0.009 -0.014 ±0.009 -0.033 ± 0.009 0.366 ± 0.009 +10.1 +0.024 ± 0.009 0.046 ± 0.009 0.123 ± 0.009 0.070 ± 0.009 0.421 ± 0.008 +10.2 -0.002 ± 0.009 0.018 ± 0.009 0.089 ± 0.009 0.041 ± 0.009 0.396 ± 0.009 +10.3 -0.113 ± 0.010 -0.094 ± 0.010 -0.029 ± 0.009 -0.073 ± 0.009 0.322 ± 0.009 +10.4 -0.013 ± 0.009 0.007 ± 0.009 0.076 ± 0.009 0.029 ± 0.009 0.389 ± 0.008 +10.5 -0.045 ± 0.009 -0.025 ± 0.009 0.041 ± 0.009 -0.004 ± 0.009 0.367 ± 0.009 +bandpass measurement by the FTS at the site. This comes from the systematic variation in +the bandpass for each detector. We calculate the uncertainty in the bandpass of each wafer +from the data in the sensitive frequency region as shown in Table III. We then calculate ¯s +5000 times using random realizations of the detector bandpass with the uncertainty evaluated +above. We take the standard deviation of this distribution as the systematic uncertainty +due to the uncertainty in the detector bandpass. +We next consider the non-vertical incident light. In the HWP model used in section V, +we assume that light is vertically incident. However, not all light is vertically incident in +the setup of the telescope. The Polarbear HWP is placed at the prime focus, which is +between the primary and secondary mirrors, of the Huan Tran Telescope. The light between +these mirrors is once focused at the prime focus and spreads again, and the incident angle +of the light incident on the HWP thus increases as the light deviates from the center of the +optical path. The non-vertical incident light will change the optical path in the HWP and +thus affect the estimate of ¯s. The maximum value of the incident angle is 16◦ at the half +width at half maximum from the geometry. We thus calculate conservatively how ¯s varies +19 + +TABLE V. Estimated ¯s and uncertainties for each wafer. The first and second columns from the +left give the average values and standard deviation of the MCMC fitting explained in section V. +The third column gives the systematic error due to the uncertainty in the detector bandpass. The +fourth column gives the systematic error due to the non-vertical incident light. These systematic +uncertainties are smaller than the standard deviation of the MCMC fitting. +Wafer +AVG +STD +bandpass +non-vertical +8.2.0 +0.133 +0.009 +0.001 +0.001 +9.4 +-0.075 +0.009 +0.001 +0.002 +10.1 +-0.024 +0.009 +0.001 +0.002 +10.2 +0.002 +0.009 +0.001 +0.003 +10.3 +-0.113 +0.010 +0.001 +0.002 +10.4 +-0.013 +0.009 +0.001 +0.003 +10.5 +-0.045 +0.009 +0.001 +0.003 +when the incident light is tilted at 16◦. In this calculation, we rotate the HWP with the +tilted incident light and extract the second harmonics in the simulation. +Table V gives the systematic uncertainties in the band-averaged s value. Here, we as- +sume that the source spectrum is the RJ spectrum. The columns from the left show the +wafer name, band-averaged s values, statistical uncertainty in the band-averaged s value, +systematic error of the uncertainty in the detector bandpass, and systematic error in the +non-vertical incident light. We find that these systematic uncertainties are smaller than the +statistical uncertainty. +B. +Possibility of cross-checking using atmospheric CP +We next consider a method of cross-checking the above result with the values obtained +from observation. The atmospheric Zeeman emission is a possible CP source with which +to measure ¯s. As described in section V, the atmospheric Zeeman emission is a bright CP +source and is expected to be observable with the Polarbear detector. Thus, we might be +able to separate the CP signal from the second harmonic signal using the method described +in section II B and estimate the leakage of the HWP by comparing the observed CP signal +20 + +with the theoretical value. +Note that because the coordinate of the atmospheric CP is fixed to the ground, the signal +of the atmospheric CP may be degenerated with the ground pickup signal. The difference +in spectra can be used to distinguish the atmospheric CP signal. The Zeeman emission has +a peak at 118.75 GHz and this results in a temperature difference of approximately 100 µK +at maximum between wafers due to slight differences in frequency characteristics. If the +spectrum of the ground pickup signal is the RJ spectrum, we can distinguish the Zeeman +emission from the difference in the observed temperature between wafers. +C. +Prospects of CP Measurement +Table IV in section V shows that ¯s is nonzero in most cases. This suggests the possibility +to probe the CP using Polarbear data. +From the mean value of the ¯s parameter in +Table IV of the CMB spectrum and noise level in B-mode observation12, we estimate that +the sensitivity of ℓ(ℓ + 1)CV V +ℓ +/(2π) is approximately 30(µK)2 at ℓ ∼ 300 in Polarbear; +this result is comparable to the sensitivity of measurements made by SPIDER. +VII. +SUMMARY +We evaluated the HWP used at Polarbear, including the leakage between linear po- +larization and CP. We constructed an HWP model from data recorded at the laboratory in +2014 and estimated the leakage between the CP and linear polarization. This model well +explained the measured spectrum of the Mueller matrix components, and the uncertainty in +the parameters of the HWP was at maximum 1/20th the design value. We thus found that +the absolute value of the band-averaged leakage from the CP obtained using the HWP, ¯s, +ranged from 0.151 to 0.021 at each wafer, and the statistical uncertainty in ¯s was approxi- +mately 0.010 for each wafer in the case of the RJ spectrum. This means that all detectors on +each wafer were capable of measuring the CP. We also considered four other spectra. The +value of ¯s was nonzero in most cases. In particular, ¯s was larger for the Zeeman spectrum +than for the other spectra. We also estimated the systematic uncertainties in ¯s. In this +paper, we considered the uncertainties in the detector bandpass and non-vertical incident +light and found that these systematic uncertainties were smaller than the statistical error. +21 + +Finally, we verified this result using the atmospheric CP signal and presented prospects of +making angular power spectrum measurements of CP anisotropy. +ACKNOWLEDGMENTS +We acknowledge M. J. Myers for creating the HWP, and Y. Inoue and H. Yamaguchi +for setup the laboratory measurement system. MH acknowledges support from the World +Premier International Research Center Initiative (WPI) of MEXT and the JSPS KAKENHI +grant No. JP22H04945. ST acknowledges support from the JSPS KAKENHI grant Nos. +JP14J01662 and JP18J02133. HN achnowledges support from the JSPS KAKENHI grant +No. JP17K18785. This work was supported by the JSPS Core-to-Core Program. We thank +Edanz (https://jp.edanz.com/ac) for editing a draft of this manuscript. +AUTHOR DECLARATIONS +Conflict of Interest +The authors have no conflicts to disclose. +Author Contributions +T. Fujino:Conceptualization (equal); Formal Analysis (lead); Writing/Original Draft +Preparation (lead). S. Takakura: Conceptualization (equal); Investigation (lead); Writ- +ing/Review & Editing (lead). Y. Chinone: Writing/Review & Editing (supporting). M. +Hasegawa: Writing/Review & Editing (equal). M. Hazumi: Writing/Review & Editing +(supporting). N. Katayama: Writing/Review & Editing (supporting). A. T. Lee: Writ- +ing/Review & Editing (supporting). T. Matsumura: Writing/Review & Editing (equal). +Y. Minami: Writing/Review & Editing (equal). H. Nishino: Writing/Review & Editing +(supporting). +22 + +REFERENCES +1A. Cooray, A. Melchiorri, +and J. Silk, “Is the cosmic microwave background circularly +polarized?” Physics Letters B 554, 1–6 (2003). +2S. De and H. 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Chuss, et al., “Two-year cosmology large angular scale +surveyor (class) observations: A first detection of atmospheric circular polarization at q +band,” The Astrophysical Journal 889, 120 (2020). +25 + diff --git a/HtA0T4oBgHgl3EQfB_9Y/content/tmp_files/load_file.txt b/HtA0T4oBgHgl3EQfB_9Y/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..bd3225e45d4ea49e2a8ac9433b866527b59f08c4 --- /dev/null +++ b/HtA0T4oBgHgl3EQfB_9Y/content/tmp_files/load_file.txt @@ -0,0 +1,949 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf,len=948 +page_content='Characterization of a half-wave plate for CMB circular polarization measurement with POLARBEAR T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Fujino,1, a) S.' metadata={'source': 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The University of Tokyo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Kashiwa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Chiba 277-8583,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Japan 5)Institute of Particle and Nuclear Studies (IPNS),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' High Energy Accelerator Research Organization (KEK),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Tsukuba,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Ibaraki 305-0801,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Japan 6)The Graduate University for Advanced Studies (SOKENDAI),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Miura District,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Kanagawa 240-0115,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Hayama,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Japan 7)Japan Aerospace Exploration Agency (JAXA),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Institute of Space and Astronautical Science (ISAS),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Sagamihara,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Kanagawa 252-5210,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Japan 8)Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' University of California,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Berkeley,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Berkeley,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' CA 94720,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' USA 9)Physics Division,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Lawrence Berkeley National Laboratory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Berkeley,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' CA 94720,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' USA 10)Research Center for Nuclear Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Osaka University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Ibaraki,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Osaka,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' 567-0047,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Japan 11)The University of Tokyo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Tokyo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Research Center for the Early Universe,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' School of Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' 113-0033,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Japan 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='01983v1 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='CO] 5 Jan 2023 (Dated: 6 January 2023) A half-wave plate (HWP) is often used as a modulator to suppress systematic error in the measurements of cosmic microwave background (CMB) polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' An HWP can also be used to measure circular polarization (CP) through its optical leakage from CP to linear polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The CP of the CMB is predicted to be produced by interactions in the Universe, such as interactions with supernova remnants of popu- lation III stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Thus, the observation of the CP of CMB is a new tool for searching for population III stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In this paper, we demonstrate the improved measurement of the leakage coefficient using the transmission spectrum measurement of an actual HWP in the laboratory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We measured the transmittance of linearly polarized light through the HWP used in the Polarbear experiment in the frequency range of 120 GHz to 160 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We evaluate properties of the HWP by fitting the data with a physical model using the Markov Chain Monte Carlo method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We then estimate the band-averaged CP leakage coefficient using the physical model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We find that the leakage coefficient strongly depends on the spectra of CP sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We thus calculate the maximum rate of leakage from CP to linear polarization as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='133 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='009 in the Rayleigh–Jeans spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The nonzero value shows that Polarbear would have sensitivity to the CP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Additionally, because we use the bandpass of detectors installed in the telescope to calculate the band-averaged values, we also consider systematic effects in the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' a)Electronic mail: fugino-takuro-yk@ynu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='jp 2 I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' INTRODUCTION Measuring the polarization of the cosmic microwave background (CMB) is a powerful method of probing the physics of the early universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The linear polarization of the CMB comes from the quadrupole anisotropy at the last scattering of CMB photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' There are two sources of quadrupole anisotropy, namely the density perturbation and primordial grav- itational wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The density perturbation makes an even-parity linear polarization pattern called the E-mode in the CMB polarization whereas the primordial gravitational wave gen- erated by cosmic inflation in the early universe makes an odd-parity linear polarization pattern called the B-mode as well as the E-mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The primordial B-mode polarization can be considered a smoking gun for the inflation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The scientific goal of many ongoing and future planed CMB experiments is finding the signal in the linear polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' CMB photons can also have circular polarization (CP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Although the CP of the CMB is not predicted by the standard models of cosmology, the so-called Λ Cold Dark Matter (ΛCDM) model, there are mechanisms that can generate the CP of the CMB photons dur- ing their propagation from the last scattering to an observer today.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Examples are Faraday conversion (FC) by the magnetic fields of galaxy clusters1, FC by relativistic plasma rem- nants of Population III stars2, scattering from the cosmic neutrino background (CνB)3, and photon-photon-scattering4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Some CMB polarization experiments have set an experimental constraint on the angular power spectrum of CP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The optics of the Cosmology Large Angular Scale Surveyor (CLASS) have sensitivity to CP because of the use of a variable-delay polarization modulator5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' SPI- DER, a balloon-borne telescope designed to search for the B-mode linear polarization of the CMB, placed a limit on the CP power spectrum even though the telescope was not designed to be sensitive to the CP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The SPIDER project utilized the imperfection of the half-wave plate (HWP) modulator6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' An ideal HWP works as a retarder of phase π, inverting the electric field of one axis of the incident linearly polarized light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The outgoing light is thus linearly polarized at a different angle from the incoming light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In practice, however, an HWP comprising single-layer birefringent material only satisfies this condition at a target frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Outside the target frequency range within the observational frequency band, the retardance is no longer π, and a coupling between linear polarization and CP is thus created.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In this case, a part of the incident CP leaks to linear polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Thus, a CMB telescope, 3 which is designed to detect a linearly polarized signal, gains sensitivity to CP as long as the properties of its HWP are well characterized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' To utilize this infinitesimal leakage, we need to know the amount of leakage precisely by calibration with known CP light or characterization from measured optical parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Because we do not have a calibrator for CP in Polarbear, in this paper, we choose to characterize the leakage of the HWP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Although there have been papers on CMB experiments using an HWP as a polarization modulator7–9, they mainly reported only the efficiency of the linear polarization and did not include the leakage between CP and linear polarization because they aimed to measure the linear polarization of the CMB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Some papers10,11 reported the leakage between the CP and linear polarization using Mueller matrix formalism;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' however, these were simulation-only results or proto-type results, not evaluation results of an HWP for actual CMB observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' A study on CP by SPIDER6 used the leakage estimated from the design values of the HWP and calculated an upper limit on the angular power spectrum of the CMB CP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In the present paper, we report the characterization of an HWP installed in the Polar- bear telescope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Polarbear is a CMB experiment that began in January 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' From May 2014 to December 2016, Polarbear performed large-angular-scale observations using the HWP, which was continuously rotated at 2 Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' With these data, we measured the CMB B-mode power spectrum over a multipole range of 50 < ℓ < 600 and put a limit on the tensor-to-scalar ratio, r < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='3312.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We evaluate the HWP using transmission spectrum taken in the laboratory in 2014 before its installation in the Polarbear telescope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We determine physical parameters of the HWP by fitting the data with a theoretical transmission model and then estimate the leakage between the CP and linear polarization using this model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Through measurement of the fringe, we determine the thickness and the difference in the refractive index between the ordinary and extra-ordinary axes of sapphire precisely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Section II presents an overview of the CMB polarization observation with the continuously rotating HWP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Section III explains the Polarbear experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Section IV details the characterization of the Polarbear HWP in the laboratory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We also present the results of the transmittance of the HWP for linearly polarized light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In section V, we explain a method of estimating the HWP leakage between CP and linear polarization and present estimation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We discuss systematic uncertainty of the leakage in section VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We also discuss the prospects of CP measurements using Polarbear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' 4 TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Design values of the HWP used in the Polarbear experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The first and second rows give values for the ordinary and extra-ordinary axes of the sapphire, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The refractive indices and loss tangents of the components come from V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Parshin (1994)13, RT/duroid (2020)14, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Lamb (1996)15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' thickness refractive index loss tangent Sapphire (o-axis) (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='1 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='1) mm 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='068 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='003 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='30 × 10−4 Sapphire (e-axis) (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='1 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='1) mm 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='402 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='003 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='25 × 10−4 Duroid 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='254 mm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='715 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='012 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='0 × 10−4 LDPE 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='038 mm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='514 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='010 ∼5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='0 × 10−4 II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' POLARIZATION OBSERVATION WITH AN HWP An HWP is an optical device that creates an optical path difference of half of the wave- length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' CMB experiments widely use HWPs made from birefringent materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' An HWP converts linearly polarized incident light with angle αin to linearly polarized light with angle 2θh − αin, where θh is the angle of the fast axis of the HWP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In Polarbear, we rotate the HWP continuously to separate the linear polarization signal from the unpolarized signal in the frequency domain for the reduction of the systematic uncertainties, which are generated in the instruments after the HWP and by the detector pair difference, and low-frequency noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In this section, we explain the optical model of the HWP and how the HWP modulates polarization signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' HWP modeling The HWP used in Polarbear comprises a 28 cm diameter 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='1 mm thick single sapphire as birefringent material, which is sandwiched between two anti-reflection coating layers of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='254 mm thick Duroid 6002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' They are attached with a glue layer comprising 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='038 mm-thick polyethylene (LDPE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The thickness of the birefringent material is determined so that the optical path difference between the slow axis and fast axis is half of the wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The HWP is shown in Figure 1 and the design values of the HWP are given in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' 5 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Photograph of the HWP in the Polarbear experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' To express the polarization state of light, we introduce the Stokes vector as P = ⟨EE†⟩ = Iσ0 + Qσ3 + Uσ1 + V σ2, (1) where E, E†, σx, and the angled brackets denote the vector of complex electric fields, its complex conjugate transposition, Pauli matrices, and time averaging, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The ele- ments of the Stokes vector, I, Q, U, and V , are respectively the intensity, linear polarization amplitude on the axes, amplitude of 45-degree-tilted linear polarization, and amplitude of CP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We also introduce the Mueller matrix, which represents the conversion of the Stokes parameter by each optical element.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' A Mueller matrix M is expressed using the Jones matrix J as Mij = 1 2Tr(σiJσjJ†), (2) where i, j are indices of the matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The Jones matrix is a 2 × 2 matrix expressing the complex transmission of the electric field of each axis, J = � �a(ν) ϵ1(ν) ϵ2(ν) b(ν)eiδ(ν) � � , (3) where a(ν) and b(ν) represent the transmittance of each axis, ϵ1(ν) and ϵ2(ν) represent the coupling of axes, and δ is the retardance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' 6 Because the HWP of Polarbear is made from a single-layer birefringent material in which the coupling of ϵ1(ν) and ϵ2(ν) vanishes, we neglect ϵ1(ν) and ϵ2(ν) hereafter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' There- fore, the Mueller matrix of the Polarbear HWP is expressed as MHWP = � � � � � � � T ρ 0 0 ρ T 0 0 0 0 c −s 0 0 s c � � � � � � � = � � � � � � � a2 + b2 a2 − b2 0 0 a2 − b2 a2 + b2 0 0 0 0 ab cos δ −ab sin δ 0 0 ab sin δ ab cos δ � � � � � � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (4) In this matrix, T, ρ, c, and s, denote the transmittance, differential transmittance between the two HWP axes, polarization efficiency, and coupling between linear polarization and CP states, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The retardance δ is the phase difference caused by this HWP as δ = 2π(ns − nf)dν/vc, where nf and ns are the indices of the fast and slow axes, d is the thickness of the birefringent material, ν is the electromagnetic frequency of the incoming radiation, and vc is the speed of light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In the case of an ideal HWP, these values are T = 1, c = −1, and ρ = s = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We follow T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Essinger-Hileman (2013)16 in calculating the Mueller matrix of the HWP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In this method, the Mueller matrix of a stack of isotropic and birefringent material layers is calculated using a generalized transfer matrix, which solves the boundary conditions of the electric and magnetic fields of the transmitted, reflected, and absorbed waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In this paper, we consider that the HWP comprises a sapphire and an anti-reflective (AR) coating (Duroid) with glue (LDPE) on both sides of the sapphire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We use the thickness, refractive index, and loss tangent of each layer of the HWP to calculate the Mueller matrix of the HWP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In this calculation, we assume that the thickness of the AR coating is the same on the two sides of the sapphire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We also assume that the HWP is in air with a refractive index of 1 and that light enters the HWP vertically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Polarization measurement with the HWP When a detector sensitive to a single linear polarization observes the sky through an HWP continuously rotating at an angular velocity of ωh, the observed quantity is the integral of the signal spectrum over the observational bandwidth: ¯d = � ∞ 0 W(ν)d(ν)dν, (5) 7 where d(ν) is the detector signal at each frequency and W(ν) is the window function for the spectral band-shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' For the incident signal with a Stokes vector of (I(ν), Q(ν), U(ν), V (ν)), the signal is derived as d(ν) = VdetMrot(−2ωht)MHWP(ν)Mrot(2ωht) (I(ν), Q(ν), U(ν), V (ν))T = d0(ν) + d2(ν) + d4(ν).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (6) Here, Vdet = (1, cos(2θdet), sin(2θdet), 0) is the vector of the detector, θdet is the angle of the detector, and Mrot is the Mueller matrix of the coordinate rotation: Mrot(θ) = � � � � � � � 1 0 0 0 0 cos(θ) sin(θ) 0 0 − sin(θ) cos(θ) 0 0 0 0 1 � � � � � � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (7) d0(ν), d2(ν), and d4(ν) are respectively the zeroth, second, and fourth harmonics signals of the HWP rotation frequency, d0(ν) =I(ν)T(ν) + Q(ν)T(ν) + c(ν) 2 cos(2θdet) − U(ν)T(ν) + c(ν) 2 sin(2θdet), (8) d2(ν) =I(ν)ρ(ν) cos(2ωht − 2θdet) + Q(ν)ρ(ν) cos(2ωht) − U(ν)ρ(ν) sin(2ωht) + V (ν)s(ν) sin(2ωht − 2θdet), (9) d4(ν) =Q(ν)T(ν) − c(ν) 2 cos(4ωht − 2θdet) − U(ν)T(ν) − c(ν) 2 sin(4ωht − 2θdet).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (10) Equation (10) shows that the Q and U signals are modulated into the fourth harmonics sig- nal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In a previous linear polarization observation17, we evaluated the polarization efficiency, which is shown as (T − c)/2 in Eq (10), by observation of the Crab Nebula and physical optics simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Equation (9) shows that the CP component V is in the second harmonics signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Unlike T(ν) and (T(ν) − c(ν))/2, which are ∼ 1 over the observational bandwidth, the other leakage coefficients, (T(ν)+c(ν))/2, ρ(ν), and s(ν), vary within the band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We therefore use the band average of the leakage coefficient for the effective leakage coefficient: ¯s ≡ � s(ν)V (ν)W(ν)dν � V (ν)W(ν)dν , (11) where V (ν) is the source spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' If this ¯s is nonzero, the detector has sensitivity to the incident CP signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' 8 From the modulated detector timestream, we extract each harmonics signal through demodulation using the recorded angle of the HWP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='18 However, unlike the fourth harmonics signal, the second harmonics signal contains not only the CP signal but also the intensity and linear polarization signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We thus need to eliminate these contaminations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We can subtract the linear polarization component considering the correlation with the second and fourth harmonic signals because the linear polarization signal is simultaneously present in the second and fourth harmonics signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The zeroth harmonics signal is available for the removal of intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The coefficient of the linear polarization in the zeroth signal T(ν) + c(ν) ≪ 1, and the intensity signal is thus dominant in the zeroth harmonics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We thus subtract the intensity component from the correlation between the zeroth and second harmonic signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' POLARBEAR EXPERIMENT Polarbear is a CMB experiment conducted at the James Ax Observatory, which is at an altitude of 5190 m in the Atacama Desert, Chile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Polarbear searched for both degree-scale and sub-degree-scale B-mode polarization signals originating from inflationary gravitational waves and the weak gravitational lensing effect, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The Huan Tran Telescope, which is equipped with the Polarbear receiver, has an off-axis Gregorian optics configuration with a 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='5 m-diameter primary mirror and secondary mirror.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The Polarbear receiver has seven wafers on the focal plane (see Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Each wafer is mounted with 182 detectors, and there is thus a total of 1274 detectors on the focal plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The detector is sensitive to the frequency band centered at 150 GHz with a fractional band width of ap- proximately 30 %.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We measured the band-pass window function at the site with a Fourier transform spectrometer (FTS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In this paper, we use the wafer-averaged values of this mea- surement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' See F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Matsuda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (2019)19 for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Polarbear began observations in January 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We placed a continuously rotating HWP between the primary and secondary mirrors to measure the degree-scale B-mode polarization from May 201418.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Note that the HWP was not installed during the FTS measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' 9 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Layout of detector wafers on the focal plane of Polarbear 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' There are seven wafers on the Polarbear focal plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Six wafers have silicon lenslets, and one wafer, which is labeled 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='0, has alumina lenslets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' LABORATORY MEASUREMENT We characterized the optical properties of the HWP installed in the Polarbear tele- scope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The characterization was conducted in a laboratory environment prior to the deploy- ment of the HWP to the Polarbear telescope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Measurement System Figure 3 shows the measurement setup for characterizing the Polarbear HWP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' A millimeter-wave source signal is generated by a continuous wave generator (12 to 18 GHz) with a multiplier (× 9) covering a frequency range from 108 to 162 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The source signal is emitted through the waveguide with a pyramidal feed horn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' After the feed horn, we place an optical chopper to chop the signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We insert a wire grid along the optical path to define the polarization angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The polarized signal is collimated by a lens before the aperture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The lens is composed of Rexolite with a sub-wave grading AR coating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The HWP is mounted on a holder that rotates about the z-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The HWP is placed normal to the incident radi- ation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' This rotational mechanism is controlled by a stepping motor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In our measurement, the HWP is rotationally stepped in intervals of 6 degrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The angle of the fast axis of the 10 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='4 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='3 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='0 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='2 19 cm 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='5 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='1 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='4Multipliers Signal Generator z x Source horn Wire grid Lens Aperture HWP Wire grid Detector horn Chopper Lock-in Amplifier FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Setup of the transmission measurement of the HWP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' HWP is originally unknown, and we thus calculate this angle in the data analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Behind the HWP, another wire grid is inserted to determine the outgoing polarized signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The detector is a diode detector that is sensitive to the input millimeter wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The detector is set on a linear stage to calibrate the effect of standing waves and moves 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='9 mm along the z-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The detected signal is read by a lock-in amplifier with a reference signal from the chopper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Methods The following measurement method was adopted using the setup in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We start the measurement by setting the frequency of the signal generator to 12 GHz and the rotation angle of the HWP to 0 degrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In this measurement, we take data by changing the detector position along the z-axis from 0 to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='9 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' After the measurement at 0 degrees and 12 GHz, we step the rotation angle of the stepping motor to 6 degrees and repeat the measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' After making measurements from 0 to 354 degrees, we step the frequency of the signal generator by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='1 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We repeat the measurements until making measurements at 18 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We also measure the transmittance of the linear polarization by taking the ratio of the output signal when the HWP is inserted into the optical system and the output signal when the HWP is not inserted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' These measurements are performed after the angle of the fast axis of the HWP is determined by the previous measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' 11 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Analysis In the analysis, we firstly remove the effect of the standing wave from the signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' For each frequency and rotation angle, we plot the signal as a function of the linear stage position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We then fit the signal with a sinusoidal wave plus a constant component and extract the constant component as the signal for this frequency and rotation angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Then, given the above setup and the measurement procedure, the data are modeled as dm(ν, θh) =G(ν) (1, 1, 0, 0) Mrot(−2θh)MHWP(ν)Mrot(2θh) (1, 1, 0, 0)T + doffset =G(ν)3T(ν) + c(ν) 2 + 2G(ν)ρ(ν) cos(2θh) + G(ν)T(ν) − c(ν) 2 cos(4θh) + doffset, (12) where θh is the rotation angle of the HWP, G(ν) is the gain of the system, and doffset is the offset of the lock-in amplifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We find that some measurements are negative and assume that this is due to the offset of the lock-in amplifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We thus include doffset as a parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Given this model, we fit the data using the equation d = A0 + A2 cos (2θh + 2φ2) + A4 cos (4θh + 4φ4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (13) Figure 4 shows a typical modulated response curve when the HWP rotates about the z-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The top panel shows the modulated power as a function of the HWP angle at 143 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The points are the measurement data, and the curve is the fit using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The middle panel shows the second harmonic component obtained by computing d−(A0 +A4 cos (4θh + 4φ4)) in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The bottom panel shows the residual of the fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Here, the peaks of the top panel correspond to the angles where the fast or slow axis of the HWP becomes parallel to the incident polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' There is a small difference in the transmission between the fast and slow axes owing to the difference in the refractive index, which is seen as the second harmonics component in the middle panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The signal becomes almost zero at the middle of the peaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' This means that the input polarization is efficiently rotated to the orthogonal polarization, and the leakage to the CP is small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We then relate the obtained amplitudes, A0, A2, and A4, to the components of the Mueller matrix of the HWP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' By comparing Eqs (12) and (13), we obtain ρ(ν) T(ν) + δ1(ν) = A2(ν) A0(ν) + A4(ν), c(ν) T(ν) + δ2(ν) = A0(ν) − 3A4(ν) A0(ν) + A4(ν) , (14) 12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='5 Output [V] fit data 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='01 A2 [V] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='0 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='0 180.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='0 270.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='0 360.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='0 rotation angle [degree] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='005 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='005 Residual [V] FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (Top) Example of the output signal for each rotation angle at an incident frequency of 143.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='1 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The blue points are the data, and the orange line shows the fit with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (Middle) The second harmonics component of the same data obtained by subtracting A0 +A4 cos(4θh +4φ4) of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (Bottom) Residual of the fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' where δ1(ν) and δ2(ν) denote the effect of the offset of the lock-in amplifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' These values are calculated using doffset: δ1(ν) = −A2(ν)doffset ((A0(ν) + A4(ν))(A0(ν) − doffset + A4(ν)), (15) δ2(ν) = 4A0(ν)doffset ((A0(ν) + A4(ν))(A0(ν) − doffset + A4(ν)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (16) We also calculate the transmittance of the linear polarization T + ρ from the ratio of the observations made with an HWP rotation angle θh = 0 and observations made without the HWP as T(ν) + ρ(ν) = dm(θh = 0)(ν) dnoHWP (ν).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (17) Finally, we fit the spectra obtained from Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (14) and (17) with the model of the Mueller matrix of the HWP described in section II A using the Markov Chain Monte Carlo (MCMC) method with the thickness, refractive index, and loss tangent of each layer of the HWP as 13 120 140 160 Frequency [GHz] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='90 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='95 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='05 T + 120 140 160 Frequency [GHz] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='04 /T 120 140 160 Frequency [GHz] 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='95 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='90 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='85 c/T FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Calculated spectra of the Mueller matrix components and results of MCMC fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Blue points are measured points with error explained in section IV A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The red dashed line and green band are the estimated mean value and one-sigma distribution respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Note that these data points and fitting lines include the effect of the offset of the lock-in amplifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' input parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' As the prior distribution of the HWP model, we use the design values given in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' To avoid negative values, we assume the exponential distribution as the prior distribution of loss tangents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We assume Gaussian distributions for the prior distributions of other parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Additionally, we include doffset as the input parameter of the MCMC fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The prior distribution of doffset is a uniform distribution because we do not know the detail of doffset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We take the following steps before performing the MCMC fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The statistical uncertainties in the observations are smaller than the actual deviations from the model, and we thus introduce the contribution of systematic uncertainties possibly due to gain fluctuations, standing waves, and stray light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We use the MCMC method only with the detector offset as an input parameter and the design values for other parameters and determine an additional error so that the reduced chi-squared becomes 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We use only data in the frequency range above 120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='6 GHz for two reasons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' One reason is that these points are away from the observation frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The other reason is that the value of c/T drops off unreasonably around 119 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' 14 TABLE II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Parameters of the HWP model obtained by MCMC fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' These values are calculated from the mean values of the posterior distributions and the uncertainties come from the samples’ standard deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' A comparison with Table I shows that all parameters are consistent within the uncertainty given in the table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The uncertainty in the sapphire thickness and the uncertainty in the refractive index difference of the sapphire become smaller than the uncertainties in the design values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' thickness refractive index loss tangent Sapphire (o-axis) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='086 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='005 mm 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='065 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='002 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='11 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='89) × 10−4 Sapphire (e-axis) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='086 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='005 mm 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='404 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='002 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='51 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='50) × 10−4 Duroid 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='255 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='002 mm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='710 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='008 (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='4 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='53) × 10−4 LDPE 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='039 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='002 mm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='514 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='010 (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='3 ± 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='7) × 10−4 D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Results The blue points in Figure 5 show measured spectra of T + ρ, ρ/T, and c/T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Figure 5 also shows the spectra calculated with the HWP model with parameters from the MCMC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The red dashed lines and green band indicate the converged average value and one-sigma band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Note that these data points and fitting lines include the effect of the offset of the lock-in amplifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Table II gives the parameters of the HWP model after the MCMC fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In this table, we give the mean values of the posterior distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' A comparison with Table I shows that the results are consistent with the fiducial values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We also find that the uncertainty in the sapphire thickness becomes 1/20 and the uncertainty in the refractive index difference of the sapphire becomes 1/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The accuracy of the model is improved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In this measurement, the uncertainties in the measured spectra are limited by the un- known systematic error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The cause of this systematic error must be understood to improve the accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Additionally, the offset of the lock-in amplifier doffset is estimated from the fitting as a nuisance parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In future measurements, it would beneficial to measure the background signal to determine the offset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Ideally, a vector network analyzer (VNA) would be used for the HWP characterization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' A VNA can measure the amplitude and phase of the electric field, allowing the calculation of the Mueller matrix directly from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' 15 120 130 140 150 160 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='4 s 120 130 140 150 160 Frequency [GHz] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='01 68% C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' of s FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Spectra of the estimated s parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The top panel shows the spectra of the mean s value (red dash line) and the range of one sigma (green band).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The bottom panel shows the one-sigma uncertainty of the s parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' LEAKAGE ESTIMATION We calculate the coupling between the CP and linear polarization, s, using the HWP model (see section II A) and the parameters obtained from the samples of the MCMC fitting in section IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Figure 6 shows the spectra of s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The s spectrum is close to zero at the obser- vation frequency, which is given in Table III, and decreases at high frequency as expected from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The frequency at which s is zero is approximately 143 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' This frequency is close to the central frequency of the Polarbear telescope (see Table III).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We show the uncertainty in this spectrum in the bottom panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The uncertainty is almost constant within the observation frequency range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We calculate the band-averaged value, ¯s, using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We give the details of the bandpass of each wafer in Table III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' For the detector band-pass window function, W(ν), we use the wafer-averaged spectrum of the FTS measurement at the site (see section III).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The detector bandpass properties are summarized in Table III for each wafer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We calculate ¯s for each wafer because ¯s is sensitive to the wafer-by-wafer variation of the band center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The 16 TABLE III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Detector bandpass of each wafer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The average (AVG) and standard deviation (STD) of the band center and bandwidth are shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We also show the uncertainty in the bandpass of each wafer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' These values are obtained from FTS measurement at the site19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Band Center (GHz) BandWidth (GHz) Uncertainty Wafer AVG STD AVG STD 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='0 136.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='7 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='4 1.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='5 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='005 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='5 145.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='4 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='006 statistical uncertainty in ¯s is calculated from the standard deviation of the samples of ¯s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Unlike the case for the linear polarization of the CMB, there is a variation in the frequency dependence of the CMB CP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Here,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' we consider four spectra of the CP of the CMB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' namely the Rayleigh–Jeans (RJ) spectrum,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' CMB spectrum,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' the frequency dependence of the FC20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' and the frequency dependence of the CP caused by CνB3: SRJ(ν) = S(ν0) � ν ν0 �2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (18) SCMB(ν) = S(ν0) � ν ν0 �4 exp(hν/kBT)/ exp(hν0/kBT) (exp(hν/kBT) − 1)2/(exp(hν0/kBT) − 1)2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (19) SFC(ν) = SCMB(ν) �ν0 ν �3 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (20) SCνB(ν) = SCMB(ν)ν0 ν ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' (21) where S(ν0) is the amplitude of the signal at the pivot frequency ν0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' and h,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' kB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' T are the Planck constant,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Boltzmann constant,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' and temperature of the CMB (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='725 K)21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We also consider the spectrum of CP due to the atmospheric Zeeman emission22,23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The Zeeman emission is a signal produced by the splitting of the energy levels of the oxygen molecules in the atmosphere by the Earth’s magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' This signal is expected in that the low- frequency side of the split level at 118.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='75 GHz is circularly polarized clockwise and the high-frequency side is circularly polarized counterclockwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' 17 Table IV presents the band- and spectral-dependence of the band-averaged s value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The values of wafer 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='0 are larger than those of other wafers because the central frequency of wafer 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='0 is lower than that of the other wafers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' This relation of ¯s among wafers is independent of the source spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Regarding the source spectrum dependence, the values of the CMB spectrum are ap- proximately 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='02 larger than those of the RJ spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The maximum absolute value of our estimates is almost the same as that of the SPIDER HWP s parameters6 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='149 in this paper versus 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='154 in SPIDER), which are also band-averaged using the CMB source spectrum and their bandpass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' However, the minimum value in this paper is larger than that in SPIDER (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='007 versus 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We also compare the uncertainty in the s parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The uncertainty in the s parameter of the SPIDER HWP is approximately 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='041 whereas the uncertainty in the s parameter obtained from the design values of Polarbear HWP (Table I) is approximately 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In contrast to these results, the uncertainty in our estimated s parameter is approximately 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The method described in this paper thus reduces the uncertainty in the HWP model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Meanwhile, the values of the FC spectrum, CνB spectrum, and Zeeman spectrum are different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Although some signs of band-integrated s values are reversed, the set of absolute values of the FC spectrum and CνB spectrum are almost the same as those of the RJ spectrum and CMB spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The band-integrated s values are larger for the Zeeman spectrum than for the other spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The CP signal of the Zeeman emission is expected to be approximately 61 µK in the Polarbear frequency band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Even with the suppression by ¯s, the apparent signal is approximately 31 µK, which is above the noise level of Polarbear (NETarray = 23 µK√s )17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' DISCUSSION A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Systematic Uncertainty We estimate the systematic uncertainties in the band-averaged s parameter of the HWP under the conditions of actual operation in the telescope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We consider the uncertainty in the bandpass dependence and the non-vertical incident light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We first consider the uncertainty in the bandpass dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' There is uncertainty in the 18 TABLE IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Band-averaged s values for various spectra of sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In this paper, we assume Rayleigh–Jeans spectrum (RJ), CMB spectrum (CMB), spectrum of the CP due to Faraday Con- version (FC), spectrum of the CP due to the cosmic neutrino background (CνB), and atmospheric Zeeman emission (Zeeman).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The difference in the values between the RJ and CMB is smaller than the differences between other spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Meanwhile, the values of FC and CνB differ largely from those of RJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Moreover, the values of the atmospheric Zeeman emission are larger than those of the other spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Wafer RJ CMB FC CνB Zeeman 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='133 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='009 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='149 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='009 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='207 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='008 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='168 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='009 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='437 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='011 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='075 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='009 -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='055 ± 0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='389 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='008 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='5 -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='045 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='009 -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='025 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='009 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='041 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='009 -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='004 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='009 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='367 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='009 bandpass measurement by the FTS at the site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' This comes from the systematic variation in the bandpass for each detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We calculate the uncertainty in the bandpass of each wafer from the data in the sensitive frequency region as shown in Table III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We then calculate ¯s 5000 times using random realizations of the detector bandpass with the uncertainty evaluated above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We take the standard deviation of this distribution as the systematic uncertainty due to the uncertainty in the detector bandpass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We next consider the non-vertical incident light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In the HWP model used in section V, we assume that light is vertically incident.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' However, not all light is vertically incident in the setup of the telescope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The Polarbear HWP is placed at the prime focus, which is between the primary and secondary mirrors, of the Huan Tran Telescope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The light between these mirrors is once focused at the prime focus and spreads again, and the incident angle of the light incident on the HWP thus increases as the light deviates from the center of the optical path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The non-vertical incident light will change the optical path in the HWP and thus affect the estimate of ¯s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The maximum value of the incident angle is 16◦ at the half width at half maximum from the geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We thus calculate conservatively how ¯s varies 19 TABLE V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Estimated ¯s and uncertainties for each wafer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The first and second columns from the left give the average values and standard deviation of the MCMC fitting explained in section V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The third column gives the systematic error due to the uncertainty in the detector bandpass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The fourth column gives the systematic error due to the non-vertical incident light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' These systematic uncertainties are smaller than the standard deviation of the MCMC fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Wafer AVG STD bandpass non-vertical 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='133 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='009 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='001 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='075 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='009 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='002 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='024 0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='003 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='113 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='010 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='002 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='013 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='009 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='003 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='045 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='009 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='003 when the incident light is tilted at 16◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In this calculation, we rotate the HWP with the tilted incident light and extract the second harmonics in the simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Table V gives the systematic uncertainties in the band-averaged s value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Here, we as- sume that the source spectrum is the RJ spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The columns from the left show the wafer name, band-averaged s values, statistical uncertainty in the band-averaged s value, systematic error of the uncertainty in the detector bandpass, and systematic error in the non-vertical incident light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We find that these systematic uncertainties are smaller than the statistical uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Possibility of cross-checking using atmospheric CP We next consider a method of cross-checking the above result with the values obtained from observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The atmospheric Zeeman emission is a possible CP source with which to measure ¯s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' As described in section V, the atmospheric Zeeman emission is a bright CP source and is expected to be observable with the Polarbear detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Thus, we might be able to separate the CP signal from the second harmonic signal using the method described in section II B and estimate the leakage of the HWP by comparing the observed CP signal 20 with the theoretical value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Note that because the coordinate of the atmospheric CP is fixed to the ground, the signal of the atmospheric CP may be degenerated with the ground pickup signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The difference in spectra can be used to distinguish the atmospheric CP signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The Zeeman emission has a peak at 118.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='75 GHz and this results in a temperature difference of approximately 100 µK at maximum between wafers due to slight differences in frequency characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' If the spectrum of the ground pickup signal is the RJ spectrum, we can distinguish the Zeeman emission from the difference in the observed temperature between wafers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Prospects of CP Measurement Table IV in section V shows that ¯s is nonzero in most cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' This suggests the possibility to probe the CP using Polarbear data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' From the mean value of the ¯s parameter in Table IV of the CMB spectrum and noise level in B-mode observation12, we estimate that the sensitivity of ℓ(ℓ + 1)CV V ℓ /(2π) is approximately 30(µK)2 at ℓ ∼ 300 in Polarbear;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' this result is comparable to the sensitivity of measurements made by SPIDER.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' SUMMARY We evaluated the HWP used at Polarbear, including the leakage between linear po- larization and CP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We constructed an HWP model from data recorded at the laboratory in 2014 and estimated the leakage between the CP and linear polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' This model well explained the measured spectrum of the Mueller matrix components, and the uncertainty in the parameters of the HWP was at maximum 1/20th the design value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We thus found that the absolute value of the band-averaged leakage from the CP obtained using the HWP, ¯s, ranged from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='151 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='021 at each wafer, and the statistical uncertainty in ¯s was approxi- mately 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='010 for each wafer in the case of the RJ spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' This means that all detectors on each wafer were capable of measuring the CP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We also considered four other spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' The value of ¯s was nonzero in most cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In particular, ¯s was larger for the Zeeman spectrum than for the other spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We also estimated the systematic uncertainties in ¯s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' In this paper, we considered the uncertainties in the detector bandpass and non-vertical incident light and found that these systematic uncertainties were smaller than the statistical error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' 21 Finally, we verified this result using the atmospheric CP signal and presented prospects of making angular power spectrum measurements of CP anisotropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' ACKNOWLEDGMENTS We acknowledge M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Myers for creating the HWP, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Inoue and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Yamaguchi for setup the laboratory measurement system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' MH acknowledges support from the World Premier International Research Center Initiative (WPI) of MEXT and the JSPS KAKENHI grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' JP22H04945.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' ST acknowledges support from the JSPS KAKENHI grant Nos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' JP14J01662 and JP18J02133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' HN achnowledges support from the JSPS KAKENHI grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' JP17K18785.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' This work was supported by the JSPS Core-to-Core Program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' We thank Edanz (https://jp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='edanz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content='com/ac) for editing a draft of this manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' AUTHOR DECLARATIONS Conflict of Interest The authors have no conflicts to disclose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Author Contributions T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Fujino:Conceptualization (equal);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Formal Analysis (lead);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Writing/Original Draft Preparation (lead).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Takakura: Conceptualization (equal);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Investigation (lead);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Writ- ing/Review & Editing (lead).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Chinone: Writing/Review & Editing (supporting).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Hasegawa: Writing/Review & Editing (equal).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Hazumi: Writing/Review & Editing (supporting).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Katayama: Writing/Review & Editing (supporting).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' Lee: Writ- ing/Review & Editing (supporting).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HtA0T4oBgHgl3EQfB_9Y/content/2301.01983v1.pdf'} +page_content=' T.' metadata={'source': 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Jan 2023 +– +Exploration in Model-based Reinforcement +Learning with Randomized Reward +. +Lingxiao Wang, Ping Li +. +Cognitive Computing Lab +. +Baidu Research +. +10900 NE 8th St, Bellevue, WA 98004, USA +Abstract +1Model-based Reinforcement Learning (MBRL) has been widely adapted due to its sample effi- +ciency. However, existing worst-case regret analysis typically requires optimistic planning, which +is not realistic in general. In contrast, motivated by the theory, empirical study utilizes ensemble of +models, which achieve state-of-the-art performance on various testing environments. Such devia- +tion between theory and empirical study leads us to question whether randomized model ensemble +guarantee optimism, and hence the optimal worst-case regret? This paper partially answers such +question from the perspective of reward randomization, a scarcely explored direction of exploration +with MBRL. We show that under the kernelized linear regulator (KNR) model, reward randomiza- +tion guarantees a partial optimism, which further yields a near-optimal worst-case regret in terms +of the number of interactions. We further extend our theory to generalized function approximation +and identified conditions for reward randomization to attain provably efficient exploration. Corre- +spondingly, we propose concrete examples of efficient reward randomization. To the best of our +knowledge, our analysis establishes the first worst-case regret analysis on randomized MBRL with +function approximation. +1. This manuscript was completed in September 2021 while both authors worked at Baidu Cognitive Computing Lab. +© . + +1. Introduction +Reinforcement learning (RL) (Sutton and Barto, 2018) aims to learn the optimal policy by iteratively +interacting with the environment. Model-based reinforcement learning (MBRL) (Osband and Roy, +2014; Luo et al., 2019; Ha and Schmidhuber, 2018; Luo et al., 2019; Sun et al., 2019; Kaiser et al., +2020; Ayoub et al., 2020; Kakade et al., 2020) achieves such a goal by fitting the environment from +the observation and obtaining the policy from the fitted environment. Incorporated with deep learn- +ing, MBRL has achieved tremendous success in real-world tasks, including video games (Ha and Schmidhuber, +2018; Kaiser et al., 2020) and control tasks (Watter et al., 2015; Williams et al., 2015; Chua et al., +2018; Hafner et al., 2019; Song and Sun, 2021). +A key factor to the success of MBRL is sample efficiency. In terms of the theoretical analysis, +such sample efficiency is characterized by the regret analysis of MBRL. Previous analysis sug- +gests that when incorporated with exploration strategies, MBRL enjoys a near-optimal �O( +√ +T) re- +gret (Jaksch et al., 2010; Ayoub et al., 2020; Kakade et al., 2020), where T is the total number of in- +teractions with the environment. However, previous provably efficient exploration typically utilizes +optimistic planning (Jaksch et al., 2010; Luo et al., 2019; Ayoub et al., 2020; Kakade et al., 2020). +Such exploration strategy requires (i) identifying a confidence set of models D, which captures the +uncertainty in model estimation, and then (ii) conducting optimistic planning by searching for the +maximal policy among all possible models within D. The key to the success of optimistic planning +is optimism under the face of the uncertainty principle (Jaksch et al., 2010). Intuitively, optimistic +planning encourages the agent to explore less visited areas, hence enhancing the sample complex- +ity of the corresponding RL algorithm. While step (i) is realizable with ensemble techniques, step +(ii) is in general impossible to implement, as it requires solving an optimization problem over a +possibly continuous space of models D. As an alternative, previous empirical study (Chua et al., +2018; Pathak et al., 2017, 2019) typically borrows the idea from optimistic planning and the study of +Thompson sampling (TS) based algorithm (Osband and Roy, 2014). A common empirical approach +is to utilize model ensembles to capture the uncertainty of model estimations. Such ensembles +are further utilized in planning through TS (Chua et al., 2018) or bonus construction (Pathak et al., +2017, 2019). Unlike optimistic planning, such approaches typically do not have a worst-case regret +guarantee. Nevertheless, they attain state-of-the-art performance in various testing environments. +Such deviation from theory and practice motivates us to propose this question: +Does randomized model ensemble guarantees optimism, and hence the optimal worst-case regret? +In this paper, we provide a partial solution to the above question from reward randomization, a +relatively less studied method for exploration in MBRL. We initiate our analysis under the kernelized +linear regulator (KNR) transition model (Mania et al., 2022; Kakade et al., 2020; Song and Sun, +2021) and known reward functions. We propose PlanEx , which conducts exploration by itera- +tively planning with the fitted transition model and a randomized reward function. We further show +that PlanEx attains the near-optimal �O( +√ +T) regret. A key observation of reward randomization is +a notion of partial optimism (Russo, 2019; Zanette et al., 2020), which ensures that a sufficient +amount of interactions are devoted to exploration under the optimism principle. Motivated by the +analysis under the KNR transition model, we extend PlanEx to general function approximation +with calibrated model (Curi et al., 2020; Kidambi et al., 2021) and propose a generic design princi- +ple of reward randomization. We further propose concrete examples of valid reward randomization + +EXPLORATION IN MODEL-BASED RL +and demonstrate the effectiveness of reward randomization theoretically. We highlight that the pro- +posed reward randomization method can be easily implemented based on the model ensembles. In +addition, the reward randomization is highly modular and can be incorporated with various SOTA +baselines. +Contribution. Our work provides a partial solution to the question we raised. Specifically, we +investigate reward randomization and propose PlanEx . Our contributions are as follows. +• We propose PlanEx , a novel exploration algorithm for MBPO with worst-case regret guar- +antee that is realizable with general function parameterizations. +• We show that PlanEx has near-optimal worst-case regret under the KNR dynamics. +To the best of our knowledge, our analysis establishes the first worst-case regret analysis on ran- +domized MBRL with function approximation. +Related Work. Our work is closely related to the regret analysis of MBRL and online control +problem (Osband and Roy, 2014; Luo et al., 2019; Sun et al., 2019; Lu and Roy, 2019; Ayoub et al., +2020; Kakade et al., 2020; Curi et al., 2020; Agarwal et al., 2020b; Song and Sun, 2021). Ayoub et al. +(2020) propose the value-target regression (VTR) algorithm, which focuses on the aspects of the +transition model that are relevant to RL. Agarwal et al. (2020b) propose FLAMBE, a provably effi- +cient MBRL algorithm under the linear MDP setting (Jin et al., 2020; Yang and Wang, 2019). Kakade et al. +(2020) propose LC3, an online control algorithm under the KNR dynamics (Mania et al., 2022) that +attains the optimal worst-case regret. Both Ayoub et al. (2020) and Kakade et al. (2020) utilizes op- +timistic planning for exploration, which is in general intractable. In contrast, we utilize reward ran- +domization for exploration, which also attains the optimal worst-case regret and is highly tractable. +To attain tractable optimistic planning, Curi et al. (2020) design HUCRL, which introduces an ex- +tra state deviation variable in the optimization for planning. In contrast, planning with randomized +reward does not introduce extra variable in optimization. Luo et al. (2019) optimizes a lower bound +of value functions, which avoids explicit uncertain quantification. Recent works also utilizes re- +ward bonus to attain optimistic planning (Kidambi et al., 2021; Song and Sun, 2021). Song and Sun +(2021) propose PC-MLP, which constructs bonus by estimating the policy cover (Agarwal et al., +2020a) and is computationally tractable. As a comparison, PC-MLP requires extra sampling to +estimate the covariate matrix of policy cover. As a consequence, PC-MLP does not attain the op- +timal �O( +√ +T)-regret. In contrast, PlanEx does not require extra sampling to construct the bonus +and can achieve the �O( +√ +T)-regret. In addition, to attain tractable realization, PC-MLP utilizes +different feature in model fitting and bonus construction, which is inconsistent with the theoretical +analysis. In contrast, the implementation of PlanEx is consistent with the theoretical analysis un- +der the calibrated model assumption. Previous work also study efficient model-free RL exploration +algorithms with function approximation. See, e.g., Jiang et al. (2017); Jin et al. (2020); Du et al. +(2020); Wang et al. (2020); Cai et al. (2020); Agarwal et al. (2020a); Modi et al. (2021) and refer- +ences therein for this line of research. +Our analysis is inspired by the recent progress in worst-case regret analysis of randomized RL +algorithms (Russo, 2019; Pacchiano et al., 2020; Zanette et al., 2020; Ishfaq et al., 2021). Our op- +timism analysis is inspired by Russo (2019) and Zanette et al. (2020). Russo (2019) propose the +first worst-case regret analysis to the randomized least-squares value iteration (RLSVI) algorithm +under the tabular setting. Zanette et al. (2020) extend the analysis of RLSVI to truncated linear + +function approximations under the general state space. Ishfaq et al. (2021) analyze the randomized +Q-learning with both linear function approximation and general function approximation. In contrast, +we focus on the randomized MBRL algorithm. Pacchiano et al. (2020) analyze the worst-case re- +gret of MBRL with both reward and transition randomization. We remark that both Pacchiano et al. +(2020) and Ishfaq et al. (2021) require drawing multiple samples for each state-action pair in plan- +ning and further maximizing over all randomized reward functions in planning. In contrast, we only +require one sample at each time step, and do not need further maximization. In addition, Pacchiano et al. +(2020) focus on the tabular setting with finite state and action spaces, whereas we consider the +generic setting with function approximation. +2. Background +2.1. Reinforcement Learning +In this paper, we model the environment by an episodic MDP (S, A, H, {rh}h∈[H], P). Here S +and A are the state spaces, H is the length of episodes, rh : S × A �→ [0, 1] is the bounded +reward function for h ∈ [H], and P is the transition kernel, which defines the transition probability +sh+1 ∼ P(· | sh, ah) for all h ∈ [H] and (sh, ah) ∈ S × A. Interaction Procedure. An agent +with a set of policies {πh}h∈[H] interacts with such environment as follows. The agent starts from +a fixed initial state s1 ∈ S. Iteratively, upon reaching the state sh ∈ S, the agent takes the action +ah = πh(sh). The agent then receives the reward rh(sh, ah). The environment transits into the next +state sh+1 according to the probability P(· | sh, ah). The process ends when the agent reaches the +state sH+1. +To describe the expected cumulative reward, for each policy π = {πh}h∈[H], we introduce the +action-value functions {Qπ +h}h∈[H] defined as follows, +Qπ +h(sh, ah; {rh}h∈[H], P) = +H +� +τ=h +E +� +rτ(sτ, aτ) +�� sh, ah, π +� +, +∀h ∈ [H], (sh, ah) ∈ S × A, +(1) +where aτ = πτ(sτ) and sτ+1 ∼ P(· | sτ, aτ) for all τ = h, . . . , H. Similarly, we define the value +functions {V π +h }h∈[H] as follows, +V π +h (sh; {rh}h∈[H], P) = +H +� +τ=h +E +� +rτ(sτ, aτ) +�� sh, π +� +, +∀h ∈ [H], (sh, ah) ∈ S × A. +(2) +We define optimal policy π∗ = {π∗ +h}h∈[H] as the maximizer of the following optimization problem, +π∗ = argmax +π +V π +1 (s1; {rh}h∈[H], P). +(3) +Correspondingly, we define V ∗ and Q∗ the value and action-value functions corresponding to the +optimal policy π∗. +The goal of reinforcement learning (RL) is to sequentially select the policy πk = {πk +h}h∈[H] +based on the previous experiences, aiming to maximize the expected cumulative reward collected +by the agent in the interaction process. Equivalently, the goal is to minimize the following regret, +R(K) = +K +� +k=1 +V ∗(s1) − V πk(s1), +(4) + +EXPLORATION IN MODEL-BASED RL +where K is the total number of interactions and s1 is the fixed initial state. Intuitively, the re- +gret R(K) describes the deviation between the policies executed in the interaction process and the +optimal policy. +2.2. The Online Nonlinear Control Problem +We consider the online nonlinear control problem with the following transition dynamics, +sh+1 = f(sh, ah) + ǫ, +where ǫ ∼ N(0, σ2 · I), +∀h ∈ [H], (sh, ah) ∈ S × A. +Here the function f : S × A �→ S belongs to a Reproducing Kernel Hilbert Space (RKHS) with +known kernel and the noise ǫ is independent across transitions. Such transition is also known as +the Kernelized Nonlinear Regulator (KNR) in previous study (Kakade et al., 2020; Song and Sun, +2021). In this work, we follow Mania et al. (2022); Kakade et al. (2020); Song and Sun (2021) and +consider a primal version of such transition dynamics as the underlying transition dynamics for the +RL problem, which is defined as follows, +sh+1 = f(sh, ah; W ∗) + ǫ, +where ǫ ∼ N(0, σ2 · I), +f(sh, ah; W ∗) = W ∗φ(sh, ah), +∀h ∈ [H], (sh, ah) ∈ S × A. +(5) +Here φ : S × A �→ Rdφ is a known feature embedding. Meanwhile, the state space S ⊆ RdS is a +subset of the Euclidean space with dimension dS and W ∗ ∈ RdS×dφ is the unknown true parameter +of the KNR transition dynamics. +Correspondingly, in the sequel, we denote by Qπ(·, ·; {rh}h∈[H], W) and V π(·; {rh}h∈[H], W) +the value functions of the policy π under the reward functions {rh}h∈[H] and the transition dynamics +defined by the matrix W ∈ RdS×dφ. For the simplicity of our analysis, we fix the following scaling +of features and parameters. +Assumption 1 (Normalized Model) We assume that ∥φ(s, a)∥2 ≤ 1/ +√ +H for all (s, a) ∈ S × A. +correspondingly, we assume that ∥W ∗∥2 = O( +√ +H), where W ∗ is the true parameter of the KNR +transition dynamics defined in (5). +Similar normalization assumptions also arises in Mania et al. (2022). We remark that the scaling +assumptions in Assumption 1 only affect the rate of H in regret, and is imposed for the simplicity +of our analysis. +2.3. Model-based RL for Unknown Transition Dynamics +In model-based RL, the agent optimizes the policy by iteratively fitting the transition dynamics +based on the data collected, and conducting optimal planning on the fitted transition dynamics. For +each iteration k, the model-based RL consists of the following steps. +• (i) Model Fitting. In this step, the agent updates the parameter Wk of transition dynamics +based on the replay buffer Dk. +• (ii) Planning. In this step, the agent conducts optimal planning based on the fitted parameter +Wk of transition dynamics. By planning with the fitted models, the agent updates the policy +πk. + +• (iii) Interaction. In this step, the agent interacts with the environment with the policy πk +and collects a trajectory ιk = (sk +1, ak +1, . . . , sk +H, ak +H, sk +H+1). The agent then updates the replay +buffer by Dk+1 = Dk ∪ ιk. +In the sequel, we raise the following assumption, which assume that we have access to a planning +oracle to handle the planning in step (ii). +Assumption 2 (Planning Oracle) We assume that we have access to the oracle Plan(·, ·, ·), which +returns the optimal policy π = Plan(s1, {rh}h∈[H], W) for any input reward functions {rh}h∈[H] +and the parameter W of the transition dynamics. +Remark 3 (Remark on Sample Complexity) In practice, the planning on fitted environment is +typically handled by deep RL algorithms (Pathak et al., 2017; Luo et al., 2019; Pathak et al., 2019; +Song and Sun, 2021) or model predictive control (Williams et al., 2015; Chua et al., 2018; Kakade et al., +2020). We remark that since such planning is conducted on the fitted environment, solving such plan- +ning problem does not raise concerns in the sample complexity of solvers. In contrast, such sample +complexity concern is raised when interacting with the real environment in step (iii). We remark +that the goal of exploration is to obtain a near-optimal policy with as few round of interactions K +as possible. When measured with the regret R(K) defined in (4), the goal of exploration is to design +algorithms to attain an regret R(K) that grows as slow as possible in terms of K. +3. Exploration with Randomized Reward +In this section, we propose PlanEx , an provably efficient and realizable algorithm for the RL +problem with KNR dynamics. In the sequel, we describe the procedure of each step in the k-th +iteration of PlanEx . +(i) Model Fitting. Given the dataset Dk = {(sτ +h, aτ +h, sτ +h+1)(h,τ)∈[H]×[k−1]}, we fit the transition +parameter W k by minimizing the prediction error of sh+1 given (sh, ah). Specifically, we minimize +the following least-squares loss, +W k ← +argmin +W ∈RdS×dφ +H +� +h=1 +k−1 +� +τ=1 +∥sτ +h+1 − Wφ(sτ +h, aτ +h)∥2 +2 + λ · ∥W∥2 +F , +(6) +where we denote by ∥ · ∥F the matrix Frobenius norm. The optimization in (6) has the following +explicit form solution, +W k ← +� H +� +h=1 +k−1 +� +τ=1 +sτ +h+1φ(sτ +h, aτ +h)⊤ +� +Λ−1 +k , +Λk = +H +� +h=1 +k−1 +� +τ=1 +φ(sτ +h, aτ +h)φ(sτ +h, aτ +h)⊤ + λI. +(7) +(ii) Planning. In the planning stage, we aim to derive a policy πk that interact with the environment. +There are two objectives that we aim to achieve in deriving the policy πk. (a) Firstly, the policy πk +should properly exploit our knowledge about the environment to optimize the cumulative reward. +(b) Secondly, the policy πk should also incorporate our uncertainty to the environment and conduct +exploration to unexplored critical events. To properly balance between (a) and (b), we need to +quantify our uncertainty to the environment. Such uncertainty quantification can be done by the + +EXPLORATION IN MODEL-BASED RL +matrix Λk defined in (7). Specifically, it is known () that the matrix Λk defines the following +confidence region +Gk = +� +W ∈ RdS×dφ : ∥(W − W k)Λ1/2 +k +∥2 +2 ≤ βk +� +. +For properly set βk, it is known that W ∗ ∈ Gk with high probability. Under such observation, previ- +ous attempts (Jaksch et al., 2010; Kakade et al., 2020) attain the balance between exploitation and +exploration by finding the maximizer π of V π(s1; {rh}h∈[H], W) for W ∈ Gk, which, however, is +computationally intractable. To propose a computationally tractable alternative, previous empirical +approaches utilizes ensemble models to estimate the epistemic uncertainty in fitting the model with +finite observations. +In this work, we investigate the approach of directly incorporating uncertainty into the reward +functions. To this end, we introduce the following perturbed reward function, +rk +h,ξ(sh, ah) = +� +rh(sh, ah) + φ(sh, ah)⊤ξk +h +�+, +∀h ∈ [H], (sh, ah) ∈ S × A, +(8) +where the noise {ξk +h}h∈[H] are sampled independently from the Gaussian distribution ξk +h ∼ N(0, σ2 +k· +Λ−1 +k ). Intuitively, such noise has larger variance in regions that are less explored by the agent, and +smaller variance in regions that are well-explored. In addition, we clip the reward to ensure that the +reward is positive. +Upon perturbing the reward, we update the policy by planning based on the estimated transition +and perturbed reward as follows, +πk = {πk +h}h∈[H] = Plan +� +s1, {rk +h,ξ}h∈[H], W k� +. +(9) +We remark that the reward perturbation in (8) is conducted before planning. The perturbed reward +defined in (8) is fixed throughout the planning stage. We summarize PlanEx in Algorithm 1. +4. Theoretical Analysis +In this section, we analyze PlanEx in Algorithm 1. Our key observations are, +• the reward perturbation in PlanEx leads to optimistic planning for at least a constant pro- +portion of the interactions, and +• such partial optimism guaranteed by PlanEx is sufficient for exploration. +4.1. Partial Optimism +In the sequel, we show that PlanEx enjoys a partial optimism. Specifically, the following lemma +holds. +Lemma 4 (Partial Optimism) +Under the good event W ∗ ∈ Gk = {W ∈ RdS×dφ : ∥(W − +W k)Λ1/2 +k +∥2 +2 ≤ βk}, for properly selected σk, it holds with probability at least Φ(−1) that +V ∗ +1 +� +s1; {rh}h∈[H], W ∗� +− V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +≤ 0, +(10) +where Φ(·) is the cumulative distribution function of the standard Gaussian distribution. + +Algorithm 1 Planning with Randomized Reward +Require: Dataset D, rewards {rh}h∈[H]. +1: Initialization: Set Λ1 = λ · I. +2: for k = 1, 2, . . . , K do +3: +Generate a set of independent noise ξk +h ∼ N(0, σ2 +k · Λ−1 +k ) for all h ∈ [H]. +4: +Obtain the perturbed rewards +rk +h,ξ(sh, ah) = {rh(sh, ah) + φ(sh, ah)⊤ξk +h}+, +∀(sh, ah) ∈ S × A, h ∈ [H]. +5: +Obtain the policy πk by calling the planning oracle, +πk = Plan(s1, {rk +h,ξ}h∈[H], W k). +6: +Execute πk to sample a trajectory τ k = {sk +1, ak +1, sk +2, ..., sk +H, ak +H, sk +H+1}. +7: +Update the dataset Dk ← Dk−1 ∪ τ k. +8: +Update the model and covariate matrix +W k+1 ← argmin +W ∈RS×d +H +� +h=1 +k +� +τ=0 +∥sτ +h+1 − Wφ(sτ +h, aτ +h)∥2 +2 + λ · ∥W∥2 +2, +Λk+1 ← Λk + +H +� +h=1 +φ(sk +h, ak +h)φ(sk +h, ak +h)⊤. +9: end for + +EXPLORATION IN MODEL-BASED RL +Proof See §A.2 for a detailed proof. +Lemma 4 ensures that at least Φ(−1) of the value function estimation in PlanEx overestimates +the optimal value function V ∗ +1 (·; {rh}h∈[H], W ∗) that we wish to obtain. As a consequence, the +randomized reward in PlanEx guarantees that at least Φ(−1) of the trajectories contributes to ex- +ploration under the optimism principle. Intuitively, such optimism holds since, (i) on the one hand, +the randomized Gaussian perturbation ensures that the perturbed reward has a sufficiently large +probability to be larger than the true reward, and (ii) on the other hand, the good event Gk ensures +that the value functions estimated under the true model ({rh}h∈[H], W ∗) does not deviate too much +from the value function estimated under the current model ({rh}h∈[H], W k) without perturbation. +4.2. Regret Analysis +We highlight that the optimism guarantee in Lemma 4 alone does not guarantee optimal regret. To +conduct reasonable exploration, in addition to optimism, we need to ensure that the overestimation +induced by perturbed reward does not deviated too far away from the value functions under the true +reward. In our work, we ensure such deviation guarantee by properly incorporating the uncertainty +into the transition dynamics. More specifically, recall that we define the reward perturbation as +follows +rk +h,ξ(sh, ah) = +� +rh(sh, ah) + φ(sh, ah)⊤ξk +h +�+, +∀h ∈ [H], (sh, ah) ∈ S × A, +where the noise {ξk +h}h∈[H] are sampled independently from the Gaussian distribution ξk +h ∼ N(0, σ2 +k· +Λ−1 +k ). Such perturbation introduces the noise ξk +h, whose variance scales with the model uncertainty +Λk. Such reward perturbation ensures that, with a high probability, the bias in value estimation un- +der the perturbed reward scales with the error in transition model estimation in (7). Thus, as long +as we have reasonable model estimation, such as minimizing least-squares error in (7), the overes- +timation induced by perturbed reward is small. Specifically, the following Theorem guarantees that +PlanEx has an optimal regret in K. +Theorem 5 Let λ = 1 and σ2 +k = H3·βk/σ2 with βk specified in Appendix A.1. Under Assumptions +1 and 2, it holds for K > 1/Φ(−1) that +E +� +R(K) +� += O +� +(dS + dφ)3/2 · H7/2 · log2(K) · +√ +K +� +, +where the expectation is taken with respect to the randomized reward perturbation and trajectory +sampling in PlanEx . +Proof See §A.4 for a detailed proof. +We remark that the rate in Theorem 5 is information-theoretically optimal in the number of inter- +actions K with the environment (Jiang et al., 2017). We remark that comparing with the optimal +planning approach such as LC3 (Kakade et al., 2020), PlanEx suffers from extra dependencies in +H, dφ and dS, which arises due to the random perturbation of rewards. In addition, we highlight +that, comparing with PC-MLP (Song and Sun, 2021), our algorithm attains the optimal O( +√ +K) +dependency with respect to K. Such stronger sample efficiency arises as PlanEx does not require +extra sampling to compute policy cover matrix, which is required by PC-MLP. + +Exploration with Model Uncertainty. We remark that the high probability optimism based on +Thompson sampling typically arises in the analysis of randomized value iterations for RL (Russo, +2019; Zanette et al., 2020). In contrast, our work utilizes such idea for model-based exploration. +To understand such counterpart in model-based exploration, we highlight that for both model-based +and model-free exploration, designing provable exploration hinges on incorporating the model un- +certainty into the value functions and its corresponding policy. In value-based approaches such +as LSVI-UCB (Jin et al., 2020), such model uncertainty is estimated via regression of target value +functions on sh+1 with respect to (sh, ah), and is incorporated into value functions as the bonus. In +model-based approaches such as UCRL and its variants (Jaksch et al., 2010; Kakade et al., 2020), +such model uncertainty is characterized by a confidence region of transition dynamics, and is incor- +porated into value functions via optimistic planning. In addition, for algorithms that utilizes policy +cover (Song and Sun, 2021; Agarwal et al., 2020a), such model uncertainty is obtained by aggre- +gating the visitation trajectories of current policies. Our work instantiates such idea by directly +perturbing the reward functions based on model uncertainty, which serves as a primitive view of all +the exploration algorithms. +5. A Generalization with General Function Approximation +A key observation from the design of PlanEx is that sufficient exploration is guaranteed as long as +at least a fixed proportion of iterations are dedicated to exploration with optimism. To further vali- +date such observation, we generalize PlanEx by general function approximation in the sequel. We +summarize the algorithm in Algorithm 2. To conduct our analysis, we assume that the estimation of +transition dynamics is sufficiently accurate and satisfies the following calibrated model assumption. +Algorithm 2 Planning with Randomized Reward +Require: Rewards {rh}h∈[H]. +1: Initialization: Initialize buffer D0 as an empty set. Initialize the transition dynamics P1. +2: for k = 1, 2, . . . , K do +3: +Generate the randomized reward {rk +h,ξ}h∈[H]. +4: +Obtain the policy πk by calling the planning oracle, πk = Plan(s1, {rk +h,ξ}h∈[H], Pk). +5: +Execute πk to sample a trajectory τ k = {sk +1, ak +1, sk +2, ..., sk +H, ak +H, sk +H+1}. +6: +Update the dataset Dk ← Dk−1 ∪ τ k. +7: +Update the transition dynamics Pk+1 based on the dataset Dk. +8: end for +Assumption 6 (Calibrated model) Let Pk be the transition dynamics estimated in the k-th itera- +tion. For all δ > 0 and k ∈ [K], it holds with probability at least 1 − δ that +∥P(· | sh, ah) − Pk(· | sh, ah)∥1 ≤ β(δ) · ιk(sh, ah), +∀k ∈ [K], (sh, ah) ∈ S × A. +Meanwhile, it holds that ιk ≤ 1 for all k ∈ [K]. +Here the parameter β(δ) characterizes the variance in concentration, which typically scales with +log(1/δ). Similar assumption also arises in the analysis under general function approximation (Curi et al., + +EXPLORATION IN MODEL-BASED RL +2020; Kidambi et al., 2021). In addition, we remark that such assumption generalizes various com- +monly adopted parametric models, including the linear MDP model (Jin et al., 2020) and the KNR +model (Kakade et al., 2020) we adopted in previous sections. Correspondingly, we propose the +following complexity metric for the RL problems, +IK = +max +{Dk}k∈[K] +K +� +k=1 +H +� +h=1 +ι2 +k(sk +h, ak +h). +(11) +Here the maximization is taken over all possible dataset {Dk}k∈[K] collected by an online learn- +ing algorithm with |Dk| = H for all k ∈ [K]. We remark that similar complexity metric also +arises in the analysis of model-based RL with general function approximations (Curi et al., 2020; +Kakade et al., 2020; Kidambi et al., 2021). +We cast the following conditions on the reward randomization that ensures sufficient explo- +ration. +Condition 7 ((Optimism)) It holds for the randomized reward function {rk +h,ξ}h∈[H] that +H +� +h=1 +rk +h,ξ(sh, ah) − rh(sh, ah) ≥ H · β(δ) · +H +� +h=1 +ιk(sh, ah), +which holds uniformly for all trajectories {(sh, ah)}h∈[H] with probability at least p0. +Condition 8 ((Concentration of Rewards)) It holds for all δ′ > 0 that |rk +h,ξ − rh| ≤ Cr(δ′) · ιk +with probability at least 1 − δ′ for all (k, h) ∈ [K] × [H], where ιk is defined in Assumption 6. +Intuition Behind Reward Randomization Conditions. We remark that Conditions 7 and 8 are the +key factors for the success of the randomized reward in PlanEx . On the one hand, Condition 7 +ensures that a constant p0 proportion of the evaluations results in optimistic value functions. Such +optimistic value estimation further allows for exploration under the optimism principle. On the +other hand, the concentration condition in Condition 8 ensures that with high probability, the value +function estimated under the randomized reward does not deviate too much from that evaluated +under the true reward. +The following Theorem upper bounds the regret of Algorithm 2 under Assumption 6. +Theorem 9 (Regret Bound) Under Assumption 6, for the randomized reward that satisfies Con- +ditions 7 and 8, the regret of Algorithm 2 is bounded as follows, +E +� +R(K) +� += O +� +Poly +� +Cr(1/K), β(1/K), H +� +· IK · +√ +K +� +. +Proof See §B for the detailed proof. +We remark that for commonly used model parameterization such as linear MDP and KNR, the +parameter β(1/K) typically scales with log(K). Meanwhile, for properly designed reward ran- +domization scheme, the term Cr(1/K) also scales with log(K). Thus, Theorem 18 shows that +Algorithm 2 has a regret bound that scales with �O(IK · +√ +K), which matches the previous regret +bound of exploration under model-based RL (). + +5.1. Design of Randomized Reward +We remark that in practice, the model uncertainty {ιk}k∈[K] defined in Assumption 6 can be esti- +mated based on disagreement of ensemble models. Thus, to instantiate Algorithm 2, it remains to +design proper reward randomization scheme that satisfies Conditions 7 and 8. In what follows, we +present examples of such randomized rewards. +Example 1 (Gaussian Perturbation) Let rk +h,ξ(sk +h, ak +h) = r(sk +h, ak +h) + ξk +h, where {ξk +h}(k,h)∈[K]×[H] +are sampled independently from the Gaussian distribution N(0, σk · ι2 +k(sk +h, ak +h)). Under regulation +conditions specified in §B.2, the randomized reward {rk +h,ξ}(k,h)∈[K]×[H] satisfies Conditions 7 and +8. +Example 2 (Bernoulli Perturbation) +Let rk +h,ξ(sk +h, ak +h) = r(sk +h, ak +h) + ξk +h · σ′ +kιk(sk +h, ak +h), where +ξk +h = 1 with probability 1/2 and ξk +h = −1 with probability 1/2. For the parameters {σ′ +k}(k)∈[K] +specified in §B.2, the randomized reward {rk +h,ξ}(k,h)∈[K]×[H] satisfies Conditions 7 and 8. +A Comparison with Bonus-based Approaches. We remark that our proposed randomized reward +is closely related to the reward bonus for model-based RL, which arises in the recent progress +of exploration under model-based RL (Kidambi et al., 2021; Song and Sun, 2021). Such bonus- +based approaches typically estimate the model uncertainty {ιk}k∈[K] and then design reward bonus +that incorporates such uncertainty estimation. Indeed, one may view the randomized rewards in +Examples 1 and 2 as a randomized generalization of such reward bonus. Specifically, both the +randomized reward and the reward bonus accomplishes exploration with optimism principle. For +randomized reward, such exploration is guaranteed by the partial optimism that we investigated in +§4.1. In contrast, for reward bonus, such exploration is guaranteed by directly enforcing optimism +with bonus. +Given the connections between the reward bonus and randomized reward, one may be prompt +to ask why using randomized reward? We highlight that adding bonus is, in fact, a pessimistic +approach in order to reduce the worst-case regret. Such approach enforces a bonus that deviates +from the true reward, aiming to introduce a bias in value estimations to achieve minimal worst-case +regret. In comparison, randomized reward allows the perturbation to be centered around the true +reward, and yields a milder deviation from the true reward. 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Good Events and Parameters +In what follows, we define the following good events for the analysis. +Definition 10 (Good Events) We define the following good events, +GW k,good = {∥W ∗ − W k∥2 +Λk ≤ βk}, +Gξk,good = {∥ξk +h∥2 +Λk ≤ βk,ξ, +∀h ∈ [H]}, +Gξk,opt = +� +V ∗ +1 +� +s1; {rh}h∈[H], W ∗� +− V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +≤ 0 +� +. +Correspondingly, we further define +GW,good = +� +k∈[K] +GW k,good, +Gξ,good = +� +k∈[K] +Gξk,good. +In the sequel, we follow Lemma 19 and set βk as follows +βk = 2λ · ∥W ∗∥2 +2 + 8σ2� +dS · log(5) + 2 log(k) + log(4) + log +� +det(Λk)/ det(Λ0) +�� +, +where σ is the noise variance that defines the transition dynamics in (5). Correspondingly, we set +the parameter σk in PlanEx as follows, +σ2 +k = H3 · βk/σ2, +Meanwhile, we set the parameter βk,ξ = 2σ2 +k · log(KH/δ) in Definition 10. It thus holds that +P(Gξ,good) ≥ 1 − δ. +A.2. Optimality +In the sequel, we present the optimality analysis of PlanEx , which is inspired by Russo (2019) +and Zanette et al. (2020). +Lemma 11 (Probability of Optimality) Under the good event GW k,good, it holds with probability +at least Φ(−1) that +V ∗ +1 +� +s1; {rh}h∈[H], W ∗� +− V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +≤ 0. +(12) +In other words, it holds that P(Gξk,opt | GW k,good) ≥ Φ(−1). +Proof Note that +V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +− V ∗ +1 +� +s1; {rh}h∈[H], W ∗� +≥ V π∗ +1 +� +s1; {rk +h,ξ}h∈[H], W k� +− V ∗ +1 +� +s1; {rh}h∈[H], W ∗� +, +≥ φ(s1, a1)⊤ξk +1 − E +� +V ∗ +2 +� +s2; {rh}h∈[H], W ∗� ��� s1, a1, W ∗� ++ E +� +V π∗ +2 +� +s2; {rk +h,ξ}h∈[H], W k� ��� s1, a1, W k� +, +(13) + +EXPLORATION IN MODEL-BASED RL +where the second inequality holds since {r1 + φ⊤ξk +1}+ − r1 = max{φ⊤ξk +1, −r1} ≥ φ⊤ξk +1. Here +we denote by π∗ the optimal policy under the model ({rh}h∈[H], W ∗) and a1 the optimal action +a1 = π∗(s1). It further holds that, +E +� +V π∗ +2 +� +s2; {rk +h,ξ}h∈[H], W k� ��� s1, a1, W k� +− E +� +V ∗ +2 +� +s2; {rh}h∈[H], W ∗� ��� s1, a1, W ∗� += E +� +V ∗ +2 +� +s2; {rh}h∈[H], W ∗� ��� s1, a1, W k� +− E +� +V ∗ +2 +� +s2; {rh}h∈[H], W ∗� ��� s1, a1, W ∗� +� +�� +� +(i) ++ E +� +V π∗ +2 +� +s2; {rk +h,ξ}h∈[H], W k� +− V ∗ +2 +� +s2; {rh}h∈[H], W ∗� ��� s1, a1, W k� +� +�� +� +(ii) +. +(14) +By Lemma 20 and the fact that V ∗ +h ≤ H for all h ∈ [H], we upper bound the absolute value of term +(i) as follows, +|(i)| ≤ H · ∥(W k − W ∗)φ(s1, a1)∥2/σ ≤ H · ∥W k − W ∗∥Λl · ∥φ(s1, a1)∥Λ−1 +k . +Thus, under the event GW k,good), it further holds that +|(i)| ≤ +� +βkH2/σ · ∥φ(s1, a1)∥Λ−1 +k . +(15) +By plugging (15) into (14) and further unrolling term (ii) based on similar computation in (13) and +(14), we conclude that +V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +− V ∗ +1 +� +s1; {rh}h∈[H], W ∗� +≥ +H +� +h=1 +E +� +φ(sh, ah)⊤ξk +h − +� +βkH2/σ · ∥φ(sh, ah)∥Λ−1 +k +�� s1, π∗, W k� +. +Note that for any given trajectory {(sh, ah)}h∈[H], it holds that +H +� +h=1 +φ(sh, ah)⊤ξk +h ∼ N(0, σ2 +k,H), +σ2 +k,H = σ2 +k · +H +� +h=1 +∥φ(sh, ah)∥2 +Λ−1 +k . +It then holds from the setup σ2 +k = H3 · βk/σ2 and Cauchy-Schwartz inequality that +σk,H = +� +� +� +�H3 · βk/σ2 · +H +� +h=1 +∥φ(sh, ah)∥2 +Λ−1 +k +≥ +� +βkH2/σ · +H +� +h=1 +∥φ(sh, ah)∥Λ−1 +k . +Thus, for any given trajectory {(sh, ah)}h∈[H], it holds with probability at least Φ(−1) that +H +� +h=1 +φ(sh, ah)⊤ξk +h ≥ σk,H ≥ +� +βkH2/σ · ∥φ(sh, ah)∥Λ−1 +k . + +Hence, upon taking integration with respect to the trajectory under s1, π∗, W k, and the good event +GW k,good, it holds with probability at least Φ(−1) that +V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +− V ∗ +1 +� +s1; {rh}h∈[H], W ∗� +≥ +H +� +h=1 +E +� +φ(sh, ah)⊤ξk +h − +� +βkH2/σ2 · ∥φ(sh, ah)∥Λ−1 +k +�� s1, π∗, W k� +≥ 0. +Thus, we complete the proof of Lemma 11. +Lemma 12 (Optimism Bound) It holds for K > 1/Φ(−1) that +E +� K +� +k=1 +V ∗ +1 +� +s1; {rh}h∈[H], W ∗� +− V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k) +���� GW,good, Gξ,good +� += � +O( +√ +K). +Proof In the sequel, we set δ = 1/K in the good events defined in Definition 10. We fix an arbitrary +k ∈ [K] and upper bound the following difference, +∆k = V ∗ +1 +� +s1; {rh}h∈[H], W ∗� +− V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k). +We construct a noise set {�ξk +h}h∈[H], which is an identical and independent copy of the noise set +{ξk +h}h∈[H]. Correspondingly, we define the good events G�ξ,good and G�ξ,opt in Definition 10. We +further define the optimal value function V �πk +1 +� +s1; {rk +h,�ξ}h∈[H], W k) under the perturbed reward set +{rh + φ⊤�ξk +h}h∈[H] and the transition W k. It thus follows from Lemma 11 that +∆k = V ∗ +1 +� +s1; {rh}h∈[H], W ∗� +− V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k) +≤ E +� +V �πk +1 +� +s1; {rk +h,�ξ}h∈[H], W k) +��� G�ξ,good, G�ξ,opt +� +− V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k). +(16) +We further define the value function corresponding to the minimal perturbation under the good +event Gξ,good as follows, +{ξk +h}h∈[H] = +argmin +∥ξk +h∥2 +Λk ≤βk,ξ +max +π +V π +1 +� +s1; {rh + φ⊤ξk +h}+ +h∈[H], W k� +. +(17) +We define rk +h,ξ = {rh + φ⊤ξk +h}+ the corresponding perturbed reward. We further define πk the +corresponding optimal policy of the model ({rk +h,ξ}h∈[H], W k). Thus, under the good event Gξ,good, +we have +∆k ≤ E +� +V �πk +1 +� +s1; {rk +h,�ξ}h∈[H], W k� +− V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� ��� G�ξ,good, G�ξ,opt +� +. +(18) +Meanwhile, note that under the good event G�ξk,good, we have +V �πk +1 +� +s1; {rk +h,�ξ}h∈[H], W k� +≥ V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +. + +EXPLORATION IN MODEL-BASED RL +In what follows, we write V �πk +1 += V �πk +1 (s1; {rk +h,�ξ}h∈[H], W k) and V πk +1 += V πk +1 (s1; {rk +h,ξ}h∈[H], W k) +for notational simplicity. It holds that +E�ξ +� +V �πk +1 +− V πk +1 +�� G�ξ,good +� += E�ξ +� +V �πk +1 +− V πk +1 +�� G�ξk,good, G�ξk,opt +� +· P(G�ξk,opt | G�ξk,good) ++ E�ξ +� +V �πk +1 +− V πk +1 +�� G�ξk,good, Gc +�ξk,opt +� +· P(Gc +�ξk,opt | G�ξk,good) +≥ E�ξ +� +V �πk +1 +− V πk +1 +�� G�ξk,good, G�ξk,opt +� +· P(G�ξk,opt | G�ξk,good). +(19) +Meanwhile, it follows from Lemma 11 that, under GW,good, +P(G�ξk,opt | G�ξk,good) ≥ P(G�ξk,opt ∩ G�ξk,good) ≥ 1 − P(Gc +�ξk,opt) − P(Gc +�ξk,good) ≥ Φ(−1) − δ. +(20) +By further plugging (19) and (20) into (18), we obtain that +∆k ≤ +� +Φ(−1) − δ +�−1 · E�ξ +� +V �πk +1 +− V πk +1 +�� G�ξk,good +� += +� +Φ(−1) − δ +�−1 · Eξ +� +V πk +1 +− V πk +1 +�� Gξk,good +� +, +(21) +where we use the fact that the noise set {�ξk +h}h∈[H] is an identical and independent copy of the noise +set {ξk +h}h∈[H]. +It now remains to upper bound the difference V πk +1 +− V πk +1 +under the good events Gξ,good and +GW,good. Note that +V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +− V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +≤ V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +− V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +, +(22) +which holds since πk is optimal for the model ({rk +h,ξ}h∈[H], W k). Meanwhile, by adding and sub- +tracting the value function V πk +1 (s1; {rh}h∈[H], W ∗) of πk under the true model ({rh}h∈[H], W ∗) in +(22), we obtain that +V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +− V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +≤ V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +− V πk +1 +� +s1; {rh}h∈[H], W ∗� +� +�� +� +(iii) +(23) ++ V πk +1 +� +s1; {rh}h∈[H], W ∗� +− V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +� +�� +� +(iv) +. +In the sequel, we upper bound terms (iii) and (iv) in (23) under the good events Gξ,good and GW,good, +respectively. + +Upper bound of term (iii). The upper bound is similar to that in the proof of Lemma 13. Note that +(iii) = V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +− V πk +1 +� +s1; {rh}h∈[H], W ∗� += max{φ(s1, a1)⊤ξk +1, −r1(s1, a1)} + φ(s1, a1)⊤ξk +h + E +� +V πk +2 +� +s2; {rk +h,ξ}h∈[H], W k� ��� s1, πk, W k� +− E +� +V πk +2 +� +s2; {rh}h∈[H], W ∗� ��� s1, πk, W ∗� +≤ ∥φ(s1, a1)∥Λ−1 +k +· ∥ξk +1∥Λk + ∆k +ξ,1 +(24) ++ E +� +V πk +2 +� +s2; {rk +h,ξ}h∈[H], W k� +− V πk +2 +� +s2; {rh}h∈[H], W ∗� ��� s1, πk, W ∗� +, +where the inequality follows from Cauchy-Schwartz inequality and the fact that r1 ≥ 0. Here we +define a1 = πk(s1) and +∆k +ξ,1 = E +� +V πk +2 +� +s2; {rk +h,ξ}h∈[H], W k� ��� s1, πk, W k� +− E +� +V πk +2 +� +s2; {rk +h,ξ}h∈[H], W k� ��� s1, πk, W ∗� +. +Note that under the good event Gξ,good, it holds for all (sh, ah) ∈ S × A and h ∈ [H] that +rk +h,ξ(sh, ah) ≤ r(sh, ah) + |φ(sh, ah)⊤ξk +h| ≤ 1 + ∥φ(sh, ah)∥Λ−1 +k +· ∥ξk +h∥Λk +≤ 1 + +� +βk,ξ/(λ2H). +Thus, it holds under the good event Gξ,good that +0 ≤ V πk +2 +� +s2; {rk +h,ξ}h∈[H], W k� +≤ H · +� +1 + +� +βk,ξ/(λ2H) +� += H + +� +βk,ξH/λ. +(25) +By Lemma 20, it further holds under good events Gξ,good and GW,good that +∆k +ξ,1 = E +� +V πk +2 +� +s2; {rk +h,ξ}h∈[H], W k� ��� s1, πk, W k� +− E +� +V πk +2 +� +s2; {rk +h,ξ}h∈[H], W k� ��� s1, πk, W ∗� +. +≤ +� +H + +� +βk,ξH/λ +� +· σ−1 · ∥(W k − W ∗)φ(s1, a1)∥2 +≤ +� +H + +� +βk,ξH/λ +� +· σ−1 · ∥W k − W ∗∥Λk · ∥φ(s1, a1)∥Λ−1 +k +≤ +� +H + +� +βk,ξH/λ +� +· σ−1 · +� +βk · ∥φ(s1, a1)∥Λ−1 +k . +(26) +Here the first inequality follows from Lemma 20 and the bounds in (25), the second inequality +follows from Cauchy-Schwartz inequality, and the third inequality follows from the definition of +the good event GW,good in Definition 10. Plugging (26) and the definition of the good event Gξ,good +into (24), we obtain that +(iii) ≤ Ck · ∥φ(s1, a1)∥Λ−1 +k +(27) ++ E +� +V πk +2 +� +s2; {rk +h,ξ}h∈[H], W k� +− V πk +2 +� +s2; {rh}h∈[H], W ∗� ��� s1, πk, W ∗� +, +where we define +Ck = +� +H + +� +βk,ξH/λ +� +· σ−1 · +� +βk + +� +βk,ξ. + +EXPLORATION IN MODEL-BASED RL +By further unrolling (27), we conclude that, under the good events Gξ,good and GW,good, we have +(iii) ≤ E +� H +� +h=1 +Ck · ∥φ(sh, ah)∥Λ−1 +k +���� s1, πk, W ∗, Gξk,good, GW k,good +� +. +(28) +Upper bound of term (iv). The upper bound of term (iv) is similar that of term (iii). Note that +(iv) = V πk +1 +� +s1; {rh}h∈[H], W ∗� +− V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� += min +� +−φ(s1, a1)⊤ξk +h, r1(s1, a1) +� ++ E +� +V πk +2 +� +s2; {rh}h∈[H], W ∗� ��� s1, πk, W ∗� +− E +� +V πk +2 +� +s2; {rk +h,ξ}h∈[H], W k� ��� s1, πk, W k� +≤ −φ(s1, a1)⊤ξk +h + ∆k +ξ,1 ++ E +� +V πk +2 +� +s2; {rh}h∈[H], W ∗� +− V πk +2 +� +s2; {rk +h,ξ}h∈[H], W k� ��� s1, πk, W ∗� +, +where we define +∆k +ξ,1 = E +� +V πk +2 +� +s2; {rk +h,ξ}h∈[H], W ∗� ��� s1, πk, W k� +− E +� +V πk +2 +� +s2; {rk +h,ξ}h∈[H], W k� ��� s1, πk, W k� +. +By the definition of the minimal perturbation in (17), it holds that ∥ξk +h∥Λk ≤ βξ for all (h, k) ∈ +[H] × [K]. Thus, we have +−φ(s1, a1)⊤ξk +h ≤ βk,ξ · ∥φ(s1, a1)∥Λ−1 +k . +The rest of the computation is almost identical to that in (iii). We omit the computation for simplicity +and conclude that, under good events Gξ,good and GW,good, we have +(iv) ≤ E +� H +� +h=1 +Ck · ∥φ(sh, ah)∥Λ−1 +k +���� s1, πk, W ∗, Gξk,good, GW k,good +� +, +(29) +where we define +Ck = +� +H + +� +βk,ξH/λ +� +· σ−1 · +� +βk + +� +βk,ξ. +(30) +Thus, by plugging (28) and (29) into (23), we conclude that +E[∆k | GW,good, Gξ,good] ≤ +� +Φ(−1) − δ +�−1 · Eξ +� +V πk +1 +− V πk +1 +�� GW k,good, Gξk,good +� +≤ +� +Φ(−1) − δ +�−1 · Cmax · E +� H +� +h=1 +∥φ(sk +h, ak +h)∥Λ−1 +k +����GW k,good, Gξk,good +� +, +where we define +Cmax = CK = +� +H + +� +βK,ξH/λ +� +· σ−1 · +� +βK + +� +βK,ξ ≥ Ck, +∀k ∈ [K], + +and the expectation is taken with respect to the trajectories of πk under the transition defined by +W ∗. Recall that we set λ = 1, δ = 1/K, and σk = H3 · βk/σ2. Thus, under Assumption 1, we +obtain that +βK = O +� +H + dS + log(K) + dφ · log(K) +� +, +βK,ξ = 2σ2 +K · log(K/δ) = O +� +H4 · log(KH) + (dS + dφ) · H3 · log2(KH) +� +. +Thus, upon computation, we have +Cmax = O +� +(dS + dφ) · H3 · log3/2(KH) +� +. +Finally, it holds that +E +� K +� +k=1 +V ∗ +1 +� +s1; {rh}h∈[H], W ∗� +− V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k) +���� GW,good, Gξ,good +� +≤ +� +Φ(−1) − 1/K +�−1 · Cmax · E +� K +� +k=1 +H +� +h=1 +∥φ(sk +h, ak +h)∥Λ−1 +k +����GW,good, Gξ,good +� +≤ +� +Φ(−1) − 1/K +�−1 · Cmax · E +�� +HK · +K +� +k=1 +H +� +h=1 +∥φ(sk +h, ak +h)∥2 +Λ−1 +k +�1/2 ����GW,good, Gξ,good +� += O +� +(dS + dφ)3/2 · H7/2 · log2(KH) · +√ +K +� +, +where the expectation is taken with respect to the trajectories of {πk}k∈[K] under the true transition +defined by W ∗, and the last inequality follows from Lemma 21 and the fact that log det(ΛK+1) ≤ +dφ · log K. Thus, we complete the proof of Lemma 12. +A.3. Estimation Error +Lemma 13 (Estimation Error Bound) It holds for K > 1/Φ(−1) that +E +� K +� +k=1 +V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +− V πk +1 +� +s1; {rh}h∈[H], W ∗) +���� GW,good, Gξ,good +� += � +O( +√ +K). +Proof Note that +V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +− V πk +1 +� +s1; {rh}h∈[H], W ∗� += max{φ(s1, a1)⊤ξk +1, −r1(s1, a1)} + φ(s1, a1)⊤ξk +h + E +� +V πk +2 +� +s2; {rk +h,ξ}h∈[H], W k� ��� s1, πk, W k� +− E +� +V πk +2 +� +s2; {rh}h∈[H], W ∗� ��� s1, πk, W ∗� +≤ ∥φ(s1, a1)∥Λ−1 +k +· ∥ξk +1∥Λk + ∆k +ξ,1 +(31) ++ E +� +V πk +2 +� +s2; {rk +h,ξ}h∈[H], W k� +− V πk +2 +� +s2; {rh}h∈[H], W ∗� ��� s1, πk, W ∗� +, + +EXPLORATION IN MODEL-BASED RL +where the inequality follows from Cauchy-Schwartz inequality and the fact that r1 ≥ 0. Here we +define a1 = πk(s1) and +∆k +ξ,1 = E +� +V πk +2 +� +s2; {rk +h,ξ}h∈[H], W k� ��� s1, πk, W k� +− E +� +V πk +2 +� +s2; {rk +h,ξ}h∈[H], W k� ��� s1, πk, W ∗� +. +Note that under the good event Gξ,good, it holds for all (sh, ah) ∈ S × A and h ∈ [H] that +rk +h,ξ(sh, ah) ≤ r(sh, ah) + |φ(sh, ah)⊤ξk +h| ≤ 1 + ∥φ(sh, ah)∥Λ−1 +k +· ∥ξk +h∥Λk +≤ 1 + βξ/λ. +Thus, it holds under the good event Gξ,good that +0 ≤ V πk +2 +� +s2; {rk +h,ξ}h∈[H], W k� +≤ H · (1 + βξ/λ). +(32) +By Lemma 20, it further holds under good events Gξ,good and GW,good that +∆k +ξ,1 = E +� +V πk +2 +� +s2; {rk +h,ξ}h∈[H], W k� ��� s1, πk, W k� +− E +� +V πk +2 +� +s2; {rk +h,ξ}h∈[H], W k� ��� s1, πk, W ∗� +. +≤ H · (1 + βξ/λ)/σ · ∥(W k − W ∗)φ(s1, a1)∥2 +≤ H · (1 + βξ/λ)/σ · ∥W k − W ∗∥Λk · ∥φ(s1, a1)∥Λ−1 +k +≤ H · (1 + βξ/λ)/σ · βk · ∥φ(s1, a1)∥Λ−1 +k . +(33) +Here the first inequality follows from Lemma 20 and the bounds in (32), the second inequality +follows from Cauchy-Schwartz inequality, and the third inequality follows from the definition of +the good event GW,good in Definition 10. Plugging (33) and the definition of the good event Gξ,good +into (31), we obtain that +V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +− V πk +1 +� +s1; {rh}h∈[H], W ∗� +≤ Ck · ∥φ(s1, a1)∥Λ−1 +k ++ E +� +V πk +2 +� +s2; {rk +h,ξ}h∈[H], W k� +− V πk +2 +� +s2; {rh}h∈[H], W ∗� ��� s1, πk, W ∗� +, +where Ck is defined in (30). By further unrolling (27) and summing over k ∈ [K], we conclude that +K +� +k=1 +V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +− V πk +1 +� +s1; {rh}h∈[H], W ∗� +≤ E +� K +� +k=1 +H +� +h=1 +Ck · ∥φ(sk +h, ak +h)∥Λ−1 +k +���� GW k,good, Gξk,good +� +, +where the expectation is taken with respect to the trajectories of {πk}k∈[K] under the true transi- +tion defined by W ∗. The rest of the computation is identical to that of Lemma 12. We omit the +computation and conclude that +E +� K +� +k=1 +V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +− V πk +1 +� +s1; {rh}h∈[H], W ∗) +���� GW,good, Gξ,good +� += � +O( +√ +K). + +A.4. Regret Analysis +Theorem 14 (Expected Regret Bound) +We set λ = 1 and σk as in §A.1. It holds for K > +1/Φ(−1) that +E +� +R(K) +� += O +� +(dS + dφ)3/2 · H7/2 · log2(KH) · +√ +K +� +. +Proof It holds that +E +� +R(K) +� += E +� K +� +k=1 +V ∗ +1 +� +s1; {rh}h∈[H], W ∗� +− V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k) ++ V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +− V πk +1 +� +s1; {rh}h∈[H], W ∗) +� +. +Thus, we have +E +� +R(K) +� +≤ Opt + Est + Vmax · +K +� +k=1 +� +P(Gc +W k,good) +� ++ Vmax · K · P(Gc +ξ,good), +(34) +where we define +Opt = E +� K +� +k=1 +V ∗ +1 +� +s1; {rh}h∈[H], W ∗� +− V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k) +���� GW,good, Gξ,good +� +, +Est = E +� K +� +k=1 +V πk +1 +� +s1; {rk +h,ξ}h∈[H], W k� +− V πk +1 +� +s1; {rh}h∈[H], W ∗) +���� GW,good, Gξ,good +� +. +Plugging the bounds of Opt and Est in Lemmas 12 and 13, respectively, the fact that Vmax = H, +and δ = 1/T into (34), we conclude that +E +� +R(K) +� += O +� +(dS + dφ)3/2 · H7/2 · log2(KH) · +√ +K +� +. +Thus, we completes the proof of Theorem 14. +Appendix B. Proof of Result in §5 +In this section, we present the proofs of results in §5. +B.1. Regret Analysis +Similar to the proofs in §A, we define the good event Ggood as follows, +Ggood = +� +|rh − rk +h,ξ| ≤ Cr(δ′) · ιk, +∥P(· | s, a) − Pk(· | s, a)∥1 ≤ βk(δ) · ιk(s, a), +∀(k, h) ∈ [K] × [H], (s, a) ∈ S × A +� +. +Under Assumption 6, it holds for the randomized reward satisfying Condition 7 that P(Ggood) ≥ +1 − δ′ − δ. + +EXPLORATION IN MODEL-BASED RL +Lemma 15 (Probability of Optimality) Under Assumptions 6 and the good event Ggood, it holds +for the randomized reward satisfying Condition 7 that +V ∗ +1 +� +s1; {rh}h∈[H], P +� +≤ V πk +1 +� +s1; {rk +h,ξ}h∈[H], Pk) ≥ 1/2 +with probability at least p0. +Proof The proof is similar to that for Lemma 11. Note that +V πk +1 +� +s1; {rk +h,ξ}h∈[H], Pk) − V ∗ +1 +� +s1; {rh}h∈[H], P +� +≥ V π∗ +1 +� +s1; {rk +h,ξ}h∈[H], Pk) − V ∗� +s1; {rh}h∈[H], P +� += rk +h,ξ +� +s1, π∗(s1) +� +− rh +� +s1, π∗(s1) +� ++ E +� +V π∗ +2 +� +s2; {rk +h,ξ}h∈[H], Pk) +��� s1, π∗, Pk� +− E +� +V ∗ +2 +� +s2; {rh}h∈[H], P +� ��� s1, π∗, P +� +, +(35) +where we denote by π∗ the optimal policy under the environment defined by ({rh}h∈[H], P), and the +first inequality follows from the optimality of πk under the environment defined by ({rk +h,ξ}h∈[H], Pk). +Meanwhile, it holds that +E +� +V π∗ +2 +� +s2; {rk +h,ξ}h∈[H], Pk) +��� s1, π∗, Pk� +− E +� +V ∗ +2 +� +s2; {rh}h∈[H], P +� ��� s1, π∗, P +� += E +� +V ∗ +2 +� +s2; {rh}h∈[H], P +� ��� s1, π∗, Pk� +− E +� +V ∗ +2 +� +s2; {rh}h∈[H], P +� ��� s1, π∗, P +� +� +�� +� +(i) ++ E +� +V π∗ +2 +� +s2; {rk +h,ξ}h∈[H], Pk) − V ∗ +2 +� +s2; {rh}h∈[H], P +� ��� s1, π∗, Pk� +� +�� +� +(ii) +. +(36) +By Assumption 6, H¨older’s inequality, and the fact that V ∗ +1 ≤ H, it holds under the good event +Ggood that +|(i)| ≤ E +� +H · ∥(P − Pk)(· | s1, a1)∥1 +�� s1, π∗� +≤ E +� +H · β(δ) · ιk(s1, a1) +�� s1, π∗� +. +By further unrolling term (ii) in (36), we conclude from (35) that +V πk +1 +� +s1; {rk +h,ξ}h∈[H], Pk) − V ∗ +1 +� +s1; {rh}h∈[H], P +� +≥ E +� H +� +h=1 +rk +h,ξ(s1, a1) − rh(s1, a1) − H · βk +H +� +h=1 +ιk(sh, ah) +����� s1, π∗, Pk +� +. +Thus, under the optimism condition in Condition 7, it holds that +V πk +1 +� +s1; {rk +h,ξ}h∈[H], Pk) − V ∗ +1 +� +s1; {rh}h∈[H], P +� +≥ 0 +with probability at least p0 − δ. + +Lemma 16 (Optimism Bound) For δ′ ≤ p0, it holds with probability at least 1 − δ − δ′ that +E +� K +� +k=1 +V ∗ +1 +� +s1; {rh}h∈[H], P +� +− V πk +1 +� +s1; {rk +h,ξ}h∈[H], Pk) +���� Ggood +� += O +� +C(δ, δ′) · IK · +√ +K +� +, +where we define C(δ, δ′) = Cr(δ′) + H · (1 + Cr(δ′)) · β(δ). +Proof The proof is similar to that of Lemma 12 in §A.2. We define the following minimal perturbed +value function, +V πk +1 += argmin +�r∈Ggood +argmax +π +V π +1 +� +s1; {�rh}h∈[H], Pk� +. +Following the same computation as in the proof of Lemma 12, we obtain that +E +� K +� +k=1 +V ∗ +1 +� +s1; {rh}h∈[H], P +� +− V πk +1 +� +s1; {rk +h,ξ}h∈[H], Pk) +���� Ggood +� +≤ (p0 − δ)−1 · E +� K +� +k=1 +V πk +1 +� +s1; {rk +h,ξ}h∈[H], Pk) − V πk +1 +� +s1; {�rh}h∈[H], Pk) +���� Ggood +� +� +�� +� +∆k +. +(37) +By further adding and subtracting V πk(s1; {rh}, P), we obtain that +∆k = E +� K +� +k=1 +V πk +1 +� +s1; {rk +h,ξ}h∈[H], Pk) − V πk(s1; {rh}, P) +���� Ggood +� +� +�� +� +(iii) ++ E +� K +� +k=1 +V πk(s1; {rh}, P) − V πk +1 +� +s1; {�rh}h∈[H], Pk) +���� Ggood +� +� +�� +� +(iv) +. +(38) +Thus, upon a similar computation to that in §A.2, under the good event Ggood, it further holds that +V πk +1 +� +s1; {rk +h,ξ}h∈[H], Pk) − V πk(s1; {rh}, P) ≤ E +� +C(δ, δ′) +H +� +h=1 +ιk(sh, ah) +���� s1, πk, P +� +, +where we define +C(δ, δ′) = Cr(δ′) + H · +� +1 + Cr(δ′) +� +· β(δ). +Here we use the fact that ∥V πk +h +� +·; {rk +h,ξ}h∈[H], Pk)∥∞ ≤ H · (1 + Cr(δ′)) under the good event +Ggood. The same bound holds for term (iv) in (38) following the fact that �r ∈ Ggood. Thus, by + +EXPLORATION IN MODEL-BASED RL +plugging (37) into (37), we conclude that +E +� K +� +k=1 +V ∗ +1 +� +s1; {rh}h∈[H], P +� +− V πk +1 +� +s1; {rk +h,ξ}h∈[H], Pk) +���� Ggood +� +≤ C(δ, δ′) · (p0 − δ)−1 · E +� K +� +k=1 +H +� +h=1 +Ck · σk(sh, ah) +���� Ggood +� +≤ C(δ, δ′) · (p0 − δ)−1 · +√ +HK · E +�� H +� +h=1 +ι2 +k(sh, ah) +�1/2 ����� Ggood +� +, +By further plugging into the definition of IK in (11), we obtain that +E +� K +� +k=1 +V ∗ +1 +� +s1; {rh}h∈[H], P +� +− V πk +1 +� +s1; {rk +h,ξ}h∈[H], Pk) +���� Ggood +� += O +� +C(δ, δ′) · IK · +√ +K +� +, +which concludes the proof of Lemma 16. +Lemma 17 (Estimation Error Bound) It holds that +E +� K +� +k=1 +V πk +1 +� +s1; {rk +h,ξ}h∈[H], Pk) − V πk +1 +� +s1; {rh}h∈[H], P) +���� Ggood +� += O +� +C(δ, δ′) · IK · +√ +K +� +. +Proof Under the good event Ggood, it holds that +V πk +1 +� +s1; {rk +h,ξ}h∈[H], Pk) − V πk +1 +� +s1; {rh}h∈[H], P) +≤ Cr · σk(s1, a1) + E +� +V πk +2 +� +s2; {rk +h,ξ}h∈[H], Pk) +��� s1, πk, Pk� +− E +� +V πk +2 +� +s2; {rh}h∈[H], P) +�� s1, πk, P +� +≤ Cr · σk(s1, a1) + ∆k +ξ,1 ++ E +� +V πk +2 +� +s2; {rk +h,ξ}h∈[H], Pk) − V πk +2 +� +s2; {rh}h∈[H], P) +�� s1, πk, P +� +, +(39) +where we define a1 = πk +1(s1) and +∆k +ξ,1 = E +� +V πk +2 +� +s2; {rk +h,ξ}h∈[H], Pk) +��� s1, πk, Pk� +− E +� +V πk +2 +� +s2; {rk +h,ξ}h∈[H], Pk) +��� s1, πk, P +� +. +Under the good event Ggood, it holds from H¨older’s inequality that +∆k +ξ,1 ≤ H · +� +1 + Cr(δ′) +� +· βk · ιk(s1, a1). +(40) +By plugging (40) into (39) and further unrolling (39), we obtain that, under the good event Ggood, +V πk +1 +� +s1; {rk +h,ξ}h∈[H], Pk) − V πk +1 +� +s1; {rh}h∈[H], P) +≤ C(δ, δ′) · E +� H +� +h=1 +ιk(sh, ah) +�� s1, πk, P +� +, +(41) + +where we define C(δ, δ′) = Cr(δ′) + H · (1+ Cr(δ′)) · β(δ). Thus, by summing (41) over k ∈ [K], +we obtain that +E +� K +� +k=1 +V πk +1 +� +s1; {rk +h,ξ}h∈[H], Pk) − V πk +1 +� +s1; {rh}h∈[H], P) +���� Ggood +� +≤ C(δ, δ′) · E +� K +� +k=1 +H +� +h=1 +σk(sk +h, ak +h) +���� Ggood +� +≤ C(δ, δ′) · +√ +HK · IK, +where IK is defined in (11). Thus, we complete the proof of Lemma 17. +Theorem 18 (Regret Bound) Let δ = δ′ = 1/K. Under Assumption 6, for the randomized reward +that satisfies Conditions 7 and 8, we have +E +� +R(K) +� += O +�� +Cr(1/K) + H · +� +1 + Cr(1/K) +� +· β(1/K) +� +· +√ +H2K · IK +� +. +Proof Combining Lemmas 16 and 17, it holds that +E +� K +� +k=1 +V ∗ +1 +� +s1; {rh}h∈[H], P +� +− V πk +1 +� +s1; {rh}h∈[H], Pk) +���� Ggood +� += O +� +C(δ, δ′) · IK · +√ +K +� +. (42) +Meanwhile, under Assumption 6, it holds for rewards that satisfies 8 that P(Ggood)1 − δ − δ′. Thus, +for δ = δ′ = 1/K, we have +E +� K +� +k=1 +V ∗ +1 +� +s1; {rh}h∈[H], P +� +− V πk +1 +� +s1; {rh}h∈[H], Pk) +���� Gc +good +� +≤ 2K · (δ + δ′) = 4. +(43) +Combining (42) and (43), it holds that +E +� +R(K) +� += O +� +C(1/K, 1/K) · +√ +H2K · IK +� += O +�� +Cr(1/K) + H · +� +1 + Cr(1/K) +� +· β(1/K) +� +· +√ +H2K · IK +� +, +which concludes the proof of Theorem 18. +B.2. Verification of Example +In the sequel, we verify that Examples 1 and 2 satisfies Conditions 7 and 8. +Example 3 (Gaussian Reward) Let +rk +h,ξ(sh, ah) ∼ N +� +rh(sh, ah), H · β(δ) · σ2 +k(sh, ah) +� +, +which are sampled independently over (sh, ah) ∈ S × A. It holds that the probability of +H +� +h=1 +rk +h,ξ(sh, ah) − rh(sh, ah) ≥ H · β(δ) +H +� +h=1 +σk(sh, ah) + +EXPLORATION IN MODEL-BASED RL +is greater than the following event, +N +� +0, H · +H +� +h=1 +σ2 +k(sh, ah) +� +≥ +� +� +� +�H · β(δ) +H +� +h=1 +σ2 +k(sh, ah), +which holds with probability at least Φ(−1). In addition, if r/σk are lipschitz functions of (s, a) ∈ +S × A and S × A has a covering number CS×A under the same metric, it further holds that +|rk +h,ξ −rh| ≤ +� +H · β(δ) · log(CS×A · HK/δ′)·σk with probability at least 1−δ′. Thus, Conditions +7 and 8 are satisfied. +Example 4 (Bernoulli Reward) Let +rk +h,ǫ(sh, ah) ∼ r(sh, ah) + 2 +√ +H · β(δ) · σk(sh, ah) · ǫh, +where ǫh = 1 with probability 1/2 and ǫh = −1 with probability 1/2. For any trajectory τ, it holds +from the Khintchine’s inequality (Veraar, 2010) that +H +� +h=1 +√ +H · β(δ) · σk(sh, ah) · ǫh/S(τ) ≥ 1/2 +with probability at least p0 = 3/16, where we define +S(τ) = H +H +� +h=1 +β2(δ) · σ2 +k(sh, ah). +Thus, it holds that +H +� +h=1 +rk +h,ǫ(sh, ah) − r(sh, ah) ≥ 2 +H +� +h=1 +√ +H · β(δ) · σk(sh, ah) · ǫh +≥ S(τ) ≥ +H +� +h=1 +β(δ) · σk(sh, ah) +with probability at least p0 = 3/16. In addition, it holds that |rk +h,ǫ(sh, ah) − r(sh, ah)| ≤ 2 +√ +H · +β(δ) · σk(sh, ah). Thus, Conditions 7 and 8 are satisfied. +Appendix C. Auxiliary Lemma +Lemma 19 (Concentration of Self-normalized Process (Abbasi-Yadkori et al., 2011; Kakade et al., 2020)) +It holds for +βk = 2λ · ∥W ∗∥2 +2 + 8σ2� +dS · log(5) + 2 log(k) + log(4) + log +� +det(Λk)/ det(Λ0) +�� +that +∞ +� +k=0 +P(Gc +W k,good) = +∞ +� +k=0 +P +� +∥W k − W ∗∥2 +Λk ≥ βk +� +≤ 1/2. + +Proof See Kakade et al. (2020) for a detailed proof. +Lemma 20 (Expected Difference Under Two Gaussian (Kakade et al., 2020)) Let z1 ∼ N(µ1, σ2) +and z2 ∼ N(µ2, σ2) be two Gaussian random variables. Let g be a positive measurable function. +It holds that +Ez1∼N(µ1,σ2) +� +g(z1) +� +− Ez2∼N(µ1,σ2) +� +g(z2) +� +≤ min{∥µ1 − µ2∥2/σ, 1} · +� +Ez1∼N(µ1,σ2) +� +g2(z1) +� +. +Proof See Kakade et al. (2020) for a detailed proof. +Lemma 21 (Elliptical Potential Lemma (Kakade et al., 2020)) Let ∥φk +h∥2 ≤ 1/ +√ +H for all (k, h) ∈ +[K] × [H]. Let Λ1 = I and Λk+1 = Λk + �H +h=1 φk +h(φk +h)⊤. It holds that +K +� +k=1 +H +� +h=1 +∥φk +h∥2 +Λ−1 +k +≤ 2 log +� +det(ΛK+1) · det(Λ0)−1� +. +Proof Note that we have Λk ≻ Λ1 = I. It thus holds that +0 ≤ +H +� +h=1 +(φk +h)⊤Λ−1 +k φk +h ≤ +H +� +h=1 +∥φk +h∥2 +2 ≤ 1, +∀k ∈ [K]. +Meanwhile, since x ≤ 2 log(1 + x) for x ∈ [0, 1], we have +2 log +� +1 + +H +� +h=1 +(φk +h)⊤Λ−1 +k φk +h +� +≥ +H +� +h=1 +(φk +h)⊤Λ−1 +k φk +h. +(44) +On the other hand, it follows from matrix determinant lemma that +log det(Λk+1) − log det(Λk) = log det +� +I + Λ−1/2 +k +H +� +h=1 +(φk +h)(φk +h)⊤Λ−1/2 +k +� +�� +� +Ξk +� +. +Let {σi}i∈[d] be the eigenvalues of the matrix Ξk. It holds that σi > 0 for all i ∈ [d] and +log det(I + Ξk) = log Πi∈[d](1 + σi) ≥ log +� +1 + +� +i∈[d] +σi +� += log det +� +1 + Tr(Ξk) +� +. +Thus, we have +log det(Λk+1) − log det(Λk) = log det(I + Ξk) ≥ log det +� +1 + Tr(Ξk) +� += log +� +1 + +H +� +h=1 +Tr +� +Λ−1/2 +k +(φk +h)(φk +h)⊤Λ−1/2 +k +�� += log +� +1 + +H +� +h=1 +(φk +h)⊤Λ−1 +k φk +h +� +. +(45) + +EXPLORATION IN MODEL-BASED RL +Combining (44) and (45), we conclude that +K +� +k=1 +H +� +h=1 +∥φk +h∥2 +Λ−1 +k +≤ +K +� +k=1 +log det(Λk+1) − log det(Λk) = 2 log +� +det(ΛK+1) · det(Λ0)−1� +, +which concludes the proof of Lemma 20. + diff --git a/K9E1T4oBgHgl3EQfYwRv/content/tmp_files/load_file.txt b/K9E1T4oBgHgl3EQfYwRv/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..81e02f16ecb7d3a9ac1cc4f758c864d618dd6e6e --- /dev/null +++ b/K9E1T4oBgHgl3EQfYwRv/content/tmp_files/load_file.txt @@ -0,0 +1,911 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf,len=910 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='03142v1 [stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='ML] 9 Jan 2023 – Exploration in Model-based Reinforcement Learning with Randomized Reward .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Lingxiao Wang, Ping Li .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Cognitive Computing Lab .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Baidu Research .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 10900 NE 8th St, Bellevue, WA 98004, USA Abstract 1Model-based Reinforcement Learning (MBRL) has been widely adapted due to its sample effi- ciency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' However, existing worst-case regret analysis typically requires optimistic planning, which is not realistic in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In contrast, motivated by the theory, empirical study utilizes ensemble of models, which achieve state-of-the-art performance on various testing environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Such devia- tion between theory and empirical study leads us to question whether randomized model ensemble guarantee optimism, and hence the optimal worst-case regret?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' This paper partially answers such question from the perspective of reward randomization, a scarcely explored direction of exploration with MBRL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We show that under the kernelized linear regulator (KNR) model, reward randomiza- tion guarantees a partial optimism, which further yields a near-optimal worst-case regret in terms of the number of interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We further extend our theory to generalized function approximation and identified conditions for reward randomization to attain provably efficient exploration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Corre- spondingly, we propose concrete examples of efficient reward randomization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' To the best of our knowledge, our analysis establishes the first worst-case regret analysis on randomized MBRL with function approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' This manuscript was completed in September 2021 while both authors worked at Baidu Cognitive Computing Lab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' © .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Introduction Reinforcement learning (RL) (Sutton and Barto, 2018) aims to learn the optimal policy by iteratively interacting with the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Model-based reinforcement learning (MBRL) (Osband and Roy, 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Luo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Ha and Schmidhuber, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Luo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Sun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Kaiser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Ayoub et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020) achieves such a goal by fitting the environment from the observation and obtaining the policy from the fitted environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Incorporated with deep learn- ing, MBRL has achieved tremendous success in real-world tasks, including video games (Ha and Schmidhuber, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Kaiser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020) and control tasks (Watter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Williams et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Chua et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Hafner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Song and Sun, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' A key factor to the success of MBRL is sample efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In terms of the theoretical analysis, such sample efficiency is characterized by the regret analysis of MBRL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Previous analysis sug- gests that when incorporated with exploration strategies, MBRL enjoys a near-optimal �O( √ T) re- gret (Jaksch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Ayoub et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020), where T is the total number of in- teractions with the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' However, previous provably efficient exploration typically utilizes optimistic planning (Jaksch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Luo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Ayoub et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Such exploration strategy requires (i) identifying a confidence set of models D, which captures the uncertainty in model estimation, and then (ii) conducting optimistic planning by searching for the maximal policy among all possible models within D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' The key to the success of optimistic planning is optimism under the face of the uncertainty principle (Jaksch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Intuitively, optimistic planning encourages the agent to explore less visited areas, hence enhancing the sample complex- ity of the corresponding RL algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' While step (i) is realizable with ensemble techniques, step (ii) is in general impossible to implement, as it requires solving an optimization problem over a possibly continuous space of models D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' As an alternative, previous empirical study (Chua et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Pathak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2017, 2019) typically borrows the idea from optimistic planning and the study of Thompson sampling (TS) based algorithm (Osband and Roy, 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' A common empirical approach is to utilize model ensembles to capture the uncertainty of model estimations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Such ensembles are further utilized in planning through TS (Chua et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2018) or bonus construction (Pathak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2017, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Unlike optimistic planning, such approaches typically do not have a worst-case regret guarantee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Nevertheless, they attain state-of-the-art performance in various testing environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Such deviation from theory and practice motivates us to propose this question: Does randomized model ensemble guarantees optimism, and hence the optimal worst-case regret?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In this paper, we provide a partial solution to the above question from reward randomization, a relatively less studied method for exploration in MBRL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We initiate our analysis under the kernelized linear regulator (KNR) transition model (Mania et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Song and Sun, 2021) and known reward functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We propose PlanEx , which conducts exploration by itera- tively planning with the fitted transition model and a randomized reward function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We further show that PlanEx attains the near-optimal �O( √ T) regret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' A key observation of reward randomization is a notion of partial optimism (Russo, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Zanette et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020), which ensures that a sufficient amount of interactions are devoted to exploration under the optimism principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Motivated by the analysis under the KNR transition model, we extend PlanEx to general function approximation with calibrated model (Curi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Kidambi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2021) and propose a generic design princi- ple of reward randomization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We further propose concrete examples of valid reward randomization EXPLORATION IN MODEL-BASED RL and demonstrate the effectiveness of reward randomization theoretically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We highlight that the pro- posed reward randomization method can be easily implemented based on the model ensembles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In addition, the reward randomization is highly modular and can be incorporated with various SOTA baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Our work provides a partial solution to the question we raised.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Specifically, we investigate reward randomization and propose PlanEx .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Our contributions are as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We propose PlanEx , a novel exploration algorithm for MBPO with worst-case regret guar- antee that is realizable with general function parameterizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We show that PlanEx has near-optimal worst-case regret under the KNR dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' To the best of our knowledge, our analysis establishes the first worst-case regret analysis on ran- domized MBRL with function approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Related Work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Our work is closely related to the regret analysis of MBRL and online control problem (Osband and Roy, 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Luo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Sun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Lu and Roy, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Ayoub et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Curi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Agarwal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Song and Sun, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Ayoub et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2020) propose the value-target regression (VTR) algorithm, which focuses on the aspects of the transition model that are relevant to RL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Agarwal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2020b) propose FLAMBE, a provably effi- cient MBRL algorithm under the linear MDP setting (Jin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Yang and Wang, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2020) propose LC3, an online control algorithm under the KNR dynamics (Mania et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2022) that attains the optimal worst-case regret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Both Ayoub et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2020) and Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2020) utilizes op- timistic planning for exploration, which is in general intractable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In contrast, we utilize reward ran- domization for exploration, which also attains the optimal worst-case regret and is highly tractable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' To attain tractable optimistic planning, Curi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2020) design HUCRL, which introduces an ex- tra state deviation variable in the optimization for planning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In contrast, planning with randomized reward does not introduce extra variable in optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Luo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2019) optimizes a lower bound of value functions, which avoids explicit uncertain quantification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Recent works also utilizes re- ward bonus to attain optimistic planning (Kidambi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Song and Sun, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Song and Sun (2021) propose PC-MLP, which constructs bonus by estimating the policy cover (Agarwal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020a) and is computationally tractable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' As a comparison, PC-MLP requires extra sampling to estimate the covariate matrix of policy cover.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' As a consequence, PC-MLP does not attain the op- timal �O( √ T)-regret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In contrast, PlanEx does not require extra sampling to construct the bonus and can achieve the �O( √ T)-regret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In addition, to attain tractable realization, PC-MLP utilizes different feature in model fitting and bonus construction, which is inconsistent with the theoretical analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In contrast, the implementation of PlanEx is consistent with the theoretical analysis un- der the calibrated model assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Previous work also study efficient model-free RL exploration algorithms with function approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' See, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Jin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2020);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Du et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2020);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2020);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Cai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2020);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Agarwal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2020a);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Modi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2021) and refer- ences therein for this line of research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Our analysis is inspired by the recent progress in worst-case regret analysis of randomized RL algorithms (Russo, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Pacchiano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Zanette et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Ishfaq et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Our op- timism analysis is inspired by Russo (2019) and Zanette et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Russo (2019) propose the first worst-case regret analysis to the randomized least-squares value iteration (RLSVI) algorithm under the tabular setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Zanette et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2020) extend the analysis of RLSVI to truncated linear function approximations under the general state space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Ishfaq et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2021) analyze the randomized Q-learning with both linear function approximation and general function approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In contrast, we focus on the randomized MBRL algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Pacchiano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2020) analyze the worst-case re- gret of MBRL with both reward and transition randomization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We remark that both Pacchiano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2020) and Ishfaq et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2021) require drawing multiple samples for each state-action pair in plan- ning and further maximizing over all randomized reward functions in planning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In contrast, we only require one sample at each time step, and do not need further maximization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In addition, Pacchiano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2020) focus on the tabular setting with finite state and action spaces, whereas we consider the generic setting with function approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Background 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Reinforcement Learning In this paper, we model the environment by an episodic MDP (S, A, H, {rh}h∈[H], P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Here S and A are the state spaces, H is the length of episodes, rh : S × A �→ [0, 1] is the bounded reward function for h ∈ [H], and P is the transition kernel, which defines the transition probability sh+1 ∼ P(· | sh, ah) for all h ∈ [H] and (sh, ah) ∈ S × A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Interaction Procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' An agent with a set of policies {πh}h∈[H] interacts with such environment as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' The agent starts from a fixed initial state s1 ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Iteratively, upon reaching the state sh ∈ S, the agent takes the action ah = πh(sh).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' The agent then receives the reward rh(sh, ah).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' The environment transits into the next state sh+1 according to the probability P(· | sh, ah).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' The process ends when the agent reaches the state sH+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' To describe the expected cumulative reward, for each policy π = {πh}h∈[H], we introduce the action-value functions {Qπ h}h∈[H] defined as follows, Qπ h(sh, ah;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P) = H � τ=h E � rτ(sτ, aτ) �� sh, ah, π � , ∀h ∈ [H], (sh, ah) ∈ S × A, (1) where aτ = πτ(sτ) and sτ+1 ∼ P(· | sτ, aτ) for all τ = h, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' , H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Similarly, we define the value functions {V π h }h∈[H] as follows, V π h (sh;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P) = H � τ=h E � rτ(sτ, aτ) �� sh, π � , ∀h ∈ [H], (sh, ah) ∈ S × A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2) We define optimal policy π∗ = {π∗ h}h∈[H] as the maximizer of the following optimization problem, π∗ = argmax π V π 1 (s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (3) Correspondingly, we define V ∗ and Q∗ the value and action-value functions corresponding to the optimal policy π∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' The goal of reinforcement learning (RL) is to sequentially select the policy πk = {πk h}h∈[H] based on the previous experiences, aiming to maximize the expected cumulative reward collected by the agent in the interaction process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Equivalently, the goal is to minimize the following regret, R(K) = K � k=1 V ∗(s1) − V πk(s1), (4) EXPLORATION IN MODEL-BASED RL where K is the total number of interactions and s1 is the fixed initial state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Intuitively, the re- gret R(K) describes the deviation between the policies executed in the interaction process and the optimal policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' The Online Nonlinear Control Problem We consider the online nonlinear control problem with the following transition dynamics, sh+1 = f(sh, ah) + ǫ, where ǫ ∼ N(0, σ2 · I), ∀h ∈ [H], (sh, ah) ∈ S × A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Here the function f : S × A �→ S belongs to a Reproducing Kernel Hilbert Space (RKHS) with known kernel and the noise ǫ is independent across transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Such transition is also known as the Kernelized Nonlinear Regulator (KNR) in previous study (Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Song and Sun, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In this work, we follow Mania et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2022);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2020);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Song and Sun (2021) and consider a primal version of such transition dynamics as the underlying transition dynamics for the RL problem, which is defined as follows, sh+1 = f(sh, ah;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' W ∗) + ǫ, where ǫ ∼ N(0, σ2 · I), f(sh, ah;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' W ∗) = W ∗φ(sh, ah), ∀h ∈ [H], (sh, ah) ∈ S × A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (5) Here φ : S × A �→ Rdφ is a known feature embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Meanwhile, the state space S ⊆ RdS is a subset of the Euclidean space with dimension dS and W ∗ ∈ RdS×dφ is the unknown true parameter of the KNR transition dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Correspondingly, in the sequel, we denote by Qπ(·, ·;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W) and V π(·;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W) the value functions of the policy π under the reward functions {rh}h∈[H] and the transition dynamics defined by the matrix W ∈ RdS×dφ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' For the simplicity of our analysis, we fix the following scaling of features and parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Assumption 1 (Normalized Model) We assume that ∥φ(s, a)∥2 ≤ 1/ √ H for all (s, a) ∈ S × A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' correspondingly, we assume that ∥W ∗∥2 = O( √ H), where W ∗ is the true parameter of the KNR transition dynamics defined in (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Similar normalization assumptions also arises in Mania et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We remark that the scaling assumptions in Assumption 1 only affect the rate of H in regret, and is imposed for the simplicity of our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Model-based RL for Unknown Transition Dynamics In model-based RL, the agent optimizes the policy by iteratively fitting the transition dynamics based on the data collected, and conducting optimal planning on the fitted transition dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' For each iteration k, the model-based RL consists of the following steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (i) Model Fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In this step, the agent updates the parameter Wk of transition dynamics based on the replay buffer Dk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (ii) Planning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In this step, the agent conducts optimal planning based on the fitted parameter Wk of transition dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' By planning with the fitted models, the agent updates the policy πk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (iii) Interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In this step, the agent interacts with the environment with the policy πk and collects a trajectory ιk = (sk 1, ak 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' , sk H, ak H, sk H+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' The agent then updates the replay buffer by Dk+1 = Dk ∪ ιk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In the sequel, we raise the following assumption, which assume that we have access to a planning oracle to handle the planning in step (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Assumption 2 (Planning Oracle) We assume that we have access to the oracle Plan(·, ·, ·), which returns the optimal policy π = Plan(s1, {rh}h∈[H], W) for any input reward functions {rh}h∈[H] and the parameter W of the transition dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Remark 3 (Remark on Sample Complexity) In practice, the planning on fitted environment is typically handled by deep RL algorithms (Pathak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Luo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Pathak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Song and Sun, 2021) or model predictive control (Williams et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Chua et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We remark that since such planning is conducted on the fitted environment, solving such plan- ning problem does not raise concerns in the sample complexity of solvers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In contrast, such sample complexity concern is raised when interacting with the real environment in step (iii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We remark that the goal of exploration is to obtain a near-optimal policy with as few round of interactions K as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' When measured with the regret R(K) defined in (4), the goal of exploration is to design algorithms to attain an regret R(K) that grows as slow as possible in terms of K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Exploration with Randomized Reward In this section, we propose PlanEx , an provably efficient and realizable algorithm for the RL problem with KNR dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In the sequel, we describe the procedure of each step in the k-th iteration of PlanEx .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (i) Model Fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Given the dataset Dk = {(sτ h, aτ h, sτ h+1)(h,τ)∈[H]×[k−1]}, we fit the transition parameter W k by minimizing the prediction error of sh+1 given (sh, ah).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Specifically, we minimize the following least-squares loss, W k ← argmin W ∈RdS×dφ H � h=1 k−1 � τ=1 ∥sτ h+1 − Wφ(sτ h, aτ h)∥2 2 + λ · ∥W∥2 F , (6) where we denote by ∥ · ∥F the matrix Frobenius norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' The optimization in (6) has the following explicit form solution, W k ← � H � h=1 k−1 � τ=1 sτ h+1φ(sτ h, aτ h)⊤ � Λ−1 k , Λk = H � h=1 k−1 � τ=1 φ(sτ h, aτ h)φ(sτ h, aτ h)⊤ + λI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (7) (ii) Planning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In the planning stage, we aim to derive a policy πk that interact with the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' There are two objectives that we aim to achieve in deriving the policy πk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (a) Firstly, the policy πk should properly exploit our knowledge about the environment to optimize the cumulative reward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (b) Secondly, the policy πk should also incorporate our uncertainty to the environment and conduct exploration to unexplored critical events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' To properly balance between (a) and (b), we need to quantify our uncertainty to the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Such uncertainty quantification can be done by the EXPLORATION IN MODEL-BASED RL matrix Λk defined in (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Specifically, it is known () that the matrix Λk defines the following confidence region Gk = � W ∈ RdS×dφ : ∥(W − W k)Λ1/2 k ∥2 2 ≤ βk � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' For properly set βk, it is known that W ∗ ∈ Gk with high probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Under such observation, previ- ous attempts (Jaksch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020) attain the balance between exploitation and exploration by finding the maximizer π of V π(s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W) for W ∈ Gk, which, however, is computationally intractable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' To propose a computationally tractable alternative, previous empirical approaches utilizes ensemble models to estimate the epistemic uncertainty in fitting the model with finite observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In this work, we investigate the approach of directly incorporating uncertainty into the reward functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' To this end, we introduce the following perturbed reward function, rk h,ξ(sh, ah) = � rh(sh, ah) + φ(sh, ah)⊤ξk h �+, ∀h ∈ [H], (sh, ah) ∈ S × A, (8) where the noise {ξk h}h∈[H] are sampled independently from the Gaussian distribution ξk h ∼ N(0, σ2 k· Λ−1 k ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Intuitively, such noise has larger variance in regions that are less explored by the agent, and smaller variance in regions that are well-explored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In addition, we clip the reward to ensure that the reward is positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Upon perturbing the reward, we update the policy by planning based on the estimated transition and perturbed reward as follows, πk = {πk h}h∈[H] = Plan � s1, {rk h,ξ}h∈[H], W k� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (9) We remark that the reward perturbation in (8) is conducted before planning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' The perturbed reward defined in (8) is fixed throughout the planning stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We summarize PlanEx in Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Theoretical Analysis In this section, we analyze PlanEx in Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Our key observations are, the reward perturbation in PlanEx leads to optimistic planning for at least a constant pro- portion of the interactions, and such partial optimism guaranteed by PlanEx is sufficient for exploration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Partial Optimism In the sequel, we show that PlanEx enjoys a partial optimism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Specifically, the following lemma holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Lemma 4 (Partial Optimism) Under the good event W ∗ ∈ Gk = {W ∈ RdS×dφ : ∥(W − W k)Λ1/2 k ∥2 2 ≤ βk}, for properly selected σk, it holds with probability at least Φ(−1) that V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ≤ 0, (10) where Φ(·) is the cumulative distribution function of the standard Gaussian distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Algorithm 1 Planning with Randomized Reward Require: Dataset D, rewards {rh}h∈[H].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 1: Initialization: Set Λ1 = λ · I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 2: for k = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' , K do 3: Generate a set of independent noise ξk h ∼ N(0, σ2 k · Λ−1 k ) for all h ∈ [H].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 4: Obtain the perturbed rewards rk h,ξ(sh, ah) = {rh(sh, ah) + φ(sh, ah)⊤ξk h}+, ∀(sh, ah) ∈ S × A, h ∈ [H].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 5: Obtain the policy πk by calling the planning oracle, πk = Plan(s1, {rk h,ξ}h∈[H], W k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 6: Execute πk to sample a trajectory τ k = {sk 1, ak 1, sk 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', sk H, ak H, sk H+1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 7: Update the dataset Dk ← Dk−1 ∪ τ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 8: Update the model and covariate matrix W k+1 ← argmin W ∈RS×d H � h=1 k � τ=0 ∥sτ h+1 − Wφ(sτ h, aτ h)∥2 2 + λ · ∥W∥2 2, Λk+1 ← Λk + H � h=1 φ(sk h, ak h)φ(sk h, ak h)⊤.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 9: end for EXPLORATION IN MODEL-BASED RL Proof See §A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='2 for a detailed proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Lemma 4 ensures that at least Φ(−1) of the value function estimation in PlanEx overestimates the optimal value function V ∗ 1 (·;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗) that we wish to obtain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' As a consequence, the randomized reward in PlanEx guarantees that at least Φ(−1) of the trajectories contributes to ex- ploration under the optimism principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Intuitively, such optimism holds since, (i) on the one hand, the randomized Gaussian perturbation ensures that the perturbed reward has a sufficiently large probability to be larger than the true reward, and (ii) on the other hand, the good event Gk ensures that the value functions estimated under the true model ({rh}h∈[H], W ∗) does not deviate too much from the value function estimated under the current model ({rh}h∈[H], W k) without perturbation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Regret Analysis We highlight that the optimism guarantee in Lemma 4 alone does not guarantee optimal regret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' To conduct reasonable exploration, in addition to optimism, we need to ensure that the overestimation induced by perturbed reward does not deviated too far away from the value functions under the true reward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In our work, we ensure such deviation guarantee by properly incorporating the uncertainty into the transition dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' More specifically, recall that we define the reward perturbation as follows rk h,ξ(sh, ah) = � rh(sh, ah) + φ(sh, ah)⊤ξk h �+, ∀h ∈ [H], (sh, ah) ∈ S × A, where the noise {ξk h}h∈[H] are sampled independently from the Gaussian distribution ξk h ∼ N(0, σ2 k· Λ−1 k ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Such perturbation introduces the noise ξk h, whose variance scales with the model uncertainty Λk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Such reward perturbation ensures that, with a high probability, the bias in value estimation un- der the perturbed reward scales with the error in transition model estimation in (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, as long as we have reasonable model estimation, such as minimizing least-squares error in (7), the overes- timation induced by perturbed reward is small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Specifically, the following Theorem guarantees that PlanEx has an optimal regret in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Theorem 5 Let λ = 1 and σ2 k = H3·βk/σ2 with βk specified in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Under Assumptions 1 and 2, it holds for K > 1/Φ(−1) that E � R(K) � = O � (dS + dφ)3/2 · H7/2 · log2(K) · √ K � , where the expectation is taken with respect to the randomized reward perturbation and trajectory sampling in PlanEx .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Proof See §A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='4 for a detailed proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We remark that the rate in Theorem 5 is information-theoretically optimal in the number of inter- actions K with the environment (Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We remark that comparing with the optimal planning approach such as LC3 (Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020), PlanEx suffers from extra dependencies in H, dφ and dS, which arises due to the random perturbation of rewards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In addition, we highlight that, comparing with PC-MLP (Song and Sun, 2021), our algorithm attains the optimal O( √ K) dependency with respect to K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Such stronger sample efficiency arises as PlanEx does not require extra sampling to compute policy cover matrix, which is required by PC-MLP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Exploration with Model Uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We remark that the high probability optimism based on Thompson sampling typically arises in the analysis of randomized value iterations for RL (Russo, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Zanette et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In contrast, our work utilizes such idea for model-based exploration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' To understand such counterpart in model-based exploration, we highlight that for both model-based and model-free exploration, designing provable exploration hinges on incorporating the model un- certainty into the value functions and its corresponding policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In value-based approaches such as LSVI-UCB (Jin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020), such model uncertainty is estimated via regression of target value functions on sh+1 with respect to (sh, ah), and is incorporated into value functions as the bonus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In model-based approaches such as UCRL and its variants (Jaksch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020), such model uncertainty is characterized by a confidence region of transition dynamics, and is incor- porated into value functions via optimistic planning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In addition, for algorithms that utilizes policy cover (Song and Sun, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Agarwal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020a), such model uncertainty is obtained by aggre- gating the visitation trajectories of current policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Our work instantiates such idea by directly perturbing the reward functions based on model uncertainty, which serves as a primitive view of all the exploration algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' A Generalization with General Function Approximation A key observation from the design of PlanEx is that sufficient exploration is guaranteed as long as at least a fixed proportion of iterations are dedicated to exploration with optimism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' To further vali- date such observation, we generalize PlanEx by general function approximation in the sequel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We summarize the algorithm in Algorithm 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' To conduct our analysis, we assume that the estimation of transition dynamics is sufficiently accurate and satisfies the following calibrated model assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Algorithm 2 Planning with Randomized Reward Require: Rewards {rh}h∈[H].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 1: Initialization: Initialize buffer D0 as an empty set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Initialize the transition dynamics P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 2: for k = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' , K do 3: Generate the randomized reward {rk h,ξ}h∈[H].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 4: Obtain the policy πk by calling the planning oracle, πk = Plan(s1, {rk h,ξ}h∈[H], Pk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 5: Execute πk to sample a trajectory τ k = {sk 1, ak 1, sk 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', sk H, ak H, sk H+1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 6: Update the dataset Dk ← Dk−1 ∪ τ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 7: Update the transition dynamics Pk+1 based on the dataset Dk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 8: end for Assumption 6 (Calibrated model) Let Pk be the transition dynamics estimated in the k-th itera- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' For all δ > 0 and k ∈ [K], it holds with probability at least 1 − δ that ∥P(· | sh, ah) − Pk(· | sh, ah)∥1 ≤ β(δ) · ιk(sh, ah), ∀k ∈ [K], (sh, ah) ∈ S × A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Meanwhile, it holds that ιk ≤ 1 for all k ∈ [K].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Here the parameter β(δ) characterizes the variance in concentration, which typically scales with log(1/δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Similar assumption also arises in the analysis under general function approximation (Curi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', EXPLORATION IN MODEL-BASED RL 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Kidambi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In addition, we remark that such assumption generalizes various com- monly adopted parametric models, including the linear MDP model (Jin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020) and the KNR model (Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020) we adopted in previous sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Correspondingly, we propose the following complexity metric for the RL problems, IK = max {Dk}k∈[K] K � k=1 H � h=1 ι2 k(sk h, ak h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (11) Here the maximization is taken over all possible dataset {Dk}k∈[K] collected by an online learn- ing algorithm with |Dk| = H for all k ∈ [K].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We remark that similar complexity metric also arises in the analysis of model-based RL with general function approximations (Curi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Kidambi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We cast the following conditions on the reward randomization that ensures sufficient explo- ration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Condition 7 ((Optimism)) It holds for the randomized reward function {rk h,ξ}h∈[H] that H � h=1 rk h,ξ(sh, ah) − rh(sh, ah) ≥ H · β(δ) · H � h=1 ιk(sh, ah), which holds uniformly for all trajectories {(sh, ah)}h∈[H] with probability at least p0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Condition 8 ((Concentration of Rewards)) It holds for all δ′ > 0 that |rk h,ξ − rh| ≤ Cr(δ′) · ιk with probability at least 1 − δ′ for all (k, h) ∈ [K] × [H], where ιk is defined in Assumption 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Intuition Behind Reward Randomization Conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We remark that Conditions 7 and 8 are the key factors for the success of the randomized reward in PlanEx .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' On the one hand, Condition 7 ensures that a constant p0 proportion of the evaluations results in optimistic value functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Such optimistic value estimation further allows for exploration under the optimism principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' On the other hand, the concentration condition in Condition 8 ensures that with high probability, the value function estimated under the randomized reward does not deviate too much from that evaluated under the true reward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' The following Theorem upper bounds the regret of Algorithm 2 under Assumption 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Theorem 9 (Regret Bound) Under Assumption 6, for the randomized reward that satisfies Con- ditions 7 and 8, the regret of Algorithm 2 is bounded as follows, E � R(K) � = O � Poly � Cr(1/K), β(1/K), H � IK · √ K � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Proof See §B for the detailed proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We remark that for commonly used model parameterization such as linear MDP and KNR, the parameter β(1/K) typically scales with log(K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Meanwhile, for properly designed reward ran- domization scheme, the term Cr(1/K) also scales with log(K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, Theorem 18 shows that Algorithm 2 has a regret bound that scales with �O(IK · √ K), which matches the previous regret bound of exploration under model-based RL ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Design of Randomized Reward We remark that in practice, the model uncertainty {ιk}k∈[K] defined in Assumption 6 can be esti- mated based on disagreement of ensemble models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, to instantiate Algorithm 2, it remains to design proper reward randomization scheme that satisfies Conditions 7 and 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In what follows, we present examples of such randomized rewards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Example 1 (Gaussian Perturbation) Let rk h,ξ(sk h, ak h) = r(sk h, ak h) + ξk h, where {ξk h}(k,h)∈[K]×[H] are sampled independently from the Gaussian distribution N(0, σk · ι2 k(sk h, ak h)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Under regulation conditions specified in §B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='2, the randomized reward {rk h,ξ}(k,h)∈[K]×[H] satisfies Conditions 7 and 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Example 2 (Bernoulli Perturbation) Let rk h,ξ(sk h, ak h) = r(sk h, ak h) + ξk h · σ′ kιk(sk h, ak h), where ξk h = 1 with probability 1/2 and ξk h = −1 with probability 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' For the parameters {σ′ k}(k)∈[K] specified in §B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='2, the randomized reward {rk h,ξ}(k,h)∈[K]×[H] satisfies Conditions 7 and 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' A Comparison with Bonus-based Approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We remark that our proposed randomized reward is closely related to the reward bonus for model-based RL, which arises in the recent progress of exploration under model-based RL (Kidambi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Song and Sun, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Such bonus- based approaches typically estimate the model uncertainty {ιk}k∈[K] and then design reward bonus that incorporates such uncertainty estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Indeed, one may view the randomized rewards in Examples 1 and 2 as a randomized generalization of such reward bonus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Specifically, both the randomized reward and the reward bonus accomplishes exploration with optimism principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' For randomized reward, such exploration is guaranteed by the partial optimism that we investigated in §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In contrast, for reward bonus, such exploration is guaranteed by directly enforcing optimism with bonus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Given the connections between the reward bonus and randomized reward, one may be prompt to ask why using randomized reward?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We highlight that adding bonus is, in fact, a pessimistic approach in order to reduce the worst-case regret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Such approach enforces a bonus that deviates from the true reward, aiming to introduce a bias in value estimations to achieve minimal worst-case regret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In comparison, randomized reward allows the perturbation to be centered around the true reward, and yields a milder deviation from the true reward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In addition, as shown in our work, such perturbation also has a worst-case regret guarantee at �O( √ K) order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' EXPLORATION IN MODEL-BASED RL References Yasin Abbasi-Yadkori, D´avid P´al, and Csaba Szepesv´ari.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Improved algorithms for linear stochas- tic bandits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems (NIPS), pages 2312–2320, Granada, Spain, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Alekh Agarwal, Mikael Henaff, Sham M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Kakade, and Wen Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' PC-PG: policy cover directed exploration for provable policy gradient learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems (NeurIPS), virtual, 2020a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Alekh Agarwal, Sham M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Kakade, Akshay Krishnamurthy, and Wen Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' FLAMBE: structural complexity and representation learning of low rank MDPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems (NeurIPS), virtual, 2020b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Alex Ayoub, Zeyu Jia, Csaba Szepesv´ari, Mengdi Wang, and Lin Yang.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Manuel Watter, Jost Tobias Springenberg, Joschka Boedecker, and Martin A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Riedmiller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Embed to control: A locally linear latent dynamics model for control from raw images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In Advances in Neural Information Processing Systems (NIPS), pages 2746–2754, Montreal, Canada, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Grady Williams, Andrew Aldrich, and Evangelos Theodorou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Model predictive path integral control using covariance variable importance sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' arXiv preprint arXiv:1509.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='01149, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Lin Yang and Mengdi Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Sample-optimal parametric q-learning using linearly additive features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In Proceedings of the 36th International Conference on Machine Learning (ICML), pages 6995– 7004, Long Beach, CA, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Andrea Zanette, David Brandfonbrener, Emma Brunskill, Matteo Pirotta, and Alessandro Lazaric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Frequentist regret bounds for randomized least-squares value iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics (AISTATS), pages 1954–1964, Online [Palermo, Sicily, Italy], 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Proof of Main Result In this section, we present the proofs of main results in §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Good Events and Parameters In what follows, we define the following good events for the analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Definition 10 (Good Events) We define the following good events, GW k,good = {∥W ∗ − W k∥2 Λk ≤ βk}, Gξk,good = {∥ξk h∥2 Λk ≤ βk,ξ, ∀h ∈ [H]}, Gξk,opt = � V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ≤ 0 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Correspondingly, we further define GW,good = � k∈[K] GW k,good, Gξ,good = � k∈[K] Gξk,good.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In the sequel, we follow Lemma 19 and set βk as follows βk = 2λ · ∥W ∗∥2 2 + 8σ2� dS · log(5) + 2 log(k) + log(4) + log � det(Λk)/ det(Λ0) �� , where σ is the noise variance that defines the transition dynamics in (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Correspondingly, we set the parameter σk in PlanEx as follows, σ2 k = H3 · βk/σ2, Meanwhile, we set the parameter βk,ξ = 2σ2 k · log(KH/δ) in Definition 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' It thus holds that P(Gξ,good) ≥ 1 − δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Optimality In the sequel, we present the optimality analysis of PlanEx , which is inspired by Russo (2019) and Zanette et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Lemma 11 (Probability of Optimality) Under the good event GW k,good, it holds with probability at least Φ(−1) that V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (12) In other words, it holds that P(Gξk,opt | GW k,good) ≥ Φ(−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Proof Note that V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� − V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� ≥ V π∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� − V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� , ≥ φ(s1, a1)⊤ξk 1 − E � V ∗ 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� ��� s1, a1, W ∗� + E � V π∗ 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ��� s1, a1, W k� , (13) EXPLORATION IN MODEL-BASED RL where the second inequality holds since {r1 + φ⊤ξk 1}+ − r1 = max{φ⊤ξk 1, −r1} ≥ φ⊤ξk 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Here we denote by π∗ the optimal policy under the model ({rh}h∈[H], W ∗) and a1 the optimal action a1 = π∗(s1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' It further holds that, E � V π∗ 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ��� s1, a1, W k� − E � V ∗ 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� ��� s1, a1, W ∗� = E � V ∗ 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� ��� s1, a1, W k� − E � V ∗ 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� ��� s1, a1, W ∗� � �� � (i) + E � V π∗ 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� − V ∗ 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� ��� s1, a1, W k� � �� � (ii) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (14) By Lemma 20 and the fact that V ∗ h ≤ H for all h ∈ [H], we upper bound the absolute value of term (i) as follows, |(i)| ≤ H · ∥(W k − W ∗)φ(s1, a1)∥2/σ ≤ H · ∥W k − W ∗∥Λl · ∥φ(s1, a1)∥Λ−1 k .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, under the event GW k,good), it further holds that |(i)| ≤ � βkH2/σ · ∥φ(s1, a1)∥Λ−1 k .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (15) By plugging (15) into (14) and further unrolling term (ii) based on similar computation in (13) and (14), we conclude that V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� − V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� ≥ H � h=1 E � φ(sh, ah)⊤ξk h − � βkH2/σ · ∥φ(sh, ah)∥Λ−1 k �� s1, π∗, W k� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Note that for any given trajectory {(sh, ah)}h∈[H], it holds that H � h=1 φ(sh, ah)⊤ξk h ∼ N(0, σ2 k,H), σ2 k,H = σ2 k · H � h=1 ∥φ(sh, ah)∥2 Λ−1 k .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' It then holds from the setup σ2 k = H3 · βk/σ2 and Cauchy-Schwartz inequality that σk,H = � � � �H3 · βk/σ2 · H � h=1 ∥φ(sh, ah)∥2 Λ−1 k ≥ � βkH2/σ · H � h=1 ∥φ(sh, ah)∥Λ−1 k .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, for any given trajectory {(sh, ah)}h∈[H], it holds with probability at least Φ(−1) that H � h=1 φ(sh, ah)⊤ξk h ≥ σk,H ≥ � βkH2/σ · ∥φ(sh, ah)∥Λ−1 k .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Hence, upon taking integration with respect to the trajectory under s1, π∗, W k, and the good event GW k,good, it holds with probability at least Φ(−1) that V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� − V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� ≥ H � h=1 E � φ(sh, ah)⊤ξk h − � βkH2/σ2 · ∥φ(sh, ah)∥Λ−1 k �� s1, π∗, W k� ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, we complete the proof of Lemma 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Lemma 12 (Optimism Bound) It holds for K > 1/Φ(−1) that E � K � k=1 V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k) ���� GW,good, Gξ,good � = � O( √ K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Proof In the sequel, we set δ = 1/K in the good events defined in Definition 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We fix an arbitrary k ∈ [K] and upper bound the following difference, ∆k = V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We construct a noise set {�ξk h}h∈[H], which is an identical and independent copy of the noise set {ξk h}h∈[H].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Correspondingly, we define the good events G�ξ,good and G�ξ,opt in Definition 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We further define the optimal value function V �πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,�ξ}h∈[H], W k) under the perturbed reward set {rh + φ⊤�ξk h}h∈[H] and the transition W k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' It thus follows from Lemma 11 that ∆k = V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k) ≤ E � V �πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,�ξ}h∈[H], W k) ��� G�ξ,good, G�ξ,opt � − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (16) We further define the value function corresponding to the minimal perturbation under the good event Gξ,good as follows, {ξk h}h∈[H] = argmin ∥ξk h∥2 Λk ≤βk,ξ max π V π 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh + φ⊤ξk h}+ h∈[H], W k� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (17) We define rk h,ξ = {rh + φ⊤ξk h}+ the corresponding perturbed reward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We further define πk the corresponding optimal policy of the model ({rk h,ξ}h∈[H], W k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, under the good event Gξ,good, we have ∆k ≤ E � V �πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,�ξ}h∈[H], W k� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ��� G�ξ,good, G�ξ,opt � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (18) Meanwhile, note that under the good event G�ξk,good, we have V �πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,�ξ}h∈[H], W k� ≥ V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' EXPLORATION IN MODEL-BASED RL In what follows, we write V �πk 1 = V �πk 1 (s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,�ξ}h∈[H], W k) and V πk 1 = V πk 1 (s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k) for notational simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' It holds that E�ξ � V �πk 1 − V πk 1 �� G�ξ,good � = E�ξ � V �πk 1 − V πk 1 �� G�ξk,good, G�ξk,opt � P(G�ξk,opt | G�ξk,good) + E�ξ � V �πk 1 − V πk 1 �� G�ξk,good, Gc �ξk,opt � P(Gc �ξk,opt | G�ξk,good) ≥ E�ξ � V �πk 1 − V πk 1 �� G�ξk,good, G�ξk,opt � P(G�ξk,opt | G�ξk,good).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (19) Meanwhile, it follows from Lemma 11 that, under GW,good, P(G�ξk,opt | G�ξk,good) ≥ P(G�ξk,opt ∩ G�ξk,good) ≥ 1 − P(Gc �ξk,opt) − P(Gc �ξk,good) ≥ Φ(−1) − δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (20) By further plugging (19) and (20) into (18), we obtain that ∆k ≤ � Φ(−1) − δ �−1 · E�ξ � V �πk 1 − V πk 1 �� G�ξk,good � = � Φ(−1) − δ �−1 · Eξ � V πk 1 − V πk 1 �� Gξk,good � , (21) where we use the fact that the noise set {�ξk h}h∈[H] is an identical and independent copy of the noise set {ξk h}h∈[H].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' It now remains to upper bound the difference V πk 1 − V πk 1 under the good events Gξ,good and GW,good.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Note that V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ≤ V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� , (22) which holds since πk is optimal for the model ({rk h,ξ}h∈[H], W k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Meanwhile, by adding and sub- tracting the value function V πk 1 (s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗) of πk under the true model ({rh}h∈[H], W ∗) in (22), we obtain that V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ≤ V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� � �� � (iii) (23) + V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� � �� � (iv) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In the sequel, we upper bound terms (iii) and (iv) in (23) under the good events Gξ,good and GW,good, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Upper bound of term (iii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' The upper bound is similar to that in the proof of Lemma 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Note that (iii) = V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� = max{φ(s1, a1)⊤ξk 1, −r1(s1, a1)} + φ(s1, a1)⊤ξk h + E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ��� s1, πk, W k� − E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� ��� s1, πk, W ∗� ≤ ∥φ(s1, a1)∥Λ−1 k ∥ξk 1∥Λk + ∆k ξ,1 (24) + E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� − V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� ��� s1, πk, W ∗� , where the inequality follows from Cauchy-Schwartz inequality and the fact that r1 ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Here we define a1 = πk(s1) and ∆k ξ,1 = E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ��� s1, πk, W k� − E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ��� s1, πk, W ∗� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Note that under the good event Gξ,good, it holds for all (sh, ah) ∈ S × A and h ∈ [H] that rk h,ξ(sh, ah) ≤ r(sh, ah) + |φ(sh, ah)⊤ξk h| ≤ 1 + ∥φ(sh, ah)∥Λ−1 k ∥ξk h∥Λk ≤ 1 + � βk,ξ/(λ2H).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, it holds under the good event Gξ,good that 0 ≤ V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ≤ H · � 1 + � βk,ξ/(λ2H) � = H + � βk,ξH/λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (25) By Lemma 20, it further holds under good events Gξ,good and GW,good that ∆k ξ,1 = E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ��� s1, πk, W k� − E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ��� s1, πk, W ∗� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' ≤ � H + � βk,ξH/λ � σ−1 · ∥(W k − W ∗)φ(s1, a1)∥2 ≤ � H + � βk,ξH/λ � σ−1 · ∥W k − W ∗∥Λk · ∥φ(s1, a1)∥Λ−1 k ≤ � H + � βk,ξH/λ � σ−1 · � βk · ∥φ(s1, a1)∥Λ−1 k .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (26) Here the first inequality follows from Lemma 20 and the bounds in (25), the second inequality follows from Cauchy-Schwartz inequality, and the third inequality follows from the definition of the good event GW,good in Definition 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Plugging (26) and the definition of the good event Gξ,good into (24), we obtain that (iii) ≤ Ck · ∥φ(s1, a1)∥Λ−1 k (27) + E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� − V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� ��� s1, πk, W ∗� , where we define Ck = � H + � βk,ξH/λ � σ−1 · � βk + � βk,ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' EXPLORATION IN MODEL-BASED RL By further unrolling (27), we conclude that, under the good events Gξ,good and GW,good, we have (iii) ≤ E � H � h=1 Ck · ∥φ(sh, ah)∥Λ−1 k ���� s1, πk, W ∗, Gξk,good, GW k,good � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (28) Upper bound of term (iv).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' The upper bound of term (iv) is similar that of term (iii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Note that (iv) = V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� = min � −φ(s1, a1)⊤ξk h, r1(s1, a1) � + E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� ��� s1, πk, W ∗� − E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ��� s1, πk, W k� ≤ −φ(s1, a1)⊤ξk h + ∆k ξ,1 + E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� − V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ��� s1, πk, W ∗� , where we define ∆k ξ,1 = E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W ∗� ��� s1, πk, W k� − E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ��� s1, πk, W k� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' By the definition of the minimal perturbation in (17), it holds that ∥ξk h∥Λk ≤ βξ for all (h, k) ∈ [H] × [K].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, we have −φ(s1, a1)⊤ξk h ≤ βk,ξ · ∥φ(s1, a1)∥Λ−1 k .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' The rest of the computation is almost identical to that in (iii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We omit the computation for simplicity and conclude that, under good events Gξ,good and GW,good, we have (iv) ≤ E � H � h=1 Ck · ∥φ(sh, ah)∥Λ−1 k ���� s1, πk, W ∗, Gξk,good, GW k,good � , (29) where we define Ck = � H + � βk,ξH/λ � σ−1 · � βk + � βk,ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (30) Thus, by plugging (28) and (29) into (23), we conclude that E[∆k | GW,good, Gξ,good] ≤ � Φ(−1) − δ �−1 · Eξ � V πk 1 − V πk 1 �� GW k,good, Gξk,good � ≤ � Φ(−1) − δ �−1 · Cmax · E � H � h=1 ∥φ(sk h, ak h)∥Λ−1 k ����GW k,good, Gξk,good � , where we define Cmax = CK = � H + � βK,ξH/λ � σ−1 · � βK + � βK,ξ ≥ Ck, ∀k ∈ [K], and the expectation is taken with respect to the trajectories of πk under the transition defined by W ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Recall that we set λ = 1, δ = 1/K, and σk = H3 · βk/σ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, under Assumption 1, we obtain that βK = O � H + dS + log(K) + dφ · log(K) � , βK,ξ = 2σ2 K · log(K/δ) = O � H4 · log(KH) + (dS + dφ) · H3 · log2(KH) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, upon computation, we have Cmax = O � (dS + dφ) · H3 · log3/2(KH) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Finally, it holds that E � K � k=1 V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='ξ}h∈[H],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' W k) ���� GW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='good,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Gξ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='good � ≤ � Φ(−1) − 1/K �−1 · Cmax · E � K � k=1 H � h=1 ∥φ(sk h,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' ak h)∥Λ−1 k ����GW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='good,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Gξ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='good � ≤ � Φ(−1) − 1/K �−1 · Cmax · E �� HK · K � k=1 H � h=1 ∥φ(sk h,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' ak h)∥2 Λ−1 k �1/2 ����GW,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='good,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Gξ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='good � = O � (dS + dφ)3/2 · H7/2 · log2(KH) · √ K � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' where the expectation is taken with respect to the trajectories of {πk}k∈[K] under the true transition defined by W ∗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' and the last inequality follows from Lemma 21 and the fact that log det(ΛK+1) ≤ dφ · log K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, we complete the proof of Lemma 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Estimation Error Lemma 13 (Estimation Error Bound) It holds for K > 1/Φ(−1) that E � K � k=1 V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗) ���� GW,good, Gξ,good � = � O( √ K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Proof Note that V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� = max{φ(s1, a1)⊤ξk 1, −r1(s1, a1)} + φ(s1, a1)⊤ξk h + E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ��� s1, πk, W k� − E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� ��� s1, πk, W ∗� ≤ ∥φ(s1, a1)∥Λ−1 k ∥ξk 1∥Λk + ∆k ξ,1 (31) + E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� − V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� ��� s1, πk, W ∗� , EXPLORATION IN MODEL-BASED RL where the inequality follows from Cauchy-Schwartz inequality and the fact that r1 ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Here we define a1 = πk(s1) and ∆k ξ,1 = E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ��� s1, πk, W k� − E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ��� s1, πk, W ∗� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Note that under the good event Gξ,good, it holds for all (sh, ah) ∈ S × A and h ∈ [H] that rk h,ξ(sh, ah) ≤ r(sh, ah) + |φ(sh, ah)⊤ξk h| ≤ 1 + ∥φ(sh, ah)∥Λ−1 k ∥ξk h∥Λk ≤ 1 + βξ/λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, it holds under the good event Gξ,good that 0 ≤ V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ≤ H · (1 + βξ/λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (32) By Lemma 20, it further holds under good events Gξ,good and GW,good that ∆k ξ,1 = E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ��� s1, πk, W k� − E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� ��� s1, πk, W ∗� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' ≤ H · (1 + βξ/λ)/σ · ∥(W k − W ∗)φ(s1, a1)∥2 ≤ H · (1 + βξ/λ)/σ · ∥W k − W ∗∥Λk · ∥φ(s1, a1)∥Λ−1 k ≤ H · (1 + βξ/λ)/σ · βk · ∥φ(s1, a1)∥Λ−1 k .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (33) Here the first inequality follows from Lemma 20 and the bounds in (32), the second inequality follows from Cauchy-Schwartz inequality, and the third inequality follows from the definition of the good event GW,good in Definition 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Plugging (33) and the definition of the good event Gξ,good into (31), we obtain that V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� ≤ Ck · ∥φ(s1, a1)∥Λ−1 k + E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� − V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� ��� s1, πk, W ∗� , where Ck is defined in (30).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' By further unrolling (27) and summing over k ∈ [K], we conclude that K � k=1 V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� ≤ E � K � k=1 H � h=1 Ck · ∥φ(sk h, ak h)∥Λ−1 k ���� GW k,good, Gξk,good � , where the expectation is taken with respect to the trajectories of {πk}k∈[K] under the true transi- tion defined by W ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' The rest of the computation is identical to that of Lemma 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We omit the computation and conclude that E � K � k=1 V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗) ���� GW,good, Gξ,good � = � O( √ K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Regret Analysis Theorem 14 (Expected Regret Bound) We set λ = 1 and σk as in §A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' It holds for K > 1/Φ(−1) that E � R(K) � = O � (dS + dφ)3/2 · H7/2 · log2(KH) · √ K � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Proof It holds that E � R(K) � = E � K � k=1 V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k) + V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, we have E � R(K) � ≤ Opt + Est + Vmax · K � k=1 � P(Gc W k,good) � + Vmax · K · P(Gc ξ,good), (34) where we define Opt = E � K � k=1 V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k) ���� GW,good, Gξ,good � , Est = E � K � k=1 V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], W k� − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], W ∗) ���� GW,good, Gξ,good � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Plugging the bounds of Opt and Est in Lemmas 12 and 13, respectively, the fact that Vmax = H, and δ = 1/T into (34), we conclude that E � R(K) � = O � (dS + dφ)3/2 · H7/2 · log2(KH) · √ K � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, we completes the proof of Theorem 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Proof of Result in §5 In this section, we present the proofs of results in §5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Regret Analysis Similar to the proofs in §A, we define the good event Ggood as follows, Ggood = � |rh − rk h,ξ| ≤ Cr(δ′) · ιk, ∥P(· | s, a) − Pk(· | s, a)∥1 ≤ βk(δ) · ιk(s, a), ∀(k, h) ∈ [K] × [H], (s, a) ∈ S × A � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Under Assumption 6, it holds for the randomized reward satisfying Condition 7 that P(Ggood) ≥ 1 − δ′ − δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' EXPLORATION IN MODEL-BASED RL Lemma 15 (Probability of Optimality) Under Assumptions 6 and the good event Ggood, it holds for the randomized reward satisfying Condition 7 that V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P � ≤ V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) ≥ 1/2 with probability at least p0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Proof The proof is similar to that for Lemma 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Note that V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) − V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P � ≥ V π∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) − V ∗� s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P � = rk h,ξ � s1, π∗(s1) � − rh � s1, π∗(s1) � + E � V π∗ 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) ��� s1, π∗, Pk� − E � V ∗ 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P � ��� s1, π∗, P � , (35) where we denote by π∗ the optimal policy under the environment defined by ({rh}h∈[H], P), and the first inequality follows from the optimality of πk under the environment defined by ({rk h,ξ}h∈[H], Pk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Meanwhile, it holds that E � V π∗ 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) ��� s1, π∗, Pk� − E � V ∗ 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P � ��� s1, π∗, P � = E � V ∗ 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P � ��� s1, π∗, Pk� − E � V ∗ 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P � ��� s1, π∗, P � � �� � (i) + E � V π∗ 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) − V ∗ 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P � ��� s1, π∗, Pk� � �� � (ii) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (36) By Assumption 6, H¨older’s inequality, and the fact that V ∗ 1 ≤ H, it holds under the good event Ggood that |(i)| ≤ E � H · ∥(P − Pk)(· | s1, a1)∥1 �� s1, π∗� ≤ E � H · β(δ) · ιk(s1, a1) �� s1, π∗� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' By further unrolling term (ii) in (36), we conclude from (35) that V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) − V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P � ≥ E � H � h=1 rk h,ξ(s1, a1) − rh(s1, a1) − H · βk H � h=1 ιk(sh, ah) ����� s1, π∗, Pk � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, under the optimism condition in Condition 7, it holds that V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) − V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P � ≥ 0 with probability at least p0 − δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Lemma 16 (Optimism Bound) For δ′ ≤ p0, it holds with probability at least 1 − δ − δ′ that E � K � k=1 V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P � − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) ���� Ggood � = O � C(δ, δ′) · IK · √ K � , where we define C(δ, δ′) = Cr(δ′) + H · (1 + Cr(δ′)) · β(δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Proof The proof is similar to that of Lemma 12 in §A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' We define the following minimal perturbed value function, V πk 1 = argmin �r∈Ggood argmax π V π 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {�rh}h∈[H], Pk� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Following the same computation as in the proof of Lemma 12, we obtain that E � K � k=1 V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P � − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) ���� Ggood � ≤ (p0 − δ)−1 · E � K � k=1 V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {�rh}h∈[H], Pk) ���� Ggood � � �� � ∆k .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (37) By further adding and subtracting V πk(s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}, P), we obtain that ∆k = E � K � k=1 V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) − V πk(s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}, P) ���� Ggood � � �� � (iii) + E � K � k=1 V πk(s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}, P) − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {�rh}h∈[H], Pk) ���� Ggood � � �� � (iv) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (38) Thus, upon a similar computation to that in §A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='2, under the good event Ggood, it further holds that V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) − V πk(s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}, P) ≤ E � C(δ, δ′) H � h=1 ιk(sh, ah) ���� s1, πk, P � , where we define C(δ, δ′) = Cr(δ′) + H · � 1 + Cr(δ′) � β(δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Here we use the fact that ∥V πk h � ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk)∥∞ ≤ H · (1 + Cr(δ′)) under the good event Ggood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' The same bound holds for term (iv) in (38) following the fact that �r ∈ Ggood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, by EXPLORATION IN MODEL-BASED RL plugging (37) into (37), we conclude that E � K � k=1 V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P � − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) ���� Ggood � ≤ C(δ, δ′) · (p0 − δ)−1 · E � K � k=1 H � h=1 Ck · σk(sh, ah) ���� Ggood � ≤ C(δ, δ′) · (p0 − δ)−1 · √ HK · E �� H � h=1 ι2 k(sh, ah) �1/2 ����� Ggood � , By further plugging into the definition of IK in (11), we obtain that E � K � k=1 V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P � − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) ���� Ggood � = O � C(δ, δ′) · IK · √ K � , which concludes the proof of Lemma 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Lemma 17 (Estimation Error Bound) It holds that E � K � k=1 V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P) ���� Ggood � = O � C(δ, δ′) · IK · √ K � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Proof Under the good event Ggood, it holds that V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P) ≤ Cr · σk(s1, a1) + E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) ��� s1, πk, Pk� − E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P) �� s1, πk, P � ≤ Cr · σk(s1, a1) + ∆k ξ,1 + E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) − V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P) �� s1, πk, P � , (39) where we define a1 = πk 1(s1) and ∆k ξ,1 = E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) ��� s1, πk, Pk� − E � V πk 2 � s2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) ��� s1, πk, P � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Under the good event Ggood, it holds from H¨older’s inequality that ∆k ξ,1 ≤ H · � 1 + Cr(δ′) � βk · ιk(s1, a1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (40) By plugging (40) into (39) and further unrolling (39), we obtain that, under the good event Ggood, V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P) ≤ C(δ, δ′) · E � H � h=1 ιk(sh, ah) �� s1, πk, P � , (41) where we define C(δ, δ′) = Cr(δ′) + H · (1+ Cr(δ′)) · β(δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, by summing (41) over k ∈ [K], we obtain that E � K � k=1 V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rk h,ξ}h∈[H], Pk) − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P) ���� Ggood � ≤ C(δ, δ′) · E � K � k=1 H � h=1 σk(sk h, ak h) ���� Ggood � ≤ C(δ, δ′) · √ HK · IK, where IK is defined in (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, we complete the proof of Lemma 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Theorem 18 (Regret Bound) Let δ = δ′ = 1/K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Under Assumption 6, for the randomized reward that satisfies Conditions 7 and 8, we have E � R(K) � = O �� Cr(1/K) + H · � 1 + Cr(1/K) � β(1/K) � √ H2K · IK � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Proof Combining Lemmas 16 and 17, it holds that E � K � k=1 V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P � − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], Pk) ���� Ggood � = O � C(δ, δ′) · IK · √ K � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (42) Meanwhile, under Assumption 6, it holds for rewards that satisfies 8 that P(Ggood)1 − δ − δ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, for δ = δ′ = 1/K, we have E � K � k=1 V ∗ 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], P � − V πk 1 � s1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' {rh}h∈[H], Pk) ���� Gc good � ≤ 2K · (δ + δ′) = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (43) Combining (42) and (43), it holds that E � R(K) � = O � C(1/K, 1/K) · √ H2K · IK � = O �� Cr(1/K) + H · � 1 + Cr(1/K) � β(1/K) � √ H2K · IK � , which concludes the proof of Theorem 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Verification of Example In the sequel, we verify that Examples 1 and 2 satisfies Conditions 7 and 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Example 3 (Gaussian Reward) Let rk h,ξ(sh, ah) ∼ N � rh(sh, ah), H · β(δ) · σ2 k(sh, ah) � , which are sampled independently over (sh, ah) ∈ S × A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' It holds that the probability of H � h=1 rk h,ξ(sh, ah) − rh(sh, ah) ≥ H · β(δ) H � h=1 σk(sh, ah) EXPLORATION IN MODEL-BASED RL is greater than the following event, N � 0, H · H � h=1 σ2 k(sh, ah) � ≥ � � � �H · β(δ) H � h=1 σ2 k(sh, ah), which holds with probability at least Φ(−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In addition, if r/σk are lipschitz functions of (s, a) ∈ S × A and S × A has a covering number CS×A under the same metric, it further holds that |rk h,ξ −rh| ≤ � H · β(δ) · log(CS×A · HK/δ′)·σk with probability at least 1−δ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, Conditions 7 and 8 are satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Example 4 (Bernoulli Reward) Let rk h,ǫ(sh, ah) ∼ r(sh, ah) + 2 √ H · β(δ) · σk(sh, ah) · ǫh, where ǫh = 1 with probability 1/2 and ǫh = −1 with probability 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' For any trajectory τ, it holds from the Khintchine’s inequality (Veraar, 2010) that H � h=1 √ H · β(δ) · σk(sh, ah) · ǫh/S(τ) ≥ 1/2 with probability at least p0 = 3/16, where we define S(τ) = H H � h=1 β2(δ) · σ2 k(sh, ah).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, it holds that H � h=1 rk h,ǫ(sh, ah) − r(sh, ah) ≥ 2 H � h=1 √ H · β(δ) · σk(sh, ah) · ǫh ≥ S(τ) ≥ H � h=1 β(δ) · σk(sh, ah) with probability at least p0 = 3/16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' In addition, it holds that |rk h,ǫ(sh, ah) − r(sh, ah)| ≤ 2 √ H · β(δ) · σk(sh, ah).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, Conditions 7 and 8 are satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Auxiliary Lemma Lemma 19 (Concentration of Self-normalized Process (Abbasi-Yadkori et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020)) It holds for βk = 2λ · ∥W ∗∥2 2 + 8σ2� dS · log(5) + 2 log(k) + log(4) + log � det(Λk)/ det(Λ0) �� that ∞ � k=0 P(Gc W k,good) = ∞ � k=0 P � ∥W k − W ∗∥2 Λk ≥ βk � ≤ 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Proof See Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2020) for a detailed proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Lemma 20 (Expected Difference Under Two Gaussian (Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020)) Let z1 ∼ N(µ1, σ2) and z2 ∼ N(µ2, σ2) be two Gaussian random variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Let g be a positive measurable function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' It holds that Ez1∼N(µ1,σ2) � g(z1) � − Ez2∼N(µ1,σ2) � g(z2) � ≤ min{∥µ1 − µ2∥2/σ, 1} · � Ez1∼N(µ1,σ2) � g2(z1) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Proof See Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (2020) for a detailed proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Lemma 21 (Elliptical Potential Lemma (Kakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=', 2020)) Let ∥φk h∥2 ≤ 1/ √ H for all (k, h) ∈ [K] × [H].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Let Λ1 = I and Λk+1 = Λk + �H h=1 φk h(φk h)⊤.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' It holds that K � k=1 H � h=1 ∥φk h∥2 Λ−1 k ≤ 2 log � det(ΛK+1) · det(Λ0)−1� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Proof Note that we have Λk ≻ Λ1 = I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' It thus holds that 0 ≤ H � h=1 (φk h)⊤Λ−1 k φk h ≤ H � h=1 ∥φk h∥2 2 ≤ 1, ∀k ∈ [K].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Meanwhile, since x ≤ 2 log(1 + x) for x ∈ [0, 1], we have 2 log � 1 + H � h=1 (φk h)⊤Λ−1 k φk h � ≥ H � h=1 (φk h)⊤Λ−1 k φk h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (44) On the other hand, it follows from matrix determinant lemma that log det(Λk+1) − log det(Λk) = log det � I + Λ−1/2 k H � h=1 (φk h)(φk h)⊤Λ−1/2 k � �� � Ξk � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Let {σi}i∈[d] be the eigenvalues of the matrix Ξk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' It holds that σi > 0 for all i ∈ [d] and log det(I + Ξk) = log Πi∈[d](1 + σi) ≥ log � 1 + � i∈[d] σi � = log det � 1 + Tr(Ξk) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' Thus, we have log det(Λk+1) − log det(Λk) = log det(I + Ξk) ≥ log det � 1 + Tr(Ξk) � = log � 1 + H � h=1 Tr � Λ−1/2 k (φk h)(φk h)⊤Λ−1/2 k �� = log � 1 + H � h=1 (φk h)⊤Λ−1 k φk h � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} +page_content=' (45) EXPLORATION IN MODEL-BASED RL Combining (44) and (45), we conclude that K � k=1 H � h=1 ∥φk h∥2 Λ−1 k ≤ K � k=1 log det(Λk+1) − log det(Λk) = 2 log � det(ΛK+1) · det(Λ0)−1� , which concludes the proof of Lemma 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/K9E1T4oBgHgl3EQfYwRv/content/2301.03142v1.pdf'} diff --git a/KdE4T4oBgHgl3EQf7w5t/content/2301.05342v1.pdf b/KdE4T4oBgHgl3EQf7w5t/content/2301.05342v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d6d97268e35495c2054e9f741733aa4344c8a128 --- /dev/null +++ b/KdE4T4oBgHgl3EQf7w5t/content/2301.05342v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e8b445aed3c8e635129ffe89748bac3f1b7e848c8f4267d83e2bc30fb95d1d6f +size 695903 diff --git a/KdE4T4oBgHgl3EQf7w5t/vector_store/index.faiss b/KdE4T4oBgHgl3EQf7w5t/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..111740b07fc8d2ade7ee4a04f40d1ec64867d902 --- /dev/null +++ b/KdE4T4oBgHgl3EQf7w5t/vector_store/index.faiss 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b/LtE3T4oBgHgl3EQfAwm8/content/tmp_files/2301.04261v1.pdf.txt @@ -0,0 +1,937 @@ +TOWARDS MICROSTRUCTURAL STATE VARIABLES IN +MATERIALS SYSTEMS +A PREPRINT +Veera Sundararaghavan∗ +Department of Aerospace Engineering +University of Michigan +Ann Arbor, MI +veeras@umich.edu +Megna Shah and Jeff Simmons +Materials and Manufacturing Directorate +Air Force Research Laboratory +Wirght Patterson Air Force Base, OH +megna.shah.1@us.af.mil +jeff.simmons.3@afrl.af.mil +January 12, 2023 +ABSTRACT +The vast combination of material properties seen in nature are achieved by the complexity of the +material microstructure. Advanced characterization and physics based simulation techniques have +led to generation of extremely large microstructural datasets. There is a need for machine learning +techniques that can manage data complexity by capturing the maximal amount of information about +the microstructure using the least number of variables. This paper aims to formulate dimensionality +and state variable estimation techniques focused on reducing microstructural image data. It is shown +that local dimensionality estimation based on nearest neighbors tend to give consistent dimension +estimates for natural images for all p-Minkowski distances. However, it is found that dimensionality +estimates have a systematic error for low-bit depth microstructural images. The use of Manhattan +distance to alleviate this issue is demonstrated. It is also shown that stacked autoencoders can recon- +struct the generator space of high dimensional microstructural data and provide a sparse set of state +variables to fully describe the variability in material microstructures. +Keywords Intrinsic dimensionality · maximum likelihood estimation · Minkowski distances · Microstructures · +autoencoders +∗Corresponding author: Prof. Sundararaghavan, Email: veeras@umich.edu, Tel: 734-615-7242 +arXiv:2301.04261v1 [cs.LG] 11 Jan 2023 + +arXiv Paper +A PREPRINT +1 +Introduction +It is widely accepted that controlling the microstructure of a material will enable control of its properties. But it is less +clear which, or even how many, of the features of the microstructure represent its variability. Recently, Chen, et al. [8] +identified intrinsic dimensions in complex and chaotic dynamical systems, using only short videos of their behavior +and proposed that state variables of complex systems may be identified in this way. This suggests the tantalizing +prospect of identification of a minimal set of microstructural state variables that would govern the material’s behavior. +This minimum number of features would encode all of the dimensions in the microstructure necessary to make design +decisions, much like when the Wright brothers ‘invented the airplane’ by discovering how to control all dimensions of +motion. Finding and controlling all dimensions of the microstructure could enable a completely new way of exploiting +design spaces. +Recent advances in characterization techniques and computing have led to generation and analysis of large datasets, +enabling improved understanding of microstructure. Much work has been done to quantify various aspects of the +microstructure, such as particle size and shape distributions, orientation distributions, n-point statistics among others +[39, 28, 5, 35], enabling significant advancements in processing-structure-properties understanding. But this has relied +on domain experts manually identifying which features should be characterized. While advancing the understanding, +this still leaves the uncertainty as to the degree to which the important variation in the structure was actually quantified. +Although each microstructure can be represented as a vector of size n, the actual dimensionality of an entire database +of microstructures is expected to be much lower. In formal terms, a data set containing points of dimensionality +n is said to have intrinsic dimensionality (ID) equal to µ < n if every point lies entirely within an µ-dimensional +manifold of ℜn. The methods of dimensionality estimation can be categorized as local and global approaches. Global +methods for ID estimation rely on the spread of the entire dataset, as exemplified by projection methods such as +the principal component analysis (PCA). Linear methods such as PCA and multidimensional scaling were explored +for microstructural data in Refs [38, 34, 36]. However, it is known that such methods tend to fail on non–linear +manifolds [15]. Other global approaches to dimension reduction such as ISOMAP and its variants treat non–linear +manifolds using geodesic distances [37] and have been used to reduce dimensionality of microstructures [15, 24]. +Local approaches use the local geometry of the high dimensional space to estimate the intrinsic dimension and tend +to be more computationally efficient [10]. Levina and Bickel [23] developed such an estimate by choosing an optimal +dimension in which the local neighborhood of points would be uniformly spaced. Pope et. al. [31] applied this +methodology to estimate the dimensionality of some well known benchmark datasets such as the MNIST [22] and +CIFAR [20] datasets and found that the information in those had a surprisingly low number of dimensions, i.e. degrees +of freedom. Estimates ranged from 10 to 25 dimensions from the simplest to most complex dataset. +Much of the work cited above relied on human judgement as to the reasonableness of the dimensionality estimates and +did not have any ground truths by which to evaluate such reasonableness. Consequently, assessing the validity of the +methods becomes problematic. This paper addresses itself to the problem of developing a self-consistent methodology +for estimating the dimensionality of random media such as microstructures through validation against datasets with +known dimensionality and by employing additional distance measures, all of which should yield the same estimated +dimensionality. The classic work of Levina and Bickel [23] and subsequent papers use the L2 norm (Euclidean +distance) to estimate the intrinsic dimension. We find that this approach is inaccurate for low bit depth images, due to +the sparsity of the data. This is a systematic error that persists in recent papers, for example in Ref. [8], where MLE +estimates are higher than the intrinsic dimension for binary images. This is especially concerning for microstructure +images that have a significantly reduced bit depth representing a handful of material phases. Ability to obtain consistent +dimensionality estimates for generalized Minkowski distances is shown, so long as the histogram of pixel values covers +a wide range, but that the estimates become inconsistent when this range is significantly reduced (known as sparsity in +the imaging literature). In this case, its is found that the L1 norm, Minkowski distance for p = 1 is the most accurate. +ID estimators provide only the true dimensionality leaving other questions such as what state variables are actually +encoded in these dimensions. More recently, deep learning generative methods have created representations that +automatically capture the key variables accounting for most of the variation in image based datasets [21, 19], and such +models have been trained on microstructural data [33, 11, 9, 4, 13, 18]. Machine learned representations are expected +to parsimoniously capture the maximal amount of information about the microstructure, as was demonstrated in Ref +[25] by combining neural network representation of images with manifold learning. In Ref. [8], a stacked autoencoder +was employed to reduce physical dynamics data to the intrinsic dimensional space. The minimum number of variables +(matching the intrinsic dimension) found from the autoencoder network are referred to as ‘state variables’ in [8], a +terminology that is adopted in this work. To test the technique, microstructure image datasets were upsampled from +a synthetic low dimensional space and passed to the stacked autoencoder. The results show a successful reduction of +the images back to space describing the state variables providing a promising route to capture useful information in +microstructures. +2 + +arXiv Paper +A PREPRINT +2 +Methodology +2.1 +Microstructures as Random Variables +In this paper, microstructures are modelled as images whose contents are outcomes of observations of random vari- +ables [27]. More formally, a random variable M is defined to describe the Microstructure. In this context, ‘Microstruc- +ture’ is that used by, say, a process engineer who wants a certain microstructure because of its desirable properties. +The outcomes (m ∈ ℜn) from sampling M represent the images that would be observed, say, by a microscopist +investigating the microstructure, where the lower case ‘m’ is used to distinguish an instance from the class. Here, n +is the number of pixels in the image. This way, one can make use of the considerable results from sampling theory, +particularly point processes[32], in the analyses. +2.2 +Microstructures on a Manifold +Modeling microstructure observations as images, an image is an outcome of sampling M to give m. If this image is, +say 256 × 256 in dimension, m ∈ ℜ256×256. This is a huge space, from which all images of this spatial resolution +may be sampled. The vast majority of these images simply represent random noise. By hypothesis, natural (or +microstructural) images occupy a very small subset of this space. That is, the valid images that would plausibly +represent a Microstructure occupy a manifold in ℜ256×256. +Speaking loosely, a manifold is a lower-dimensional space that is contained in our ℜ256×256 space, but having fewer +total number of dimensions. A plane embedded in a 3-D space is an example of a linear manifold, having only 2 +dimensions. More generally, the term ‘manifold’ means some non-linear subspace that can be distorted within the +embedding space. Figure 1(a) shows an example of a manifold in ℜ3, which is known as the ‘swiss roll’ manifold. +Essentially, this is a plane that contains all of the data, but has been ‘rolled up’ into a spiral, so that it exists in ℜ3, +but the points, themselves only occupy ℜ2. In this work, the manifold is referred to as a latent space and the high– +dimensional embedding space as the ambient space. This is motivated by the fact that one would observe the images +in the ambient space (ℜ256×256 in the current example). +x +y +z +0 +1 +2D plane containing images with +volume fraction of 2/3 (binary +images a,b,c) +Cube with vertices representing all +possible 3 pixel binary images +(ii) +T1 +T2 +Low dimensional data in a +high dimensional space +Nearest neighbor shells +around a data point, Tk +represents the radius of the +hypersphere to the kth +nearest neighbor +(i) +L2 +L1 +a +b +c +Figure 1: (i) A ‘swiss roll’ manifold containing image data represented as points. Near–neighbor shells around a +data point are illustrated which can be used to estimate the intrinsic dimensionality. (ii) A mainifold representation of +binary images with n pixels, which exist on vertices of a cube of dimension n. The space of 3 pixel images are shown +with a 2D domain representing images (marked a,b,c) with pixel values that sum to two. +Visualizing images on a latent manifold becomes problematic for greater than three dimensions: very simple images +must be used for illustration, with the extension to higher dimensions being made in a more abstract sense. Using a very +simple image, consisting of only 3 pixels, one can illustrate a latent manifold in an embedding space in Figure 1(b). +The actual ambient space is the closed set +A = {(x, y, z) ∈ ℜ3|x ∈ [0, 1], y ∈ [0, 1], z ∈ [0, 1]} +(1) +The ‘corners’ of A represent binary images, i.e. 1-bit images, where the pixels can only have values of 0 or 1. +Within this space, a (linear) manifold is embedded as: +B = {(x, y, z) ∈ A|x + y + z = 2} +(2) +which represents binary images in which one of the pixels has a value of 0 and two have a value of 1, as well as all +convex combinations [6] of these images to form a constrained set of grayscale images. +3 + +arXiv Paper +A PREPRINT +By hypothesis, microstructure images occupy some latent manifold in an enormous ambient space. Obtaining this +manifold is the subject of manifold learning[30, 26]. Our hypothesis is that the Microstructure may be controlled by +identifying state variables for its description and that these may be enumerated if one knows the dimensionality of the +latent manifold on which the microstructure images lie. It is the subject of disentanglement, an active area of research +in machine learning [17, 14], to make these dimensions interpretable. +2.3 +Nearest Neighbor Approach to Dimensionality Estimation +The nearest neighbor method [29] is a geometric estimator of the intrinsic dimensionality of the manifold on which the +data lies. The assumptions behind this approach are (1) that the samples are independent and identically distributed +(iid) from some distribution, (2) that, in a space of proper dimension, they will be uniformly distributed, (3) that the +mapping between the latent space and the ambient space is continuous, and (4) that the distance between two points +in the ambient space is the same as that in the latent space. +The intuitive meaning of ‘random placement,’ where there is no bias towards one area in space or another. This is +a common one made with modeling, say, trees in a forest. The unique point process that will assure such a random +placement is the Poisson process [2]. The intuitive meaning of ‘continuous’ is that neighboring points in the latent +space correspond to neighboring points in the ambient space. Topology[7] provides a more precise statement of this, +but the essential intuitive interpretation is this. +There is one subtle complication that arises because data is generally not on a linear manifold, but on one that is curved +and twisted. The distance between two points on a curved manifold would be measured as its geodesic distance, +whereas, in the ambient space, it would be measured as a Euclidean distance or similar. Since differentiable manifolds +are approximately Euclidean for small distances, this amounts to a requirement that the distance between points be +made small. +With these assumptions, the dimensionality of a dataset may be made, knowing only a distance between the points. +Levina and Bickel used the Euclidean distance, but we use the generalized p-norm approach of Minkowski, which +reduces to the Euclidean distance for p = 2. All p-norms are required to estimate the same dimensionality, which +yields a ‘best practice’ for intrinsic dimensionality estimation. +The nearest neighbor (NN) method aims to find the intrinsic dimensionality µ ≤ n using the number of nearest +neighbors k of each data point [23]. The data are modeled as being iid samples from a probability density in the low +dimensional latent space ℜµ. By hypothesis, there is a locally homogeneous Poisson process, of dimension µ, such +that the density is constant within a neighborhood of m [32], which will uniformly (at least, locally) distribute the data +points in this space. +Let m1, m2, .., ms ∈ ℜn be the instances of s microstructures. Under these assumptions, the average number of data +points (¯k) that fall into a hypersphere in ℜµ around a point mi will be proportional to the volume of the hypersphere: +¯k = f(m)V(µ, p) +(3) +where the proportionality constant, f(m), defines the uniform probability density defining number of points per unit +volume in ℜµ and V(µ, p) refers to the volume of the hypersphere of dimensionality µ that has an expected number ¯k +nearest neighbors with distances represented using a Lp norm. +The volume of the hypersphere is given by the particular choice of the distance measure. Levina and Bickel[23] used +the Euclidean distance measure (p = 2) where the volume is given by the formula: +V(µ, 2) = V (µ, 2)[Tk(2)]µ +(4) +Where V (µ, 2) is the volume of a hypersphere of unit radius in ℜµ, Tk(2) is the distance from a fixed point m to its kth +nearest neighbor in the ambient space, and the constant 2 within brackets in Eq. 4 indicates the Minkowski 2-norm, +which is the Euclidean distance measure, is being used. By the locally isometric hypothesis, this is the same as the +distance would be measured in the latent space. +2.3.1 +Generalized Distance Measures +For the Euclidean distance, the volume of a unit hypersphere is +πµ/2 +Γ(µ/2+1)[23]. We extend this analysis to apply to the +general Minkowski distances of order p, (dp). +4 + +arXiv Paper +A PREPRINT +Between points mq and ml, dp is defined as: +dp(mq, ml) ≜ +� n +� +i=1 +|mq,i − ml,i|p +�1/p +(5) +Particular cases of the Minkowski distance family are d1, commonly known as the Manhattan distance or the L1 norm +and d2, commonly known as the Euclidean distances or the L2 norm. A geometric representation of a 2D circle for +p = 1, 2, 4, and ∞ is shown in Fig. 2(a), where the surface describes all points equidistant from the origin under the +respective dp. +(a) +L1 +L2 +L4L∞ +x1 +x2 +(b) +Figure 2: (a) Minkowski circles (b) Our estimation of the ratio of average distances to jth and kth nearest neighbor +shells for the swiss roll dataset as a function of the Minkowski parameter. +The volume of a hypersphere of dimensionality µ when using a dp distance measure (see below) is: +V(µ, p) = V (µ, p)[Tk(p)]µ +(6) +where, V (µ, p) = 2µ[Γ(1/p+1)]µ +Γ(µ/p+1) +is the volume of a hypersphere of unit radius in ℜµ and Tk(p) is the distance to the +kth nearest neighbor, both being measured in terms of the dp distance. +For a choice of the Minkowski parameter p, the relationship in Eq. 3 can be used to estimate the dimension by +regressing log ¯Tk(p) on log k over a suitable range of k (eg. from k = ka to k = kb), where ¯Tk(p) denotes the mean +dp distance of points to their kth nearest neighbor. The intrinsic dimension is obtained as the slope: +µ = +log kb − log ka +log Tkb(p) − log Tka(p) = log +� kb +ka +� � +log Tkb(p) +Tka(p) +�−1 +(7) +Since µ is a unique intrinsic dimension, the above equation implies that the ratio +Tkb(p) +Tka(p) is independent of p. +This can be seen as follows, based on a Poisson point process. Using Eq. 3 and Eq. 6, the expected number of points +within a distance rp from a point m can be written as: +¯k = c(p)rµ +p +(8) +where c(p) = f(m)V (µ, p). The hypersphere defined by the points between m and the kth neighbor contains k − 1 +points in its interior, the kth being on the boundary, itself. The Poisson distribution (P) for finding k − 1 points within +a distance of rp from point m is given by: +P(k − 1) = (c(p)rµ +p )k−1 +Γ(k) +exp(−c(p)rµ +p ) +(9) +5 + +arXiv Paper +A PREPRINT +From which one can infer that the rate of the Poisson process is λ(p) = +d +dr(c(p)rµ +p ). +The density function (Fk) of a distance rp from m to its kth neighbor can be written as (using Eq. 8 and 9, and +performing change of variables for the probability density), [29]: +Fk(rp) = +� +(c(p)rµ +p )k−1 +Γ(k) +exp(−c(p)rµ +p ) +� +c(p)µrµ−1 +p +(10) +From this expression, the expectation of a distance rp from m to its kth neighbor can be found as (see appendix 2): +Ek(rp) = +� ∞ +0 +rpFk(rp)drp = c(p)− 1 +µ Γ(k + 1 +µ) +Γ(k) +(11) +The leading term c(p)− 1 +µ , which is a function of Minkowski parameter p, is independent of k. This implies that the +ratio of average distances for different values of k (eg. in Eq. 7) will be independent of the Minkowski parameter. +This is, indeed, correct, as our estimates of the ratio of average distances to jth and kth nearest neighbor shells ( Tj(p) +Tk(p)) +for different Minkowski parameters for the swiss roll shows, Fig. 2(b). +2.4 +MLE estimation using the p–norm +The intrinsic dimensionality estimator in Ref. [23] is a variant of the nearest neighbor theory which seeks a maximum +likelihood estimate (MLE) instead of a mean estimate. The difference is subtle: The nearest neighbor approach esti- +mates the dimension as a statistic that can be computed from data (as in Eq. 7), while the MLE approach seeks the +optimum parameter in the Poisson distribution (eq. 9), which in practise yields a more robust estimate of dimension- +ality. +The log likelihood of the Poisson process can be written as: +L(µ, θ, p) = +� R +0 +log(λ(p)) dN(rp) − +� R +0 +λ(p) drp +(12) +where N(rp) is the number of points within a distance rp from m and θ = log f(m). Maximizing the likelihood +using ∂L +∂θ = 0 and ∂L +∂µ = 0, an optimal value of µ is obtained, also containing ratios of distances [23]: +µk(mi, p) = +1 +k − 1 +� +� +k−1 +� +j=1 +log +�Tk(p) +Tj(p) +�� +� +−1 +(13) +As described in Levina and Bickel, a denominator of k − 2 instead of k − 1 gives an unbiased estimate and is +employed in this work. Fig. 3 shows the variation of computed intrinsic dimension by this approach against the choice +of Minkowski parameter for a Helix and a broken swiss roll dataset. The correct intrinsic dimension is found for all +Minkowski parameters tested: 1 for the helix and 2 for the broken swiss roll. +2.5 +Numerical considerations +Datasets of interest in this work are material microstructures that typically consist of two phases (eg. a fiber composite, +containing a fiber and a matrix) or a finite number of phases (eg. steels containing austenite, martensite, ferrite etc.). +In two phase images, pixels are labeled such that the precipitate is one and the matrix is zero (binary image). Note that +the independence of intrinsic dimensionality to Minkowski parameter is true only if the distance r is non-discrete (eg. +cases in Fig. 3). Here, we show an example where this breaks down using the case of binary images. Here, one has a +discrete manifold where images occupy vertices of a cube as shown in Fig. 1(ii). Consider the distance between any +two images under the Minkowski distance family for the case of binary image. Since the absolute difference between +any two pixels is either zero or one, the distance between any two image instances mq and ml can be written as: +dp(mq, ml) = (||mq − ml||1)1/p +(14) +Here, ||..||1 refers to the L1 norm (Manhattan distance) which derives from using mq,i − ml,i in eq. 14 is either zero +or one for binary images. For Minkowski parameter p = 1, lets say that fitting log ¯Tk(1) against log k would give +the slope as the intrinsic dimension µ∗. When using p = 2, substituting Tk(2) = (Tk(1))1/2 (eq. 14) would give +an intrinsic dimension (slope) of 2µ∗ instead. The same behavior is also obtained with the MLE equation (Eq. 13). +6 + +arXiv Paper +A PREPRINT +Figure 3: MLE based intrinsic dimension for different Minkowski parameters: (left) Helix, µ = 1 (right) Broken swiss +roll, µ = 2. +In general, an intrinsic dimension of pµ∗ would be obtained for the p-Minkowski measure. This inconsistency in our +computed value of intrinsic dimension for binary images is related to a discretization error. One of the objectives +of this paper is to identify a p-Minkowski measure that mitigates this issue in binary microstructural images (or in +general, images with low bit depth) via numerical examples. +3 +Results +The results employ the MLE estimate in Eq. 13. In this equation, every data point mi gives a dimension estimate +for every neighbor count k. A dimension estimate matrix of size k × n is obtained where n is the number of images +in the dataset. The intrinsic dimension is estimated as the mean of the values in the dimension estimate matrix. An +important aspect in dimensionality estimation is removing duplicates from the dataset so that the same datapoint is not +double–counted as its own neighbor. This was done on all datasets before computing the intrinsic dimension. +3.1 +Binary Datasets +In rest of the results, the datasets are split into four categories: +• Dataset 1. Rectangles and squares in a matrix. Ten different synthetic datasets were tested containing +rectangular and square shapes in a matrix following different size and positional constraints which dictate +the intrinsic dimensionality (shown in Fig. 5). Images are of size 128 × 128. In cases A, B, F, G, the shapes +were randomly placed leading to two free dimensions of x and y coordinates of the center of the shape. In +addition, for cases A and B varying sizes were used adding one more dimension in the case of squares (the +width) and two more in the case of rectangles (width and height). In cases C, D, H and I, the shapes were +placed linearly along a horizontal axis at the center, eliminating one intrinsic dimension (the y-coordinate +of center) from cases A, B, F, G, respectively. The last two cases, E and J, include centered shapes with a +variation only in the size of the object. In all cases, the shapes in the images are complete, ie, they are not +cutoff by the image boundary. +• Dataset 2. Randomly centered circles of a constant radius in a matrix. The coordinates of the center (x, y) +are independently sampled using uniform random variables. Images are of size 256 × 256. Four datasets 2A, +2B, 2C, 2D containing radii of r = 24, 36, 48 and 58 pixels, respectively were generated with circle centers +((x, y)) selected within a range such that the circles do not intersect the boundaries. +{(x, y) ∈ ℜ2|r < x < 256 − r, r < y < 256 − r} +(15) +• Dataset 3. A known 3D point cloud is used as the generator for microstructural images, where each point +in the 3D cloud (x1, x2, x3) is mapped to (x, y, R) in a binary image of a circle in a matrix, where R is the +circle radius, (x, y) is the center of the circle. In this way, the radius is no longer a free variable and is related +7 + +arXiv Paper +A PREPRINT +to the center of the circle via the topology of the point cloud (termed the ‘generator space’ to differentiate +from the latent space, which could be lower in dimension). The mapping for the circle from the generator +space to the ambient space would be f : ℜ3 → ℜ128×128. Two cases were used +(i) Dataset 3A (swiss roll circles). The generator space is a 3D swiss roll given as: +x = t cos t + c1, y = 30η2 + c2, z = t sin t + c3 +(16) +where t = 3π +2 (1 + 2η1), η1 and η2 are uniform random variables in the range of 0 to 1 and (c1, c2, c3) are +translation factors chosen as (62, 50, 20) respectively. The latent space will be two dimensional, governed by +the choice of the two random variables η1 and η2. +(ii) Dataset 3B (helix circles). Generator space is a 3D helix, given by the equations: +x = 5(13 + (2 + cos 8t)(cos t)), y = 5(13 + (2 + cos 8t)(sin t)), z = 9(4 + sin 8t) +(17) +where t = 2πη, η being a uniform random variable in the range of 0 to 1. The latent space will be one +dimensional, with the location in the manifold governed by the choice of η. Note that the coordinates of +points in the generator space of Dataset 3A and 3B are rounded before mapping to images because of the +integer (pixel) representation of the centers and radii. +• Dataset 4: Contains results from a phase field simulation of grain growth based on the Allen-Cahn equation +following the numerical formulation of Fan and Chen [12]. The data is in the form of binary images (128 × +128) containing grain boundaries at different time steps of a single simulation. Since all the model parameters +are fixed at the start of the simulation and images are only a function of time, the intrinsic dimensionality of +all images from a single simulation run is expected to be one. Dataset contains results from three different +simulation runs. +3.2 +Intrinsic dimension estimates +Fig. 4(a) shows the variation of intrinsic dimension with the choice of Minkowski parameter for binary image dataset– +2D. The intrinsic dimension is two, and corresponds to the (x, y) coordinate of the center of the circle. In the binary +case, a linear increase in the intrinsic dimension with Minkowski parameter is obtained as explained previously. While +it was expected that the L1 norm gives the minimum intrinsic dimension estimate among these cases, it is also seen +that the L1 distance measure matches the expected intrinsic dimensionality. To further confirm this, the circle is +replaced with a Gaussian distribution centered at the circle origin and with a constant standard deviation (of 20) for all +datasets. Since each of the four cases in dataset 2 contains a circle of different radii, each case spans different number +of grayscale levels. An example is shown in Fig. 4(e) with the blue line spanning a part of the Gaussian curve, distance +between the blue lines is the circle diameter). Cases with radii of 24, 36, 48 and 58 pixels contain 201, 419, 706 and +1001 grayscale levels, respectively. As the number of grayscale levels increase, the intrinsic dimension obtained from +the use of higher p-Minkowski distance measures converge toward the true estimate as given by the L1 norm. +To further test the use of L1 norm for MLE estimation of binary images, all ten cases in dataset 1 were tested (results +shown in Fig. 5). The intrinsic dimension expected for each case is indicated by numbers in green near the cases +in Fig. 5. A histogram of values in the dimension estimate matrix is also plotted and the standard deviation of the +histogram is reported in addition to the mean. As seen from these results, the MLE approach with the L1 norm gives +a sound estimate of the intrinsic dimension in all cases. +3.3 +Retrieving state variables using an autoencoder +While the MLE algorithm recovers the intrinsic dimensionality, it is of interest to identify the geometry of the latent +space and to correlate the dimensions to microstructural features. A variety of applications can benefit from such +analysis, including identification of novel processing paths and inverse design of microstructures for a given property +as shown in Ref. [33]. To generate a proof–of–concept, synthetic dataset C and D are used where the generator space +is known. Our objective was to check if the generator space can be retrieved solely from the image data. +The state variables were identified using an autoencoder architecture. An autoencoder (AE) [3] is a multi-layer neural +network that learns the identity function, such that the output ˆx approximates the input x. In the architecture, the +hidden layers have fewer nodes than the input dimension and act as a bottleneck. In the first few layers, the autoencoder +compresses the input to a compressed (latent space) representation in a process called ‘encoding’. At its simplest, a +single hidden layer operates on the input x ∈ ℜn and generates an encoding y1 ∈ ℜj, j < n such that: +y1 = σ(W1x + b1) +(18) +where W1 represents the j × n weight matrix, b1 is the j × 1 bias vector for the first layer. The function σ is typically +a non-linear activation function and a logistic sigmoid function is used in this work. +8 + +arXiv Paper +A PREPRINT +b +d +a +c +e +a +Figure 4: a. Variation of intrinsic dimension with the choice of Minkowski parameter for a circle with varying position, +represented as binary and grayscale images. The true dimensionality is 2. b. Shows a binary microstructure c. Intensity +across the dotted line in (b) is shown. (d) A grayscale microstructure based on a Gaussian intensity profile. As the +number of grayscale levels increase, the answers for higher p-Minkowski distance measures converge toward the true +estimate. +Later layers reconstruct the output from this latent space representation in a process called ‘decoding’. An example is +another layer that maps the latent vector y1 in the previous step to output ˆx ∈ ℜn such that +ˆx = σ(W2y1 + b2) +(19) +where W2 represents the n × j weight matrix, b2 is the n × 1 bias vector of the second layer. Multiple layers can be +used to develop a deep network. The parameters in W and b are found by minimizing the cost, 1 +2(||x − ˆx||2)2, by +training via backpropagation. +In this work, a stacked autoencoder configuration comprised of four layers in total as shown in Fig. 6(c) is employed. +The first autoencoder comprised of two layers (encoder and decoder) was trained to reduce the dimensions to 100 +first. This was followed by a second autoencoder with two layers (encoder and decoder) that uses the 100 dimensional +feature from the first autoencoder as input and reduces it to the intrinsic dimension identified by the MLE algorithm +or the generator dimension. The two autoencoders were sequentially trained first, followed by re–training a combined +four–layer autoencoder. +Fig. 6 shows a schematic of the approach using dataset 3A (circles sampled from a swiss roll, Fig. 6(b)). The stacked +autoencoder reads in the images into a network with a bottleneck equal to the generator space dimension (=3). The +decoded images from the last layer are shown in Fig. 6(d). The three variables corresponding to each image are plotted +in Fig. 6(e) which shows that the generated topology is similar to the actual generator space in Fig. 6(a). The points +shown are colored according to the circle radius in the images. Note that the autoencoder, by default, restricts the +range of values to between 0 and 1. However, the topology of the space is generally well reconstructed demonstrating +a proof–of–concept that variables that define the microstructural state can be identified using stacked autoencoders. +Figure 7(b,c) shows both the computed generator space and the 1D latent space for the helix circles dataset 3B (Figure +7(a) shows the actual generator space from which the images were sampled with (x1, x2, x3) coordinate equal to +(r, x, y) in the image). As in the swiss roll case, the generator space for the helix data set also looks similar to the +generator space considering that the points are mapped in the range [0, 1] by the autoencoder. The computed latent +spaces are colored according to a microstructural feature, the radius of the circle. Clustering of this feature in the +latent space demonstrates promise towards the use of proximity analysis to find new microstructures with interesting +properties through interpolation. Such an application will form a part of our future efforts. +The last example is from dataset 4 (phase field data). In the results from this dataset in Fig. 8, one simulation +trajectory was used in two stacked autoencoders of bottleneck 3 and 2. Fig. 8(a) compares the reconstructions from +the autoencoder against the original images at five randomly chosen time steps from this trajectory. Each consecutive +time step in the phase field data results in incremental changes in topology of grain boundaries, hence it is expected +9 + +arXiv Paper +A PREPRINT +Randomly placed rectangles, vary size +Linearly placed rectangle, vary size +Randomly placed squares, same size +Linearly placed squares, vary size +Randomly placed rectangles, same size +Linearly placed rectangles, same size +Linearly placed squares, same size +A +B +C +D +F +G +H +I +2 / 2 +1 / 1 +2.9 / 3 +2 / 2 +2 / 2 +1 / 1 +3.6 / 4 +2.8/ 3 +Centered rectangles, vary size +1.9 /2 +E +Randomly placed squares, vary size +Centered squares, vary size +1 / 1 +J +Figure 5: Variation of MLE based intrinsic dimension for a variety of synthetic datasets using L1 norm. The predicted +dimension for various data points are shown as a histogram. The numbers in red indicate mean predictions for each +case. The numbers in green are the expected dimensionality. +that data points are arranged in the order of time steps in the latent space. This is indeed seen in the topologies of +the space constructed by the autoencoder as shown in Fig. 8(b,c). Similar to the helix case seen earlier, the intrinsic +dimensionality is expected to be one which is confirmed by the results of the MLE algorithm in Fig. 8(c). +In the last example, the complete dataset containing three different phase field simulations is employed with an au- +toencoder bottleneck of 3. The resulting latent space is shown in Fig. 9. In all three simulations, the initial image was +the same represented by the central point in the latent space. The trajectories from the three simulations emerge in +different directions from the initial point, resulting in different final microstructures. This latent space is an example +of a microstructural space for a grain coarsening process. To estimate the true dimensionality of the processing space, +a large number of trajectories need to be superposed. Although a simplistic set of three trajectories are shown, this +example shows how the framework can be used to visualize a multitude of complex processes within a single graph. +Past work in [36, 1] employed similar visualization of linear PCA components to perform process design, the use of +non–linear manifolds as demonstrated here is expected to significantly improve state–of–the–art and will form part of +our future work. +4 +Conclusions +A methodology for reliably estimating the intrinsic dimensionality of random media is developed. The method re- +solves the ambiguity in results for images with low bit depth when using state–of–the–art techniques that employ the +Euclidean (L2) norm. Particular novel contributions of this work are listed below: +• It is shown that the NN and MLE formulae for intrinsic dimensionality estimation can work with all +Minkowski distance measures. Further, the examples show that all Minkowski measures give the same in- +trinsic dimensionality for non-discrete datasets. +• Dimensionality estimates are dependent on distance measures for image data with discrete levels as was +shown for binary images. Through examples, it is shown that the use of L1 distance in the MLE estimate +produces a reliable estimate in such cases. +10 + +d = 3.6 +/- 0.7 +1500 +500 +0 +10 +20 +30 +Dimensionality2000 +d = 2.0 +/- 0.3 +1500 +500 +0 +0 +10 +20 +30 +Dimensionality2000 +d = 2.8 +/- 0.6 +Counts +1500 +1000 +500 +0 +0 +10 +20 +30 +Dimensionality600 +d = 1.0 +/- 0.1 +200 +0 +0 +10 +20 +30 +Dimensionality2500 +d = 2.9 +/- 0.8 +2000 +uno +1500 + 1000 +500 +0 +10 +20 +30 +Dimensionality2000 +d = 2.0 +/- 0.3 +1500 +500 +0 +10 +20 +30 +Dimensionality1500 +d = 2.0 +/- 0.3 +Counts +1000 +500 +0 +0 +10 +20 +30 +Dimensionalityd = 1.0 +/- 0.1 +400 +2300 +uno +8200 +100 +0 +0 +10 +20 +30 +Dimensionality500 +d = 1.9 +/- 0.2 +400 +200 +100 +0 +0 +10 +20 +30 +Dimensionality30 +d = 1.0 +/- 0.2 +Counts +20 +10 +0 +0 +10 +20 +30 +DimensionalityarXiv Paper +A PREPRINT +Generator space (swiss roll) +Plot latent representation +16384 +16384 +100 +3 +100 +Sample circle center (x,y) +and radius (z) from swiss roll +Ambient space (Training data) +Decoded images +Reconstructed generator space +Stacked Autoencoder +(a) +(b) +(c) +(d) +(e) +radius +radius +Figure 6: +Use of autoencoders for building a generator space is shown using a synthetic dataset. (a) The swiss roll +is the generator space, each point has a (x1, x2, x3) coordinate equal to (R, x, y) in an image where R is the circle +radius, (x, y) is the center of the circle. (b) Shows images from the database. (c) Stacked autoencoder reads in the +images into a network with a bottleneck equal to the generator space dimension (=3) (d) Decoded images from the +last layer of the network. (e) The 1000 images are reduced to three variables in the bottleneck. These variables when +plotted show the generator space. +a +b +c +Generator space +Autoencoder: generator space +Autoencoder: latent space +Figure 7: Helix circles dataset 3B: (a) Generator space where images are sampled (b) Generator space computed from +the images using the stacked autoencoder (c) Intrinsic dimensional (1D) space computed by the stacked autoencoder. +• Examples show that stacked autoencoders can reconstruct the low dimensional generator spaces of mi- +crostructures and provide a sparse set of state variables to fully describe material microstructures. +Use of these state variables to quantify microstructure–property–process relationships will form a part of our future +work. +Data availability +Codes and datasets will be made freely available upon publication in a peer–reviewed journal. +11 + +arXiv Paper +A PREPRINT +Original data +Decoder output (3D latent space) +Decoder output (2D latent space) +(a) +(b) +(c) +3D autoencoder representation +2D autoencoder representation +(d) +Figure 8: (a) Decoder outputs for a single phase field trajectory (b) Comparison of 3D versus 2D representation of the +autoencoder (c) MLE estimate of dimensionality +Original data +Decoder output (3D latent space) +(b) +3D autoencoder representation +(a) +Figure 9: (a) Decoder outputs for combined dataset containing all three phase field trajectories (b) 3D representation +from autoencoder showing all three trajectories. +Acknowledgements +This research was supported in part by the Air Force Research Laboratory Materials and Manufacturing Directorate, +through the Air Force Office of Scientific Research Summer Faculty Fellowship Program, Contract Numbers FA8750- +15-3-6003 and FA9550-15-0001. This research was supported in part through computational resources and services +provided by Advanced Research Computing at the University of Michigan, Ann Arbor. +References +[1] Pinar Acar and Veera Sundararaghavan. Linear solution scheme for microstructure design with process con- +straints. AIAA Journal, 54(12):4022 – 4031, 2016. +[2] Adrian Baddeley, Imre Bárány, and Rolf Schneider. Spatial point processes and their applications. Stochastic +Geometry: Lectures Given at the CIME Summer School Held in Martina Franca, Italy, September 13–18, 2004, +pages 1–75, 2007. +[3] Pierre Baldi and Kurt Hornik. Neural networks and principal component analysis: Learning from examples +without local minima. Neural networks, 2(1):53–58, 1989. +[4] Ramin Bostanabad. Reconstruction of 3d microstructures from 2d images via transfer learning. 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In general, image boundaries can play a role in biasing the intrinsic +dimension. Consider the case of a single circular shape placed in a matrix. If the shape intersects the boundary, only +a part of the shape is seen and the intrinsic dimensionality of three as judged from the dataset assumes that the shape +always remains a circle. To test this, we have plotted results from two datasets, one with and one without boundary +intersections. We consider sufficiently high sample size (3000 images) and image size (128 × 128) for each case. +The histogram of estimated dimension per data point is plotted in Fig. S1a showing that the algorithm is able to +predict the correct mean dimension for both cases. The key difference being that the histogram is broader and a higher +standard deviation is obtained when the circles intersect the boundary. Another case is shown in Fig. S1b where the +circle is linearly placed along the centerline. Here, two distinct peaks are seen in the histogram where the circles are +freely placed, with the first peak at a lower intrinsic dimension. the mean dimension is again correctly estimated for +both cases with a higher standard deviation for the case where circles intersect the image boundaries. A case where +the circles are periodic is also shown here, where the circles wrap around on the opposite side when they intersect +the boundary. While this case shows a single sharp peak as in the case where boundaries are avoided, the standard +deviation is higher than that case. +Appendix 2 +Equation (10) simplifies to: +Fk(rp) = +� +(c(p)rµ +p )k−1 +Γ(k) +e−c(p)rµ +p +� +c(p)µrµ−1 +p += +� +c(p)kµ +� +1 +Γ(k) +�� +rµk−1 +p +e−c(p)rµ +p +14 + +arXiv Paper +A PREPRINT +Figure S1: Histograms of estimated dimension per data point (a) Two cases are considered, a circle of varying radii +is freely placed in one case and avoids boundary in another case. (b) Here, the circle is linearly placed along the +centerline. A case with periodicity is included. Inset images show superposition of a few different images in each +dataset. +Inserting this into Equation (11): +Ek(rp) = +� ∞ +0 +rpFk(rp)drp += +� +c(p)kµ +� +1 +Γ(k) +�� � ∞ +0 +rµk +p e−c(p)rµ +p drp +Changing the integration variable with ξ ≜ c(p)rµ +p (rp = ξ1/µc(p)−1/µ): +Ek(rp) = +� +c(p)kµ +� +1 +Γ(k) +�� � ∞ +0 +(ξ1/µc(p)−1/µ)µke−ξd(ξ1/µc(p)−1/µ) += c(p)−1/µ +� +1 +Γ(k) +� � ∞ +0 +ξk+1/µ−1e−ξdξ +The integral is, by definition, Γ(k + 1/µ) [16]. Substituting: +Ek(rp) = c(p)−1/µ Γ(k + 1/µ) +Γ(k) +15 + diff --git a/LtE3T4oBgHgl3EQfAwm8/content/tmp_files/load_file.txt b/LtE3T4oBgHgl3EQfAwm8/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..1afdeea32b050588d36ad11f5298e7518e1329e6 --- /dev/null +++ b/LtE3T4oBgHgl3EQfAwm8/content/tmp_files/load_file.txt @@ -0,0 +1,522 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf,len=521 +page_content='TOWARDS MICROSTRUCTURAL STATE VARIABLES IN MATERIALS SYSTEMS A PREPRINT Veera Sundararaghavan∗ Department of Aerospace Engineering University of Michigan Ann Arbor, MI veeras@umich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='edu Megna Shah and Jeff Simmons Materials and Manufacturing Directorate Air Force Research Laboratory Wirght Patterson Air Force Base, OH megna.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='shah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='1@us.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='af.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='mil jeff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='simmons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='3@afrl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='af.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='mil January 12, 2023 ABSTRACT The vast combination of material properties seen in nature are achieved by the complexity of the material microstructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Advanced characterization and physics based simulation techniques have led to generation of extremely large microstructural datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' There is a need for machine learning techniques that can manage data complexity by capturing the maximal amount of information about the microstructure using the least number of variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' This paper aims to formulate dimensionality and state variable estimation techniques focused on reducing microstructural image data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' It is shown that local dimensionality estimation based on nearest neighbors tend to give consistent dimension estimates for natural images for all p-Minkowski distances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' However, it is found that dimensionality estimates have a systematic error for low-bit depth microstructural images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The use of Manhattan distance to alleviate this issue is demonstrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' It is also shown that stacked autoencoders can recon- struct the generator space of high dimensional microstructural data and provide a sparse set of state variables to fully describe the variability in material microstructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Keywords Intrinsic dimensionality · maximum likelihood estimation · Minkowski distances · Microstructures · autoencoders ∗Corresponding author: Prof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Sundararaghavan, Email: veeras@umich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='edu, Tel: 734-615-7242 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='04261v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='LG] 11 Jan 2023 arXiv Paper A PREPRINT 1 Introduction It is widely accepted that controlling the microstructure of a material will enable control of its properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' But it is less clear which, or even how many, of the features of the microstructure represent its variability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Recently, Chen, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' [8] identified intrinsic dimensions in complex and chaotic dynamical systems, using only short videos of their behavior and proposed that state variables of complex systems may be identified in this way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' This suggests the tantalizing prospect of identification of a minimal set of microstructural state variables that would govern the material’s behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' This minimum number of features would encode all of the dimensions in the microstructure necessary to make design decisions, much like when the Wright brothers ‘invented the airplane’ by discovering how to control all dimensions of motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Finding and controlling all dimensions of the microstructure could enable a completely new way of exploiting design spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Recent advances in characterization techniques and computing have led to generation and analysis of large datasets, enabling improved understanding of microstructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Much work has been done to quantify various aspects of the microstructure, such as particle size and shape distributions, orientation distributions, n-point statistics among others [39, 28, 5, 35], enabling significant advancements in processing-structure-properties understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' But this has relied on domain experts manually identifying which features should be characterized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' While advancing the understanding, this still leaves the uncertainty as to the degree to which the important variation in the structure was actually quantified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Although each microstructure can be represented as a vector of size n, the actual dimensionality of an entire database of microstructures is expected to be much lower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' In formal terms, a data set containing points of dimensionality n is said to have intrinsic dimensionality (ID) equal to µ < n if every point lies entirely within an µ-dimensional manifold of ℜn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The methods of dimensionality estimation can be categorized as local and global approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Global methods for ID estimation rely on the spread of the entire dataset, as exemplified by projection methods such as the principal component analysis (PCA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Linear methods such as PCA and multidimensional scaling were explored for microstructural data in Refs [38, 34, 36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' However, it is known that such methods tend to fail on non–linear manifolds [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Other global approaches to dimension reduction such as ISOMAP and its variants treat non–linear manifolds using geodesic distances [37] and have been used to reduce dimensionality of microstructures [15, 24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Local approaches use the local geometry of the high dimensional space to estimate the intrinsic dimension and tend to be more computationally efficient [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Levina and Bickel [23] developed such an estimate by choosing an optimal dimension in which the local neighborhood of points would be uniformly spaced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Pope et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' [31] applied this methodology to estimate the dimensionality of some well known benchmark datasets such as the MNIST [22] and CIFAR [20] datasets and found that the information in those had a surprisingly low number of dimensions, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Estimates ranged from 10 to 25 dimensions from the simplest to most complex dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Much of the work cited above relied on human judgement as to the reasonableness of the dimensionality estimates and did not have any ground truths by which to evaluate such reasonableness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Consequently, assessing the validity of the methods becomes problematic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' This paper addresses itself to the problem of developing a self-consistent methodology for estimating the dimensionality of random media such as microstructures through validation against datasets with known dimensionality and by employing additional distance measures, all of which should yield the same estimated dimensionality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The classic work of Levina and Bickel [23] and subsequent papers use the L2 norm (Euclidean distance) to estimate the intrinsic dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' We find that this approach is inaccurate for low bit depth images, due to the sparsity of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' This is a systematic error that persists in recent papers, for example in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' [8], where MLE estimates are higher than the intrinsic dimension for binary images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' This is especially concerning for microstructure images that have a significantly reduced bit depth representing a handful of material phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Ability to obtain consistent dimensionality estimates for generalized Minkowski distances is shown, so long as the histogram of pixel values covers a wide range, but that the estimates become inconsistent when this range is significantly reduced (known as sparsity in the imaging literature).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' In this case, its is found that the L1 norm, Minkowski distance for p = 1 is the most accurate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' ID estimators provide only the true dimensionality leaving other questions such as what state variables are actually encoded in these dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' More recently, deep learning generative methods have created representations that automatically capture the key variables accounting for most of the variation in image based datasets [21, 19], and such models have been trained on microstructural data [33, 11, 9, 4, 13, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Machine learned representations are expected to parsimoniously capture the maximal amount of information about the microstructure, as was demonstrated in Ref [25] by combining neural network representation of images with manifold learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' In Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' [8], a stacked autoencoder was employed to reduce physical dynamics data to the intrinsic dimensional space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The minimum number of variables (matching the intrinsic dimension) found from the autoencoder network are referred to as ‘state variables’ in [8], a terminology that is adopted in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' To test the technique, microstructure image datasets were upsampled from a synthetic low dimensional space and passed to the stacked autoencoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The results show a successful reduction of the images back to space describing the state variables providing a promising route to capture useful information in microstructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 2 arXiv Paper A PREPRINT 2 Methodology 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='1 Microstructures as Random Variables In this paper, microstructures are modelled as images whose contents are outcomes of observations of random vari- ables [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' More formally, a random variable M is defined to describe the Microstructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' In this context, ‘Microstruc- ture’ is that used by, say, a process engineer who wants a certain microstructure because of its desirable properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The outcomes (m ∈ ℜn) from sampling M represent the images that would be observed, say, by a microscopist investigating the microstructure, where the lower case ‘m’ is used to distinguish an instance from the class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Here, n is the number of pixels in the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' This way, one can make use of the considerable results from sampling theory, particularly point processes[32], in the analyses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='2 Microstructures on a Manifold Modeling microstructure observations as images, an image is an outcome of sampling M to give m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' If this image is, say 256 × 256 in dimension, m ∈ ℜ256×256.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' This is a huge space, from which all images of this spatial resolution may be sampled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The vast majority of these images simply represent random noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' By hypothesis, natural (or microstructural) images occupy a very small subset of this space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' That is, the valid images that would plausibly represent a Microstructure occupy a manifold in ℜ256×256.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Speaking loosely, a manifold is a lower-dimensional space that is contained in our ℜ256×256 space, but having fewer total number of dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' A plane embedded in a 3-D space is an example of a linear manifold, having only 2 dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' More generally, the term ‘manifold’ means some non-linear subspace that can be distorted within the embedding space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Figure 1(a) shows an example of a manifold in ℜ3, which is known as the ‘swiss roll’ manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Essentially, this is a plane that contains all of the data, but has been ‘rolled up’ into a spiral, so that it exists in ℜ3, but the points, themselves only occupy ℜ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' In this work, the manifold is referred to as a latent space and the high– dimensional embedding space as the ambient space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' This is motivated by the fact that one would observe the images in the ambient space (ℜ256×256 in the current example).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' x y z 0 1 2D plane containing images with volume fraction of 2/3 (binary images a,b,c) Cube with vertices representing all possible 3 pixel binary images (ii) T1 T2 Low dimensional data in a high dimensional space Nearest neighbor shells around a data point, Tk represents the radius of the hypersphere to the kth nearest neighbor (i) L2 L1 a b c Figure 1: (i) A ‘swiss roll’ manifold containing image data represented as points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Near–neighbor shells around a data point are illustrated which can be used to estimate the intrinsic dimensionality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' (ii) A mainifold representation of binary images with n pixels, which exist on vertices of a cube of dimension n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The space of 3 pixel images are shown with a 2D domain representing images (marked a,b,c) with pixel values that sum to two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Visualizing images on a latent manifold becomes problematic for greater than three dimensions: very simple images must be used for illustration, with the extension to higher dimensions being made in a more abstract sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Using a very simple image, consisting of only 3 pixels, one can illustrate a latent manifold in an embedding space in Figure 1(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The actual ambient space is the closed set A = {(x, y, z) ∈ ℜ3|x ∈ [0, 1], y ∈ [0, 1], z ∈ [0, 1]} (1) The ‘corners’ of A represent binary images, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 1-bit images, where the pixels can only have values of 0 or 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Within this space, a (linear) manifold is embedded as: B = {(x, y, z) ∈ A|x + y + z = 2} (2) which represents binary images in which one of the pixels has a value of 0 and two have a value of 1, as well as all convex combinations [6] of these images to form a constrained set of grayscale images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 3 arXiv Paper A PREPRINT By hypothesis, microstructure images occupy some latent manifold in an enormous ambient space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Obtaining this manifold is the subject of manifold learning[30, 26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Our hypothesis is that the Microstructure may be controlled by identifying state variables for its description and that these may be enumerated if one knows the dimensionality of the latent manifold on which the microstructure images lie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' It is the subject of disentanglement, an active area of research in machine learning [17, 14], to make these dimensions interpretable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='3 Nearest Neighbor Approach to Dimensionality Estimation The nearest neighbor method [29] is a geometric estimator of the intrinsic dimensionality of the manifold on which the data lies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The assumptions behind this approach are (1) that the samples are independent and identically distributed (iid) from some distribution, (2) that, in a space of proper dimension, they will be uniformly distributed, (3) that the mapping between the latent space and the ambient space is continuous, and (4) that the distance between two points in the ambient space is the same as that in the latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The intuitive meaning of ‘random placement,’ where there is no bias towards one area in space or another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' This is a common one made with modeling, say, trees in a forest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The unique point process that will assure such a random placement is the Poisson process [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The intuitive meaning of ‘continuous’ is that neighboring points in the latent space correspond to neighboring points in the ambient space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Topology[7] provides a more precise statement of this, but the essential intuitive interpretation is this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' There is one subtle complication that arises because data is generally not on a linear manifold, but on one that is curved and twisted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The distance between two points on a curved manifold would be measured as its geodesic distance, whereas, in the ambient space, it would be measured as a Euclidean distance or similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Since differentiable manifolds are approximately Euclidean for small distances, this amounts to a requirement that the distance between points be made small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' With these assumptions, the dimensionality of a dataset may be made, knowing only a distance between the points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Levina and Bickel used the Euclidean distance, but we use the generalized p-norm approach of Minkowski, which reduces to the Euclidean distance for p = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' All p-norms are required to estimate the same dimensionality, which yields a ‘best practice’ for intrinsic dimensionality estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The nearest neighbor (NN) method aims to find the intrinsic dimensionality µ ≤ n using the number of nearest neighbors k of each data point [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The data are modeled as being iid samples from a probability density in the low dimensional latent space ℜµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' By hypothesis, there is a locally homogeneous Poisson process, of dimension µ, such that the density is constant within a neighborhood of m [32], which will uniformly (at least, locally) distribute the data points in this space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Let m1, m2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='., ms ∈ ℜn be the instances of s microstructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Under these assumptions, the average number of data points (¯k) that fall into a hypersphere in ℜµ around a point mi will be proportional to the volume of the hypersphere: ¯k = f(m)V(µ, p) (3) where the proportionality constant, f(m), defines the uniform probability density defining number of points per unit volume in ℜµ and V(µ, p) refers to the volume of the hypersphere of dimensionality µ that has an expected number ¯k nearest neighbors with distances represented using a Lp norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The volume of the hypersphere is given by the particular choice of the distance measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Levina and Bickel[23] used the Euclidean distance measure (p = 2) where the volume is given by the formula: V(µ, 2) = V (µ, 2)[Tk(2)]µ (4) Where V (µ, 2) is the volume of a hypersphere of unit radius in ℜµ, Tk(2) is the distance from a fixed point m to its kth nearest neighbor in the ambient space, and the constant 2 within brackets in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 4 indicates the Minkowski 2-norm, which is the Euclidean distance measure, is being used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' By the locally isometric hypothesis, this is the same as the distance would be measured in the latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='1 Generalized Distance Measures For the Euclidean distance, the volume of a unit hypersphere is πµ/2 Γ(µ/2+1)[23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' We extend this analysis to apply to the general Minkowski distances of order p, (dp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 4 arXiv Paper A PREPRINT Between points mq and ml, dp is defined as: dp(mq, ml) ≜ � n � i=1 |mq,i − ml,i|p �1/p (5) Particular cases of the Minkowski distance family are d1, commonly known as the Manhattan distance or the L1 norm and d2, commonly known as the Euclidean distances or the L2 norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' A geometric representation of a 2D circle for p = 1, 2, 4, and ∞ is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 2(a), where the surface describes all points equidistant from the origin under the respective dp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' (a) L1 L2 L4L∞ x1 x2 (b) Figure 2: (a) Minkowski circles (b) Our estimation of the ratio of average distances to jth and kth nearest neighbor shells for the swiss roll dataset as a function of the Minkowski parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The volume of a hypersphere of dimensionality µ when using a dp distance measure (see below) is: V(µ, p) = V (µ, p)[Tk(p)]µ (6) where, V (µ, p) = 2µ[Γ(1/p+1)]µ Γ(µ/p+1) is the volume of a hypersphere of unit radius in ℜµ and Tk(p) is the distance to the kth nearest neighbor, both being measured in terms of the dp distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' For a choice of the Minkowski parameter p, the relationship in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 3 can be used to estimate the dimension by regressing log ¯Tk(p) on log k over a suitable range of k (eg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' from k = ka to k = kb), where ¯Tk(p) denotes the mean dp distance of points to their kth nearest neighbor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The intrinsic dimension is obtained as the slope: µ = log kb − log ka log Tkb(p) − log Tka(p) = log � kb ka � � log Tkb(p) Tka(p) �−1 (7) Since µ is a unique intrinsic dimension, the above equation implies that the ratio Tkb(p) Tka(p) is independent of p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' This can be seen as follows, based on a Poisson point process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 3 and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 6, the expected number of points within a distance rp from a point m can be written as: ¯k = c(p)rµ p (8) where c(p) = f(m)V (µ, p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The hypersphere defined by the points between m and the kth neighbor contains k − 1 points in its interior, the kth being on the boundary, itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The Poisson distribution (P) for finding k − 1 points within a distance of rp from point m is given by: P(k − 1) = (c(p)rµ p )k−1 Γ(k) exp(−c(p)rµ p ) (9) 5 arXiv Paper A PREPRINT From which one can infer that the rate of the Poisson process is λ(p) = d dr(c(p)rµ p ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The density function (Fk) of a distance rp from m to its kth neighbor can be written as (using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 8 and 9, and performing change of variables for the probability density), [29]: Fk(rp) = � (c(p)rµ p )k−1 Γ(k) exp(−c(p)rµ p ) � c(p)µrµ−1 p (10) From this expression, the expectation of a distance rp from m to its kth neighbor can be found as (see appendix 2): Ek(rp) = � ∞ 0 rpFk(rp)drp = c(p)− 1 µ Γ(k + 1 µ) Γ(k) (11) The leading term c(p)− 1 µ , which is a function of Minkowski parameter p, is independent of k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' This implies that the ratio of average distances for different values of k (eg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 7) will be independent of the Minkowski parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' This is, indeed, correct, as our estimates of the ratio of average distances to jth and kth nearest neighbor shells ( Tj(p) Tk(p)) for different Minkowski parameters for the swiss roll shows, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 2(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='4 MLE estimation using the p–norm The intrinsic dimensionality estimator in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' [23] is a variant of the nearest neighbor theory which seeks a maximum likelihood estimate (MLE) instead of a mean estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The difference is subtle: The nearest neighbor approach esti- mates the dimension as a statistic that can be computed from data (as in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 7), while the MLE approach seeks the optimum parameter in the Poisson distribution (eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 9), which in practise yields a more robust estimate of dimension- ality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The log likelihood of the Poisson process can be written as: L(µ, θ, p) = � R 0 log(λ(p)) dN(rp) − � R 0 λ(p) drp (12) where N(rp) is the number of points within a distance rp from m and θ = log f(m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Maximizing the likelihood using ∂L ∂θ = 0 and ∂L ∂µ = 0, an optimal value of µ is obtained, also containing ratios of distances [23]: µk(mi, p) = 1 k − 1 � � k−1 � j=1 log �Tk(p) Tj(p) �� � −1 (13) As described in Levina and Bickel, a denominator of k − 2 instead of k − 1 gives an unbiased estimate and is employed in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 3 shows the variation of computed intrinsic dimension by this approach against the choice of Minkowski parameter for a Helix and a broken swiss roll dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The correct intrinsic dimension is found for all Minkowski parameters tested: 1 for the helix and 2 for the broken swiss roll.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='5 Numerical considerations Datasets of interest in this work are material microstructures that typically consist of two phases (eg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' a fiber composite, containing a fiber and a matrix) or a finite number of phases (eg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' steels containing austenite, martensite, ferrite etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' In two phase images, pixels are labeled such that the precipitate is one and the matrix is zero (binary image).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Note that the independence of intrinsic dimensionality to Minkowski parameter is true only if the distance r is non-discrete (eg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' cases in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Here, we show an example where this breaks down using the case of binary images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Here, one has a discrete manifold where images occupy vertices of a cube as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 1(ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Consider the distance between any two images under the Minkowski distance family for the case of binary image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Since the absolute difference between any two pixels is either zero or one, the distance between any two image instances mq and ml can be written as: dp(mq, ml) = (||mq − ml||1)1/p (14) Here, ||.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='.||1 refers to the L1 norm (Manhattan distance) which derives from using mq,i − ml,i in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 14 is either zero or one for binary images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' For Minkowski parameter p = 1, lets say that fitting log ¯Tk(1) against log k would give the slope as the intrinsic dimension µ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' When using p = 2, substituting Tk(2) = (Tk(1))1/2 (eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 14) would give an intrinsic dimension (slope) of 2µ∗ instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The same behavior is also obtained with the MLE equation (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 6 arXiv Paper A PREPRINT Figure 3: MLE based intrinsic dimension for different Minkowski parameters: (left) Helix, µ = 1 (right) Broken swiss roll, µ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' In general, an intrinsic dimension of pµ∗ would be obtained for the p-Minkowski measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' This inconsistency in our computed value of intrinsic dimension for binary images is related to a discretization error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' One of the objectives of this paper is to identify a p-Minkowski measure that mitigates this issue in binary microstructural images (or in general, images with low bit depth) via numerical examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 3 Results The results employ the MLE estimate in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' In this equation, every data point mi gives a dimension estimate for every neighbor count k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' A dimension estimate matrix of size k × n is obtained where n is the number of images in the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The intrinsic dimension is estimated as the mean of the values in the dimension estimate matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' An important aspect in dimensionality estimation is removing duplicates from the dataset so that the same datapoint is not double–counted as its own neighbor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' This was done on all datasets before computing the intrinsic dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='1 Binary Datasets In rest of the results, the datasets are split into four categories: Dataset 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Rectangles and squares in a matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Ten different synthetic datasets were tested containing rectangular and square shapes in a matrix following different size and positional constraints which dictate the intrinsic dimensionality (shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Images are of size 128 × 128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' In cases A, B, F, G, the shapes were randomly placed leading to two free dimensions of x and y coordinates of the center of the shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' In addition, for cases A and B varying sizes were used adding one more dimension in the case of squares (the width) and two more in the case of rectangles (width and height).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' In cases C, D, H and I, the shapes were placed linearly along a horizontal axis at the center, eliminating one intrinsic dimension (the y-coordinate of center) from cases A, B, F, G, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The last two cases, E and J, include centered shapes with a variation only in the size of the object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' In all cases, the shapes in the images are complete, ie, they are not cutoff by the image boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Dataset 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Randomly centered circles of a constant radius in a matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The coordinates of the center (x, y) are independently sampled using uniform random variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Images are of size 256 × 256.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Four datasets 2A, 2B, 2C, 2D containing radii of r = 24, 36, 48 and 58 pixels, respectively were generated with circle centers ((x, y)) selected within a range such that the circles do not intersect the boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' {(x, y) ∈ ℜ2|r < x < 256 − r, r < y < 256 − r} (15) Dataset 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' A known 3D point cloud is used as the generator for microstructural images, where each point in the 3D cloud (x1, x2, x3) is mapped to (x, y, R) in a binary image of a circle in a matrix, where R is the circle radius, (x, y) is the center of the circle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' In this way, the radius is no longer a free variable and is related 7 arXiv Paper A PREPRINT to the center of the circle via the topology of the point cloud (termed the ‘generator space’ to differentiate from the latent space, which could be lower in dimension).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The mapping for the circle from the generator space to the ambient space would be f : ℜ3 → ℜ128×128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Two cases were used (i) Dataset 3A (swiss roll circles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The generator space is a 3D swiss roll given as: x = t cos t + c1, y = 30η2 + c2, z = t sin t + c3 (16) where t = 3π 2 (1 + 2η1), η1 and η2 are uniform random variables in the range of 0 to 1 and (c1, c2, c3) are translation factors chosen as (62, 50, 20) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The latent space will be two dimensional, governed by the choice of the two random variables η1 and η2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' (ii) Dataset 3B (helix circles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Generator space is a 3D helix, given by the equations: x = 5(13 + (2 + cos 8t)(cos t)), y = 5(13 + (2 + cos 8t)(sin t)), z = 9(4 + sin 8t) (17) where t = 2πη, η being a uniform random variable in the range of 0 to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The latent space will be one dimensional, with the location in the manifold governed by the choice of η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Note that the coordinates of points in the generator space of Dataset 3A and 3B are rounded before mapping to images because of the integer (pixel) representation of the centers and radii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Dataset 4: Contains results from a phase field simulation of grain growth based on the Allen-Cahn equation following the numerical formulation of Fan and Chen [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The data is in the form of binary images (128 × 128) containing grain boundaries at different time steps of a single simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Since all the model parameters are fixed at the start of the simulation and images are only a function of time, the intrinsic dimensionality of all images from a single simulation run is expected to be one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Dataset contains results from three different simulation runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='2 Intrinsic dimension estimates Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 4(a) shows the variation of intrinsic dimension with the choice of Minkowski parameter for binary image dataset– 2D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The intrinsic dimension is two, and corresponds to the (x, y) coordinate of the center of the circle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' In the binary case, a linear increase in the intrinsic dimension with Minkowski parameter is obtained as explained previously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' While it was expected that the L1 norm gives the minimum intrinsic dimension estimate among these cases, it is also seen that the L1 distance measure matches the expected intrinsic dimensionality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' To further confirm this, the circle is replaced with a Gaussian distribution centered at the circle origin and with a constant standard deviation (of 20) for all datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Since each of the four cases in dataset 2 contains a circle of different radii, each case spans different number of grayscale levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' An example is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 4(e) with the blue line spanning a part of the Gaussian curve, distance between the blue lines is the circle diameter).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Cases with radii of 24, 36, 48 and 58 pixels contain 201, 419, 706 and 1001 grayscale levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' As the number of grayscale levels increase, the intrinsic dimension obtained from the use of higher p-Minkowski distance measures converge toward the true estimate as given by the L1 norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' To further test the use of L1 norm for MLE estimation of binary images, all ten cases in dataset 1 were tested (results shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The intrinsic dimension expected for each case is indicated by numbers in green near the cases in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' A histogram of values in the dimension estimate matrix is also plotted and the standard deviation of the histogram is reported in addition to the mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' As seen from these results, the MLE approach with the L1 norm gives a sound estimate of the intrinsic dimension in all cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='3 Retrieving state variables using an autoencoder While the MLE algorithm recovers the intrinsic dimensionality, it is of interest to identify the geometry of the latent space and to correlate the dimensions to microstructural features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' A variety of applications can benefit from such analysis, including identification of novel processing paths and inverse design of microstructures for a given property as shown in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' To generate a proof–of–concept, synthetic dataset C and D are used where the generator space is known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Our objective was to check if the generator space can be retrieved solely from the image data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The state variables were identified using an autoencoder architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' An autoencoder (AE) [3] is a multi-layer neural network that learns the identity function, such that the output ˆx approximates the input x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' In the architecture, the hidden layers have fewer nodes than the input dimension and act as a bottleneck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' In the first few layers, the autoencoder compresses the input to a compressed (latent space) representation in a process called ‘encoding’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' At its simplest, a single hidden layer operates on the input x ∈ ℜn and generates an encoding y1 ∈ ℜj, j < n such that: y1 = σ(W1x + b1) (18) where W1 represents the j × n weight matrix, b1 is the j × 1 bias vector for the first layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The function σ is typically a non-linear activation function and a logistic sigmoid function is used in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 8 arXiv Paper A PREPRINT b d a c e a Figure 4: a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Variation of intrinsic dimension with the choice of Minkowski parameter for a circle with varying position, represented as binary and grayscale images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The true dimensionality is 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Shows a binary microstructure c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Intensity across the dotted line in (b) is shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' (d) A grayscale microstructure based on a Gaussian intensity profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' As the number of grayscale levels increase, the answers for higher p-Minkowski distance measures converge toward the true estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Later layers reconstruct the output from this latent space representation in a process called ‘decoding’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' An example is another layer that maps the latent vector y1 in the previous step to output ˆx ∈ ℜn such that ˆx = σ(W2y1 + b2) (19) where W2 represents the n × j weight matrix, b2 is the n × 1 bias vector of the second layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Multiple layers can be used to develop a deep network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The parameters in W and b are found by minimizing the cost, 1 2(||x − ˆx||2)2, by training via backpropagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' In this work, a stacked autoencoder configuration comprised of four layers in total as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 6(c) is employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The first autoencoder comprised of two layers (encoder and decoder) was trained to reduce the dimensions to 100 first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' This was followed by a second autoencoder with two layers (encoder and decoder) that uses the 100 dimensional feature from the first autoencoder as input and reduces it to the intrinsic dimension identified by the MLE algorithm or the generator dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The two autoencoders were sequentially trained first, followed by re–training a combined four–layer autoencoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 6 shows a schematic of the approach using dataset 3A (circles sampled from a swiss roll, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 6(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The stacked autoencoder reads in the images into a network with a bottleneck equal to the generator space dimension (=3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The decoded images from the last layer are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 6(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The three variables corresponding to each image are plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 6(e) which shows that the generated topology is similar to the actual generator space in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 6(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The points shown are colored according to the circle radius in the images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Note that the autoencoder, by default, restricts the range of values to between 0 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' However, the topology of the space is generally well reconstructed demonstrating a proof–of–concept that variables that define the microstructural state can be identified using stacked autoencoders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Figure 7(b,c) shows both the computed generator space and the 1D latent space for the helix circles dataset 3B (Figure 7(a) shows the actual generator space from which the images were sampled with (x1, x2, x3) coordinate equal to (r, x, y) in the image).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' As in the swiss roll case, the generator space for the helix data set also looks similar to the generator space considering that the points are mapped in the range [0, 1] by the autoencoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The computed latent spaces are colored according to a microstructural feature, the radius of the circle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Clustering of this feature in the latent space demonstrates promise towards the use of proximity analysis to find new microstructures with interesting properties through interpolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Such an application will form a part of our future efforts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The last example is from dataset 4 (phase field data).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' In the results from this dataset in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 8, one simulation trajectory was used in two stacked autoencoders of bottleneck 3 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 8(a) compares the reconstructions from the autoencoder against the original images at five randomly chosen time steps from this trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Each consecutive time step in the phase field data results in incremental changes in topology of grain boundaries, hence it is expected 9 arXiv Paper A PREPRINT Randomly placed rectangles, vary size Linearly placed rectangle, vary size Randomly placed squares, same size Linearly placed squares, vary size Randomly placed rectangles, same size Linearly placed rectangles, same size Linearly placed squares, same size A B C D F G H I 2 / 2 1 / 1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='9 / 3 2 / 2 2 / 2 1 / 1 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='6 / 4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='8/ 3 Centered rectangles, vary size 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='9 /2 E Randomly placed squares, vary size Centered squares, vary size 1 / 1 J Figure 5: Variation of MLE based intrinsic dimension for a variety of synthetic datasets using L1 norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The predicted dimension for various data points are shown as a histogram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The numbers in red indicate mean predictions for each case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The numbers in green are the expected dimensionality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' that data points are arranged in the order of time steps in the latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' This is indeed seen in the topologies of the space constructed by the autoencoder as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 8(b,c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Similar to the helix case seen earlier, the intrinsic dimensionality is expected to be one which is confirmed by the results of the MLE algorithm in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 8(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' In the last example, the complete dataset containing three different phase field simulations is employed with an au- toencoder bottleneck of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The resulting latent space is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' In all three simulations, the initial image was the same represented by the central point in the latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The trajectories from the three simulations emerge in different directions from the initial point, resulting in different final microstructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' This latent space is an example of a microstructural space for a grain coarsening process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' To estimate the true dimensionality of the processing space, a large number of trajectories need to be superposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Although a simplistic set of three trajectories are shown, this example shows how the framework can be used to visualize a multitude of complex processes within a single graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Past work in [36, 1] employed similar visualization of linear PCA components to perform process design, the use of non–linear manifolds as demonstrated here is expected to significantly improve state–of–the–art and will form part of our future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 4 Conclusions A methodology for reliably estimating the intrinsic dimensionality of random media is developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The method re- solves the ambiguity in results for images with low bit depth when using state–of–the–art techniques that employ the Euclidean (L2) norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Particular novel contributions of this work are listed below: It is shown that the NN and MLE formulae for intrinsic dimensionality estimation can work with all Minkowski distance measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Further, the examples show that all Minkowski measures give the same in- trinsic dimensionality for non-discrete datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Dimensionality estimates are dependent on distance measures for image data with discrete levels as was shown for binary images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Through examples, it is shown that the use of L1 distance in the MLE estimate produces a reliable estimate in such cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' 10 d = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='6 +/- 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='7 1500 500 0 10 20 30 Dimensionality2000 d = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='0 +/- 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='3 1500 500 0 0 10 20 30 Dimensionality2000 d = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='8 +/- 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='6 Counts 1500 1000 500 0 0 10 20 30 Dimensionality600 d = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='0 +/- 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='1 200 0 0 10 20 30 Dimensionality2500 d = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='9 +/- 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='8 2000 uno 1500 1000 500 0 10 20 30 Dimensionality2000 d = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='0 +/- 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='3 1500 500 0 10 20 30 Dimensionality1500 d = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='0 +/- 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='3 Counts 1000 500 0 0 10 20 30 Dimensionalityd = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='0 +/- 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='1 400 2300 uno 8200 100 0 0 10 20 30 Dimensionality500 d = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='9 +/- 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='2 400 200 100 0 0 10 20 30 Dimensionality30 d = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='0 +/- 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='2 Counts 20 10 0 0 10 20 30 DimensionalityarXiv Paper A PREPRINT Generator space (swiss roll) Plot latent representation 16384 16384 100 3 100 Sample circle center (x,y) and radius (z) from swiss roll Ambient space (Training data) Decoded images Reconstructed generator space Stacked Autoencoder (a) (b) (c) (d) (e) radius radius Figure 6: Use of autoencoders for building a generator space is shown using a synthetic dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' (a) The swiss roll is the generator space, each point has a (x1, x2, x3) coordinate equal to (R, x, y) in an image where R is the circle radius, (x, y) is the center of the circle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' (b) Shows images from the database.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' (c) Stacked autoencoder reads in the images into a network with a bottleneck equal to the generator space dimension (=3) (d) Decoded images from the last layer of the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' (e) The 1000 images are reduced to three variables in the bottleneck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' These variables when plotted show the generator space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' a b c Generator space Autoencoder: generator space Autoencoder: latent space Figure 7: Helix circles dataset 3B: (a) Generator space where images are sampled (b) Generator space computed from the images using the stacked autoencoder (c) Intrinsic dimensional (1D) space computed by the stacked autoencoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Examples show that stacked autoencoders can reconstruct the low dimensional generator spaces of mi- crostructures and provide a sparse set of state variables to fully describe material microstructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Use of these state variables to quantify microstructure–property–process relationships will form a part of our future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Data availability Codes and datasets will be made freely available upon publication in a peer–reviewed journal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='11 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='arXiv Paper ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='A PREPRINT ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='Original data ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='Decoder output (3D latent space) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='Decoder output (2D latent space) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='(a) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='(b) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='(c) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='3D autoencoder representation ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='2D autoencoder representation ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='(d) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='Figure 8: (a) Decoder outputs for a single phase field trajectory (b) Comparison of 3D versus 2D representation of the ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='autoencoder (c) MLE estimate of dimensionality ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='Original data ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='Decoder output (3D latent space) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='(b) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='3D autoencoder representation ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='(a) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='Figure 9: (a) Decoder outputs for combined dataset containing all three phase field trajectories (b) 3D representation ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content='from autoencoder showing all three trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Acknowledgements This research was supported in part by the Air Force Research Laboratory Materials and Manufacturing Directorate, through the Air Force Office of Scientific Research Summer Faculty Fellowship Program, Contract Numbers FA8750- 15-3-6003 and FA9550-15-0001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' This research was supported in part through computational resources and services provided by Advanced Research Computing at the University of Michigan, Ann Arbor.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' [38] Sanket Thakre, Vishnu Harshith, and Anand K Kanjarla.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Intrinsic dimensionality of microstructure data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Inte- grating Materials and Manufacturing Innovation, 10(1):44–57, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' [39] Salvatore Torquato.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Random heterogeneous materials: Microstructure and macroscopic properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Springer- Verlag, New York, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Appendix 1 In the datasets used in this paper, we avoided the intersection of the particle shape with the image boundary to get an unbiased estimation of the dimensionality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' In general, image boundaries can play a role in biasing the intrinsic dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Consider the case of a single circular shape placed in a matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' If the shape intersects the boundary, only a part of the shape is seen and the intrinsic dimensionality of three as judged from the dataset assumes that the shape always remains a circle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' To test this, we have plotted results from two datasets, one with and one without boundary intersections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' We consider sufficiently high sample size (3000 images) and image size (128 × 128) for each case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The histogram of estimated dimension per data point is plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' S1a showing that the algorithm is able to predict the correct mean dimension for both cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' The key difference being that the histogram is broader and a higher standard deviation is obtained when the circles intersect the boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Another case is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' S1b where the circle is linearly placed along the centerline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Here, two distinct peaks are seen in the histogram where the circles are freely placed, with the first peak at a lower intrinsic dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' the mean dimension is again correctly estimated for both cases with a higher standard deviation for the case where circles intersect the image boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' A case where the circles are periodic is also shown here, where the circles wrap around on the opposite side when they intersect the boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' While this case shows a single sharp peak as in the case where boundaries are avoided, the standard deviation is higher than that case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Appendix 2 Equation (10) simplifies to: Fk(rp) = � (c(p)rµ p )k−1 Γ(k) e−c(p)rµ p � c(p)µrµ−1 p = � c(p)kµ � 1 Γ(k) �� rµk−1 p e−c(p)rµ p 14 arXiv Paper A PREPRINT Figure S1: Histograms of estimated dimension per data point (a) Two cases are considered, a circle of varying radii is freely placed in one case and avoids boundary in another case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' (b) Here, the circle is linearly placed along the centerline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' A case with periodicity is included.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Inset images show superposition of a few different images in each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Inserting this into Equation (11): Ek(rp) = � ∞ 0 rpFk(rp)drp = � c(p)kµ � 1 Γ(k) �� � ∞ 0 rµk p e−c(p)rµ p drp Changing the integration variable with ξ ≜ c(p)rµ p (rp = ξ1/µc(p)−1/µ): Ek(rp) = � c(p)kµ � 1 Γ(k) �� � ∞ 0 (ξ1/µc(p)−1/µ)µke−ξd(ξ1/µc(p)−1/µ) = c(p)−1/µ � 1 Γ(k) � � ∞ 0 ξk+1/µ−1e−ξdξ The integral is, by definition, Γ(k + 1/µ) [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} +page_content=' Substituting: Ek(rp) = c(p)−1/µ Γ(k + 1/µ) Γ(k) 15' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LtE3T4oBgHgl3EQfAwm8/content/2301.04261v1.pdf'} diff --git a/PNE4T4oBgHgl3EQf-A73/content/tmp_files/2301.05361v1.pdf.txt b/PNE4T4oBgHgl3EQf-A73/content/tmp_files/2301.05361v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..4c905ed92d2fe7aed48afcacc00d34fb7933d822 --- /dev/null +++ b/PNE4T4oBgHgl3EQf-A73/content/tmp_files/2301.05361v1.pdf.txt @@ -0,0 +1,2075 @@ +ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY +WITH TANGENTIAL ANCHORING +STAN ALAMA, LIA BRONSARD AND LEE VAN BRUSSEL +Department of Mathematics and Statistics, McMaster University, Hamilton, ON, +Canada +Abstract. We analyze Ginzburg–Landau minimization problems in two dimen- +sions with either a “strong or weak” tangential boundary condition. These prob- +lems are motivated by experiments in liquid crystal with boundary defects. +In +the singular limit when the correlation length tends to zero, we show that bound- +ary defects will be observed for weak anchoring, while both boundary and interior +vortices are possible for strong anchoring in the first order limit. +1. Introduction +In this paper we study minimizers of two variational problems motivated by the +study of defects in a nematic liquid crystal. We consider a two-dimensional setting, +related to a thin-film reduction of the three dimensional Landau–de Gennes model +to two dimensions. The special feature we are interested in comes from the work +of Volovik and Lavrentovich [VL83] where nematic drops are placed in an isotropic +medium, allowing for the control of nematic boundary behaviour. In this way, the +liquid crystal and its associated defect dynamics are studied as the nematic boundary +molecules are transformed from having a forced angle of α = π/2 with respect to +the unit normal n to the boundary of the droplet to α = 0. In this paper, we return +to the well-studied Ginzburg-Landau functional but with new tangential types of +boundary conditions, inspired by this physical phenomena. +We begin by describing the variational problem in mathematical terms, and stating +our main results in Theorems 1.1 and 1.2. We consider a two-dimensional, bounded, +simply connected domain Ω ⊂ R2 ∼= C representing the space occupied by the liquid +crystal with C3,α-smooth boundary Γ := ∂Ω. +Let g : Γ → S1 be C3,α-smooth +E-mail address: alama@mcmaster.ca, bronsard@mcmaster.ca, vanbrulw@mcmaster.ca. +Date: January 16, 2023. +1 +arXiv:2301.05361v1 [math.AP] 13 Jan 2023 + +2 +ALAMA, BRONSARD AND VAN BRUSSEL +boundary data with positive degree +D := deg(g; Γ) > 0. +A natural example is to choose g to parametrize the (positively oriented) unit tangent +vector to ∂Ω, but this need not be the case. In order to force the order parameter u +to be parallel (or close to parallel) with respect to g, we will be using two methods. +The first method is to impose that u have zero projection along a vector orthogonal +to g, that is, impose the pointwise scalar product condition ⟨u, g⊥⟩ = 0 on Γ. With +this, we consider the Ginzburg–Landau energy defined for H1(Ω; R2) mappings +Eε(u) := 1 +2 +ˆ +Ω +� +|∇u|2 + 1 +2ε2 +� +1 − |u|2�2 +� +dx +where ε > 0 and observe the behaviour of solutions to the strong tangential mini- +mization problem +inf +� +Eε(u) : u ∈ Hg(Ω) := {u ∈ H1(Ω; R2) : ⟨u, g⊥⟩ = 0 on Γ} +� +, +(1.1) +in the limit as ε → 0. In this way, we can observe the topological defects associated +to the limiting map by analyzing a sequence of energy minimizing configurations +{uε} where the nematic material is asked to be precisely (strongly) parallel to g +along Γ for each ε > 0. It turns out that asking such a condition to hold does not +quite translate to a standard Dirichlet or Neumann problem for the associated Euler– +Lagrange equations, but rather a mixture of the two within appropriate coordinates. +To see this, we make the additional assumption that g be defined on a tubular +neighborhood +NΓ := {x ∈ Ω : dist(x, Γ) < δ} +with δ > 0 is small. Using this assumption, there exists a natural decomposition for +functions u in NΓ using the orthonormal frame {g(x), g⊥(x)} via +u = u∥g + u⊥g⊥ +(1.2) +where u∥ := ⟨u, g⟩ and u⊥ := ⟨u, g⊥⟩. In using this decomposition, we find that +solutions to the strong tangential problem (1.1) satisfy the Euler–Lagrange system +� +� +� +� +� +� +� +−∆u = 1 +ε2(1 − |u|2)u +in Ω, +u⊥ = 0 +on Γ, +∂nu∥ = 0 +on Γ. +(1.3) +The second method for enforcing parallelity is done through boundary energy penal- +ization (see e.g. Moser [Mos03]). Indeed, define +Eg,s +ε (u) := Eε(u) + 1 +2εs +ˆ +Γ +⟨u, g⊥⟩2 ds + +ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING3 +where s ∈ (0, 1], so that solutions of the weak tangential minimization problem +inf +� +Eg,s +ε (u) : u ∈ H1(Ω; R2) +� +(1.4) +are energetically induced to decrease their projection along g⊥. By calculating the +first variation for Eg,s +ε , it can be easily shown that minimizers uε satisfy the weak +anchoring system +� +� +� +� +� +−∆u = 1 +ε2(1 − |u|2)u +in Ω, +∂nu = − 1 +εsu⊥g⊥ +on Γ. +(1.5) +For either minimization problem, solutions to (1.1) and (1.4) are guaranteed by the +direct method from the calculus of variations. Moreover, it can also be shown that +strong tangential minimizers, in some sense, are weak limits of solutions to a cer- +tain modified weakly tangential minimization problem. Therefore, both problems +are naturally connected and it is reasonable to analyze the solutions of both. +It is well known from the literature (see Bethuel-Brezis-H´elein [BBH94], for exam- +ple) that the local winding behaviour of minimizers about vortices and the global +winding behaviour of the boundary data g are directly linked to the energy of a mini- +mizing configuration. Thus, given that our interest is in the observation of boundary +defects, we must grasp, in some way, the winding behaviour of minimizers near +boundary vortices. Indeed, when a defect is located in the interior, this winding is +easily quantifiable by calculating the standard topological degree of the minimizer’s +normalization about a small circle centered at the defect. However, since a closed +curve cannot be made about a boundary vortex, it is not immediately clear how +one should proceed in this case. To combat this, we develop a topological quantity +called the boundary index, which essentially counts the net number of approximate +π-rotations that are made from one side of the vortex to the other on the boundary. +In this way, a boundary defect with an associated boundary index d will resemble +an interior vortex of degree d cut in half, and thus carry a “half-integer” degree (see +Definition (4.3)). A rigorous construction of the boundary index is given in Sec- +tion 4. Using the notion of the boundary index, the main results of this paper are +summarized in Theorems 1.1 and 1.2. +Theorem 1.1. Suppose {uε}ε>0 is a sequence of solutions to (1.1) with associated +boundary function g : NΓ → S1 of degree D = deg(g; Γ) ≥ 1. +Then there is a +subsequence εn → 0, a finite number of point singularities Σ ⊂ Ω and a harmonic +map u0 ∈ H1(Ω \ Σ; S1) such that +uεn ⇀ u0 +weakly in H1 +loc(Ω \ Σ; R2) + +4 +ALAMA, BRONSARD AND VAN BRUSSEL +with each defect contained in Σ having either associated degree, or boundary index, +equal to one. In the particular case where D = 1, then one and only one of the +following scenarios hold: +(1) Σ = {p} with p ∈ Ω, +(2) Σ = {q1, q2} with q1, q2 ∈ Γ. +For the last part of Theorem 1.1, we remind the reader that our primary motiva- +tion for studying this problem came from the topological observations made on 3D +samples, by Volovik and Lavrentovich in [VL83]. In particular, they found experi- +mentally single interior hedgehog defect when molecules are asked to be normal to +the boundary and a bipolar boojum pair when requiring tangential conditions. In +either case, the normal and tangential boundary data are of degree one and thus +our theoretical treatment of the problem weakly recovers this observation. To get +a complete picture, a renormalized energy analysis would need to be conducted in +order to show when one defect type is preferred over another. To this end, in the last +section of this work, we provide a concrete example of strong tangential anchoring +in the case Ω = B1(0), the unit disc, with g = τ the positively oriented unit tangent +vector to the boundary Γ, to highlight that the boundary vortex pair may give the +preferable energy minimizing configuration. Such a result in 2D would be a first step +in obtaining theoretically results coinciding with the found experimental data. +Next we state our result in case of weak tangential boundary conditions: +Theorem 1.2. Suppose {uε}ε>0 is a sequence of solutions to (1.4) with associated +boundary function g : NΓ → S1 of degree D = deg(g; Γ) ≥ 1. +Then there is a +subsequence εn → 0, a finite number of point singularities Σ ⊂ Ω and a harmonic +map u0 ∈ H1(Ω \ Σ; S1) such that +uεn ⇀ u0 +weakly in H1 +loc(Ω \ Σ; R2) +with each defect contained in Σ having associated degree or boundary index equal to +one. If s ∈ (0, 1), it holds that Σ ⊂ Γ with |Σ| = 2D. +The primary takeaway of Theorem 1.2 comes from the observation that the expo- +nent s ∈ (0, 1] almost completely dictates the allocation of defects in Ω. In particular, +the Theorem states that independent of the winding behaviour of g and the geometry +of Ω, giving vortices ‘more room’ along the boundary (on the scale of εs as opposed +to ε) is enough for boundary vortex pairs to always be energetically preferable when +compared to interior vortices. +A related model is that of a thin ferromagnetic film as obtained in an appropri- +ate limiting regime by DeSimone, Kohn, Muller and Otto [DKMO02]. This limiting + +ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING5 +ferromagnetic thin film was studied by Moser [Mos03], and by Kurzke [Kur06] in +certain settings. In those problems, they impose tangential weak anchoring condi- +tions with g = τ the unit tangent, and find critical anchoring strength at which +boundary vortices are favored over interior vortices. In our case, we also consider a +strong tangential anchoring, and generalize their results to weak anchoring for any g. +More recently, Ignat-Kurzke [IK21] have obtained Γ-convergence results for the weak +tangential anchoring problem using a notion of global Jacobian in a different limit- +ing regime where interior vortices cost more energy than boundary vortices. In the +context of polarization-modulated orthogonal smectic liquid crystal, Garcia-Cervera, +Giorgi and Joo [GCGJ20] have studied boundary vortices in a square domain with +mixed weak and strong boundary conditions on the edges. +In the work of Volovik and Lavrentovich [VL83] the topological dynamics of the +nematic material are observed as the boundary molecules are changed from being +parallel to the boundary to perpendicular, by varying the aperture α of the cone +formed by the molecule with the normal to the boundary. When the angle α = π/2, +a bipolar structure is noticed with two point defects occurring along the boundary +called boojums. At the other extreme with α = 0, a single interior hedgehog defect is +realized. Using a vector-valued order parameter u for modelling the molecular align- +ment of the liquid crystal, the authors note that a surface energy density proportional +to +[⟨u, n⟩2 − cos2 α]2 +(1.6) +can be used in comparison to an interior gradient energy for determining the energy +preference of boojum defects to hedgehog defects and vice versa. A generalization of +this setup was analyzed by Alama, Bronsard and Golovaty in [ABG20] where they +replaced the boundary’s normal vector n in expression (1.6) with general smooth +S1-valued boundary data g, possessing a positive associated winding number along +the boundary, and restricting α ∈ (0, π/2), the relative angle made between g and +the order parameter u. In this present work, we aim to answer the question of how +this generalization operates for the specific case of α = π/2 using Ginzburg-Landau +as a toy model for nematic material. In particular, we are interested in obtaining +conditions for which minimizing configurations prefer boundary defects over interior +defects in this setting. +The rest of the paper is organized as follows: in Section 2 we present upper bounds +for the energy of minimizers to each problem, as well as a priori pointwise bounds +for all solutions of the associated Euler-Lagrange equations, adapted for our new +settings. In Section 3, we present our η compactness results adapted from Struwe +[Str94] to handle each type of boundary conditions and use it to define the “bad balls” +for each type, and show that they are contained in a finite number of very small balls. + +6 +ALAMA, BRONSARD AND VAN BRUSSEL +Next in Section 4, we analyze the winding behaviour of minimizers around boundary +defects and introduce our notion of boundary index and use it to obtain the important +“degree Proposition and Lemma” (Proposition 4.1 and Lemma 4.2) which will be +essential in proving the lower bound on the energy of boundary defects in terms of +the degree of the boundary data. In Section 5, we obtain an energy lower bound +for each type of tangential conditions over the appropriate ball collections, and we +put everything together and prove our two main theorems. Finally in Section 6, we +present an example with strong tangential anchoring on the unit disc which suggest +that two antipodal boundary defect would be favored. +2. Preliminary Facts for Minimizers +We begin by showing an important pointwise bound on solutions of the Euler– +Lagrange systems (1.3) and (1.5). The proof follows familiar lines, (see [BBH94, +ABGS15, ABG20]) and so we provide a sketch to highlight the differences with +previous papers. +Lemma 2.1. Suppose u is a solution of (1.3) or (1.5). Then |u| ≤ 1 and there is a +constant C0 > 0 independent of ε for which ε|∇u| ≤ C0 for all x ∈ Ω. +Proof. Define V := |u|2 − 1 and V+ := max{V, 0}. Using the Euler–Lagrange equa- +tions and integrating by parts over Ω we obtain +0 ≤ +ˆ +Ω +|u|2V 2 ++ dx ≤ 1 +2 +ˆ +Γ +V+∂nV ds − 1 +2 +ˆ +Ω +|∇V+|2 dx. +If u is a solution of (1.3), it follows that V+ ≡ 0. If u is a solution of (1.5), then +∂nV = 2⟨u, ∂nu⟩ = − 2 +εs(u⊥)2 ≤ 0 +and we obtain V+ ≡ 0 again. Thus, |u| ≤ 1 in Ω. +The gradient bound can be obtained by contradiction: suppose that there exists +sequences εk → 0 and xk ∈ Ω so that tk := |∇uk(xk)| = ∥∇uk∥∞ satisfies tkεk → ∞ +as k → ∞. Let +vk(x) := uk +� +xk + x +tk +� +which is defined whenever y := xk+x/tk ∈ Ω. Likewise, define h(x) := g(y) whenever +y ∈ Γ. By the uniform bound on u proven above and the choice of scaling, we have +∥vk∥∞ ≤ 1 and +|∇vk(0)| = 1 ∀k. +(2.1) + +ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING7 +By the uniform bound ∥vk∥∞ ≤ 1 and using the fact that vk solves +−∆vk = +1 +(tkεk)2(1 − |vk|2)vk +for x ∈ tk[Ω − xk], +we conclude ∆vk → 0 uniformly on Ω. There are two blow-up cases to consider. +If along some subsequence tk dist(xk, Γ) → +∞, then vk → v with v bounded and +harmonic in all of R2, and hence constant, contradicting (2.1). +Suppose now tk dist(xk, Γ) is bounded uniformly so that the domains of vk converge +to the half-space +tk[Ω − xk] → R2 ++ as k → ∞. +For each k, the weak tangential problem becomes +� +� +� +� +� +� +� +� +� +−∆vk = +1 +(tkεk)2(1 − |vk|2)vk +in tk[Ω − xk], +∂nvk = − 1 +tkεs +k +⟨vk, h⊥⟩h⊥ +on tk[Γ − xk], +(2.2) +while the strong tangential problem is written +� +� +� +� +� +� +� +� +� +� +� +−∆vk = +1 +(tkεk)2(1 − |vk|2)vk +in tk[Ω − xk], +⟨vk, h⊥⟩ = 0 +on tk[Γ − xk], +∂n⟨vk, h⟩ = 0 +on tk[Γ − xk]. +(2.3) +Both problems yield a bounded harmonic limit v defined on R2 ++ with vk → v in Ck +loc. +Since vk and h are bounded uniformly, the normal derivative of system (2.2) has the +limit ∂nvk → 0 as k → ∞ and so the limiting harmonic map v satisfies the Neumann +condition ∂nv = 0 on ∂R2 ++. By the reflection principle, there exists a bounded har- +monic extension of v to all of R2 which again contradicts (2.1) by Liouville’s theorem. +For system (2.3), the boundary data h converges to a constant vector field on ∂R2 ++ +and the boundary conditions imply ⟨v, h⊥⟩ = ∂n⟨v, h⟩ = 0 along ∂R2 ++. Let ˜h denote +the extension of h to R2 ++ and note that ⟨v, ˜h⟩ is a harmonic scalar function defined on +R2 ++. By the reflection principle and Liouville’s theorem, ⟨v, ˜h⟩ extends to a constant +function on R2. Next, since ⟨v, h⊥⟩ = 0 on ∂R2 ++ and ⟨v, ˜h⟩ is constant, it must be +that ⟨v, ˜h⟩ = ±|v| on all of R2 and thus v is constant. Condition (2.1) is contradicted +once again giving ε|∇u| ≤ C0 for all x ∈ Ω where C0 is a constant independent of +ε. +□ + +8 +ALAMA, BRONSARD AND VAN BRUSSEL +Proposition 2.2. If uε is a strongly tangential minimizer for Eε, then +Eε(uε) ≤ πD| ln ε| + C +(2.4) +with C > 0 a constant independent of ε. If uε is a weakly tangential minimizer for +Eg,s +ε , then there is a constant C > 0 independent of ε so that +Eg,s +ε (uε) ≤ πsD| ln ε| + C. +(2.5) +The proof of this proposition utilizes a local polar coordinate system near the +boundary which is defined in [ABGS15, ABG20, Kur06] and which we will use +throughout the paper. For convenience, we provide a brief description here. Let +x0 ∈ Ω and R > 0. Set +ωR(x0) := BR(x0) ∩ Ω +and in the case where x0 ∈ Γ, define +ΓR(x0) := ωR(x0) ∩ Γ. +Whenever x0 ∈ Γ, τ(x0) will denote the positively oriented unit tangent vector to Γ +at x0. Using τ(x0) as a reference, the polar coordinates (r, θ) centered at x0 can be +defined so that θ is the angle measured from the ray defined by τ(x0) and r = |x−x0|. +By the smoothness of Γ, note that R can be chosen small enough so that +ωR(x0) = {(r, θ) : θ1(r) < θ < θ2(r), 0 < r < R} +where θ1(r) and θ2(r) are smooth functions satisfying +|θ1(r)|, |π − θ2(r)| ≤ cr +(2.6) +for some constant c = c(Γ) ≥ 0. These coordinates allow us to parametrize ΓR(x0) \ +{x0} in two pieces: +Γ+ +R(x0) := {(r, θ1(r)) : 0 < r < R}, +Γ− +R(x0) := {(r, θ2(r)) : 0 < r < R}. +Annular regions are defined similarly. For any x0 ∈ Ω set +Ar1,r2(x0) := ωr2(x0) \ ωr1(x0), +0 < r1 < r2. +When x0 ∈ Γ and r2 > 0 is taken small enough, the intersection Ar1,r2(x0)∩Γ consists +of two disjoint smooth arcs +Γ+ +r1,r2(x0) = {(r, θ1(r)) : r1 < r < r2}, +Γ− +r1,r2(x0) = {(r, θ2(r)) : r1 < r < r2}, +(2.7) +where θ1(r) and θ2(r) are as in (2.6). For notational convenience, we also set +Γ± +r1,r2(x0) := Ar1,r2(x0) ∩ Γ = Γ+ +r1,r2(x0) ∪ Γ− +r1,r2(x0). + +ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING9 +Lastly, we define a localized energy on subsets ωr(x0) by +Eε(u; ωr) := 1 +2 +ˆ +ωr +� +|∇u|2 + 1 +2ε2(1 − |u|2)2 +� +dx, +Eg,s +ε (u; ωr) := Eε(u; ωr) + 1 +2εs +ˆ +Γ∩ωr +⟨u, g⊥⟩2 ds. +Proof of Proposition 2.2. +For inequality (2.4), the desired bound is a consequence of [Str94, Lemma 2.1]. Let +vε be a minimizer for Eε over H1 +g(Ω) = {v ∈ H1(Ω; R2) : v = g on Γ}. The inclusion +H1 +g(Ω) ⊂ Hg(Ω) implies Eε(uε) ≤ Eε(vε) and applying [Str94, Lemma 2.1] to Eε(vε) +yields +Eε(uε) ≤ Eε(vε) ≤ πD| ln ε| + C. +For weakly tangential minimizers, a test function is constructed following [ABGS15, +Lemma 3.1] and [Kur06, Proposition 3.1]. Consider 2D sets of the form ωR(qj) where +{qj}2D +j=1 are well-separated points on Γ and R is chosen so that +2εs < R < 1 +2|qi − qi| +for all indices i ̸= j. Assume that the points {qj}2D +j=1 are labeled such that qj+1 is +the first point found by following the positively oriented tangent vector field along Γ +starting from qj. These points partition Γ into 2D smooth segments Cj in the sense +that Γ = ∪2D +j=1Cj with Cj being the curve connecting qj and qj+1. Let γ be a lifting +of g on the curve ΓR(qj), that is, g = eiγ on ΓR(qj), and define +h1(r) = γ +� +reiθ1(r)� ++ (j − 1)π, +h2(r) = γ +� +reiθ2(r)� ++ jπ, +φ(r, θ) = h2(r) − h1(r) +θ2(r) − θ1(r) (θ − θ1(r)) + h1(r), +where θ1(r) and θ2(r) are as in (2.6). In this way we have eiφ(r,θ) = g on Γ+ +R(qj) for j +odd and on Γ− +R(qj) for j even. Similarly, we get eiφ(r,θ) = −g for the opposite parities. +Next, let ηε(r) ∈ C∞ be a cut-off function near qj satisfying 0 ≤ ηε ≤ 1 for all r, +ηε(r) = 1 for r ≥ 2εs and ηε(r) = 0 for r < εs. In setting +ψj(r, θ) := ηε(r)φ(r, θ) + (1 − ηε(r))(γ(qj) + (j − 1)π) +we may define the S1-valued test function v(j) +ε += eiψj(r,θ) on ωR(qj), which by construc- +tion, simulates a half-vortex in the annular region A2εs,R(qj). Using the properties of + +10 +ALAMA, BRONSARD AND VAN BRUSSEL +the cut-off function along with Cauchy-Schwarz and the fact that v(j) +ε +is S1-valued, +1 +2ε2 +ˆ +ωR(qj) +(1 − |vε|2)2 dx = 0 +and +1 +2εs +ˆ +ΓR(qj) +⟨vε, g⊥⟩2 ds ≤ C +where C > 0 is a constant independent of ε. The Dirichlet energy of v(j) +ε +on ωR(qj), +can be conveniently estimated using polar coordinates: it is a straightforward calcu- +lation to confirm that the radial component +´ +ωR(qj) |∂rvε|2 dx is uniformly bounded +in ε. To bound the angular energy over ω2εs(qj), we note that by (2.6) and the +smoothness of γ, there is a constant c > 0 so that +|h2(r) − h1(r)| ≤ π + cr, +and +|θ2(r) − θ1(r)| ≥ π − cr. +Thus, we have: +ˆ +ω2εs(qj) +1 +r2|∂θv|2 dx ≤ (π + cR)2 +(π − cR) ln 2 < ∞. +Therefore it must be that the primary energy contribution comes from the subset +A2εs,R(qj). Using the same estimates as above, +ˆ +ωR(qj) +1 +r2|∂θvε|2 dx ≤ πs| ln ε| + C +for C > 0 independent of ε and so +Eg,s +ε (vε; ωR(qj)) ≤ π +2 s| ln ε| + C +on each ωR(qj). Finally, we must connect these local test functions in a way that is +independent of ε. Consider the punctured domain +˜Ω := Ω \ +2D +� +j=1 +ωR(qj) +with boundary given by +˜Γ := ∂ ˜Ω = +� +Γ \ ∪2D +j=1ΓR(qj) +� � � +∪2D +j=1∂BR(qj) ∩ Ω +� +. +We set the orientation of ˜Γ to match that of Γ where they coincide. +With this +orientation, the function ˜g : ˜Γ → S1 defined by +˜g := +� +� +� +� +� +� +� +g +on ˜Γ ∩ Cj for j odd +−g +on ˜Γ ∩ Cj for j even +v(j) +ε +on ∂BR(qj) ∩ Ω for each j = 1, . . . , 2D, + +ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING +11 +satisfies deg(˜g; ˜Γ) = 0 by construction and therefore we may let V be the S1-valued +harmonic extension of ˜g to ˜Ω which has uniformly bounded Dirichlet energy. Setting +Hε = +� +V +in ˜Ω, +v(j) +ε +in ωR(qj) for each j = 1, . . . , 2D, +we obtain a bound on Eg,s +ε (uε) via +Eg,s +ε (uε) ≤ Eg,s +ε (Hε) = +2D +� +j=1 +Eg,s +ε (v(j) +ε ; ωR(qj)) + Eg,s +ε (V ; ˜Ω) ≤ πsD| ln ε| + C +as desired. +□ +3. η-Compactness and Related Consequences +In this section, we prove an η-compactness result which allows one to relate an +energy bound to the non-existence of vortices. The idea here is that for two concen- +tric balls, if the energy on the larger ball is small enough, then it is impossible for +a vortex to exist in the smaller ball. This fact is pivotal in proving that the set of +points x ∈ Ω for which |uε| is small can be covered by a finite set of ε-balls whose +number is bounded independent of ε. We begin by stating a Pohosaev-type identity +for solutions of (1.3) or (1.5) which is obtained via integrating by parts against a +smooth function. This identity will be needed to obtain an η-compactness result +which will be developed in the next section. +Define +eε(u) := 1 +2|∇u|2 + 1 +4ε2 +� +1 − |u|2�2 . +Proposition 3.1. Let ψ ∈ C2(Ω; R2). If u is a solution of (1.5) or (1.3), then +ˆ +∂ωr +{eε(u)⟨ψ, n⟩ − ⟨∂nu, ψ · ∇u⟩} ds = +ˆ +ωr +� +eε(u) div ψ − +� +j,l +ψl +xj⟨∂xju, ∂xlu⟩ +� +dx. +(3.1) +Theorem 3.2 (η-Compactness). [Strong Tangental Case] Let 3 +4 ≤ β < γ < 1. There +exists constants η, ˜C, ε0 > 0 such that for any solution uε of (1.3) with ε ∈ (0, ε0), +if x0 ∈ Ω and Eε(uε; ω2εβ(x0)) ≤ η| ln ε|, then +|uε| ≥ 1 +2 +in ωεγ(x0), +(3.2) +1 +4ε2 +ˆ +ωεγ (x0) +(1 − |uε|2)2 dx ≤ ˜Cη. +(3.3) + +12 +ALAMA, BRONSARD AND VAN BRUSSEL +[Weak Tangential Case] Let +3 +4s ≤ β < γ < s ≤ 1. There exists constants η, ˜C, +ε0 > 0 such that for any solution uε of (1.5) with ε ∈ (0, ε0), if x0 ∈ Ω and +Eg,s +ε (uε; ω2εβ(x0)) ≤ η| ln ε|, then +|uε| ≥ 1 +2 +in ωεγ(x0), +(3.4) +|⟨uε, g⊥⟩| ≤ 1 +4 +on Γ ∩ ωεγ(x0), +(3.5) +1 +4ε2 +ˆ +ωεγ (x0) +(1 − |uε|2)2 dx + 1 +2εs +ˆ +Γ∩ωεγ (x0) +⟨uε, g⊥⟩2 ds ≤ ˜Cη. +(3.6) +The proof for Theorem 3.2 is heavily dependent on a crucial estimate. For x0 ∈ Ω, +define as in [Str94, Mos03] the functions +F(r) = F(r; x0, u, ε) := r +ˆ +∂Br(x0)∩Ω +eε(u) ds, +FΓ(r) := F(r) + r +2εs +� +x∈∂Γr(x0) +⟨u, g⊥⟩2 +where the second function above is defined when x0 ∈ Γ. +Lemma 3.3. Let x0 ∈ Ω. There exists constants C > 0 and r0 > 0 such that for +ε ∈ (0, 1) and r ∈ (0, r0) we have: +(1) If x0 ∈ Ω, ωr(x0) ∩ Γ = ∅ and u is a solution of either (1.5) or (1.3), then +1 +4ε2 +ˆ +ωr +(1 − |u|2)2 dx ≤ r +ˆ +ωr +1 +2|∇u|2dx + F(r). +(2) If x0 ∈ Γ and u is a solution of (1.3), then +1 +4ε2 +ˆ +ωr +(1 − |u|2)2 dx ≤ C +� +r +ˆ +ωr +1 +2|∇u|2 dx + F(r) + r2 +ε +� +. +(3.7) +(3) If x0 ∈ Γ and u is a solution of (1.5), then +1 +4ε2 +ˆ +ωr +(1−|u|2)2 dx+ 1 +2εs +ˆ +Γr +⟨u, g⊥⟩2 ds ≤ C +� +r +ˆ +ωr +1 +2|∇u|2 dx + FΓ(r) + r2 +εs +� +. (3.8) +Proof. The proof for case (1) is shown in [Str94, Lemma 2]. Inequality (3.8) follows +from [Mos03, Lemma 5.4] or by changing every instance of |u − g|2 with ⟨u, g⊥⟩2 +throughout [ABGS15, Lemma 4.2]. Thus, it only remains to prove (3.7). Let r0 > 0 +be chosen small enough so that Γ ∩ Br(x0) consists of a single smooth arc satisfying +|Γr| ≤ Cr for all 0 < r ≤ r0. As in [ABGS15] we let N be a 2r0-neighbourhood of +Γ, and by taking r0 smaller if necessary, there exists a vector field X ∈ C2(N; R2) + +ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING +13 +satisfying +⟨X, n⟩ = Xn = 0 +for all x ∈ Γr, +(3.9) +|X − (x − x0)| ≤ C|x − x0|2 +for all x ∈ ωr, +(3.10) +|∂xiXj − δij| ≤ C|x − x0| +for all x ∈ ωr, +(3.11) +for a constant C > 0 and for any x0 ∈ Γ. To obtain inequality (3.7) we consider the +Pohosaev-type identity (3.1) with ψ = X and estimate. Using the boundary decom- +position ∂ωr = Γr ∪ (∂Br(x0) ∩ Ω), it will be convenient to perform these estimates +on Γr and ∂Br(x0) ∩ Ω separately. +Estimates Along Γr: +By (3.9) we may write X = ⟨X, τ⟩τ = Xττ where τ is the unit tangent vector to Γr +and so X · ∇u = Xτ∂τu on Γr. With this, the lefthand side of (3.1) becomes +ˆ +Γr +{eε(u)Xn − ⟨∂nu, X · ∇u⟩} ds = − +ˆ +Γr +⟨∂nu, Xτ∂τu⟩ ds. +Using the derivative representations +∂nu = ∂n(u∥g + u⊥g⊥) = u∥∂ng + ∂nu∥g + u⊥∂ng⊥ + ∂nu⊥g⊥, +∂τu = ∂τ(u∥g + u⊥g⊥) = u∥∂τg + ∂τu∥g + u⊥∂τg⊥ + ∂τu⊥g⊥, +with the known conditions u⊥ = ∂nu∥ = ∂τu⊥ = 0, we obtain +⟨∂nu, Xτ∂τu⟩ = Xτ⟨u∥∂ng + ∂nu⊥g⊥, u∥∂τg + ∂τu∥g⟩ += Xτ((u∥)2⟨∂ng, ∂τg⟩ + u∥∂nu⊥⟨g⊥, ∂τg⟩). +Applying Lemma 2.1 and Cauchy-Schwarz, +|(u∥)2⟨∂ng, ∂τg⟩| ≤ |∂ng||∂τg| ≤ |∇g|2 ≤ C = C(g), +|u∥∂nu⊥⟨g⊥, ∂τg⟩| ≤ |∂nu⊥||g⊥||∂τg| ≤ |∇u||∇g| ≤ CC0ε−1. +Therefore, there is a constant c for which +|⟨∂nu, Xτ∂τu⟩| ≤ |Xτ|c +ε. +Moreover since |Xτ| ≤ Cr and |Γr| ≤ Cr we have another constant C (independent +of ε) so that +���� +ˆ +Γr +⟨∂nu, X · ∇u⟩ ds +���� ≤ +ˆ +Γr +|Xτ|c +ε ds ≤ Cr2 +ε . +Estimates Along ∂Br(x0) ∩ Ω: + +14 +ALAMA, BRONSARD AND VAN BRUSSEL +The lefthand side of (3.1) along ∂Br(x0) ∩ Ω can be written as the sum of integrals +I1 + I2 which we estimate separately. +First, by (3.10), |Xn|, |Xτ| ≤ Cr and by +applying Cauchy-Schwarz we get +I1 = +ˆ +∂Br(x0)∩Ω +�1 +2|∇u|2Xn − Xn|∂nu|2 − Xτ⟨∂nu, ∂τu⟩ +� +ds +≤ Cr +ˆ +∂Br(x0)∩Ω +�1 +2|∂τu|2 + 1 +2|∂nu|2 + 1 +2|∂nu|2 + 1 +2|∂τu|2 +� +ds += Cr +ˆ +∂Br(x0)∩Ω +|∇u|2 ds. +An easy estimate for I2 is given by +I2 = +1 +4ε2 +ˆ +∂Br(x0)∩Ω +(1 − |u|2)2Xn ds ≤ Cr +4ε2 +ˆ +∂Br(x0)∩Ω +(1 − |u|2)2 ds. +Thus, for C > 0 large enough +I1 + I2 ≤ Cr +ˆ +∂Br(x0)∩Ω +1 +2 +� +|∇u|2 + 1 +2ε2(1 − |u|2)2 +� +ds = CF(r) +and so the lefthand side of (3.1) has the estimate +ˆ +∂ωr +{eε(u)Xn − ⟨∂nu, X · ∇u⟩} ds = I1 + I2 − +ˆ +Γr +⟨∂nu, X · ∇u⟩ ds +≤ C +� +F(r) + r2 +ε +� +. +Estimates on ωr: +The righthand side of (3.1) can be written as the sum of integrals J1 + J2 which +again we estimate separately. By (3.11) and Cauchy-Schwarz, +� +j,l +Xl +xj⟨∂xju, ∂xlu⟩ ≤ |∇u|2 + 2Cr|∇u|2 + +ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING +15 +and since div X ≥ 2 − 2Cr we have +J1 = +ˆ +ωr +� +1 +2|∇u|2 div X − +� +j,l +Xl +xj⟨∂xju, ∂xlu⟩ +� +dx +≥ +ˆ +ωr +�1 +2|∇u|2 div X − |∇u|2 − 2Cr|∇u|2 +� +dx +≥ −Cr +ˆ +ωr +|∇u|2 dx. +For the integral J2, one can choose r0 smaller if necessary so that div X ≥ 2−2Cr ≥ 1 +and +J2 = +1 +4ε2 +ˆ +ωr +(1 − |u|2)2 div X dx ≥ +1 +4ε2 +ˆ +ωr +(1 − |u|2)2 dx. +Putting these estimates together, +1 +4ε2 +ˆ +ωr +(1 − |u|2)2 dx − Cr +ˆ +ωr +1 +2|∇u|2 dx ≤ J1 + J2 = I1 + I2 ≤ C +� +F(r) + r2 +ε +� +which completes the proof for inequality (3.7). +□ +We now prove Theorem 3.2. +Proof of Theorem 3.2. The case where x0 ∈ Ω and ω2εβ(x0) ∩ Γ = ∅ is shown in +[Str94, Lemma 2.3]. Therefore, it is sufficient to prove the result for x0 ∈ Γ. We +begin by proving (3.3) for strong tangential solutions. +Inequality (3.6) for weak +tangential solutions is done similarly. Using the mean value theorem for integrals, +there exists rε ∈ (2εγ, 2εβ) such that F(rε) ≤ η(γ − β)−1. Using the radius r = rε in +(3.7) gives +1 +4ε2 +ˆ +ωrε(x0) +(1 − |uε|2)2 dx ≤ C +� +rε +ˆ +ωrε(x0) +1 +2|∇u|2 dx + F(rε) + r2 +ε +ε +� +≤ C +� +2ε3/4η| ln ε| + +η +γ − β + 4√ε +� +. +Then for ε < ε0 with appropriately chosen ε0 > 0, we get (3.3). Inequalities (3.2) +and (3.4) can be obtained using a contradiction argument. By assuming there is +some x1 ∈ ωεγ(x0) such that |u(x1)| < 1/2, standard methods involving the mean +value theorem and smoothness properties of Γ [BBH94] allow us to conclude that +there is a radius r = cε and a constant c′ > 0 independent of η and ε such that +˜Cη ≥ +1 +4ε2 +ˆ +ω2εγ (x0) +(1 − |u|2)2dx ≥ +1 +4ε2 +ˆ +ωcε(x1) +(1 − |u|2)2dx ≥ c′. + +16 +ALAMA, BRONSARD AND VAN BRUSSEL +Taking η smaller if necessary gives the contradiction. For inequality (3.5), suppose +r0 > 0 is taken small enough so that ωr(x0) is strictly starshaped with respect to +some point x2 ∈ ωr(x0). By setting ψ = x − x2 in (3.1) and following [ABGS15, +Proposition 4.1] or [ABG20, Proposition 4.1], one can find the estimate +|uε(x) − uε(y)| ≤ C +� +|x − y|ε−s/2 +(3.12) +holding for all x, y ∈ Γrε with C a constant independent of ε and x0 . As in the +interior case, suppose there is some point x3 ∈ Γrε such that |⟨uε(x3), g⊥(x3)⟩| > 1/4. +Then by the triangle inequality, Cauchy-Schwarz and the uniform bound of Lemma +2.1: +|⟨uε(x), g⊥(x)⟩| > 1/4 − |uε(x) − uε(x3)| − |g⊥(x) − g⊥(x3)|. +By (3.12) and the smoothness of g, a radius ρ proportional to εs can be chosen so +that +|uε(x) − uε(x3)|, |g⊥(x) − g⊥(x3)| < 1 +16 +for all x ∈ Γrε ∩Bρ(x3) and so |⟨uε(x), g⊥(x)⟩| > 1/8 on this set. Applying inequality +(3.6) along with the estimate |Γrε ∩ Bρ(x3)| ≥ c′′εs with c′′ independent of ε and η, +we have +˜Cη ≥ 1 +2εs +ˆ +Γrε∩Bρ(x3) +⟨uε, g⊥⟩2 ds > c′′ +128. +As before, we choose η small enough to obtain a contradiction. +□ +Define the family of bad sets +Sε := +� +x ∈ Ω : |uε(x)| < 1 +2 +� +, +Sg,s +ε +:= Sε ∪ +� +x ∈ Γ : |⟨uε(x), g⊥(x)⟩| > 1 +4 +� +. +Proposition 3.4. [Strong Tangential Case] There exists ˜N ∈ N depending only on +Ω, a constant λ > 1 independent of ε and points pε,1, . . . , pε,Iε ∈ Sε∩Ω, qε,1, . . . , qε,Jε ∈ +Sε ∩ Γ such that +(i) Iε + Jε ≤ ˜N, +(ii) Sε ⊂ �Iε +i=1 Bλε(pε,i) ∪ �Jε +j=1 Bλε(qε,j), +(iii) {Bλε(pε,i), Bλε(qε,j)}1≤i≤Iε,1≤j≤Jε are mutually disjoint with centers satisfying +|pε,i − pε,j|, |qε,i − qε,j|, |pε,i − qε,j| > 8λε, +(iv) Bλε(pε,i) ∩ Γ = ∅ for all i = 1, . . . , Iε. +[Weak Tangential Case] There exists ˜N ∈ N depending only on Ω, a constant λ > 1 +independent of ε and points pε,1, . . . , pε,Iε ∈ Sg,s +ε +∩ Ω, qε,1, . . . , qε,Jε ∈ Sg,s +ε +∩ Γ such +that + +ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING +17 +(i) Iε + Jε ≤ ˜N, +(ii) Sg,s +ε +⊂ �Iε +i=1 Bλε(pε,i) ∪ �Jε +j=1 Bλεs(qε,j), +(iii) {Bλε(pε,i), Bλεs(qε,j)}1≤i≤Iε,1≤j≤Jε are mutually disjoint with centers satisfying +|pε,i − pε,j| > 8λε, +|qε,i − qε,j| > 8λεs, +and +|pε,i − qε,j| > 8λεs, +(iv) Bλε(pε,i) ∩ Γ = ∅ for all i = 1, . . . , Iε. +The proof is exactly as in [ABG20, Lemma 4.4] which is based on the method of +[Str94, Section 3] and a ball merging method which is presented in [BBH94, Theorem +IV.1]. As a consequence of Balzano-Weierstrass, we also have a result which states +that the bad sets Sε, Sg,s +ε +can eventually be covered by a static ball covering (along +a subsequence εn → 0). +Proposition 3.5. [Strong Tangential Case] For any sequence of ε → 0 there is a +subsequence εn → 0, a constant σ0 > 0 and a finite collection of points {p1, . . . , pI} ⊂ +Ω, {q1, . . . , qJ} ⊂ Γ such that for any 0 < σ < σ0 and for all n ∈ N, the collection of +sets +Sσ := {Bσ(pi)}I +i=1 ∪ {Bσ(qj)}J +j=1 +(3.13) +are mutually disjoint and cover Sεn. +[Weak Tangential Case] The same result holds for the bad set Sg,s +εn but with Sσ replaced +by +Sg,s +σ +:= {Bσ(pi)}I +i=1 ∪ {Bσs(qj)}J +j=1. +(3.14) +4. Local Orientation and Defect Windings +Now that the bad sets Sε and Sg,s +ε +have been shown to have finite bad ball coverings, +we are in a position to analyze the winding behaviour of minimizers around defects. +When dealing with interior bad balls, we may quantify the winding of uε on ∂Bλε(pi,ε) +in the usual way since |uε| ≥ 1/2 on this curve. In particular, we define the degree +of uε around ∂Bλε(pi,ε) to be the degree of the normalization of uε about ∂Bλε(pi,ε): +di = di,ε = deg(uε; ∂Bλε(pi,ε)) := deg(uε/|uε|; ∂Bλε(pi,ε)). +Analyzing the winding of uε about boundary bad balls is slightly more subtle, how- +ever. As mentioned in the introduction, we define the notion of a boundary index, +whose function is analogous to the degree of interior defects. Specifically, the bound- +ary index aims to quantify the turning behaviour of uε along circular arcs lying in the +interior Ω that connect two nearby points on Γ. To begin constructing this quantity, +we place focus on strong tangential solutions and then show the necessary modifica- +tions for weak tangential solutions. + +18 +ALAMA, BRONSARD AND VAN BRUSSEL +Consider again the local polar coordinate system found in Section 2 as defined +by the angular bounds (2.6) with center point qε,j ∈ Γ. Let Bλε(qε,j) be some fixed +boundary bad ball for a strong tangential solution uε and fix R > λε so that for all +ρ ∈ [λε, R] the closure of ωρ(qε,j) does not intersect the closure of any other bad ball. +Since |uε| ≥ 1/2 outside Bλε(qε,j), there is a single-valued function ψ with +uε +|uε| = eiψ +on Aλε,R(qε,j). +Likewise, there is a lifting γ of g for which g = eiγ on Aλε,R(qε,j) since g : NΓ → S1. +Looking along the curve Γ+ +λε,R(qε,j) and using the definition Hg(Ω), it holds that +either +|ψ(ρ, θ1(ρ)) − γ(ρ, θ1(ρ))| = 0 +or +|ψ(ρ, θ1(ρ)) − γ(ρ, θ1(ρ)) ± π| = 0. +(4.1) +These two possible conditions comes down the observation that uε has either a phase +equal to that of g or to −g. This fact induces a sense of orientation for uε with respect +to g along boundary components outside of bad balls. In particular, we say that uε +is positively oriented with respect to g at x ∈ Γ (p.o.) provided ⟨u(x), g(x)⟩ > 0 +(which corresponds to the first condition of (4.1)) and that uε is negatively oriented +(n.o.) in the opposite case ⟨u(x), g(x)⟩ < 0 (the second condition of (4.1)). +g +−g +u +Γ +x0 +Figure 1. Depiction of negative orientation with respect to g for a strong +tangential solution u at a point x0 ∈ Γ away from bad balls. +Upon starting at the point +q+ +ε,j = q+ +ε,j(ρ) := ∂Bρ(qε,j) ∩ Γ+ +λε,R(qε,j) +and traveling along the arc ∂Bρ(qε,j) ∩ Ω, one arrives at the point +q− +ε,j = q− +ε,j(ρ) := ∂Bρ(qε,j) ∩ Γ− +λε,R(qε,j) +for which uε has accumulated an approximate net number of π-rotations. +More +precisely, there exists a unique integer k ∈ Z such that +|ψ(ρ, θ2(ρ)) − γ(ρ, θ2(ρ)) − kπ| = 0 +on Γ− +λε,R(qε,j). +(4.2) + +ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING +19 +With this information, we may now define the boundary index. Let w : Aλε,R(qε,j) → +S1 be defined by +w := +� uε +|uε| +�2 += e2iψ. +Using (4.1) and (4.2), +� +� +� +� +� +| arg(w) − 2γ| = 2|ψ − γ| = 0 +on Γ+ +λε,R(qε,j) if uε is p.o., +| arg(w) − 2γ ± 2π| = 2|ψ − γ ± π| = 0 +on Γ+ +λε,R(qε,j) if uε is n.o., +| arg(w) − 2γ − 2πk| = 2|ψ − γ − kπ| = 0 +on Γ− +λε,R(qε,j), +and so w has preserved orientation on Γ± +λε,R(qε,j) with respect to g2. Therefore we +may extend w to x ∈ Γλε(qε,j) as an S1-valued, piecewise C2 map by simply setting +w = g2 along Γλε(qε,j). The reader can refer to Figure 2 for an illustration. Next, +g +λε +Γ+(qε,j) +Γ−(qε,j) +qε,j +u +(a) Possible profile of a strong tangential +solution u outside a boundary bad ball +g2 +Γ+(qε,j) +Γ−(qε,j) +qε,j +λε +w +(b) Corresponding profile of w outside a +boundary bad ball with interior extension +Figure 2. Relationship between u, w, g and g2. +for any ρ ∈ [λε, R], form the closed curve +Cρ := (∂Bρ(qε,j) ∩ Ω) ∪ Γρ(qε,j) +with positive orientation. By construction of w we may define +Dj = Dj(qε,j) := deg(w; Cρ) +(4.3) +whose value is independent of ρ ∈ [λ, R] for any particular extension of w by prop- +erties of the degree. Returning to the local polar coordinate system (ρ, θ) centered +at qε,j, we note that +arg(w) = 2ψ = 2Djθ + ˜φ(ρ, θ) +where ˜φ is a single-valued function in Aλε,R(qε,j). Therefore uε = f(ρ, θ)eiψ with +ψ(ρ, θ) = Djθ + φ(ρ, θ) +(4.4) + +20 +ALAMA, BRONSARD AND VAN BRUSSEL +and φ a single-valued function in Aλε,R(qε,j). The integer Dj ∈ Z is what we define +as the boundary index. In some cases, we will use the notation +Dj := ind(uε; ∂Bρ(qε,j) ∩ Ω). +The boundary index for weakly tangential solutions can be constructed in the same +way, but now with boundary bad balls having radii ρ = λεs. However, the phase +of uε along Γ± +λεs,R(qε,j) no longer satisfies the strict conditions of (4.1) and (4.2). In +this case, the definition of Sg,s +ε +can be used to show that +|ψ(ρ, θ1(ρ)) − γ(ρ, θ1(ρ))| < π +6 +or +|ψ(ρ, θ1(ρ)) − γ(ρ, θ1(ρ)) ± π| < π +6 +(4.5) +on Γ+ +λεs,R(qε,j) (depending on the orientation of u with respect to g), and that there +is a unique integer k ∈ Z such that +|ψ(ρ, θ2(ρ)) − γ(ρ, θ2(ρ)) − kπ| < π +6 +on Γ− +˜r,R(qε,j). +(4.6) +g +−g +u +Γ +π +6 +x0 +Figure 3. Illustration of positive orientation with respect to g for a weakly +tangential solution u at a point x0 ∈ Γ away from bad balls. By definition +of Sg,s +ε , the vector u(x0) may only reside within the shaded double cone +with axis defined by g. +Again, by defining the S1-valued function w = (u/|u|)2 on Aλεs,R(qε,j), from (4.5) +and (4.6) we have +� +� +� +� +� +| arg(w) − 2γ| = 2|ψ − γ| < π +3 +on Γ+ +λεs,R(qε,j) if uε is p.o., +| arg(w) − 2γ ± 2π| = 2|ψ − γ ± π| < π +3 +on Γ+ +λεs,R(qε,j) if uε is n.o., +| arg(w) − 2γ − 2πk| = 2|ψ − γ − kπ| < π +3 +on Γ− +λεs,R(qε,j), +which as before, shows that the orientation of w with respect to g2 is preserved on +Γ± +λεs,R(qε,j). We can now extend w to x ∈ Γλεs(qε,j) as an S1-valued, piecewise C2 +map satisfying | arg(w) − 2γ| < π/3 which can be done via interpolating the phase +linearly across Γλεs(qε,j), for example. The boundary index can now be defined in + +ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING +21 +the same way as the strong tangential case. +The first main identity we obtain from this definition connects the sum of all +associated bad ball boundary indices with D = deg(g; Γ) and the sum of degrees for +the interior bad balls. +Proposition 4.1. [Strong Tangential Case] Suppose uε is a solution of (1.3) with +associated bad ball covering {Bλε(pε,i), Bλε(qε,j)}1≤i≤Iε,1≤j≤Jε. Let +di = deg(uε; ∂Bλε(pε,i)) +and +Dj = ind(uε; ∂Bλε(qε,j) ∩ Ω) +be the degrees and boundary indices for uε about its interior and boundary bad balls +respectively. Then +D = +Iε +� +i=1 +di + 1 +2 +Jε +� +j=1 +Dj. +(4.7) +[Weak Tangential Case] Identity (4.7) holds for solutions of (1.5) and its associated +bad ball covering {Bλε(pε,i), Bλεs(qε,j)}1≤i≤Iε,1≤j≤Jε. +The proof for the weak tangential case is done identically to that of the strong +tangential case simply by replacing the radii λε of the boundary bad balls with λεs. +Thus, we provide a proof only for strong tangential solutions. +Proof. Define the domain +˜Ω := Ω \ +� Jε +� +j=1 +ωλε(qε,j) +� +and let ˜Γ = ∂ ˜Ω, C(qε,j) = ∂ωλε(qε,j) ∩ Ω. As in the definition of boundary index +(4.3), the function w = (uε/|uε|)2 is defined on ˜Ω and ˜Γ and can be extended across +each segment Γλε(qε,j). By the construction of the extension w, we have deg(w; Γ) = +deg(g2; Γ) = 2D and so by the definition of boundary index, +deg(w; ˜Γ) = 1 +2π +ˆ +Γ\∪jΓλε(qj) +(iw, ∂τw) ds + +Jε +� +j=1 +1 +2π +ˆ +C(qj) +(iw, ∂τw) ds += 1 +2π +ˆ +Γ +(iw, ∂τw) ds − +Jε +� +j=1 +1 +2π +ˆ +∂ωλε(qj) +(iw, ∂τw) ds += deg(w; Γ) − +Jε +� +j=1 +Dj = 2D − +Jε +� +j=1 +Dj. + +22 +ALAMA, BRONSARD AND VAN BRUSSEL +Lastly, the vortices pε,i are contained inside ˜Γ and so deg(w; ˜Γ) = �Iε +i=1 2di where we +note that the degree along each interior bad ball is doubled by the definition of w. +Thus, we obtain (4.7) by equating the two quantities for deg(w; ˜Γ) and dividing by +2. +□ +We also have a local summation property holding between degrees and boundary +indices: +Lemma 4.2. [Strong Tangential Case] Let I and J be sets of indices for a collection +of bad balls {Bλε(pε,i)}i∈I ∪ {Bλε(qε,j)}j∈J for a strongly tangential solution u and +suppose there is a point y0 ∈ Γ and radius R > 0 such that the ball BR(y0) satisfies +�� +i∈I +Bλε(pε,i) ∪ +� +j∈J +Bλε(qε,j) +� +⊂ BR(y0) +where BR(y0) does not intersect the closure of any other bad ball. Then if D = +ind(uε; ∂BR(y0) ∩ Ω), di = deg(uε; ∂Bλε(pε,i)) and Dj = ind(uε; ∂Bλε(qε,j) ∩ Ω), we +have +D = +� +j∈J +Dj + 2 +� +i∈I +di. +[Weak Tangential Case] Under the same hypotheses but with boundary bad ball radii +replaced by λεs, the above identity also holds for a collection of bad balls {Bλε(pε,i)}i∈I∪ +{Bλεs(qε,j)}j∈J for weakly tangential solutions. +The proof of this Lemma follows the same lines as Proposition 4.1, but can also +be shown using longer methods found in [vB22, Lemma 4.7]. As above, the proof +for the weak tangential case is done identically to that of the strong tangential case +by replacing the radii scaling of the boundary bad balls accordingly. To this end, we +proceed with the strong tangential case only. +Proof. Let ˜Ω = BR(y0) \ ∪j∈J ωλε(qj), ˜Γ = ∂ ˜Ω and C(qj) = ∂ωλε(qj) ∩ Ω. Since +|u| ≥ 1/2 in ˜Ω, the function w = (u/|u|)2 is defined on ˜Ω. As in the construction of +the boundary index, w can be appropriately extended across each segment Γλε(qj), +j ∈ J , and so we take w to be defined on ˜Γ∪j∈J Γλε(qj). In particular, this extension +of w is defined on ∂BR(y0) and so by definition of the boundary index, +D = ind(u; ∂BR(y0) ∩ Ω) = deg(w; ∂BR(y0)). +(4.8) + +ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING +23 +Calculating the degree of w along ˜Γ, we have by (4.8) +deg(w; ˜Γ) = 1 +2π +ˆ +∂BR(y0)\∪jΓλε(qj) +(iw, ∂τw) ds + +� +j∈J +1 +2π +ˆ +C(qj) +(iw, ∂τw) ds += 1 +2π +ˆ +∂BR(y0) +(iw, ∂τw) ds − +� +j∈J +1 +2π +ˆ +∂ωλε(qj) +(iw, ∂τw) ds += D − +� +j∈J +Dj. +On the other hand, each circle ∂ωλε(pi), i ∈ I, is contained inside ˜Γ and so +deg(w; ˜Γ) = +� +i∈I +deg(w; ∂ωλε(pi)) = 2 +� +i∈I +di +proving the desired identity. +□ +5. Lower Bounds for the Energy and Convergence +In this section, we display the details needed to complete the proof of Theorems +1.1 and 1.2, which mainly comes down to providing a lower bound for the energies +Eε and Eg,s +ε +on the ball collections Sσ and Sg,s +σ +respectively. This result is given in +Lemma 5.3 at the end of this section. The first step in our analysis is to calculate +the cost of a vortex locally on annular regions Ar,R with r < R. To do this, it is +useful to begin by characterizing solutions of (1.3) and (1.5) in terms of a local polar +representation with central point x0 ∈ Ω. Depending on whether x0 ∈ Ω or x0 ∈ Γ, +the representation for the phase of uε will look slightly different. In any case, the +general form for uε on Ar,R(x0), x0 ∈ Ω can be given by +uε(ρ, θ) = f(ρ, θ)eiψ(ρ,θ) on Ar,R(x0), ρ ∈ [r, R] +where ρ = |x − x0|, θ is an appropriately chosen polar angle and f(ρ, θ) = |uε|. In +the specific case when x0 ∈ Γ there are four general scenarios which can occur for +solutions on Γ± +r,R(x0) when ⟨u, g⟩ ̸= 0: +(a) u is p.o. on Γ+ +r,R and n.o. on Γ− +r,R, +(b) u is p.o. on Γ+ +r,R and on Γ− +r,R, +(c) u is n.o. on Γ+ +r,R and p.o. on Γ− +r,R, +(d) u is n.o. on Γ+ +r,R and on Γ− +r,R. +To accommodate for these four cases, we define a polar representation for uε on +Ar,R(x0) whose phase depends on the orientation with respect to g when near the +boundary. Let γ(x) be such that g(x) = eiγ(x) along ΓR(x0) with γ0 = γ(x0) provided + +24 +ALAMA, BRONSARD AND VAN BRUSSEL +x0 ∈ Γ. By modifying the single-valued function φ from (4.4) if necessary, the phase +ψ for uε can be given as +ψ(ρ, θ) = +� +� +� +� +� +dθ + φ(ρ, θ) +if BR(x0) ⊂ Ω +Dθ + γ0 + φ(ρ, θ) +if x0 ∈ Γ and u is p.o. on Γ+ +r,R, +Dθ + γ0 + φ(ρ, θ) ± π +if x0 ∈ Γ and u is n.o. on Γ+ +r,R. +(5.1) +In this form, φ is a smooth, single-valued function defined on Ar,R(x0) and can +be thought of strictly as a function of ρ > 0 on Γ± +r,R by the choice of coordinates +given in (2.7). That is, φ = φ(ρ, θ(ρ)) on Γ± +r,R. The integers d = deg(u; ∂Bρ(x0)), +D = ind(u; ∂Bρ(x0) ∩ Ω) ∈ Z are the associated degree and boundary index for uε +respectively. Through representation (5.1), the boundary index D determines the +orientation of u along Γ− +r,R. Indeed, when R is taken to be small and D is even, the +phase difference across Γ± +r,R will be approximately an even multiple of π. In this case, +the orientation of uε with respect to g will be maintained along Γ± +r,R (cases (b) and +(d)). When D is odd, the orientation of uε with respect to g changes sign, giving +cases (a) and (c). +The function φ plays an important role in estimating the energy contribution of +a defect and it is critical to show that it is appropriately bounded. The following +proposition is needed for this estimation process. +Proposition 5.1. Let φ be as defined in (5.1) and suppose |u| ≥ 1/2, |⟨u, g⊥⟩| ≤ 1/4 +on Γ± +r,R. Then there exists a constant C > 0 for which |φ| ≤ C(|⟨u, g⊥⟩| + ρ). In the +special case that ⟨u, g⊥⟩ = 0 on Γ± +r,R, we have the simplified bound |φ| ≤ Cρ. +The result of Proposition 5.1 is claimed in [Mos03] for g⊥ = n in the weak tangen- +tial case, but is not explicitly shown. We prove it here for completeness. +Proof. Observe the inner product +|⟨u, g⊥⟩| = |u|| cos(ψ − (γ − π/2))| = |u|| sin(ψ − γ)| = |u|| sin(ψ − γ ± π)|. +When |⟨u, g⊥⟩| ≤ 1/4 and using the bound |u| ≥ 1/2, we obtain |ψ − γ| ≤ π/6 +or |ψ − γ ± π| ≤ π/6 for all x ∈ Γ± +r,R depending on orientation. If ⟨u, g⊥⟩ = 0, +then we precisely get |ψ − γ| = 0 or |ψ − γ ± π| = 0 which again depends on the +orientation of u with respect to g. By considering the four possible orientations for +uε (cases (a)–(d)) separately, it can be shown that there is a constant c > 0 such +that |φ| ≤ π/6 + cρ on Γ± +r,R in the weak tangential case and |φ| ≤ cρ in the strong +tangential case. To see this, we analyze case (a) from above and claim the other +cases follow similarly. When uε is positively oriented on Γ+ +r,R and negatively oriented + +ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING +25 +on Γ− +r,R there is ξ ∈ [−π/6, π/6] such that, +ψ − γ = Dθ + γ0 − γ + φ = ξ +on Γ+ +r,R +with D ∈ 2Z + 1. The triangle inequality gives +|φ| ≤ |ξ| + |Dθ| + |γ0 − γ| ≤ π +6 + cρ. +On Γ− +r,R, we have Dθ + γ0 − γ + φ = Dπ + ξ and a similar estimate yields +|φ| ≤ |ξ| + |D||π − θ| + |γ0 − γ| ≤ π +6 + cρ. +The strong tangential condition corresponds to the scenario where ξ = 0 for each of +the four cases (a)–(d), and so the estimate above can be reduced to |φ| ≤ Cρ in this +case, which finishes the proof for solutions satisfying ⟨u, g⊥⟩ = 0 on Γ± +r,R. +Assume R is chosen small enough such that cρ ≤ π/12, for example, so that |φ| ≤ π/4 +on Γ± +r,R. Returning to the inner product and omitting the cases where we consider +±π in the argument, the reverse triangle inequality gives +|⟨u, g⊥⟩| = |u|| sin(ψ−γ)| ≥ 1 +2| sin(φ)|| cos(Dθ+γ0−γ)|− 1 +2| cos(φ)|| sin(Dθ+γ0−γ)| +which holds on Γ± +r,R for any of the four orientation scenarios. Since Γ and γ are +smooth, for R taken small enough it holds that +| sin(Dθ + γ0 − γ)|, |1 − | cos(Dθ + γ0 − γ)|| ≤ Cρ, +and so we may assume | cos(Dθ + γ0 − γ)| ≥ 1/2 on Γ± +r,R. Thus, +|⟨u, g⊥⟩| ≥ 1 +4| sin(φ)| − 1 +2Cρ. +Finally, since |φ| ≤ π/4 we have +|⟨u, g⊥⟩| ≥ 1 +8|φ| − 1 +2Cρ +which finishes the proof. +□ +As described in much of the surrounding literature, the energy contribution of +a non-trivial interior defect for solutions of the Ginzburg–Landau equations on an +annulus Ar,R is known to be logarithmic in the ratio R/r and depends on the square +of the degree d of u around the vortex. A similar result holds for boundary defects +with associated boundary index D. This result is given in Theorem 5.2 below. + +26 +ALAMA, BRONSARD AND VAN BRUSSEL +Theorem 5.2. [Strong Tangential Case] Suppose x0 ∈ Ω and assume that 1/2 ≤ +|u| ≤ 1 in Ar,R(x0). Additionally, suppose ⟨u, g⊥⟩ = 0 on Γ± +r,R(x0) and that there is +some number K such that +Eε(u) ≤ K| ln ε| + K, +1 +ε2 +ˆ +ωεγ (x0) +(1 − |u|2)2 dx ≤ K, +where εγ is as in Theorem 3.2. Then there exists a constant C depending only on Ω, +γ and K such that: +(i) If BR(x0) ⊂ Ω, ε ≤ r < R ≤ r0 and d = deg(u; ∂Br(x0)) ̸= 0, +ˆ +Ar,R(x0) +|∇u|2 dx ≥ 2d2π ln +�R +r +� +− C. +(5.2) +(ii) If x0 ∈ Γ, ε ≤ r < R ≤ r0 and D = ind(u; ∂Br(x0) ∩ Ω) ̸= 0, +ˆ +Ar,R(x0) +|∇u|2 dx ≥ D2π ln +�R +r +� +− C. +(5.3) +[Weak Tangential Case] Suppose x0 ∈ Ω and assume that 1/2 ≤ |u| ≤ 1 in Ar,R(x0). +Additionally, suppose |⟨u, g⊥⟩| ≤ 1/4 on Γ± +r,R and that there is some number K such +that +Eg,s +ε (u) ≤ K| ln ε| + K, +1 +ε2 +ˆ +ωεγ (x0) +(1 − |u|2)2 dx + 1 +εs +ˆ +Γεγ +⟨u, g⊥⟩2 ds ≤ K, +where εγ is as in Theorem 3.2. Then there exists a constant C depending only on Ω, +γ and K such that: +(i) If BR(x0) ⊂ Ω, ε ≤ r < R ≤ r0 and d = deg(u; ∂Br(x0)) ̸= 0, then (5.2) holds. +(ii) If x0 ∈ Γ, εs ≤ r < R ≤ r0 and D = ind(u; ∂Br(x0) ∩ Ω) ̸= 0, then (5.3) holds. +Proof. The proof of inequality (5.2) is omitted since it follows identically to that of +[Str94, Proposition 3.4] and [Str95, Proposition 3.4’]. For (5.3), we provide a brief +sketch to show how the boundary index appears and how the boundary conditions +are handled. With this, we assume x0 ∈ Γ. Using the polar representation for u on + +ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING +27 +Ar,R(x0), +ˆ +Ar,R +|∇u|2 dx = +ˆ +Ar,R +� +f 2|∇ψ|2 + |∇f|2� +dx +≥ +ˆ +Ar,R +f 2|∇Dθ + ∇φ|2 dx += +ˆ +Ar,R +D2f 2 +ρ2 +dx + +ˆ +Ar,R +2Df 2 +ρ2 +∂θφ dx + +ˆ +Ar,R +f 2|∇φ|2 dx += I1 + I2 + I3. +The lower estimates for I1 and I3 primarily follow [Str94, Proposition 3.4] and [Str95, +Proposition 3.4’], with details regarding the boundary given in [Mos03, Proposition +5.6] and [ABGS15, Proposition 4.3]. Specifically, +I1 ≥ D2π2 ln +�R +r +� +− C, +I3 ≥ 1 +4 +ˆ +Ar,R(x0) +|∇φ|2 dx +where C is a constant independent of ε. For the integral I2, Proposition 5.1 implies +|φ(ρ, θ2) − φ(ρ, θ1)| ≤ 2C +� +� � +x∈∂Γ± +ρ +|u⊥(ρ, θi(ρ))| + ρ +� +� +with u⊥ = 0 for strong tangential solutions. Applying bounding methods found in +[Mos03, Proposition 5.6] and [Str94, Proposition 3.4], +|I2| ≤ +����� +ˆ +Ar,R +2D +ρ2 ∂θφ dx +����� + 2 +����� +ˆ +Ar,R +D(1 − f 2) +ρ2 +∂θφ dx +����� +≤ +ˆ R +r +2|D||φ(ρ, θ2) − φ(ρ, θ1)| +ρ +dρ + 1 +4 +ˆ +Ar,R +|∇φ|2 dx + C +≤ 4|D|C +ˆ +Γ± +r,R +|⟨u, g⊥⟩| +ρ +dρ + 1 +4 +ˆ +Ar,R +|∇φ|2 dx + C′. +If u is a strong tangential solution, the first integral in the last line above does not +appear and so the estimate ends there. If u is a weak tangential solution, the proof of +[Mos03, Proposition 5.6] can be followed with |f ·ν| replaced by |⟨u, g⊥⟩| throughout, +giving +|I2| ≤ C + 1 +4 +ˆ +Ar,R(x0) +|∇φ|2 dx. + +28 +ALAMA, BRONSARD AND VAN BRUSSEL +The desired lower bound is then estimated by +ˆ +Ar,R +|∇u|2 dx ≥ I1 − |I2| + I3 ≥ D2π ln +�R +r +� +− C. +□ +At this point, we are ready to describe a lower bound for the energy on the sets +comprising Sσ and Sg,s +σ +as defined in (3.13) and (3.14) respectively. +Lemma 5.3. [Strong Tangential Case] Suppose εn is the subsequence taken in Propo- +sition 3.5 and let di = deg(uεn; ∂Bσ(pi)) and Dj = ind(uεn; ∂Bσ(qj)∩Ω). There exists +a constant C, independent of εn and σ such that: +Eεn(uεn; Bσ(pi)) ≥ π|di| ln +� σ +εn +� +− C, +i = 1, . . . , I, +Eεn(uεn; Bσ(qj)) ≥ π +2 |Dj| ln +� σ +εn +� +− C, +j = 1, . . . , J. +[Weak Tangential Case] Suppose εn is the subsequence taken in Proposition 3.5 and +let di = deg(uεn; ∂Bσ(pi)) and Dj = ind(uεn; ∂Bσs(qj) ∩ Ω). There exists a constant +C, independent of εn and σ such that: +Eg,s +εn (uεn; Bσ(pi)) ≥ π|di| ln +� σ +εn +� +− C, +i = 1, . . . , I, +Eg,s +εn (uεn; Bσs(qj)) ≥ πs +2 |Dj| ln +� σ +εn +� +− C, +j = 1, . . . , J. +The proof for this lemma comes from a result developed by Sandier [San98] (Jer- +rard [Jer99] gives a similar result) which uses techniques involving the logarithmic +lower bound as found in Theorem 5.2. The method involves a two-step approach +where balls containing subsets of Sε (or Sg,s +ε ) are expanded and fused such that +the energy on these balls can be estimated from below while preserving the natural +scaling by ε. A fundamental difference between our work and that of Sandier’s are +details regarding boundary data. Indeed, Sandier’s work assumes Dirichlet bound- +ary conditions and thus one does not obtain boundary vortices in this case. For our +problem, boundary vortices are expected and thus some extra care needs to be taken +when one performs the ball expansion and fusion argument. We refer the reader to +[ABM20] and [ABG20, Lemma 7.1] for a proof on how to modify Sandier’s result to +accommodate for boundary vortices. In particular, the proof not only removes the +assumption of Dirichlet boundary data, but also explains how one can deal with the +different radial scalings ε and εs of the bad balls. However, it is worth noting that +the proof of [ABG20, Lemma 7.1] is done in a global sense due to the way boojums + +ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING +29 +must be dealt with. For our case, thanks to Lemma 4.2, the arguments of [ABG20, +Lemma 7.1] can be applied to each σ-ball separately which results in Lemma 5.3. +As a consequence of Lemma 5.3 and Proposition 2.2, we have +π +� +I +� +i=1 +|di| + 1 +2 +J +� +j=1 +|Dj| +� +| ln εn| − C ≤ Eε(uεn; Sσ) ≤ πsD| ln ε| + C +(5.4) +for strong tangential solutions and +π +� +I +� +i=1 +|di| + s +2 +J +� +j=1 +|Dj| +� +| ln εn| − C ≤ Eg,s +ε (uεn; Sg,s +σ ) ≤ πsD| ln ε| + C +(5.5) +for weak tangential solutions. Using these estimates, we find that each degree di +and boundary index Dj are uniformly bounded in ε and therefore can be taken to +be constant along a subsequence εn → 0. It is also clear from (5.4) and (5.5) that +all σ-balls constituting Sσ and Sg,s +σ +respectively, which satisfy di = Dj = 0 do not +contribute substantial energy. Therefore, the associated balls can be seen to belong +to the set where uεn converges. By relabeling the approximate vortices if necessary, +we define +Σ := {p1, . . . , pI} ∪ {q1, . . . , qJ} +to be the collection of all σ-ball centers with non-trivial degree or boundary index. +Upon dividing by π| ln ε| and taking ε → 0 in (5.4) and (5.5), it holds that +I +� +i=1 +|di| + 1 +2 +J +� +j=1 +|Dj| ≤ D +for strong tangential solutions and +I +� +i=1 +|di| + s +2 +J +� +j=1 +|Dj| ≤ sD +for weak tangential solutions. Using identity (4.7) in combination with the above +inequalities shows all integers di and Dj must be positive (since we’ve assumed +D > 0). In fact, we have the equalities +D = +I +� +i=1 +di + 1 +2 +J +� +j=1 +Dj +(5.6) +and +sD = +I +� +i=1 +di + s +2 +J +� +j=1 +Dj +(5.7) + +30 +ALAMA, BRONSARD AND VAN BRUSSEL +for the strong and weak cases respectively. This allows us to conclude the following: +Let +Ωσ := Ω \ Sσ, +Ωg,s +σ +:= Ω \ Sg,s +σ . +Corollary 5.4. [Strong Tangential Case] For any σ ∈ (0, σ0), there exists a constant +C independent of ε and σ such that +Eεn(uεn; Ωσ) ≤ πD| ln σ| + C. +Moreover, there is a constant C′ independent of ε such that +1 +4ε2 +n +ˆ +Ω +� +1 − |uεn|2�2 dx ≤ C′. +[Weak Tangential Case] For any σ ∈ (0, σ0), there exists a constant C independent +of ε and σ such that +Eg,s +εn (uεn; Ωg,s +σ ) ≤ πsD| ln σ| + C. +There is also a constant C′ independent of ε such that +1 +4ε2 +n +ˆ +Ω +� +1 − |uεn|2�2 dx + 1 +2εs +n +ˆ +Γ +⟨uεn, g⊥⟩2 ds ≤ C′. +Upon taking an appropriate subsequence σn → 0, Corollary 5.4 and following +the methods of [BBH94] and [Str94] allows us to conclude that uεn ⇀ u0 weakly +in H1 +loc(Ω \ Σ; R2) as εn → 0 where u0 ∈ H1(Ω \ Σ; S1) is harmonic. By observing +annular regions in Ωσ (and Ωg,s +σ ) and applying Corollary 5.4 and Theorem 5.2, it is +easy to show that vortices of degree or boundary index larger than 1 require too +much energy, and therefore we conclude di = Dj = 1 for all 1 ≤ i ≤ I, 1 ≤ j ≤ J. +In light of equation (5.6), making the further assumption that D = 1 forces that +either Σ = {p1} ⊂ Ω or Σ = {q1, q2} ⊂ Γ which finishes the proof of Theorem 1.1. +Moreover, equation (5.7) can be rewritten +sD = +I +� +i=1 +di + s +2 +J +� +j=1 +Dj = (1 − s) +I +� +i=1 +di + sD +which immediately implies Σ ⊂ Γ whenever 0 < s < 1. The fact that each Dj = 1 +also implies |Σ| = J = 2D which then completes the proof of Theorem 1.2. +6. Defect Locations on a Disc when g = τ +This final section is dedicated to analyzing a strong tangential anchoring example. +The primary point of studying this case is to shed light on the fact that certain +domain geometries may exist for which boundary vortices could still be energetically +preferable to those in the interior, even when all vortices are given equal scaling. We +consider the special case where g = τ, the positively oriented unit tangent vector + +ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING +31 +to Γ, and take Ω = B1(0) to be the unit disc for simplicity. In this scenario, D = +deg(τ, Γ) = 1 and so in light of equation (4.7) there are only two possibilities for +defect locations, exactly one in the interior or exactly two along the boundary. To +investigate this further, we observe a renormalized energy. +One Defect in Ω +Let p ∈ Ω denote the interior singularity and assume the limiting harmonic map +u0 = τ on Γ. Following [ABGS15, Section 6] and [Riv99], consider the solution Φp +to +� +� +� +∆Φp = 2πδp(x) +in Ω, +∂Φp +∂n = g × gτ +on Γ, +with associated asymptotic energy expansion +Eg,1 +ε (uε) = π| ln ε| + W(p) + cΩ + o(1) +where +W(p) = lim +ρ→0 +� +1 +2 +ˆ +Ωρ +|∇Φp|2 dx − π ln +�1 +ρ +�� +is the renormalized energy and cΩ is the vortex core energy associated to p. It can be +shown (see [BBH94] for example) that the renormalized energy W has a minimum +value of zero at the origin p = 0. +Two Defects on Γ +Let q1, q2 ∈ Γ be the boundary singularities and consider the PDE +� +� +� +∆Φq = 0 +in Ω, +∂Φq +∂n = g × ∂τg − π(δq1(x) + δq2(x)) +on Γ +which has solution Φq(x) = ln |x − q1| + ln |x − q2|. +The energy expansion and +renormalized energy are +Eg,1 +ε (uε) = π| ln ε| + W(q1, q2) + 2cΓ + o(1), +W(q1, q2) = lim +ρ→0 +� +1 +2 +ˆ +Ωρ +|∇Φq|2 dx − π ln +�1 +ρ +�� +, +and cΓ represents the vortex core energy associated to each qj. By the identity +ˆ +Ωρ +|∇Φq|2 dx = +2 +� +j=1 +ˆ +∂Bρ(qj)∩Ω +Φq +∂Φq +∂nqj +ds + +ˆ +Γ\(Γρ(q1)∪Γρ(q2)) +Φq +∂Φq +∂n ds + +32 +ALAMA, BRONSARD AND VAN BRUSSEL +it can be shown via direct calculation that +W(q1, q2) = −π ln |q1 − q2| +which is minimized whenever q1 and q2 are antipodal. In particular, +min +q1,q2∈Γ W(q1, q2) = −π ln |2q1| < 0 = min +p∈Ω W(p). +This calculation suggests that the case where Σ = {q1, q2} gives the energetically +preferable singularity allocation. To conclude that this is indeed the case, it must be +shown that the core energy associated to a boundary vortex is not too large compared +to cΩ/2. Although we do not have a rigorous proof for this, we believe it is possible +to show using estimates such as those found in [ABM20]. +References +[ABG20] +Stan Alama, Lia Bronsard, and Dmitry Golovaty. Thin film liquid crystals with oblique +anchoring and boojums. In Annales de l’Institut Henri Poincar´e C, Analyse non +lin´eaire. Elsevier, 2020. +[ABGS15] +Stan Alama, Lia Bronsard, and Bernardo Galv˜ao-Sousa. Weak anchoring for a two- +dimensional liquid crystal. Nonlinear Analysis: +Theory, Methods & Applications, +119:74–97, 2015. +[ABM20] +Stan Alama, Lia Bronsard, and Petru Mironescu. Inside the light boojums: a journey +to the land of boundary defects. Analysis in Theory and Applications, 36(2):128–160, +2020. +[BBH94] +Fabrice Bethuel, Ha¨ım Brezis, and Fr´ed´eric H´elein. Ginzburg-Landau Vortices, vol- +ume 13. Springer, 1994. +[DKMO02] Antonio DeSimone, Robert V Kohn, Stefan M¨uller, and Felix Otto. A reduced theory +for thin-film micromagnetics. Communications on Pure and Applied Mathematics: A +Journal Issued by the Courant Institute of Mathematical Sciences, 55(11):1408–1460, +2002. +[GCGJ20] +Carlos J. Garc´ıa-Cervera, Tiziana Giorgi, and Sookyung Joo. Boundary vortex for- +mation in polarization-modulated orthogonal smectic liquid crystals. SIAM J. Appl. +Math., 80(5):2024–2044, 2020. +[IK21] +Radu Ignat and Matthias Kurzke. Global Jacobian and Γ-convergence in a two- +dimensional Ginzburg-Landau model for boundary vortices. J. Funct. Anal., 280(8):Pa- +per No. 108928, 66, 2021. +[Jer99] +Robert L Jerrard. Lower bounds for generalized ginzburg–landau functionals. SIAM +Journal on Mathematical Analysis, 30(4):721–746, 1999. +[Kur06] +Matthias Kurzke. Boundary vortices in thin magnetic films. Calculus of Variations and +Partial Differential Equations, 26(1):1–28, 2006. +[Mos03] +Roger Moser. Ginzburg-Landau vortices for thin ferromagnetic films. Applied Mathe- +matics Research eXpress, 2003(1):1–32, 01 2003. +[Riv99] +Tristan Rivi`ere. Asymptotic analysis for the ginzburg-landau equations. Bollettino +dell’Unione Matematica Italiana, 2-B(3):537–575, 10 1999. +[San98] +Etienne Sandier. Lower bounds for the energy of unit vector fields and applications. +Journal of functional analysis, 152(2):379–403, 1998. + +ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING +33 +[Str94] +Michael Struwe. On the asymptotic behavior of minimizers of the ginzburg-landau +model in 2 dimensions. Differential and Integral Equations, 7(5-6):1613–1624, 1994. +[Str95] +Michael Struwe. Erratum: “on the asymptotic behavior of minimizers of the ginzburg– +landau model in 2 dimensions”. Differential and Integral Equations, 8(1):224, 1995. +[vB22] +Lee van Brussel. Boundary Versus Interior Defects for a Ginzburg–Landau Model with +Tangential Anchoring Conditions. PhD thesis, McMaster University, Hamilton, ON. +Canada, June 2022. +[VL83] +G.E. Volovik and O.D. Lavrentovich. Topological dynamics of defects: boojums in +nematic drops. Zh Eksp Teor Fiz, 85(6):1997–2010, 1983. + diff --git a/PNE4T4oBgHgl3EQf-A73/content/tmp_files/load_file.txt b/PNE4T4oBgHgl3EQf-A73/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..accb0b61259a9cceae5fa0aced688bdf38e02a76 --- /dev/null +++ b/PNE4T4oBgHgl3EQf-A73/content/tmp_files/load_file.txt @@ -0,0 +1,813 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf,len=812 +page_content='ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING STAN ALAMA, LIA BRONSARD AND LEE VAN BRUSSEL Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' We analyze Ginzburg–Landau minimization problems in two dimen- sions with either a “strong or weak” tangential boundary condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' These prob- lems are motivated by experiments in liquid crystal with boundary defects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In the singular limit when the correlation length tends to zero, we show that bound- ary defects will be observed for weak anchoring, while both boundary and interior vortices are possible for strong anchoring in the first order limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Introduction In this paper we study minimizers of two variational problems motivated by the study of defects in a nematic liquid crystal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' We consider a two-dimensional setting, related to a thin-film reduction of the three dimensional Landau–de Gennes model to two dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The special feature we are interested in comes from the work of Volovik and Lavrentovich [VL83] where nematic drops are placed in an isotropic medium, allowing for the control of nematic boundary behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In this way, the liquid crystal and its associated defect dynamics are studied as the nematic boundary molecules are transformed from having a forced angle of α = π/2 with respect to the unit normal n to the boundary of the droplet to α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In this paper, we return to the well-studied Ginzburg-Landau functional but with new tangential types of boundary conditions, inspired by this physical phenomena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' We begin by describing the variational problem in mathematical terms, and stating our main results in Theorems 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' We consider a two-dimensional, bounded, simply connected domain Ω ⊂ R2 ∼= C representing the space occupied by the liquid crystal with C3,α-smooth boundary Γ := ∂Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Let g : Γ → S1 be C3,α-smooth E-mail address: alama@mcmaster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='ca, bronsard@mcmaster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='ca, vanbrulw@mcmaster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='ca.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Date: January 16, 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='05361v1 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='AP] 13 Jan 2023 2 ALAMA, BRONSARD AND VAN BRUSSEL boundary data with positive degree D := deg(g;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Γ) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' A natural example is to choose g to parametrize the (positively oriented) unit tangent vector to ∂Ω, but this need not be the case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In order to force the order parameter u to be parallel (or close to parallel) with respect to g, we will be using two methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The first method is to impose that u have zero projection along a vector orthogonal to g, that is, impose the pointwise scalar product condition ⟨u, g⊥⟩ = 0 on Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' With this, we consider the Ginzburg–Landau energy defined for H1(Ω;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' R2) mappings Eε(u) := 1 2 ˆ Ω � |∇u|2 + 1 2ε2 � 1 − |u|2�2 � dx where ε > 0 and observe the behaviour of solutions to the strong tangential mini- mization problem inf � Eε(u) : u ∈ Hg(Ω) := {u ∈ H1(Ω;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' R2) : ⟨u, g⊥⟩ = 0 on Γ} � , (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1) in the limit as ε → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In this way, we can observe the topological defects associated to the limiting map by analyzing a sequence of energy minimizing configurations {uε} where the nematic material is asked to be precisely (strongly) parallel to g along Γ for each ε > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' It turns out that asking such a condition to hold does not quite translate to a standard Dirichlet or Neumann problem for the associated Euler– Lagrange equations, but rather a mixture of the two within appropriate coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' To see this, we make the additional assumption that g be defined on a tubular neighborhood NΓ := {x ∈ Ω : dist(x, Γ) < δ} with δ > 0 is small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Using this assumption, there exists a natural decomposition for functions u in NΓ using the orthonormal frame {g(x), g⊥(x)} via u = u∥g + u⊥g⊥ (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2) where u∥ := ⟨u, g⟩ and u⊥ := ⟨u, g⊥⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In using this decomposition, we find that solutions to the strong tangential problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1) satisfy the Euler–Lagrange system � � � � � � � −∆u = 1 ε2(1 − |u|2)u in Ω, u⊥ = 0 on Γ, ∂nu∥ = 0 on Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3) The second method for enforcing parallelity is done through boundary energy penal- ization (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Moser [Mos03]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Indeed, define Eg,s ε (u) := Eε(u) + 1 2εs ˆ Γ ⟨u, g⊥⟩2 ds ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING3 where s ∈ (0, 1], so that solutions of the weak tangential minimization problem inf � Eg,s ε (u) : u ∈ H1(Ω;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' R2) � (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4) are energetically induced to decrease their projection along g⊥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' By calculating the first variation for Eg,s ε , it can be easily shown that minimizers uε satisfy the weak anchoring system � � � � � −∆u = 1 ε2(1 − |u|2)u in Ω, ∂nu = − 1 εsu⊥g⊥ on Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5) For either minimization problem, solutions to (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1) and (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4) are guaranteed by the direct method from the calculus of variations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Moreover, it can also be shown that strong tangential minimizers, in some sense, are weak limits of solutions to a cer- tain modified weakly tangential minimization problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Therefore, both problems are naturally connected and it is reasonable to analyze the solutions of both.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' It is well known from the literature (see Bethuel-Brezis-H´elein [BBH94], for exam- ple) that the local winding behaviour of minimizers about vortices and the global winding behaviour of the boundary data g are directly linked to the energy of a mini- mizing configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Thus, given that our interest is in the observation of boundary defects, we must grasp, in some way, the winding behaviour of minimizers near boundary vortices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Indeed, when a defect is located in the interior, this winding is easily quantifiable by calculating the standard topological degree of the minimizer’s normalization about a small circle centered at the defect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' However, since a closed curve cannot be made about a boundary vortex, it is not immediately clear how one should proceed in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' To combat this, we develop a topological quantity called the boundary index, which essentially counts the net number of approximate π-rotations that are made from one side of the vortex to the other on the boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In this way, a boundary defect with an associated boundary index d will resemble an interior vortex of degree d cut in half, and thus carry a “half-integer” degree (see Definition (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' A rigorous construction of the boundary index is given in Sec- tion 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Using the notion of the boundary index, the main results of this paper are summarized in Theorems 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Suppose {uε}ε>0 is a sequence of solutions to (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1) with associated boundary function g : NΓ → S1 of degree D = deg(g;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Γ) ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Then there is a subsequence εn → 0, a finite number of point singularities Σ ⊂ Ω and a harmonic map u0 ∈ H1(Ω \\ Σ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' S1) such that uεn ⇀ u0 weakly in H1 loc(Ω \\ Σ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' R2) 4 ALAMA, BRONSARD AND VAN BRUSSEL with each defect contained in Σ having either associated degree, or boundary index, equal to one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In the particular case where D = 1, then one and only one of the following scenarios hold: (1) Σ = {p} with p ∈ Ω, (2) Σ = {q1, q2} with q1, q2 ∈ Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' For the last part of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1, we remind the reader that our primary motiva- tion for studying this problem came from the topological observations made on 3D samples, by Volovik and Lavrentovich in [VL83].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In particular, they found experi- mentally single interior hedgehog defect when molecules are asked to be normal to the boundary and a bipolar boojum pair when requiring tangential conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In either case, the normal and tangential boundary data are of degree one and thus our theoretical treatment of the problem weakly recovers this observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' To get a complete picture, a renormalized energy analysis would need to be conducted in order to show when one defect type is preferred over another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' To this end, in the last section of this work, we provide a concrete example of strong tangential anchoring in the case Ω = B1(0), the unit disc, with g = τ the positively oriented unit tangent vector to the boundary Γ, to highlight that the boundary vortex pair may give the preferable energy minimizing configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Such a result in 2D would be a first step in obtaining theoretically results coinciding with the found experimental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Next we state our result in case of weak tangential boundary conditions: Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Suppose {uε}ε>0 is a sequence of solutions to (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4) with associated boundary function g : NΓ → S1 of degree D = deg(g;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Γ) ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Then there is a subsequence εn → 0, a finite number of point singularities Σ ⊂ Ω and a harmonic map u0 ∈ H1(Ω \\ Σ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' S1) such that uεn ⇀ u0 weakly in H1 loc(Ω \\ Σ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' R2) with each defect contained in Σ having associated degree or boundary index equal to one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' If s ∈ (0, 1), it holds that Σ ⊂ Γ with |Σ| = 2D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The primary takeaway of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2 comes from the observation that the expo- nent s ∈ (0, 1] almost completely dictates the allocation of defects in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In particular, the Theorem states that independent of the winding behaviour of g and the geometry of Ω, giving vortices ‘more room’ along the boundary (on the scale of εs as opposed to ε) is enough for boundary vortex pairs to always be energetically preferable when compared to interior vortices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' A related model is that of a thin ferromagnetic film as obtained in an appropri- ate limiting regime by DeSimone, Kohn, Muller and Otto [DKMO02].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' This limiting ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING5 ferromagnetic thin film was studied by Moser [Mos03], and by Kurzke [Kur06] in certain settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In those problems, they impose tangential weak anchoring condi- tions with g = τ the unit tangent, and find critical anchoring strength at which boundary vortices are favored over interior vortices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In our case, we also consider a strong tangential anchoring, and generalize their results to weak anchoring for any g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' More recently, Ignat-Kurzke [IK21] have obtained Γ-convergence results for the weak tangential anchoring problem using a notion of global Jacobian in a different limit- ing regime where interior vortices cost more energy than boundary vortices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In the context of polarization-modulated orthogonal smectic liquid crystal, Garcia-Cervera, Giorgi and Joo [GCGJ20] have studied boundary vortices in a square domain with mixed weak and strong boundary conditions on the edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In the work of Volovik and Lavrentovich [VL83] the topological dynamics of the nematic material are observed as the boundary molecules are changed from being parallel to the boundary to perpendicular, by varying the aperture α of the cone formed by the molecule with the normal to the boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' When the angle α = π/2, a bipolar structure is noticed with two point defects occurring along the boundary called boojums.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' At the other extreme with α = 0, a single interior hedgehog defect is realized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Using a vector-valued order parameter u for modelling the molecular align- ment of the liquid crystal, the authors note that a surface energy density proportional to [⟨u, n⟩2 − cos2 α]2 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='6) can be used in comparison to an interior gradient energy for determining the energy preference of boojum defects to hedgehog defects and vice versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' A generalization of this setup was analyzed by Alama, Bronsard and Golovaty in [ABG20] where they replaced the boundary’s normal vector n in expression (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='6) with general smooth S1-valued boundary data g, possessing a positive associated winding number along the boundary, and restricting α ∈ (0, π/2), the relative angle made between g and the order parameter u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In this present work, we aim to answer the question of how this generalization operates for the specific case of α = π/2 using Ginzburg-Landau as a toy model for nematic material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In particular, we are interested in obtaining conditions for which minimizing configurations prefer boundary defects over interior defects in this setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The rest of the paper is organized as follows: in Section 2 we present upper bounds for the energy of minimizers to each problem, as well as a priori pointwise bounds for all solutions of the associated Euler-Lagrange equations, adapted for our new settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In Section 3, we present our η compactness results adapted from Struwe [Str94] to handle each type of boundary conditions and use it to define the “bad balls” for each type, and show that they are contained in a finite number of very small balls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' 6 ALAMA, BRONSARD AND VAN BRUSSEL Next in Section 4, we analyze the winding behaviour of minimizers around boundary defects and introduce our notion of boundary index and use it to obtain the important “degree Proposition and Lemma” (Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1 and Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2) which will be essential in proving the lower bound on the energy of boundary defects in terms of the degree of the boundary data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In Section 5, we obtain an energy lower bound for each type of tangential conditions over the appropriate ball collections, and we put everything together and prove our two main theorems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Finally in Section 6, we present an example with strong tangential anchoring on the unit disc which suggest that two antipodal boundary defect would be favored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Preliminary Facts for Minimizers We begin by showing an important pointwise bound on solutions of the Euler– Lagrange systems (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3) and (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The proof follows familiar lines, (see [BBH94, ABGS15, ABG20]) and so we provide a sketch to highlight the differences with previous papers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Suppose u is a solution of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3) or (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Then |u| ≤ 1 and there is a constant C0 > 0 independent of ε for which ε|∇u| ≤ C0 for all x ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Define V := |u|2 − 1 and V+ := max{V, 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Using the Euler–Lagrange equa- tions and integrating by parts over Ω we obtain 0 ≤ ˆ Ω |u|2V 2 + dx ≤ 1 2 ˆ Γ V+∂nV ds − 1 2 ˆ Ω |∇V+|2 dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' If u is a solution of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3), it follows that V+ ≡ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' If u is a solution of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5), then ∂nV = 2⟨u, ∂nu⟩ = − 2 εs(u⊥)2 ≤ 0 and we obtain V+ ≡ 0 again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Thus, |u| ≤ 1 in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The gradient bound can be obtained by contradiction: suppose that there exists sequences εk → 0 and xk ∈ Ω so that tk := |∇uk(xk)| = ∥∇uk∥∞ satisfies tkεk → ∞ as k → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Let vk(x) := uk � xk + x tk � which is defined whenever y := xk+x/tk ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Likewise, define h(x) := g(y) whenever y ∈ Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' By the uniform bound on u proven above and the choice of scaling, we have ∥vk∥∞ ≤ 1 and |∇vk(0)| = 1 ∀k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1) ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING7 By the uniform bound ∥vk∥∞ ≤ 1 and using the fact that vk solves −∆vk = 1 (tkεk)2(1 − |vk|2)vk for x ∈ tk[Ω − xk], we conclude ∆vk → 0 uniformly on Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' There are two blow-up cases to consider.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' If along some subsequence tk dist(xk, Γ) → +∞, then vk → v with v bounded and harmonic in all of R2, and hence constant, contradicting (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Suppose now tk dist(xk, Γ) is bounded uniformly so that the domains of vk converge to the half-space tk[Ω − xk] → R2 + as k → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' For each k, the weak tangential problem becomes � � � � � � � � � −∆vk = 1 (tkεk)2(1 − |vk|2)vk in tk[Ω − xk], ∂nvk = − 1 tkεs k ⟨vk, h⊥⟩h⊥ on tk[Γ − xk], (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2) while the strong tangential problem is written � � � � � � � � � � � −∆vk = 1 (tkεk)2(1 − |vk|2)vk in tk[Ω − xk], ⟨vk, h⊥⟩ = 0 on tk[Γ − xk], ∂n⟨vk, h⟩ = 0 on tk[Γ − xk].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3) Both problems yield a bounded harmonic limit v defined on R2 + with vk → v in Ck loc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Since vk and h are bounded uniformly, the normal derivative of system (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2) has the limit ∂nvk → 0 as k → ∞ and so the limiting harmonic map v satisfies the Neumann condition ∂nv = 0 on ∂R2 +.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' By the reflection principle, there exists a bounded har- monic extension of v to all of R2 which again contradicts (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1) by Liouville’s theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' For system (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3), the boundary data h converges to a constant vector field on ∂R2 + and the boundary conditions imply ⟨v, h⊥⟩ = ∂n⟨v, h⟩ = 0 along ∂R2 +.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Let ˜h denote the extension of h to R2 + and note that ⟨v, ˜h⟩ is a harmonic scalar function defined on R2 +.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' By the reflection principle and Liouville’s theorem, ⟨v, ˜h⟩ extends to a constant function on R2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Next, since ⟨v, h⊥⟩ = 0 on ∂R2 + and ⟨v, ˜h⟩ is constant, it must be that ⟨v, ˜h⟩ = ±|v| on all of R2 and thus v is constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Condition (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1) is contradicted once again giving ε|∇u| ≤ C0 for all x ∈ Ω where C0 is a constant independent of ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' □ 8 ALAMA, BRONSARD AND VAN BRUSSEL Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' If uε is a strongly tangential minimizer for Eε, then Eε(uε) ≤ πD| ln ε| + C (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4) with C > 0 a constant independent of ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' If uε is a weakly tangential minimizer for Eg,s ε , then there is a constant C > 0 independent of ε so that Eg,s ε (uε) ≤ πsD| ln ε| + C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5) The proof of this proposition utilizes a local polar coordinate system near the boundary which is defined in [ABGS15, ABG20, Kur06] and which we will use throughout the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' For convenience, we provide a brief description here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Let x0 ∈ Ω and R > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Set ωR(x0) := BR(x0) ∩ Ω and in the case where x0 ∈ Γ, define ΓR(x0) := ωR(x0) ∩ Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Whenever x0 ∈ Γ, τ(x0) will denote the positively oriented unit tangent vector to Γ at x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Using τ(x0) as a reference, the polar coordinates (r, θ) centered at x0 can be defined so that θ is the angle measured from the ray defined by τ(x0) and r = |x−x0|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' By the smoothness of Γ, note that R can be chosen small enough so that ωR(x0) = {(r, θ) : θ1(r) < θ < θ2(r), 0 < r < R} where θ1(r) and θ2(r) are smooth functions satisfying |θ1(r)|, |π − θ2(r)| ≤ cr (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='6) for some constant c = c(Γ) ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' These coordinates allow us to parametrize ΓR(x0) \\ {x0} in two pieces: Γ+ R(x0) := {(r, θ1(r)) : 0 < r < R}, Γ− R(x0) := {(r, θ2(r)) : 0 < r < R}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Annular regions are defined similarly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' For any x0 ∈ Ω set Ar1,r2(x0) := ωr2(x0) \\ ωr1(x0), 0 < r1 < r2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' When x0 ∈ Γ and r2 > 0 is taken small enough, the intersection Ar1,r2(x0)∩Γ consists of two disjoint smooth arcs Γ+ r1,r2(x0) = {(r, θ1(r)) : r1 < r < r2}, Γ− r1,r2(x0) = {(r, θ2(r)) : r1 < r < r2}, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='7) where θ1(r) and θ2(r) are as in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' For notational convenience, we also set Γ± r1,r2(x0) := Ar1,r2(x0) ∩ Γ = Γ+ r1,r2(x0) ∪ Γ− r1,r2(x0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING9 Lastly, we define a localized energy on subsets ωr(x0) by Eε(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ωr) := 1 2 ˆ ωr � |∇u|2 + 1 2ε2(1 − |u|2)2 � dx, Eg,s ε (u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ωr) := Eε(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ωr) + 1 2εs ˆ Γ∩ωr ⟨u, g⊥⟩2 ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Proof of Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' For inequality (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4), the desired bound is a consequence of [Str94, Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Let vε be a minimizer for Eε over H1 g(Ω) = {v ∈ H1(Ω;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' R2) : v = g on Γ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The inclusion H1 g(Ω) ⊂ Hg(Ω) implies Eε(uε) ≤ Eε(vε) and applying [Str94, Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1] to Eε(vε) yields Eε(uε) ≤ Eε(vε) ≤ πD| ln ε| + C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' For weakly tangential minimizers, a test function is constructed following [ABGS15, Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1] and [Kur06, Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Consider 2D sets of the form ωR(qj) where {qj}2D j=1 are well-separated points on Γ and R is chosen so that 2εs < R < 1 2|qi − qi| for all indices i ̸= j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Assume that the points {qj}2D j=1 are labeled such that qj+1 is the first point found by following the positively oriented tangent vector field along Γ starting from qj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' These points partition Γ into 2D smooth segments Cj in the sense that Γ = ∪2D j=1Cj with Cj being the curve connecting qj and qj+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Let γ be a lifting of g on the curve ΓR(qj), that is, g = eiγ on ΓR(qj), and define h1(r) = γ � reiθ1(r)� + (j − 1)π, h2(r) = γ � reiθ2(r)� + jπ, φ(r, θ) = h2(r) − h1(r) θ2(r) − θ1(r) (θ − θ1(r)) + h1(r), where θ1(r) and θ2(r) are as in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In this way we have eiφ(r,θ) = g on Γ+ R(qj) for j odd and on Γ− R(qj) for j even.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Similarly, we get eiφ(r,θ) = −g for the opposite parities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Next, let ηε(r) ∈ C∞ be a cut-off function near qj satisfying 0 ≤ ηε ≤ 1 for all r, ηε(r) = 1 for r ≥ 2εs and ηε(r) = 0 for r < εs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In setting ψj(r, θ) := ηε(r)φ(r, θ) + (1 − ηε(r))(γ(qj) + (j − 1)π) we may define the S1-valued test function v(j) ε = eiψj(r,θ) on ωR(qj), which by construc- tion, simulates a half-vortex in the annular region A2εs,R(qj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Using the properties of 10 ALAMA, BRONSARD AND VAN BRUSSEL the cut-off function along with Cauchy-Schwarz and the fact that v(j) ε is S1-valued, 1 2ε2 ˆ ωR(qj) (1 − |vε|2)2 dx = 0 and 1 2εs ˆ ΓR(qj) ⟨vε, g⊥⟩2 ds ≤ C where C > 0 is a constant independent of ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The Dirichlet energy of v(j) ε on ωR(qj), can be conveniently estimated using polar coordinates: it is a straightforward calcu- lation to confirm that the radial component ´ ωR(qj) |∂rvε|2 dx is uniformly bounded in ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' To bound the angular energy over ω2εs(qj), we note that by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='6) and the smoothness of γ, there is a constant c > 0 so that |h2(r) − h1(r)| ≤ π + cr, and |θ2(r) − θ1(r)| ≥ π − cr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Thus, we have: ˆ ω2εs(qj) 1 r2|∂θv|2 dx ≤ (π + cR)2 (π − cR) ln 2 < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Therefore it must be that the primary energy contribution comes from the subset A2εs,R(qj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Using the same estimates as above, ˆ ωR(qj) 1 r2|∂θvε|2 dx ≤ πs| ln ε| + C for C > 0 independent of ε and so Eg,s ε (vε;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ωR(qj)) ≤ π 2 s| ln ε| + C on each ωR(qj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Finally, we must connect these local test functions in a way that is independent of ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Consider the punctured domain ˜Ω := Ω \\ 2D � j=1 ωR(qj) with boundary given by ˜Γ := ∂ ˜Ω = � Γ \\ ∪2D j=1ΓR(qj) � � � ∪2D j=1∂BR(qj) ∩ Ω � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' We set the orientation of ˜Γ to match that of Γ where they coincide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' With this orientation, the function ˜g : ˜Γ → S1 defined by ˜g := � � � � � � � g on ˜Γ ∩ Cj for j odd −g on ˜Γ ∩ Cj for j even v(j) ε on ∂BR(qj) ∩ Ω for each j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' , 2D, ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING 11 satisfies deg(˜g;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ˜Γ) = 0 by construction and therefore we may let V be the S1-valued harmonic extension of ˜g to ˜Ω which has uniformly bounded Dirichlet energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Setting Hε = � V in ˜Ω, v(j) ε in ωR(qj) for each j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' , 2D, we obtain a bound on Eg,s ε (uε) via Eg,s ε (uε) ≤ Eg,s ε (Hε) = 2D � j=1 Eg,s ε (v(j) ε ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ωR(qj)) + Eg,s ε (V ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ˜Ω) ≤ πsD| ln ε| + C as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' □ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' η-Compactness and Related Consequences In this section, we prove an η-compactness result which allows one to relate an energy bound to the non-existence of vortices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The idea here is that for two concen- tric balls, if the energy on the larger ball is small enough, then it is impossible for a vortex to exist in the smaller ball.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' This fact is pivotal in proving that the set of points x ∈ Ω for which |uε| is small can be covered by a finite set of ε-balls whose number is bounded independent of ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' We begin by stating a Pohosaev-type identity for solutions of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3) or (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5) which is obtained via integrating by parts against a smooth function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' This identity will be needed to obtain an η-compactness result which will be developed in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Define eε(u) := 1 2|∇u|2 + 1 4ε2 � 1 − |u|2�2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Let ψ ∈ C2(Ω;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' R2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' If u is a solution of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5) or (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3), then ˆ ∂ωr {eε(u)⟨ψ, n⟩ − ⟨∂nu, ψ · ∇u⟩} ds = ˆ ωr � eε(u) div ψ − � j,l ψl xj⟨∂xju, ∂xlu⟩ � dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1) Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2 (η-Compactness).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' [Strong Tangental Case] Let 3 4 ≤ β < γ < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' There exists constants η, ˜C, ε0 > 0 such that for any solution uε of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3) with ε ∈ (0, ε0), if x0 ∈ Ω and Eε(uε;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ω2εβ(x0)) ≤ η| ln ε|, then |uε| ≥ 1 2 in ωεγ(x0), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2) 1 4ε2 ˆ ωεγ (x0) (1 − |uε|2)2 dx ≤ ˜Cη.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3) 12 ALAMA, BRONSARD AND VAN BRUSSEL [Weak Tangential Case] Let 3 4s ≤ β < γ < s ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' There exists constants η, ˜C, ε0 > 0 such that for any solution uε of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5) with ε ∈ (0, ε0), if x0 ∈ Ω and Eg,s ε (uε;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ω2εβ(x0)) ≤ η| ln ε|, then |uε| ≥ 1 2 in ωεγ(x0), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4) |⟨uε, g⊥⟩| ≤ 1 4 on Γ ∩ ωεγ(x0), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5) 1 4ε2 ˆ ωεγ (x0) (1 − |uε|2)2 dx + 1 2εs ˆ Γ∩ωεγ (x0) ⟨uε, g⊥⟩2 ds ≤ ˜Cη.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='6) The proof for Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2 is heavily dependent on a crucial estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' For x0 ∈ Ω, define as in [Str94, Mos03] the functions F(r) = F(r;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' x0, u, ε) := r ˆ ∂Br(x0)∩Ω eε(u) ds, FΓ(r) := F(r) + r 2εs � x∈∂Γr(x0) ⟨u, g⊥⟩2 where the second function above is defined when x0 ∈ Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Let x0 ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' There exists constants C > 0 and r0 > 0 such that for ε ∈ (0, 1) and r ∈ (0, r0) we have: (1) If x0 ∈ Ω, ωr(x0) ∩ Γ = ∅ and u is a solution of either (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5) or (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3), then 1 4ε2 ˆ ωr (1 − |u|2)2 dx ≤ r ˆ ωr 1 2|∇u|2dx + F(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' (2) If x0 ∈ Γ and u is a solution of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3), then 1 4ε2 ˆ ωr (1 − |u|2)2 dx ≤ C � r ˆ ωr 1 2|∇u|2 dx + F(r) + r2 ε � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='7) (3) If x0 ∈ Γ and u is a solution of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5), then 1 4ε2 ˆ ωr (1−|u|2)2 dx+ 1 2εs ˆ Γr ⟨u, g⊥⟩2 ds ≤ C � r ˆ ωr 1 2|∇u|2 dx + FΓ(r) + r2 εs � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='8) Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The proof for case (1) is shown in [Str94, Lemma 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Inequality (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='8) follows from [Mos03, Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4] or by changing every instance of |u − g|2 with ⟨u, g⊥⟩2 throughout [ABGS15, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Thus, it only remains to prove (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Let r0 > 0 be chosen small enough so that Γ ∩ Br(x0) consists of a single smooth arc satisfying |Γr| ≤ Cr for all 0 < r ≤ r0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' As in [ABGS15] we let N be a 2r0-neighbourhood of Γ, and by taking r0 smaller if necessary, there exists a vector field X ∈ C2(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' R2) ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING 13 satisfying ⟨X, n⟩ = Xn = 0 for all x ∈ Γr, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='9) |X − (x − x0)| ≤ C|x − x0|2 for all x ∈ ωr, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='10) |∂xiXj − δij| ≤ C|x − x0| for all x ∈ ωr, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='11) for a constant C > 0 and for any x0 ∈ Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' To obtain inequality (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='7) we consider the Pohosaev-type identity (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1) with ψ = X and estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Using the boundary decom- position ∂ωr = Γr ∪ (∂Br(x0) ∩ Ω), it will be convenient to perform these estimates on Γr and ∂Br(x0) ∩ Ω separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Estimates Along Γr: By (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='9) we may write X = ⟨X, τ⟩τ = Xττ where τ is the unit tangent vector to Γr and so X · ∇u = Xτ∂τu on Γr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' With this, the lefthand side of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1) becomes ˆ Γr {eε(u)Xn − ⟨∂nu, X · ∇u⟩} ds = − ˆ Γr ⟨∂nu, Xτ∂τu⟩ ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Using the derivative representations ∂nu = ∂n(u∥g + u⊥g⊥) = u∥∂ng + ∂nu∥g + u⊥∂ng⊥ + ∂nu⊥g⊥, ∂τu = ∂τ(u∥g + u⊥g⊥) = u∥∂τg + ∂τu∥g + u⊥∂τg⊥ + ∂τu⊥g⊥, with the known conditions u⊥ = ∂nu∥ = ∂τu⊥ = 0, we obtain ⟨∂nu, Xτ∂τu⟩ = Xτ⟨u∥∂ng + ∂nu⊥g⊥, u∥∂τg + ∂τu∥g⟩ = Xτ((u∥)2⟨∂ng, ∂τg⟩ + u∥∂nu⊥⟨g⊥, ∂τg⟩).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Applying Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1 and Cauchy-Schwarz, |(u∥)2⟨∂ng, ∂τg⟩| ≤ |∂ng||∂τg| ≤ |∇g|2 ≤ C = C(g), |u∥∂nu⊥⟨g⊥, ∂τg⟩| ≤ |∂nu⊥||g⊥||∂τg| ≤ |∇u||∇g| ≤ CC0ε−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Therefore, there is a constant c for which |⟨∂nu, Xτ∂τu⟩| ≤ |Xτ|c ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Moreover since |Xτ| ≤ Cr and |Γr| ≤ Cr we have another constant C (independent of ε) so that ���� ˆ Γr ⟨∂nu, X · ∇u⟩ ds ���� ≤ ˆ Γr |Xτ|c ε ds ≤ Cr2 ε .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Estimates Along ∂Br(x0) ∩ Ω: 14 ALAMA, BRONSARD AND VAN BRUSSEL The lefthand side of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1) along ∂Br(x0) ∩ Ω can be written as the sum of integrals I1 + I2 which we estimate separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' First, by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='10), |Xn|, |Xτ| ≤ Cr and by applying Cauchy-Schwarz we get I1 = ˆ ∂Br(x0)∩Ω �1 2|∇u|2Xn − Xn|∂nu|2 − Xτ⟨∂nu, ∂τu⟩ � ds ≤ Cr ˆ ∂Br(x0)∩Ω �1 2|∂τu|2 + 1 2|∂nu|2 + 1 2|∂nu|2 + 1 2|∂τu|2 � ds = Cr ˆ ∂Br(x0)∩Ω |∇u|2 ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' An easy estimate for I2 is given by I2 = 1 4ε2 ˆ ∂Br(x0)∩Ω (1 − |u|2)2Xn ds ≤ Cr 4ε2 ˆ ∂Br(x0)∩Ω (1 − |u|2)2 ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Thus, for C > 0 large enough I1 + I2 ≤ Cr ˆ ∂Br(x0)∩Ω 1 2 � |∇u|2 + 1 2ε2(1 − |u|2)2 � ds = CF(r) and so the lefthand side of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1) has the estimate ˆ ∂ωr {eε(u)Xn − ⟨∂nu, X · ∇u⟩} ds = I1 + I2 − ˆ Γr ⟨∂nu, X · ∇u⟩ ds ≤ C � F(r) + r2 ε � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Estimates on ωr: The righthand side of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1) can be written as the sum of integrals J1 + J2 which again we estimate separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' By (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='11) and Cauchy-Schwarz, � j,l Xl xj⟨∂xju, ∂xlu⟩ ≤ |∇u|2 + 2Cr|∇u|2 ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING 15 and since div X ≥ 2 − 2Cr we have J1 = ˆ ωr � 1 2|∇u|2 div X − � j,l Xl xj⟨∂xju, ∂xlu⟩ � dx ≥ ˆ ωr �1 2|∇u|2 div X − |∇u|2 − 2Cr|∇u|2 � dx ≥ −Cr ˆ ωr |∇u|2 dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' For the integral J2, one can choose r0 smaller if necessary so that div X ≥ 2−2Cr ≥ 1 and J2 = 1 4ε2 ˆ ωr (1 − |u|2)2 div X dx ≥ 1 4ε2 ˆ ωr (1 − |u|2)2 dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Putting these estimates together, 1 4ε2 ˆ ωr (1 − |u|2)2 dx − Cr ˆ ωr 1 2|∇u|2 dx ≤ J1 + J2 = I1 + I2 ≤ C � F(r) + r2 ε � which completes the proof for inequality (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' □ We now prove Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The case where x0 ∈ Ω and ω2εβ(x0) ∩ Γ = ∅ is shown in [Str94, Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Therefore, it is sufficient to prove the result for x0 ∈ Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' We begin by proving (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3) for strong tangential solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Inequality (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='6) for weak tangential solutions is done similarly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Using the mean value theorem for integrals, there exists rε ∈ (2εγ, 2εβ) such that F(rε) ≤ η(γ − β)−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Using the radius r = rε in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='7) gives 1 4ε2 ˆ ωrε(x0) (1 − |uε|2)2 dx ≤ C � rε ˆ ωrε(x0) 1 2|∇u|2 dx + F(rε) + r2 ε ε � ≤ C � 2ε3/4η| ln ε| + η γ − β + 4√ε � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Then for ε < ε0 with appropriately chosen ε0 > 0, we get (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Inequalities (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4) can be obtained using a contradiction argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' By assuming there is some x1 ∈ ωεγ(x0) such that |u(x1)| < 1/2, standard methods involving the mean value theorem and smoothness properties of Γ [BBH94] allow us to conclude that there is a radius r = cε and a constant c′ > 0 independent of η and ε such that ˜Cη ≥ 1 4ε2 ˆ ω2εγ (x0) (1 − |u|2)2dx ≥ 1 4ε2 ˆ ωcε(x1) (1 − |u|2)2dx ≥ c′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' 16 ALAMA, BRONSARD AND VAN BRUSSEL Taking η smaller if necessary gives the contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' For inequality (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5), suppose r0 > 0 is taken small enough so that ωr(x0) is strictly starshaped with respect to some point x2 ∈ ωr(x0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' By setting ψ = x − x2 in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1) and following [ABGS15, Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1] or [ABG20, Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1], one can find the estimate |uε(x) − uε(y)| ≤ C � |x − y|ε−s/2 (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='12) holding for all x, y ∈ Γrε with C a constant independent of ε and x0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' As in the interior case, suppose there is some point x3 ∈ Γrε such that |⟨uε(x3), g⊥(x3)⟩| > 1/4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Then by the triangle inequality, Cauchy-Schwarz and the uniform bound of Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1: |⟨uε(x), g⊥(x)⟩| > 1/4 − |uε(x) − uε(x3)| − |g⊥(x) − g⊥(x3)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' By (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='12) and the smoothness of g, a radius ρ proportional to εs can be chosen so that |uε(x) − uε(x3)|, |g⊥(x) − g⊥(x3)| < 1 16 for all x ∈ Γrε ∩Bρ(x3) and so |⟨uε(x), g⊥(x)⟩| > 1/8 on this set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Applying inequality (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='6) along with the estimate |Γrε ∩ Bρ(x3)| ≥ c′′εs with c′′ independent of ε and η, we have ˜Cη ≥ 1 2εs ˆ Γrε∩Bρ(x3) ⟨uε, g⊥⟩2 ds > c′′ 128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' As before, we choose η small enough to obtain a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' □ Define the family of bad sets Sε := � x ∈ Ω : |uε(x)| < 1 2 � , Sg,s ε := Sε ∪ � x ∈ Γ : |⟨uε(x), g⊥(x)⟩| > 1 4 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' [Strong Tangential Case] There exists ˜N ∈ N depending only on Ω, a constant λ > 1 independent of ε and points pε,1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' , pε,Iε ∈ Sε∩Ω, qε,1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' , qε,Jε ∈ Sε ∩ Γ such that (i) Iε + Jε ≤ ˜N, (ii) Sε ⊂ �Iε i=1 Bλε(pε,i) ∪ �Jε j=1 Bλε(qε,j), (iii) {Bλε(pε,i), Bλε(qε,j)}1≤i≤Iε,1≤j≤Jε are mutually disjoint with centers satisfying |pε,i − pε,j|, |qε,i − qε,j|, |pε,i − qε,j| > 8λε, (iv) Bλε(pε,i) ∩ Γ = ∅ for all i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' , Iε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' [Weak Tangential Case] There exists ˜N ∈ N depending only on Ω, a constant λ > 1 independent of ε and points pε,1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' , pε,Iε ∈ Sg,s ε ∩ Ω, qε,1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' , qε,Jε ∈ Sg,s ε ∩ Γ such that ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING 17 (i) Iε + Jε ≤ ˜N, (ii) Sg,s ε ⊂ �Iε i=1 Bλε(pε,i) ∪ �Jε j=1 Bλεs(qε,j), (iii) {Bλε(pε,i), Bλεs(qε,j)}1≤i≤Iε,1≤j≤Jε are mutually disjoint with centers satisfying |pε,i − pε,j| > 8λε, |qε,i − qε,j| > 8λεs, and |pε,i − qε,j| > 8λεs, (iv) Bλε(pε,i) ∩ Γ = ∅ for all i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' , Iε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The proof is exactly as in [ABG20, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4] which is based on the method of [Str94, Section 3] and a ball merging method which is presented in [BBH94, Theorem IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' As a consequence of Balzano-Weierstrass, we also have a result which states that the bad sets Sε, Sg,s ε can eventually be covered by a static ball covering (along a subsequence εn → 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' [Strong Tangential Case] For any sequence of ε → 0 there is a subsequence εn → 0, a constant σ0 > 0 and a finite collection of points {p1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' , pI} ⊂ Ω, {q1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' , qJ} ⊂ Γ such that for any 0 < σ < σ0 and for all n ∈ N, the collection of sets Sσ := {Bσ(pi)}I i=1 ∪ {Bσ(qj)}J j=1 (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='13) are mutually disjoint and cover Sεn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' [Weak Tangential Case] The same result holds for the bad set Sg,s εn but with Sσ replaced by Sg,s σ := {Bσ(pi)}I i=1 ∪ {Bσs(qj)}J j=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='14) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Local Orientation and Defect Windings Now that the bad sets Sε and Sg,s ε have been shown to have finite bad ball coverings, we are in a position to analyze the winding behaviour of minimizers around defects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' When dealing with interior bad balls, we may quantify the winding of uε on ∂Bλε(pi,ε) in the usual way since |uε| ≥ 1/2 on this curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In particular, we define the degree of uε around ∂Bλε(pi,ε) to be the degree of the normalization of uε about ∂Bλε(pi,ε): di = di,ε = deg(uε;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ∂Bλε(pi,ε)) := deg(uε/|uε|;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ∂Bλε(pi,ε)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Analyzing the winding of uε about boundary bad balls is slightly more subtle, how- ever.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' As mentioned in the introduction, we define the notion of a boundary index, whose function is analogous to the degree of interior defects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Specifically, the bound- ary index aims to quantify the turning behaviour of uε along circular arcs lying in the interior Ω that connect two nearby points on Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' To begin constructing this quantity, we place focus on strong tangential solutions and then show the necessary modifica- tions for weak tangential solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' 18 ALAMA, BRONSARD AND VAN BRUSSEL Consider again the local polar coordinate system found in Section 2 as defined by the angular bounds (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='6) with center point qε,j ∈ Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Let Bλε(qε,j) be some fixed boundary bad ball for a strong tangential solution uε and fix R > λε so that for all ρ ∈ [λε, R] the closure of ωρ(qε,j) does not intersect the closure of any other bad ball.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Since |uε| ≥ 1/2 outside Bλε(qε,j), there is a single-valued function ψ with uε |uε| = eiψ on Aλε,R(qε,j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Likewise, there is a lifting γ of g for which g = eiγ on Aλε,R(qε,j) since g : NΓ → S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Looking along the curve Γ+ λε,R(qε,j) and using the definition Hg(Ω), it holds that either |ψ(ρ, θ1(ρ)) − γ(ρ, θ1(ρ))| = 0 or |ψ(ρ, θ1(ρ)) − γ(ρ, θ1(ρ)) ± π| = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1) These two possible conditions comes down the observation that uε has either a phase equal to that of g or to −g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' This fact induces a sense of orientation for uε with respect to g along boundary components outside of bad balls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In particular, we say that uε is positively oriented with respect to g at x ∈ Γ (p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=') provided ⟨u(x), g(x)⟩ > 0 (which corresponds to the first condition of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1)) and that uε is negatively oriented (n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=') in the opposite case ⟨u(x), g(x)⟩ < 0 (the second condition of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' g −g u Γ x0 Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Depiction of negative orientation with respect to g for a strong tangential solution u at a point x0 ∈ Γ away from bad balls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Upon starting at the point q+ ε,j = q+ ε,j(ρ) := ∂Bρ(qε,j) ∩ Γ+ λε,R(qε,j) and traveling along the arc ∂Bρ(qε,j) ∩ Ω, one arrives at the point q− ε,j = q− ε,j(ρ) := ∂Bρ(qε,j) ∩ Γ− λε,R(qε,j) for which uε has accumulated an approximate net number of π-rotations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' More precisely, there exists a unique integer k ∈ Z such that |ψ(ρ, θ2(ρ)) − γ(ρ, θ2(ρ)) − kπ| = 0 on Γ− λε,R(qε,j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2) ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING 19 With this information, we may now define the boundary index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Let w : Aλε,R(qε,j) → S1 be defined by w := � uε |uε| �2 = e2iψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Using (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2), � � � � � | arg(w) − 2γ| = 2|ψ − γ| = 0 on Γ+ λε,R(qε,j) if uε is p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=', | arg(w) − 2γ ± 2π| = 2|ψ − γ ± π| = 0 on Γ+ λε,R(qε,j) if uε is n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=', | arg(w) − 2γ − 2πk| = 2|ψ − γ − kπ| = 0 on Γ− λε,R(qε,j), and so w has preserved orientation on Γ± λε,R(qε,j) with respect to g2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Therefore we may extend w to x ∈ Γλε(qε,j) as an S1-valued, piecewise C2 map by simply setting w = g2 along Γλε(qε,j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The reader can refer to Figure 2 for an illustration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Next, g λε Γ+(qε,j) Γ−(qε,j) qε,j u (a) Possible profile of a strong tangential solution u outside a boundary bad ball g2 Γ+(qε,j) Γ−(qε,j) qε,j λε w (b) Corresponding profile of w outside a boundary bad ball with interior extension Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Relationship between u, w, g and g2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' for any ρ ∈ [λε, R], form the closed curve Cρ := (∂Bρ(qε,j) ∩ Ω) ∪ Γρ(qε,j) with positive orientation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' By construction of w we may define Dj = Dj(qε,j) := deg(w;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Cρ) (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3) whose value is independent of ρ ∈ [λ, R] for any particular extension of w by prop- erties of the degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Returning to the local polar coordinate system (ρ, θ) centered at qε,j, we note that arg(w) = 2ψ = 2Djθ + ˜φ(ρ, θ) where ˜φ is a single-valued function in Aλε,R(qε,j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Therefore uε = f(ρ, θ)eiψ with ψ(ρ, θ) = Djθ + φ(ρ, θ) (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4) 20 ALAMA, BRONSARD AND VAN BRUSSEL and φ a single-valued function in Aλε,R(qε,j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The integer Dj ∈ Z is what we define as the boundary index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In some cases, we will use the notation Dj := ind(uε;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ∂Bρ(qε,j) ∩ Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The boundary index for weakly tangential solutions can be constructed in the same way, but now with boundary bad balls having radii ρ = λεs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' However, the phase of uε along Γ± λεs,R(qε,j) no longer satisfies the strict conditions of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In this case, the definition of Sg,s ε can be used to show that |ψ(ρ, θ1(ρ)) − γ(ρ, θ1(ρ))| < π 6 or |ψ(ρ, θ1(ρ)) − γ(ρ, θ1(ρ)) ± π| < π 6 (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5) on Γ+ λεs,R(qε,j) (depending on the orientation of u with respect to g), and that there is a unique integer k ∈ Z such that |ψ(ρ, θ2(ρ)) − γ(ρ, θ2(ρ)) − kπ| < π 6 on Γ− ˜r,R(qε,j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='6) g −g u Γ π 6 x0 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Illustration of positive orientation with respect to g for a weakly tangential solution u at a point x0 ∈ Γ away from bad balls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' By definition of Sg,s ε , the vector u(x0) may only reside within the shaded double cone with axis defined by g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Again, by defining the S1-valued function w = (u/|u|)2 on Aλεs,R(qε,j), from (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='6) we have � � � � � | arg(w) − 2γ| = 2|ψ − γ| < π 3 on Γ+ λεs,R(qε,j) if uε is p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=', | arg(w) − 2γ ± 2π| = 2|ψ − γ ± π| < π 3 on Γ+ λεs,R(qε,j) if uε is n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=', | arg(w) − 2γ − 2πk| = 2|ψ − γ − kπ| < π 3 on Γ− λεs,R(qε,j), which as before, shows that the orientation of w with respect to g2 is preserved on Γ± λεs,R(qε,j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' We can now extend w to x ∈ Γλεs(qε,j) as an S1-valued, piecewise C2 map satisfying | arg(w) − 2γ| < π/3 which can be done via interpolating the phase linearly across Γλεs(qε,j), for example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The boundary index can now be defined in ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING 21 the same way as the strong tangential case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The first main identity we obtain from this definition connects the sum of all associated bad ball boundary indices with D = deg(g;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Γ) and the sum of degrees for the interior bad balls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' [Strong Tangential Case] Suppose uε is a solution of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3) with associated bad ball covering {Bλε(pε,i), Bλε(qε,j)}1≤i≤Iε,1≤j≤Jε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Let di = deg(uε;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ∂Bλε(pε,i)) and Dj = ind(uε;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ∂Bλε(qε,j) ∩ Ω) be the degrees and boundary indices for uε about its interior and boundary bad balls respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Then D = Iε � i=1 di + 1 2 Jε � j=1 Dj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='7) [Weak Tangential Case] Identity (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='7) holds for solutions of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5) and its associated bad ball covering {Bλε(pε,i), Bλεs(qε,j)}1≤i≤Iε,1≤j≤Jε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The proof for the weak tangential case is done identically to that of the strong tangential case simply by replacing the radii λε of the boundary bad balls with λεs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Thus, we provide a proof only for strong tangential solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Define the domain ˜Ω := Ω \\ � Jε � j=1 ωλε(qε,j) � and let ˜Γ = ∂ ˜Ω, C(qε,j) = ∂ωλε(qε,j) ∩ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' As in the definition of boundary index (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3), the function w = (uε/|uε|)2 is defined on ˜Ω and ˜Γ and can be extended across each segment Γλε(qε,j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' By the construction of the extension w, we have deg(w;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Γ) = deg(g2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Γ) = 2D and so by the definition of boundary index, deg(w;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ˜Γ) = 1 2π ˆ Γ\\∪jΓλε(qj) (iw, ∂τw) ds + Jε � j=1 1 2π ˆ C(qj) (iw, ∂τw) ds = 1 2π ˆ Γ (iw, ∂τw) ds − Jε � j=1 1 2π ˆ ∂ωλε(qj) (iw, ∂τw) ds = deg(w;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Γ) − Jε � j=1 Dj = 2D − Jε � j=1 Dj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' 22 ALAMA, BRONSARD AND VAN BRUSSEL Lastly, the vortices pε,i are contained inside ˜Γ and so deg(w;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ˜Γ) = �Iε i=1 2di where we note that the degree along each interior bad ball is doubled by the definition of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Thus, we obtain (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='7) by equating the two quantities for deg(w;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ˜Γ) and dividing by 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' □ We also have a local summation property holding between degrees and boundary indices: Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' [Strong Tangential Case] Let I and J be sets of indices for a collection of bad balls {Bλε(pε,i)}i∈I ∪ {Bλε(qε,j)}j∈J for a strongly tangential solution u and suppose there is a point y0 ∈ Γ and radius R > 0 such that the ball BR(y0) satisfies �� i∈I Bλε(pε,i) ∪ � j∈J Bλε(qε,j) � ⊂ BR(y0) where BR(y0) does not intersect the closure of any other bad ball.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Then if D = ind(uε;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ∂BR(y0) ∩ Ω), di = deg(uε;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ∂Bλε(pε,i)) and Dj = ind(uε;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ∂Bλε(qε,j) ∩ Ω), we have D = � j∈J Dj + 2 � i∈I di.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' [Weak Tangential Case] Under the same hypotheses but with boundary bad ball radii replaced by λεs, the above identity also holds for a collection of bad balls {Bλε(pε,i)}i∈I∪ {Bλεs(qε,j)}j∈J for weakly tangential solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The proof of this Lemma follows the same lines as Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1, but can also be shown using longer methods found in [vB22, Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' As above, the proof for the weak tangential case is done identically to that of the strong tangential case by replacing the radii scaling of the boundary bad balls accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' To this end, we proceed with the strong tangential case only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Let ˜Ω = BR(y0) \\ ∪j∈J ωλε(qj), ˜Γ = ∂ ˜Ω and C(qj) = ∂ωλε(qj) ∩ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Since |u| ≥ 1/2 in ˜Ω, the function w = (u/|u|)2 is defined on ˜Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' As in the construction of the boundary index, w can be appropriately extended across each segment Γλε(qj), j ∈ J , and so we take w to be defined on ˜Γ∪j∈J Γλε(qj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In particular, this extension of w is defined on ∂BR(y0) and so by definition of the boundary index, D = ind(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ∂BR(y0) ∩ Ω) = deg(w;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ∂BR(y0)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='8) ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING 23 Calculating the degree of w along ˜Γ, we have by (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='8) deg(w;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ˜Γ) = 1 2π ˆ ∂BR(y0)\\∪jΓλε(qj) (iw, ∂τw) ds + � j∈J 1 2π ˆ C(qj) (iw, ∂τw) ds = 1 2π ˆ ∂BR(y0) (iw, ∂τw) ds − � j∈J 1 2π ˆ ∂ωλε(qj) (iw, ∂τw) ds = D − � j∈J Dj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' On the other hand, each circle ∂ωλε(pi), i ∈ I, is contained inside ˜Γ and so deg(w;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ˜Γ) = � i∈I deg(w;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ∂ωλε(pi)) = 2 � i∈I di proving the desired identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' □ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Lower Bounds for the Energy and Convergence In this section, we display the details needed to complete the proof of Theorems 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2, which mainly comes down to providing a lower bound for the energies Eε and Eg,s ε on the ball collections Sσ and Sg,s σ respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' This result is given in Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3 at the end of this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The first step in our analysis is to calculate the cost of a vortex locally on annular regions Ar,R with r < R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' To do this, it is useful to begin by characterizing solutions of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3) and (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5) in terms of a local polar representation with central point x0 ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Depending on whether x0 ∈ Ω or x0 ∈ Γ, the representation for the phase of uε will look slightly different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In any case, the general form for uε on Ar,R(x0), x0 ∈ Ω can be given by uε(ρ, θ) = f(ρ, θ)eiψ(ρ,θ) on Ar,R(x0), ρ ∈ [r, R] where ρ = |x − x0|, θ is an appropriately chosen polar angle and f(ρ, θ) = |uε|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In the specific case when x0 ∈ Γ there are four general scenarios which can occur for solutions on Γ± r,R(x0) when ⟨u, g⟩ ̸= 0: (a) u is p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' on Γ+ r,R and n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' on Γ− r,R, (b) u is p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' on Γ+ r,R and on Γ− r,R, (c) u is n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' on Γ+ r,R and p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' on Γ− r,R, (d) u is n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' on Γ+ r,R and on Γ− r,R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' To accommodate for these four cases, we define a polar representation for uε on Ar,R(x0) whose phase depends on the orientation with respect to g when near the boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Let γ(x) be such that g(x) = eiγ(x) along ΓR(x0) with γ0 = γ(x0) provided 24 ALAMA, BRONSARD AND VAN BRUSSEL x0 ∈ Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' By modifying the single-valued function φ from (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4) if necessary, the phase ψ for uε can be given as ψ(ρ, θ) = � � � � � dθ + φ(ρ, θ) if BR(x0) ⊂ Ω Dθ + γ0 + φ(ρ, θ) if x0 ∈ Γ and u is p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' on Γ+ r,R, Dθ + γ0 + φ(ρ, θ) ± π if x0 ∈ Γ and u is n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' on Γ+ r,R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1) In this form, φ is a smooth, single-valued function defined on Ar,R(x0) and can be thought of strictly as a function of ρ > 0 on Γ± r,R by the choice of coordinates given in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' That is, φ = φ(ρ, θ(ρ)) on Γ± r,R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The integers d = deg(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ∂Bρ(x0)), D = ind(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ∂Bρ(x0) ∩ Ω) ∈ Z are the associated degree and boundary index for uε respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Through representation (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1), the boundary index D determines the orientation of u along Γ− r,R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Indeed, when R is taken to be small and D is even, the phase difference across Γ± r,R will be approximately an even multiple of π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In this case, the orientation of uε with respect to g will be maintained along Γ± r,R (cases (b) and (d)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' When D is odd, the orientation of uε with respect to g changes sign, giving cases (a) and (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The function φ plays an important role in estimating the energy contribution of a defect and it is critical to show that it is appropriately bounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The following proposition is needed for this estimation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Let φ be as defined in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1) and suppose |u| ≥ 1/2, |⟨u, g⊥⟩| ≤ 1/4 on Γ± r,R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Then there exists a constant C > 0 for which |φ| ≤ C(|⟨u, g⊥⟩| + ρ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In the special case that ⟨u, g⊥⟩ = 0 on Γ± r,R, we have the simplified bound |φ| ≤ Cρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The result of Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1 is claimed in [Mos03] for g⊥ = n in the weak tangen- tial case, but is not explicitly shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' We prove it here for completeness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Observe the inner product |⟨u, g⊥⟩| = |u|| cos(ψ − (γ − π/2))| = |u|| sin(ψ − γ)| = |u|| sin(ψ − γ ± π)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' When |⟨u, g⊥⟩| ≤ 1/4 and using the bound |u| ≥ 1/2, we obtain |ψ − γ| ≤ π/6 or |ψ − γ ± π| ≤ π/6 for all x ∈ Γ± r,R depending on orientation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' If ⟨u, g⊥⟩ = 0, then we precisely get |ψ − γ| = 0 or |ψ − γ ± π| = 0 which again depends on the orientation of u with respect to g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' By considering the four possible orientations for uε (cases (a)–(d)) separately, it can be shown that there is a constant c > 0 such that |φ| ≤ π/6 + cρ on Γ± r,R in the weak tangential case and |φ| ≤ cρ in the strong tangential case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' To see this, we analyze case (a) from above and claim the other cases follow similarly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' When uε is positively oriented on Γ+ r,R and negatively oriented ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING 25 on Γ− r,R there is ξ ∈ [−π/6, π/6] such that, ψ − γ = Dθ + γ0 − γ + φ = ξ on Γ+ r,R with D ∈ 2Z + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The triangle inequality gives |φ| ≤ |ξ| + |Dθ| + |γ0 − γ| ≤ π 6 + cρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' On Γ− r,R, we have Dθ + γ0 − γ + φ = Dπ + ξ and a similar estimate yields |φ| ≤ |ξ| + |D||π − θ| + |γ0 − γ| ≤ π 6 + cρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The strong tangential condition corresponds to the scenario where ξ = 0 for each of the four cases (a)–(d), and so the estimate above can be reduced to |φ| ≤ Cρ in this case, which finishes the proof for solutions satisfying ⟨u, g⊥⟩ = 0 on Γ± r,R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Assume R is chosen small enough such that cρ ≤ π/12, for example, so that |φ| ≤ π/4 on Γ± r,R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Returning to the inner product and omitting the cases where we consider ±π in the argument, the reverse triangle inequality gives |⟨u, g⊥⟩| = |u|| sin(ψ−γ)| ≥ 1 2| sin(φ)|| cos(Dθ+γ0−γ)|− 1 2| cos(φ)|| sin(Dθ+γ0−γ)| which holds on Γ± r,R for any of the four orientation scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Since Γ and γ are smooth, for R taken small enough it holds that | sin(Dθ + γ0 − γ)|, |1 − | cos(Dθ + γ0 − γ)|| ≤ Cρ, and so we may assume | cos(Dθ + γ0 − γ)| ≥ 1/2 on Γ± r,R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Thus, |⟨u, g⊥⟩| ≥ 1 4| sin(φ)| − 1 2Cρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Finally, since |φ| ≤ π/4 we have |⟨u, g⊥⟩| ≥ 1 8|φ| − 1 2Cρ which finishes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' □ As described in much of the surrounding literature, the energy contribution of a non-trivial interior defect for solutions of the Ginzburg–Landau equations on an annulus Ar,R is known to be logarithmic in the ratio R/r and depends on the square of the degree d of u around the vortex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' A similar result holds for boundary defects with associated boundary index D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' This result is given in Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2 below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' 26 ALAMA, BRONSARD AND VAN BRUSSEL Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' [Strong Tangential Case] Suppose x0 ∈ Ω and assume that 1/2 ≤ |u| ≤ 1 in Ar,R(x0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Additionally, suppose ⟨u, g⊥⟩ = 0 on Γ± r,R(x0) and that there is some number K such that Eε(u) ≤ K| ln ε| + K, 1 ε2 ˆ ωεγ (x0) (1 − |u|2)2 dx ≤ K, where εγ is as in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Then there exists a constant C depending only on Ω, γ and K such that: (i) If BR(x0) ⊂ Ω, ε ≤ r < R ≤ r0 and d = deg(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ∂Br(x0)) ̸= 0, ˆ Ar,R(x0) |∇u|2 dx ≥ 2d2π ln �R r � − C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2) (ii) If x0 ∈ Γ, ε ≤ r < R ≤ r0 and D = ind(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ∂Br(x0) ∩ Ω) ̸= 0, ˆ Ar,R(x0) |∇u|2 dx ≥ D2π ln �R r � − C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3) [Weak Tangential Case] Suppose x0 ∈ Ω and assume that 1/2 ≤ |u| ≤ 1 in Ar,R(x0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Additionally, suppose |⟨u, g⊥⟩| ≤ 1/4 on Γ± r,R and that there is some number K such that Eg,s ε (u) ≤ K| ln ε| + K, 1 ε2 ˆ ωεγ (x0) (1 − |u|2)2 dx + 1 εs ˆ Γεγ ⟨u, g⊥⟩2 ds ≤ K, where εγ is as in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Then there exists a constant C depending only on Ω, γ and K such that: (i) If BR(x0) ⊂ Ω, ε ≤ r < R ≤ r0 and d = deg(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ∂Br(x0)) ̸= 0, then (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2) holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' (ii) If x0 ∈ Γ, εs ≤ r < R ≤ r0 and D = ind(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ∂Br(x0) ∩ Ω) ̸= 0, then (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3) holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The proof of inequality (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2) is omitted since it follows identically to that of [Str94, Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4] and [Str95, Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4’].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' For (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3), we provide a brief sketch to show how the boundary index appears and how the boundary conditions are handled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' With this, we assume x0 ∈ Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Using the polar representation for u on ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING 27 Ar,R(x0), ˆ Ar,R |∇u|2 dx = ˆ Ar,R � f 2|∇ψ|2 + |∇f|2� dx ≥ ˆ Ar,R f 2|∇Dθ + ∇φ|2 dx = ˆ Ar,R D2f 2 ρ2 dx + ˆ Ar,R 2Df 2 ρ2 ∂θφ dx + ˆ Ar,R f 2|∇φ|2 dx = I1 + I2 + I3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The lower estimates for I1 and I3 primarily follow [Str94, Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4] and [Str95, Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4’], with details regarding the boundary given in [Mos03, Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='6] and [ABGS15, Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Specifically, I1 ≥ D2π2 ln �R r � − C, I3 ≥ 1 4 ˆ Ar,R(x0) |∇φ|2 dx where C is a constant independent of ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' For the integral I2, Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1 implies |φ(ρ, θ2) − φ(ρ, θ1)| ≤ 2C � � � x∈∂Γ± ρ |u⊥(ρ, θi(ρ))| + ρ � � with u⊥ = 0 for strong tangential solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Applying bounding methods found in [Mos03, Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='6] and [Str94, Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4], |I2| ≤ ����� ˆ Ar,R 2D ρ2 ∂θφ dx ����� + 2 ����� ˆ Ar,R D(1 − f 2) ρ2 ∂θφ dx ����� ≤ ˆ R r 2|D||φ(ρ, θ2) − φ(ρ, θ1)| ρ dρ + 1 4 ˆ Ar,R |∇φ|2 dx + C ≤ 4|D|C ˆ Γ± r,R |⟨u, g⊥⟩| ρ dρ + 1 4 ˆ Ar,R |∇φ|2 dx + C′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' If u is a strong tangential solution, the first integral in the last line above does not appear and so the estimate ends there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' If u is a weak tangential solution, the proof of [Mos03, Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='6] can be followed with |f ·ν| replaced by |⟨u, g⊥⟩| throughout, giving |I2| ≤ C + 1 4 ˆ Ar,R(x0) |∇φ|2 dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' 28 ALAMA, BRONSARD AND VAN BRUSSEL The desired lower bound is then estimated by ˆ Ar,R |∇u|2 dx ≥ I1 − |I2| + I3 ≥ D2π ln �R r � − C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' □ At this point, we are ready to describe a lower bound for the energy on the sets comprising Sσ and Sg,s σ as defined in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='13) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='14) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' [Strong Tangential Case] Suppose εn is the subsequence taken in Propo- sition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5 and let di = deg(uεn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ∂Bσ(pi)) and Dj = ind(uεn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ∂Bσ(qj)∩Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' There exists a constant C, independent of εn and σ such that: Eεn(uεn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Bσ(pi)) ≥ π|di| ln � σ εn � − C, i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' , I, Eεn(uεn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Bσ(qj)) ≥ π 2 |Dj| ln � σ εn � − C, j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' , J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' [Weak Tangential Case] Suppose εn is the subsequence taken in Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5 and let di = deg(uεn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ∂Bσ(pi)) and Dj = ind(uεn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' ∂Bσs(qj) ∩ Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' There exists a constant C, independent of εn and σ such that: Eg,s εn (uεn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Bσ(pi)) ≥ π|di| ln � σ εn � − C, i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' , I, Eg,s εn (uεn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Bσs(qj)) ≥ πs 2 |Dj| ln � σ εn � − C, j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' , J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The proof for this lemma comes from a result developed by Sandier [San98] (Jer- rard [Jer99] gives a similar result) which uses techniques involving the logarithmic lower bound as found in Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The method involves a two-step approach where balls containing subsets of Sε (or Sg,s ε ) are expanded and fused such that the energy on these balls can be estimated from below while preserving the natural scaling by ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' A fundamental difference between our work and that of Sandier’s are details regarding boundary data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Indeed, Sandier’s work assumes Dirichlet bound- ary conditions and thus one does not obtain boundary vortices in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' For our problem, boundary vortices are expected and thus some extra care needs to be taken when one performs the ball expansion and fusion argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' We refer the reader to [ABM20] and [ABG20, Lemma 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1] for a proof on how to modify Sandier’s result to accommodate for boundary vortices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In particular, the proof not only removes the assumption of Dirichlet boundary data, but also explains how one can deal with the different radial scalings ε and εs of the bad balls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' However, it is worth noting that the proof of [ABG20, Lemma 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1] is done in a global sense due to the way boojums ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING 29 must be dealt with.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' For our case, thanks to Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2, the arguments of [ABG20, Lemma 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1] can be applied to each σ-ball separately which results in Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' As a consequence of Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='3 and Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2, we have π � I � i=1 |di| + 1 2 J � j=1 |Dj| � | ln εn| − C ≤ Eε(uεn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Sσ) ≤ πsD| ln ε| + C (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4) for strong tangential solutions and π � I � i=1 |di| + s 2 J � j=1 |Dj| � | ln εn| − C ≤ Eg,s ε (uεn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Sg,s σ ) ≤ πsD| ln ε| + C (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5) for weak tangential solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Using these estimates, we find that each degree di and boundary index Dj are uniformly bounded in ε and therefore can be taken to be constant along a subsequence εn → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' It is also clear from (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4) and (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5) that all σ-balls constituting Sσ and Sg,s σ respectively, which satisfy di = Dj = 0 do not contribute substantial energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Therefore, the associated balls can be seen to belong to the set where uεn converges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' By relabeling the approximate vortices if necessary, we define Σ := {p1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' , pI} ∪ {q1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' , qJ} to be the collection of all σ-ball centers with non-trivial degree or boundary index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Upon dividing by π| ln ε| and taking ε → 0 in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4) and (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='5), it holds that I � i=1 |di| + 1 2 J � j=1 |Dj| ≤ D for strong tangential solutions and I � i=1 |di| + s 2 J � j=1 |Dj| ≤ sD for weak tangential solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Using identity (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='7) in combination with the above inequalities shows all integers di and Dj must be positive (since we’ve assumed D > 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In fact, we have the equalities D = I � i=1 di + 1 2 J � j=1 Dj (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='6) and sD = I � i=1 di + s 2 J � j=1 Dj (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='7) 30 ALAMA, BRONSARD AND VAN BRUSSEL for the strong and weak cases respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' This allows us to conclude the following: Let Ωσ := Ω \\ Sσ, Ωg,s σ := Ω \\ Sg,s σ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' [Strong Tangential Case] For any σ ∈ (0, σ0), there exists a constant C independent of ε and σ such that Eεn(uεn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Ωσ) ≤ πD| ln σ| + C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Moreover, there is a constant C′ independent of ε such that 1 4ε2 n ˆ Ω � 1 − |uεn|2�2 dx ≤ C′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' [Weak Tangential Case] For any σ ∈ (0, σ0), there exists a constant C independent of ε and σ such that Eg,s εn (uεn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Ωg,s σ ) ≤ πsD| ln σ| + C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' There is also a constant C′ independent of ε such that 1 4ε2 n ˆ Ω � 1 − |uεn|2�2 dx + 1 2εs n ˆ Γ ⟨uεn, g⊥⟩2 ds ≤ C′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Upon taking an appropriate subsequence σn → 0, Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4 and following the methods of [BBH94] and [Str94] allows us to conclude that uεn ⇀ u0 weakly in H1 loc(Ω \\ Σ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' R2) as εn → 0 where u0 ∈ H1(Ω \\ Σ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' S1) is harmonic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' By observing annular regions in Ωσ (and Ωg,s σ ) and applying Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='4 and Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2, it is easy to show that vortices of degree or boundary index larger than 1 require too much energy, and therefore we conclude di = Dj = 1 for all 1 ≤ i ≤ I, 1 ≤ j ≤ J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In light of equation (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='6), making the further assumption that D = 1 forces that either Σ = {p1} ⊂ Ω or Σ = {q1, q2} ⊂ Γ which finishes the proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Moreover, equation (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='7) can be rewritten sD = I � i=1 di + s 2 J � j=1 Dj = (1 − s) I � i=1 di + sD which immediately implies Σ ⊂ Γ whenever 0 < s < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The fact that each Dj = 1 also implies |Σ| = J = 2D which then completes the proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Defect Locations on a Disc when g = τ This final section is dedicated to analyzing a strong tangential anchoring example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The primary point of studying this case is to shed light on the fact that certain domain geometries may exist for which boundary vortices could still be energetically preferable to those in the interior, even when all vortices are given equal scaling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' We consider the special case where g = τ, the positively oriented unit tangent vector ON MINIMIZERS OF THE 2D GINZBURG-LANDAU ENERGY WITH TANGENTIAL ANCHORING 31 to Γ, and take Ω = B1(0) to be the unit disc for simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In this scenario, D = deg(τ, Γ) = 1 and so in light of equation (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='7) there are only two possibilities for defect locations, exactly one in the interior or exactly two along the boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' To investigate this further, we observe a renormalized energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' One Defect in Ω Let p ∈ Ω denote the interior singularity and assume the limiting harmonic map u0 = τ on Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Following [ABGS15, Section 6] and [Riv99], consider the solution Φp to � � � ∆Φp = 2πδp(x) in Ω, ∂Φp ∂n = g × gτ on Γ, with associated asymptotic energy expansion Eg,1 ε (uε) = π| ln ε| + W(p) + cΩ + o(1) where W(p) = lim ρ→0 � 1 2 ˆ Ωρ |∇Φp|2 dx − π ln �1 ρ �� is the renormalized energy and cΩ is the vortex core energy associated to p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' It can be shown (see [BBH94] for example) that the renormalized energy W has a minimum value of zero at the origin p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Two Defects on Γ Let q1, q2 ∈ Γ be the boundary singularities and consider the PDE � � � ∆Φq = 0 in Ω, ∂Φq ∂n = g × ∂τg − π(δq1(x) + δq2(x)) on Γ which has solution Φq(x) = ln |x − q1| + ln |x − q2|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' The energy expansion and renormalized energy are Eg,1 ε (uε) = π| ln ε| + W(q1, q2) + 2cΓ + o(1), W(q1, q2) = lim ρ→0 � 1 2 ˆ Ωρ |∇Φq|2 dx − π ln �1 ρ �� , and cΓ represents the vortex core energy associated to each qj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' By the identity ˆ Ωρ |∇Φq|2 dx = 2 � j=1 ˆ ∂Bρ(qj)∩Ω Φq ∂Φq ∂nqj ds + ˆ Γ\\(Γρ(q1)∪Γρ(q2)) Φq ∂Φq ∂n ds 32 ALAMA, BRONSARD AND VAN BRUSSEL it can be shown via direct calculation that W(q1, q2) = −π ln |q1 − q2| which is minimized whenever q1 and q2 are antipodal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In particular, min q1,q2∈Γ W(q1, q2) = −π ln |2q1| < 0 = min p∈Ω W(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' This calculation suggests that the case where Σ = {q1, q2} gives the energetically preferable singularity allocation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' To conclude that this is indeed the case, it must be shown that the core energy associated to a boundary vortex is not too large compared to cΩ/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Although we do not have a rigorous proof for this, we believe it is possible to show using estimates such as those found in [ABM20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' References [ABG20] Stan Alama, Lia Bronsard, and Dmitry Golovaty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Thin film liquid crystals with oblique anchoring and boojums.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' In Annales de l’Institut Henri Poincar´e C, Analyse non lin´eaire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Elsevier, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' [ABGS15] Stan Alama, Lia Bronsard, and Bernardo Galv˜ao-Sousa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Weak anchoring for a two- dimensional liquid crystal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Nonlinear Analysis: Theory, Methods & Applications, 119:74–97, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' [ABM20] Stan Alama, Lia Bronsard, and Petru Mironescu.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' On the asymptotic behavior of minimizers of the ginzburg-landau model in 2 dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Differential and Integral Equations, 7(5-6):1613–1624, 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' [Str95] Michael Struwe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Erratum: “on the asymptotic behavior of minimizers of the ginzburg– landau model in 2 dimensions”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Differential and Integral Equations, 8(1):224, 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' [vB22] Lee van Brussel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Boundary Versus Interior Defects for a Ginzburg–Landau Model with Tangential Anchoring Conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' PhD thesis, McMaster University, Hamilton, ON.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Canada, June 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' [VL83] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Volovik and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Lavrentovich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Topological dynamics of defects: boojums in nematic drops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} +page_content=' Zh Eksp Teor Fiz, 85(6):1997–2010, 1983.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PNE4T4oBgHgl3EQf-A73/content/2301.05361v1.pdf'} diff --git a/StFJT4oBgHgl3EQfLywb/content/tmp_files/2301.11470v1.pdf.txt b/StFJT4oBgHgl3EQfLywb/content/tmp_files/2301.11470v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..381fe5bf53b838098bf266e6ef310f9c4ff4ac9b --- /dev/null +++ b/StFJT4oBgHgl3EQfLywb/content/tmp_files/2301.11470v1.pdf.txt @@ -0,0 +1,2708 @@ +Prepared for submission to JCAP +Photons from dark photon solitons +via parametric resonance +Mustafa A. Amin, Andrew J. Long, and Enrico D. Schiappacasse +Department of Physics and Astronomy, Rice University, Houston, Texas 77005, U.S.A. +E-mail: mustafa.a.amin@rice.edu, andrewjlong@rice.edu, enrico.d.schiappacasse@rice.edu +Abstract. Wave-like dark matter made of spin-1 particles (dark photons) is expected to form ground +state clumps called “vector solitons,” which can have different polarizations. In this work, we con- +sider the interaction of dark photons with photons, expressed as dimension-6 operators, and study +the electromagnetic radiation that arises from an isolated vector soliton due to parametric resonant +amplification of the ambient electromagnetic field. We characterize the directional dependence and po- +larization of the outgoing radiation, which depends on the operator as well as the polarization state of +the underlying vector soliton. We discuss the implications of this radiation for the stability of solitons +and as a possible channel for detecting mergers of vector solitons through astrophysical observations. +arXiv:2301.11470v1 [hep-ph] 27 Jan 2023 + +Contents +1 +Introduction +1 +2 +Modeling dark photon interactions with light +3 +2.1 +Non-relativistic modes of the dark photon field +3 +2.2 +Interactions with electromagnetism +4 +2.3 +Ultraviolet embedding +5 +2.4 +Polarized vector solitons +5 +3 +Electromagnetic radiation via parametric resonance +7 +3.1 +Electromagnetic equation of motion +7 +3.2 +Applying Floquet theory +8 +3.3 +Linearly polarized dark photon field +10 +3.4 +Circularly polarized dark photon field +11 +4 +Radiation from polarized vector solitons +13 +4.1 +Condition for parametric resonance +13 +4.2 +Vector soliton decay +14 +4.3 +Astrophysical signatures from soliton mergers +15 +5 +Summary and conclusion +17 +A Details of the Floquet analysis +19 +A.1 Homogeneous and linearly-polarized dark photon field for O3 +19 +A.2 Homogeneous and circularly-polarized dark photon field for O3 +20 +B Floquet analysis for spherical soliton profile +21 +C Fuzzy dark photon dark matter +26 +Contents +1 +Introduction +Astrophysical and cosmological observations provide strong evidence for the existence of dark matter [1, +2]. However, we do not as yet know the mass, charge, and spin of the constituent dark matter particles. +What do astrophysical observations tell us about such properties, especially spin? The electric charge of +dark matter cannot be too large [3], whereas the mass cannot be lighter than O(10−19−10−18 eV) eV [4, +5]. While we do not know the spin of dark matter, an important piece of information connecting the +spin and mass of dark matter is known: if dark matter is sufficiently light, it cannot be fermionic since +the required occupation number in phase space would be too large [6]. For bosons, however, light masses +are allowed. In the regime when the dark matter mass is sufficiently light (m ≪ eV), the occupation +number of the field in astrophysical settings becomes so large that dark matter is adequately described +– 1 – + +by a classical, non-relativistic field. Classical, wave dynamical effects become relevant in such settings. +Can such wave-effects then be used to infer the spin of bosonic dark matter? +The past decade has seen a resurgence of effort in exploring wave dynamical effects in non- +relativistic, spin-0 (i.e. scalar) dark matter. See refs. [7, 8] for recent reviews, and [9–14] for examples +of numerical simulations in a structure formation context. In the case of vector (spin-1 or dark photon) +dark matter [15, 16] a similar numerical exploration is still in its nascent stage [17, 18]. While in a +broad sense, the governing equations and the resulting gravitational clustering and growth of structure +in non-relativistic vector dark matter is similar to scalars [19, 20], the additional number of components +in higher spin dark matter (2s + 1 for a spin-s field) can lead to observationally relevant differences. A +larger number of components leads to reduced wave interference, which reduces the variance of density +fluctuations in dark matter [17]. Such fluctuations can, for example, be probed by dynamical heating +of stars [4, 21]. Such effects; however, can also be mimicked to an extent by n = 2s + 1 scalar fields +with similar masses [22]. Furthermore, initial conditions in the early universe do rely on the intrinsic +nature (including spin) of the field [23–33], however, the intrinsic spin (as a spatial vector) is not +directly accessible to Newtonian gravity relevant for dark matter in the contemporary universe when +it is characteristically non-relativistic. +To access spin more directly, one must include non-gravitational interactions within the field +and/or introduce interactions with other Standard Model fields (or include relativistic corrections). +All such effects are typically expected to be small in the case of dark matter. Nevertheless, the effects +of such non-gravitational interactions, even if weak, can be enhanced by the large occupation numbers, +densities and coherence length of the dark matter field. These conditions are possible in solitons — +coherent field configurations that are long-lived, spatially localized and whose central amplitudes can +be much larger than the background density (since the amplitudes do not decay with expansion). For +a detailed recent discussion of non-relativistic scalar solitons, see for example ref. [34] and references +therein. +Such solitons have been shown to readily form in light scalar field dark matter via gravitational +interactions alone [9, 35], and recently, also in vector dark matter from cosmological and astrophysical +initial conditions [5, 18]. Unlike scalar solitons, solitons in vector fields have a richer structure due to +the vector nature of the field [19, 20, 36]. They can be polarized [19, 20], with no particular preference +for the polarization in the case of purely gravitational interactions. Such vector solitons typically carry +macroscopic amounts of intrinsic spin [20]. Non-gravitational self-interactions can lead to preference +for one polarization over another, and have been explored in refs. [37–40]. This richness in structure +arising from the vector nature of the field provides hope that interactions with Standard Model fields +in environments with solitons might lead to interesting, and potentially large spin-dependent effects. +With these considerations in mind, we consider the direct coupling of spin-1 dark matter to +photons, and explore their implications in an astrophysical environment where solitons are present. +We show that such interactions, while very weak, can still lead to resonant production of photons +when certain conditions are met. This aspect is similar to the case of resonant photon production from +axion stars and miniclusters [41–44]. However, in our case, the polarization pattern of the radiation +carries information about the underlying polarization state of the solitons as well as as the specific +nature of the interaction. +With this preliminary investigation, we elucidate characteristic features +of the electromagnetic radiation (frequency, polarization, spatial patterns of radiation etc.), and the +conditions under which such signals are produced. If detected, such signals could provide insight into +the underlying spin of dark matter. +We study resonant photon production from dark photon (i.e. vector) solitons via a variety of +– 2 – + +dimension-6 operators that couple photons and dark photons, within the framework of effective field +theory. We focus on dimension-6 operators since we find that such interactions lead to significant photon +production from solitons even in vacuum. Astrophysical implications of a more natural dimension-4 +operator: gauge kinetic mixing [45, 46], has been explored extensively in the literature (e.g. [47– +50]), albeit in non-solitonic settings. Photon production from such a coupling is also of interest in the +presence of solitons, and might lead to enhanced signals. Furthermore, our effort here is complementary +to the significant ongoing effort to detect light dark photon dark matter in terrestrial settings [51]. +The remainder of the article is organized as follows. The content of section 2 establishes the scope +of the problem: we specify the model for massive dark photons interacting with electromagnetism, +we discuss a possible ultraviolet embedding for the dimension-6 operators that we study, and we +present the spatially-localized polarized vector soliton configurations. The core results of our study are +presented in section 3, which includes our analysis of the electromagnetic field’s equation of motion +using Floquet theory and our predictions for the Floquet exponents arising from parametric resonance +of a dark photon homogeneous configuration with either linear or circular polarization. In section 4, +we apply previous results to study electromagnetic radiation from polarized vector solitons and discuss +the possible astrophysical signatures. In section 5, we conclude and summarize key points of our work. +Appendix A contains details of the homogeneous Floquet analysis, appendix B contains the modified +Floquet analysis for an inhomogeneous vector soliton, and appendix C includes an extension of our +work to the case of fuzzy dark photon dark matter. +2 +Modeling dark photon interactions with light +We are interested in the interactions of a massive spin-1 dark photon with electromagnetism. Consider +a massive real vector field Xµ(x), which we call the dark photon field. The properties and interactions +of these particles are encoded in the action +S[Xµ(x), Aµ(x), gµν(x)] = +� +d4x √−g +� +−1 +4XµνXµν − 1 +2m2XµXµ − 1 +4FµνF µν + 1 +2m2 +plR + Lint +� +(2.1) +where Xµν = ∇µXν − ∇νXµ is the dark photon field strength tensor, Fµν = ∇µAν − ∇νAµ is the +electromagnetic field strength tensor, R is the Ricci scalar, and indices are raised and lowered with +the metric gµν(x). We work in natural units where ℏ = c = 1 are set to one, mpl = 1/√8πGN is +the reduced Planck mass, and (- + + +) is the metric signature. We also write Xµ = (X0, X) and +∂µf = ( ˙f, ∇f). We consider small values of the mass parameter m ≪ 10 eV corresponding to light +dark photons. Extending earlier work on dark photons, we allow for interactions between Xµ(x) and +the electromagnetic field Aµ(x), which is represented by Lint. We enumerate the relevant interaction +operators in Sec. 2.2; these include Lint ⊃ FµνFρσXαXβ and FµνFρσ∂αXβ where the Lorentz indices +may be contracted with various combinations of the inverse metric and Levi-Civita symbol. +2.1 +Non-relativistic modes of the dark photon field +We are interested in the dark photon as a candidate for the cold dark matter. +In the systems of +interest, only non-relativistic modes of the dark photon field will propagate; these modes have small +wavenumbers k ≪ m and large de Broglie wavelengths λ ≫ 2π/m. +This observation motivates a +perturbative expansion in powers of the dark photon field’s spatial gradient; the parametric relations are +|∇Xµ| ∼ λ−1Xµ ≪ mXµ ∼ ˙Xµ. We work to leading order in this expansion, which effectively amounts +– 3 – + +to setting ∇Xµ = 0.1 The temporal component of the dark photon field, X0(x), is non-dynamical in +the theories that we study. Its equation of motion is an algebraic constraint equation, which has the +solution X0 = +� +∇2−m2�−1� +∇· ˙X), neglecting gravitational and electromagnetic interactions. Working +to leading order in the gradient expansion, we set X0(x) = 0. +2.2 +Interactions with electromagnetism +Since we seek to study electromagnetic radiation from vector solitons, it is necessary to introduce a +coupling between the dark photon field Xµ(x) and the electromagnetic field Aµ(x). Working in the +context of effective field theory (EFT), we consider all operators that are consistent with electromagnetic +gauge invariance, and we organize the operators based on their mass dimension. The only such operator +with mass dimension-4 is the so-called gauge-kinetic mixing [45, 46] +L (4) +int ⊃ FµνXαβ , +(2.2) +where Fµν = ∂µAν − ∂νAµ is the usual electromagnetic field strength tensor and Xαβ = ∂αXβ − ∂βXα. +The Lorentz indices can be contracted using any combination of the diagonal inverse Minkowski metric +ηµν and the totally-antisymmetric Levi-Civita symbol ϵµνρσ; we normalize −η00 = η11 = η22 = η33 = +ϵ0123 = 1. The gauge kinetic mixing can be exchanged for a coupling to charged matter by performing a +field redefinition. In this work we consider systems in the absence of free charges, and the gauge-kinetic +mixing operators do not lead to electromagnetic radiation from a dark photon field. At mass dimension- +5 there are no operators coupling the vector soliton to electromagnetism, since such operators would +carry an odd number of Lorentz indices, which cannot be fully contracted using only the two-index +metric and the four-index Levi-Civita symbol. At dimension-6 the following operators are available: +L (6) +int ⊃ FµνFρσXαXβ , +FµνFρσ∂αXβ , +FµνXρXσ∂αXβ , +Fµν∂ρXσ∂αXβ , +Fµν∂ρ∂σ∂αXβ . (2.3) +The third, fourth, and fifth operators involve only one factor of the electromagnetic field Aµ(x). In the +presence of a background dark photon field Xµ(x), these operators provide a source for Aµ(x). The +radiation arising from such source terms is highly suppressed for long-wavelength background fields if +plasma effects can be neglected [52], and we do not discuss these operators further here. +The dimension-6 operators that we study are summarized as follows:2 +O1 = − 1 +2Fµν ˜F µν(X · X) +≈ 2(E · B)(X · X) +(2.4a) +O2 = − 1 +2FµνF µν(X · X) +≈ (E · E)(X · X) − (B · B)(X · X) +(2.4b) +O3 = FµρF νρXµXν +≈ (B · B)(X · X) − (E · X)2 − (B · X)2 +(2.4c) +O4 = ˜Fµρ ˜F νρXµXν +≈ (E · E)(X · X) − (E · X)2 − (B · X)2 +(2.4d) +O5 = FµρF νρ∂µXν +≈ (E × B) · ˙X . +(2.4e) +To move from the Lorentz-covariant expressions to the 3-vector expressions, we have dropped terms +containing X0 and spatial gradients ∇Xµ, which is an excellent approximation for non-relativistic +modes of the dark photon field. +1We work in the zero spatial gradient approximation locally, but indirectly take spatial gradients into account by +including the finite size effects of dark photon configurations in the phenomenology. +2Some of these operators are related to one another using integration by parts (dropping total derivatives) and equa- +tions of motion. For the non-relativistic dark photon field, a few other operators reduce to one of these; for instance +Fµρ ˜F νρXµXν ≈ −O1. +– 4 – + +We write Lint = g2Oi and we study the effect of each operator one at a time. Validity of the +effective field theory, which allows us to neglect the effects of dimension-8 (and higher-order) operators, +requires the coupling g2 to remain sufficiently small. Moreover, we consider systems in which the dark +photon field acquires a nonzero vacuum expectation value ⟨X⟩ ∼ ¯X, which causes these dimension-6 +operators to renormalize lower-order operators; for instance, O2 modifies the electromagnetic kinetic +term. To ensure that these modifications are negligible, and that the EFT remains valid, we impose +g2 ¯X2 ≪ 1 , +(2.5) +where ¯X is interpreted as the typical amplitude of the dark photon field X(t, x). +2.3 +Ultraviolet embedding +Each of the operators in eq. (2.4) is used to construct an effective field theory with Lint = g2Oi, and we +study the resultant electromagnetic radiation from a non-relativistic dark photon field. Our analysis +is independent of the EFT’s ultraviolet (UV) embedding, except insofar as we are justified to ‘turn +on’ each operator, one at a time. Nevertheless, it is interesting to remark that these operators can +arise from a simple, renormalizable theory in the UV. In the remainder of this short section, we offer +a concrete UV embedding for operator O2. +Consider the following theory. Suppose that Xµ is the vector potential associated with a dark +U(1)d gauge symmetry, and suppose that the UV theory includes a dark Higgs field φ(x) with Dµφ = +∂µφ − igdXµφ. If the dark Higgs acquires a nonzero vacuum expectation value ⟨φ⟩ = vd/ +√ +2, then +operator O2 can arise from the dimension-8 operator: +L8 = − 1 +8 M−4 ��Dαφ +��2FµνF µν . +(2.6) +The operator coefficients in our EFT are parametrically g2 ∼ g2 +dv2/M 4 ∼ m2/M 4 where m ∼ gdv is +the mass scale of the dark photon and M is the UV scale of new physics. The dimension-8 operator, +in turn, may arise from a renormalizable theory of charged fermions ψ and χ with a Yukawa coupling +−yφ ¯ψχ + h.c.. +A one-loop box graph generates L8 upon integrating out the fermions. +Assuming +that the fermions have comparable mass mχ ∼ mψ and electromagnetic charge qψe, the box graph is +parametrically M−4 ∼ y2q2 +ψe2/16π2m4 +ψ. Finally we arrive at a parametric estimate for the operator +coefficients in our EFT: g ∼ yqψem/4πm2 +ψ. +In the next section, we show that operators O1 through O4 lead to resonance as long as gmpl ≫ 1. +For a fiducial set of parameters, we estimate gmpl ∼ (y/1)(qψ/10−14)(m/10−6 eV)(mψ/keV)−2. These +parameters are chosen to reflect the constraints on millicharged particles, which place tight upper +limits on qψ across a wide range of mψ values [53]. The strongest limits from stellar cooling plateau to +qψ ≲ 10−14 for mψ below 10 keV; lowering mψ further does not strengthen the qψ limit. These estimates +imply that a sufficiently large dimensionless coupling gmpl ≫ 1 can be achieved if the ‘UV’ embedding +includes sufficiently light and weakly-charged fermions. Despite the small value of mψ compared to +the Standard Model particle content, the EFT approach remains valid while the fermion mass is much +larger than the dark photon mass, i.e. mψ ∼ keV ≫ m ∼ µeV. +2.4 +Polarized vector solitons +In the nonrelativistic regime, the equations of motion for the dark photon field X(t, x) and the gravita- +tional field is a Schr¨odinger-Poisson system [19, 20]. These equations admit spatially-localized solutions +with spherically-symmetric density profiles, which correspond to gravitationally-bounded and coherent +– 5 – + +clumps of dark photons that are ground states of the system at fixed particle number [19]. Such soli- +tons have spatially-independent polarization of the field, with linear and circular polarization being the +extremal cases. These have been called polarized vector solitons, and they typically carry macroscopic +amount of spin angular momentum [20]. A general polarized vector soliton field configuration takes +the form +X(t, x) = 1 +2 +� +a +� +c(a) X(r) e−i(m−µ)t ϵ(a) + h.c. +� +, +(2.7) +where r = |x| is the radial distance from the center of the soliton, the index a labels the three +polarization modes, ϵ(a) are the corresponding polarization unit vectors that are constants, and c(a) are +c-number coefficients that are normalized by � +a |c(a)|2 = 1. The real and positive parameter µ, called +the chemical potential, controls the field amplitude via the radial field profile X(r). Note that the +field amplitude oscillates in time with an angular frequency ω = m − µ. Validity of the non-relativistic +approximation requires +µ/m ≪ 1 +and +ω ≈ m . +(2.8) +For instance, vector soliton formation by the collapse of Hubble-scale inhomogeneities at radiation- +matter equality [18] would give µ ∼ Heq ≈ 2 × 10−28 eV, which is far below the fiducial mass scale +m ≈ 10−6 eV. For solitons forming in nonlinear environments inside dark matter halos, the chemical +potential is expected to be comparable to the typical kinetic energy per particle in the environment +leading to µ/m ∼ v2 ∼ 10−6 [9, 35]. +The radial field profile X(r) and the non-dynamical Newtonian potential Φ(r) are required to +solve the static Schr¨odinger-Poisson system of equations. For each polarization mode, a one-parameter +family of solutions are labeled by the chemical potential µ, which sets the amplitude of X(r) and thus +also X(t, x). These solutions are well-approximated by the empirical fitting formula [9, 17] +X(r) ≃ +¯X +(1 + 0.077 µmr2)4 +with +¯X ≃ 2.04 mpl +� µ +m +� +. +(2.9) +The localized soliton solution has a finite gravitational binding energy E, total mass M, and full width +at half maximum R that are given by [20]3 +E ≈ −20.8 +m2 +pl +m +� µ +m +�3/2 +, +M ≈ 62.3 +m2 +pl +m +� µ +m +�1/2 +, +and +R ≈ 3.16 1 +m +� µ +m +�−1/2 +. +(2.10) +which have an error of ≲ 10%. Since µ/m ≪ 1 it follows that |E| ≪ M, implying that the particles +in the vector soliton are cold, and that there are approximately N ≈ M/m constituent particles. The +average binding energy per particle is E/N ≈ −0.33m(µ/m). To ensure that the soliton is a many- +particle state, N ≫ 1, the chemical potential is bounded from below as µ/m ≫ (m/mpl)4, which is +easily satisfied, since m ≪ mpl for the parameters of interest. +The three polarization unit vectors ϵ(a)(ˆx) form an orthonormal basis. +Two convenient basis +choices are +ϵ(x) = +� +� +1 +0 +0 +� +�, +ϵ(y) = +� +� +0 +1 +0 +� +�, +ϵ(z) = +� +� +0 +0 +1 +� +� +and +ϵ(−) = +1 +√ +2 +� +� +1 +−i +0 +� +�, +ϵ(0) = +� +� +0 +0 +1 +� +�, +ϵ(+) = +1 +√ +2 +� +� +1 +i +0 +� +� . +(2.11) +3The numerical factors are more accurate than those provided in [17, 38]. +– 6 – + +They correspond to linear polarization along each of the three coordinate axes and circular polarization +with respect to the third z axis. +If non-gravitational interactions can be neglected, each of these +six modes is degenerate [20]. We do not consider the ‘hedgehog’ configuration ϵ = ˆx [36], since it +corresponds to a state of higher energy. For example, using the circular polarization basis allows the +polarized vector soliton field configuration to be written as +X(t, r) = X(r) +� +�|c(−)| +√ +2 +� +� +cos(ωt − arg c(−)) +− sin(ωt − arg c(−)) +0 +� +� + |c(0)| +� +� +0 +0 +cos(ωt − arg c(0)) +� +� + |c(+)| +√ +2 +� +� +cos(ωt − arg c(+)) +sin(ωt − arg c(+)) +0 +� +� +� +� . +(2.12) +where c(a) = |c(a)|ei arg c(a) and ω = m − µ. +3 +Electromagnetic radiation via parametric resonance +Interactions between the dark photon field and the electromagnetic field allow for electromagnetic radi- +ation to arise from a dynamical dark photon field configuration, even in the absence of charged matter. +We are concerned with the operators appearing in eq. (2.4). In the background of the oscillating dark +photon field X(t, x), these operators induce a time-dependent equation of motion for the electromag- +netic field. This leads to the phenomenon of parametric resonance, which can be studied using Floquet +theory. Fourier modes of the electromagnetic field that fall into resonance bands experience an expo- +nential amplification Ak(t) ∝ eµkt, where µk are the Floquet exponents, allowing a weak seed field to +be transformed into electromagnetic radiation. This radiation extracts energy from the dark photon +field, which impacts its lifetime while also providing a signal that would make dark photon evaporation +possibly detectable from Earth. +In the remainder of this section, we apply known techniques from Floquet theory to develop an +analytical formalism that allows us to study parametric resonance of the electromagnetic field coupled to +a dark photon field. We derive expressions for the Floquet exponents µk assuming different polarization +configurations for the dark photon field. As a simplifying approximation, throughout this section we +treat the dark photon field as spatially homogeneous: X(t, x) = X(t). In the following sections, we +discuss how our results should be adapted for the study of inhomogeneous polarized vector solitons. +3.1 +Electromagnetic equation of motion +For each of the five operators that we study, the electromagnetic field’s equation of motion is linear. +Working in the Coulomb gauge ∇ · A = 0, the equation of motion admits a Fourier representation: +Oij ¨Aj + Pij ˙Aj + QijAj = 0 , +(3.1) +– 7 – + +where the matrix coefficients are +Oij = +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +δij +, Lint = g2O1 +δij + +� +2g2|X|2� +δij +, Lint = g2O2 +δij + +� +−2g2� +XiXj + +� +2g2 k·X +|k|2 +� +kiXj +, Lint = g2O3 +δij + +� +2g2|X|2� +δij + +� +2g2 k·X +|k|2 +� +kiXj + +� +−2g2� +XiXj +, Lint = g2O4 +δij +, Lint = g2O5 +(3.2a) +Pij = +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +0 +, Lint = g2O1 +� +4g2X · ˙X +� +δij +, Lint = g2O2 +� +−2g2� ˙XiXj + +� +−2g2� +Xi ˙Xj + +� +2g2 k·X +|k|2 +� +ki ˙Xj + +� +2g2 k· ˙X +|k|2 +� +kiXj +, Lint = g2O3 +� +4g2X · ˙X +� +δij + +� +−2g2� ˙XiXj + +� +−2g2� +Xi ˙Xj + +� +2g2 k· ˙X +|k|2 +� +kiXj + +� +2g2 k·X +|k|2 +� +ki ˙Xj +, Lint = g2O4 +� +−2ig2k · ˙X +� +δij +, Lint = g2O5 +(3.2b) +Qij = +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +|k|2 δij + +� +4ig2X · ˙X +� +ϵijkkk +, Lint = g2O1 +|k|2 δij + +� +2g2|k|2 |X|2� +δij +, Lint = g2O2 +|k|2 δij + +� +−2g2(k · X)2� +δij + +� +−2g2|k|2� +XiXj + +� +2g2k · X +� +kiXj +, Lint = g2O3 +|k|2 δij + +� +−2g2(k · X)2 + 2g2|k|2 |X|2� +δij + +� +−2g2|k|2� +XiXj + +� +2g2k · X +� +kiXj +, Lint = g2O4 +|k|2 δij + +� +−ig2k · ¨ +X +� +δij +, Lint = g2O5 +. +(3.2c) +Here ki = (k)i and Xi = [X(t)]i and Ai = [Ak(t)]i with A(t, x) = +� +d3k Ak(t) eik·x/(2π)3. To derive +these expressions we have made two simplifying assumptions. First, we work to leading order in powers +of the coupling g2. If the dimensionless combination g2|X|2 were to become O(1), our EFT expansion +would be invalid, and we are safe to assume g2|X|2 ≪ 1, which lets us work to leading order in g2. +Second, we neglect gradients of the dark photon field. Whereas for a vector soliton, the dark photon +field is inhomogeneous on a scale ∼ R, the modes that exhibit parametric resonance are inhomogeneous +on a much shorter length scale λ = 2π/k ≪ R. To study electromagnetic radiation in these modes and +calculate their Floquet exponent, it is a good approximation to neglect spatial gradients of X [42]. At +the end of the calculation, we validate this condition and thereby justify our approach. +3.2 +Applying Floquet theory +To identify the growing solutions of eq. (3.1), we adapt known techniques from Floquet theory. Floquet +theory is well established, however, our system is somewhat non-trivial compared to the usual textbook +examples because of the coupling of different components as well as constraints that must be respected. +Here, we follow sec. 3.2.1-3.2.3 in Ref. [54], where a general framework to compute Floquet solutions +was presented and is most easily adapted to our needs. +Reduced system: Before applying Floquet theory to analyse the solutions of eq. (3.1), we impose +the Coulomb constraint k · A = 0 and eliminate A3. Explicitly, A3 = −k−1 +3 (k2A2 + k1A1) for k3 ̸= 0. +– 8 – + +With this substitution, eq. (3.1) becomes +˜Oij ¨Aj + ˜Pij ˙Aj + ˜QijAj = 0, +where +˜Oij ≡ Oij − Oi3kj/k3 +(similarly for ˜P, ˜Q and i, j = 1, 2). +(3.3) +Eq. (3.3) is a system of two, second order differential equations which can be written as four first order +equations: +˙q(t) = ˜U(t) q(t) +with +q(t) = +� A(t) +˙A(t) +� +and +˜U(t) = +� +0 +1 +−˜O−1 ˜Q −˜O−1˜P +� +. +(3.4) +If ˜U(t + T) = ˜U(t) is periodic with period T, then Floquet’s theorem guarantees a general solution of +the form q(t) = �4 +s=1 cs Ps(t) eµst where Ps(t + T) = Ps(t), and µs are called the Floquet exponents. +If ℜ[µs] > 0 for any s, then the equation of motion admits exponentially growing solutions. +Floquet Exponents: The Floquet exponents may be calculated by solving the matrix equation +˙F(t) = ˜U(t) F(t) with the initial condition F(0) = 1 (numerically if necessary). The matrix solution +F(t) with this initial condition is often referred to as the fundamental solution. The fundamental so- +lution evaluated at t = T is called the Monodromy matrix F(T). Let fs = |fs|eiθs, with s = 1 to 4, be +the (complex) eigenvalues of the Monodromy matrix F(T). Then, the Floquet exponents are given by +µs = T −1 [ln |fs| + iθs]. Since det(F) = 1, it follows that �4 +s=1 µs = 0. +Fastest growing solutions: Eigenvectors ϵs of the Monodromy matrix provide the functions Ps(t) = +F(t)ϵse−µst. Since Ps(t + T) = Ps(t) is periodic, if one solves the equation numerically, a solution is +only needed for one period (as is the case for calculating Floquet exponents). If we order the eigenvalues +by the largest real part, then q1(t) = c1P1(t)eµ1t provides the fastest growing solution. +So far we have suppressed the dependence of our quantities of interest on k to reduce clutter in the +equations. Let us re-instate this dependence to discuss the fastest growing solutions more explicitly. For +each Fourier mode, indexed by a wavevector k, there are four Floquet exponents, and four eigenvectors +corresponding to particular polarizations of the outgoing electromagnetic field. We label the Floquet +exponents by µk,s with arbitrary 3-vector k and with s = 1 − 4 (similarly for the eigenvectors ϵk,s). +If the equation of motion admits exponentially growing solutions, the dynamics will be dominated by +the solution that grows most quickly. Therefore it is useful to identify +µk,max = max +s +ℜ[µk,s] +and +µmax = max +k, s ℜ[µk,s] . +(3.5) +The quantity µk,max gives the largest real part of the four Floquet exponents for a given wavevector k, +and the quantity µmax gives the largest Floquet exponent among all possible wavevectors. In a given +system, µmax parametrizes the growth rate of electromagnetic radiation, while µk,max parametrizes the +radiation emitted in a particular direction and with a particular wavelength λ = 2π/|k|. For a given +k, the polarization of the radiation is determined by inspecting ϵk,max, which denotes the eigenvector +corresponding to the Floquet exponent with the largest real part for fixed k. +Analytical Approximations: Since ˜O−1 ˜Q and ˜O−1˜P are periodic functions with period T = 2π/ω0, +they can be expanded as a Fourier series ˜O−1 ˜Q = � +l[˜O−1 ˜Q]leilω0t and ˜O−1˜P = � +l[˜O−1˜P]leilω0t, +where l is an integer. +In the small source amplitude regime, we expect a solution of the form +– 9 – + +˜ +A(t) = ˜ +A+(t)eiω0t + ˜ +A−(t)e−iω0t, with a slowly varying ˜ +A±(t). Since interaction operators O1 through +O4 are quadratic in the photon and dark photon fields, at leading order, this ansatz corresponds to the +process X +X → A+A. Here, the X particles are at rest with initial energy ω0. The emitted photons +have the same energy k + O(g2) = ω0. Plugging this ansatz in the reduced system of equations, and +collecting terms ∝ e±iω0t, we arrive at +˙˜y(t) = ˜M˜y(t) +with +˜y(t) = +� ˜ +A+(t) +˜ +A−(t) +� +, +(3.6) +where +˜M = +� +� +� +− i(ω2 +0−|k|2) +2ω0 +1 − (ω2 +0+|k|2) +4ω2 +0 +[˜O−1˜P]0 + +i +2ω0 +� +O−1Q +� +0 +(ω2 +0+|k|2) +4ω2 +0 +[˜O−1˜P]2 + +i +2ω0 +� +˜O−1 ˜Q +� +2 +(ω2 +0+|k|2) +4ω2 +0 +[˜O−1˜P]−2 − +i +2ω0 +� +˜O−1 ˜Q +� +−2 +i(ω2 +0−|k|2) +2ω0 +1 − (ω2 +0+|k|2) +4ω2 +0 +[˜O−1˜P]0 − +i +2ω0 +� +O−1Q +� +0 +� +� +� . +(3.7) +Here, we have only kept terms up to O(g2) and use ˜O−1˜P = O(g2), [O−1Q]0 = [˜O−1 ˜Q]0−|k|21 = O(g2). +Note that these considerations mean that all entries in the above matrix are O(g2), and so are the +eigenvalues. The four eigenvalues of ˜M are the Floquet exponents µs for s = 1 − 4. +3.3 +Linearly polarized dark photon field +We consider a homogeneous and linearly-polarized dark photon field, which is written as +X(t, x) = ¯X cos(mt) ˆz , +(3.8) +where X has a constant orientation and varying magnitude. We have set the temporal oscillation +frequency ω0 = m which is an excellent approximation in the non-relativistic limit. For each of the +operators, O1 through O5, we perform the Floquet analysis described above, working to leading order +in powers of the coupling g2. To illustrate the details of these analytic calculations, we work through +the derivation for operator O3 in appendix A.1; the calculations for other operators are similar. For +each operator, the maximum Floquet exponent (real part) is found to be +µmax = +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +1 +2g2 ¯X2m +, +for Lint = g2O1 +1 +2g2 ¯X2m +, +for Lint = g2O2 +1 +2g2 ¯X2m +, +for Lint = g2O3 +1 +2g2 ¯X2m +, +for Lint = g2O4 +O(g4) +, +for Lint = g2O5 +, +(3.9) +where the maximization is performed over all possible wavevectors k and all possible polarizations of +the outgoing radiation. The results are equivalent for operators O1 through O4, and we discuss these +results further below. For O5, the real part of the Floquet exponent is parametrically higher order in +the coupling. This is because the additional time derivative in O5, see eq. (2.4), brings a factor of i +which renders the leading-order Floquet exponent imaginary. +First we discuss operators O1 and O2. For both of these operators, the dark photon field enters +via X · X, so its indices are not ‘entangled’ with the electromagnetic field. Consequently both O1 and +O2 have the same behavior in regard to the direction and polarization of the radiation. We find that +– 10 – + +µk,max is independent of the wavevector’s orientation, and the electromagnetic radiation is emitted +isotropically. Since the operators only depend on |X|, the radiation doesn’t ‘know’ about the dark +photon field’s orientation, and we obtain the same radiation pattern as if the condensate had been a +scalar field [42]. Our numerical results for operator O2 are illustrated in the top-left panel of figure 1, +and the chart for O1 is indistinguishable. The dominant Floquet band is centered at k = m. The +isotropic emission is reflected in the ‘vertical’ nature of the Floquet band, which is independent of the +angle θ between k and X. For both operators, the emitted radiation has no preferred polarization +direction as shown in the left bottom panel in figure 1. +Next we discuss operators O3 and O4. Here the indices for the dark photon field contract with +the indices for the electric and magnetic fields, and this leads to a richer structure in the Floquet +chart. The top-middle panel of figure 1 shows the Floquet charts for O3 and O4 which are identical. +The maximal Floquet exponent g2 ¯X2m/2 is obtained for θ = π/2, corresponding to emission that +is normal to the dark photon field’s orientation, k ⊥ ˆz. Whereas for θ = 0 or π, corresponding to +k = kz ˆz, the Floquet exponent is smaller by a factor of 2. More generally, our analytical analysis +yields an expression (A.11) for the maximal Floquet exponent (maximizing over orientations of the +electromagnetic field’s polarization) with an arbitrary angle θ between k and ˆz, which is given by +µk,max(θ) = 1 +2g2 ¯X2m +� +1 − 1 +2 cos2 θ +� +. +(3.10) +The radiation’s polarization is found to be different for the two operators. For operator O3 the outgoing +radiation at θ = π/2 is polarized in the direction of the dark photon field X ∝ ˆz, and for operator O4 +it is normal to the dark photon field in the azimuthal direction ˆφ, as indicated in the bottom-middle +panel of figure 1. +3.4 +Circularly polarized dark photon field +We consider a homogeneous and circularly-polarized dark photon field, which is written as +X(t, x) = +¯X +√ +2 +� +cos(mt) ˆx + sin(mt) ˆy +� +, +(3.11) +where X has a constant magnitude and varying orientation. +By performing the Floquet analysis +described above, we calculate the Floquet exponents µk,s. We provide some details of this derivation +for O3 in appendix A.2. Maximizing the real part over all possible directions and polarizations of the +outgoing radiation yields +µmax = +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +0 +, +for Lint = g2O1 +0 +, +for Lint = g2O2 +1 +2g2 ¯X2m +, +for Lint = g2O3 +1 +2g2 ¯X2m +, +for Lint = g2O4 +O(g4) +, +for Lint = g2O5 +. +(3.12) +Operators O1 and O2 do not lead to parametric resonance for a circularly polarized dark photon field, +hence µmax = 0. For these operators, the dark photon field enters through |X|, which remains constant +in the circularly-polarized configuration (3.11). For operator O5, the Floquet exponent is imaginary at +O(g2); see section 3.3. +– 11 – + +AB+3icbVC7TsMwFHXKq4RXKCOLRYXEVCUIAWMFC2OR6ENqo8pxndaqH5HtIKov8LCAEKs/Agbf4PTZoCWMx2dc6/uSdKGNXG97+dytr6xuZWdvd2d3bP/AOax0tU4VJG0smVS9CmjAqSNtQw0gvUQTxiJFuNL0t/O4jUZpK8WCyhIQcj +QWNKUbGSkOvNoilMDHilGU542rm+kOv7jf8OeAqCUpSByVaQ+9rMJI45UQYzJDW/cBPTJgjZShmZOYOUk0ShKdoTPqWCsSJDvN59hk8tcoIxlLBIgicq783csS1znhkJzkyE73sFeJ/Xj818XWYU5Gkhgi8OBSnDBoJiyLgiCqCDcsQVhRmxXiCVIG1uXa0sIl9eJZ3zRnDZuLi/qDdvyjq4BicgDMQgCvQBHegBdoAgyfwDF7BmzNzXpx352MxWnHKnSPwB87nDxctlHo=0 +AB/XicbVC7TsMwFHV4lvAKj43FokJihJUHmMFC2OR6ENqo8pxndaqHUe2gxSil9hYQAhVv6Djb/BaTNAy5mOzrlX9wTJowq7Xnf1tLyuraemXD3tza3tl19vZbSqQSkyYWTMhOiBRhNCZNTUjnUQSxENG2uH4pvDbD0QqKuJ7nSUk4GgY04hipI3 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+I6FDxClLM6Zlbs9HTt1tuAvAdeKVpA5KtEfO13Ac4YQToTFDSg08N9Z+hqSmJHcHiaKxAjP0IQMDBWIE+Vni+w5PDfKGIaRhEUQuFB/b2SIK5XywExypKdq1SvE/7xBosMbP6MiTjQReHkoTBjUESyKgGMqCdYsNQRhS +U1WiKdIqxNXbYpwVt9eZ10LxveVaP50Ky3bs6quAUnIEL4IFr0AL3oA06AIM5eAav4M3KrRfr3fpYjlascucE/IH1+QOPBZTJx +O2 +Figure 1: Electromagnetic radiation arising from a homogeneous dark photon field coupled to electro- +magnetism though several dimension-6 operators via the phenomenon of parametric resonance. Top: +The maximal Floquet exponent µk,max is shown as a function of the wavenumber k of the electro- +magnetic radiation and the polar angle θ such that cos θ = k · ˆz/k. The dominant Floquet band is +centered at k ≈ m and has width O(g2 ¯X2m), where m is the dark photon mass, ¯X is the field am- +plitude, and g is the coupling to electromagnetism with Lint = g2Oi. The three panels correspond to +different operators Oi and different polarizations for the dark photon field. Bottom: These graphics +illustrate the orientation of the radiation’s polarization. The green arrows denote the polarization of +the dark photon field (e.g., vector soliton), while the red and blue arrows denote the polarization of +the emitted radiation (for different operators). For operators O1 and O2 (bottom-left) the radiation +is emitted isotropically, and has no preferred polarization direction. For operators O3 and O4 with +a linearly-polarized dark photon field (bottom-middle) the radiation is predominatly emitted in the +directions normal to ˆz, whereas for a circularly-polarized dark photon field (bottom-right) the emission +is predominantly aligned with ±ˆz. +Next we discuss operators O3 and O4. The analytic calculations are facilitated by moving to a +circular polarization basis for the outgoing radiation. The top-right panel of figure 1 shows the Floquet +chart for operator O3, and the chart for O4 is indistinguishable. The Floquet exponent is maximized for +θ = 0 and π, corresponding to radiation in the direction normal to the plane of the dark photon field, +– 12 – + +k = kz ˆz, as shown in the right bottom panel of figure 1. The radiation carries circular polarization +with the same handedness as the dark photon field. This means that the radiation emitted from θ = 0 +and θ = π have opposite helicity. +4 +Radiation from polarized vector solitons +In this section we adapt the results of our Floquet analysis to study electromagnetic radiation from +polarized vector solitons. +4.1 +Condition for parametric resonance +Our Floquet analysis is performed assuming a homogeneous dark photon field X(t, x) = X(t). Of +course, a vector soliton is not a homogeneous field configuration; rather, the field’s amplitude drops +smoothly to zero beyond a distance r ≈ R away from the soliton’s center. Nevertheless, earlier work [42] +has established that for scalar solitons the maximal Floquet exponent is insensitive to the soliton’s +finite size provided that the soliton is sufficiently large. Here we show that these arguments carry over +to vector solitons as well. Specifically, we claim that the maximum Floquet exponent µ(sol.) +max of the +electromagnetic radiation emitted by a polarized vector soliton can be approximated by +µ(sol.) +max ≈ +� +µ(hom.) +max +− R−1 +, +µ(hom.) +max +R ≳ 1 +0 +, +µ(hom.) +max +R ≲ 1 +(4.1) +where τlc ≈ 2R is the light-crossing time of a soliton with radius R. +In this relation µ(hom.) +max +is +the maximal Floquet exponent in a homogeneous system with X(t, x) = X(t, 0) equal to the dark +photon field at the soliton’s center. We have already presented results for µ(hom.) +max +assuming that the +homogeneous dark photon field is either linearly or circularly polarized; see eqs. (3.9) and (3.12). We +motivate the approximation in eq. (4.1) by directly calculating the Floquet exponent using a spherical +soliton profile for operator O1; we present these results in appendix B. +The condition µ(hom.) +max +R > 1 must be satisfied in order for parametric resonance to occur. Since +µ(hom.) +max +is the instability growth rate and R is the soliton’s light-crossing time, this condition expresses +the fact that radiation is being generated more quickly than it is leaving the system, and parametric +resonance results from the associated Bose enhancement. This condition imposes a lower limit on the +strength of the coupling. Using the expression for ¯X from eq. (2.9) and the expression for R from +eq. (2.10), the parametric resonance condition is expressed as +g2 ¯X2 > +� µ +m +�1/2 +and +gmpl > +� µ +m +�−3/4 +(4.2) +where µ is the chemical potential for the soliton solution. In addition, the coupling must remain small +to justify truncating the EFT at dimension-6 operators; see eq. (2.5). Taken together, the conditions +for valid EFT and successful parametric resonance imply (µ/m)1/2 < g2 ¯X2 ≪ 1 and (µ/m)−3/4 < +gmpl ≪ (µ/m)−1. Both conditions can be satisfied provided that µ/m ≪ 1. Recall that µ/m < 1 is +required for validity of the non-relativistic expansion, and µ/m ≪ 1 is typical for soliton solutions. +It is instructive to compare the above resonance condition with the case when we have a scalar +soliton. The resonance phenomenon for scalar (or pseudoscalar) solitons is different in several aspects +from that for vector solitons. The spatially-localized configuration with spherically-symmetric density +– 13 – + +profiles for such solitons takes the form φ(t, r) = ( +� +2/m)ψ(r)cos(ωt), where ψ(r) is well-approximated +by the empirical fitting formula given in eq. (2.9), under the replacement ¯X → ¯φ. The dimension-5 +operators which enter in play are ¯O1 = −(1/4)Fµν ˜F µνφ and ¯O2 = −(1/4)FµνF µνφ, where Lint = g ¯O1 +and Lint = g ¯O2, respectively. +The resonance condition takes the same form as eq. (4.1), but now +µ(hom.) +max +is the maximal Floquet exponent in a homogeneous system with φ(t, x) = φ(t, 0) equal to the +scalar field at the soliton’s center. Since only one scalar connects to two photons, the maximal Floquet +exponent for both operators is proportional to only one power of the product between the constant field +amplitude and the coupling constant. Moreover, the dominant Floquet band is centered at k = m/2. +For both operators, we have µ(hom.) +max += g ¯φm/4. As a result, the parametric resonance condition is +expressed as (again ignoring factors of order unity): g ¯φ > (µ/m)1/2 +and +gmpl > (µ/m)−1/2 +where µ is the chemical potential of the scalar soliton solution. For the same value of µ/m for scalar +and vector solitons, the resonance phenomenon requires a larger g in vector solitons compared to the +scalar case. Conversely for the same g, the resonance condition can be satisfied for larger values of +µ/m for scalars compared to vectors (ie. for fixed m, smaller radii solitons). +4.2 +Vector soliton decay +Electromagnetic radiation via parametric resonance extracts energy from the vector soliton. If this +emission continues for a sufficiently long time, it would eventually cause the vector soliton to decay. +For each of the dimension-6 operators, and for both the linearly- and circularly-polarized soliton con- +figurations, we estimate the vector soliton’s lifetime as τ = 1/µ(sol.) +max ≈ 1/µ(hom.) +max +. Assuming that the +condition for parametric resonance (4.2) is satisfied, and using the results in eqs. (3.9) and (3.12), the +soliton lifetime is calculated as +τ = +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +2/g2 ¯X2m +, +for Lint = g2O1 +2/g2 ¯X2m +, +for Lint = g2O2 +2/g2 ¯X2m +, +for Lint = g2O3 +2/g2 ¯X2m +, +for Lint = g2O4 +O(g−4) +, +for Lint = g2O5 +and +τ = +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +∞ +, +for Lint = g2O1 +∞ +, +for Lint = g2O2 +2/g2 ¯X2m +, +for Lint = g2O3 +2/g2 ¯X2m +, +for Lint = g2O4 +O(g−4) +, +for Lint = g2O5 +(4.3) +for the linearly-polarized and circularly-polarized vector solitons, respectively. Recall that operators +O1 and O2 do not lead to electromagnetic radiation from a circularly-polarized vector soliton, and we +write τ = ∞. +With these estimates, we turn to the question of vector soliton stability and decay. Since T ≈ +2π/m is the oscillation period of the non-relativistic dark photon field, and for g2 ¯X2 ≪ 1, these +formulas reveal that the vector soliton survives for many cycles of oscillation, ∼ τ/T ≈ 1/g2 ¯X2 ≫ 1. +However, for parameters that are typical of dark photon dark matter, m−1 ∼ (10−6 eV)−1 ∼ 10−9 s, +the lifetime τ is still very short compared to the age of the universe today t0 ∼ 1017 s. The conclusion +is that any solitons in the Universe today must fail to meet the parametric resonance condition (4.2), +which shuts off the channel for their decay into electromagnetic radiation. The observation has been +noted previously for axion dark matter with a dimension-5 coupling to electromagnetism [42, 55]. +The condition for soliton stability is the converse of the condition for parametric resonance (4.2). +A stable soliton must have a weak coupling to electromagnetism such that gmpl ≲ (µ/m)−3/4. Using +– 14 – + +eq. (2.10) this condition is expressed as an upper limit on the mass of the soliton: +M ≲ Mc ≡ +102m4/3 +pl +g2/3m +∼ +� +3 × 1021 kg +�� +m +10−6 eV +�−1� +g +10−10 GeV−1 +�−2/3 +. +(4.4) +For these fiducial parameters, we also have ¯X ∼ (1 × 108 GeV) g−4/3 +10 +, N ∼ (2 × 1063)g−2/3 +10 +m−2 +6 , and +R ∼ (100 km)g2/3 +10 m−1 +6 +where m6 ≡ m/10−6 eV and g10 ≡ g/10−10 GeV−1. Eq. (4.4) gives an upper +limit on the mass of polarized vector solitons that we should expect to find in the Universe today. +Finally let us address the cosmological history of vector soliton decay. At the time of soliton +formation, there maybe be solitons with M > Mc. The parametric resonance is ineffective until the +age of the Universe reaches τ, and subsequently these solitons begin to decay. However, their decay is +halted when M decreases below Mc and the channel for parametric resonance is blocked. Consequently, +we expect that any solitons formed with M > Mc should have M ≈ Mc today, just below the threshold +for parametric resonance. A similar cosmological evolution has been discussed previously in the context +of scalar solitons coupled to electromagnetism [55]. +4.3 +Astrophysical signatures from soliton mergers +In light of the discussion from the preceding section, isolated vector solitons in the Universe today +are not expected to produce electromagnetic radiation since the condition for parametric resonance +is not met: M < Mc. However, it is reasonable to expect that an appreciable population of vector +solitons with masses just below the threshold for parametric resonance may reside in the Milky Way +halo. The merger of these sub-critical vector solitons may trigger a burst of electromagnetic radiation. +This radiation can be understood to arise from a temporary ‘activation’ of parametric resonance when +the mass of the merged pair exceeds the threshold: M1 + M2 > Mc although M1, M2 < Mc. +The collision and merger of two solitons is a complicated non-linear process, and it is challenging +to obtain accurate predictions with analytical methods. Nevertheless, 3-dimensional simulations have +been performed using numerical lattice techniques; see Refs. [55–57] for work on scalar solitons and +Ref. [17, 38] for work on vector solitons. For both the scalar and vector soliton studies, the collision +induces radiation that carries away an O(1) fraction of the constituent particles and mass, leaving an +approximately spherically-symmetric condensate. The simulations reported in Refs. [55, 56] exhibit a +mass for the merged system that is approximately Mfinal ≈ 0.7(M1 + M2) in terms of the progenitor +masses (similar results were also seen for vector solitons in [17]). This relation would allow Mfinal > Mc +while M1, M2 < Mc, meaning that the merger could ‘trigger’ parametric resonance. Although it is +worth noting that these simulations do not allow for the coupling to electromagnetism that we study +here, and any potential back reaction effects have been neglected. +For collisions of vector solitons, the polarization state (or spin density) of the transient and +final dark photon configuration can impact the electromagnetic signatures from the merger. +Our +calculations have assumed maximally-polarized configurations with spin |S| = 0 and ℏN in the linearly- +and circularly-polarized configurations, respectively. During the merger process, it is likely that the +system is better characterized as a fractionally polarized soliton [20] with 0 < |S| < ℏN or as an excited, +non-solitonic state. It is straightforward to extend our calculation to fractionally polarized solitons; +however, we have not attempted to characterize excited states and their signatures. Simulations of +collisions and mergers will help to reveal the realistic range of initial conditions for parametric resonance, +leading to more robust predictions for the associated electromagnetic radiation. +– 15 – + +We are interested in the spectrum of electromagnetic radiation resulting from vector soliton col- +lisions. For these estimates, we model the radiation as ‘triggered’ parametric resonance. That is to +say, once the merger has ‘completed’ the radiation is emitted as a sudden burst that carries away an +O(1) fraction of the excess mass ∆M = Mfinal − Mc. These dynamics have been observed previously +in simulated collisions of non-gravitationally-bounded scalar solitons with a coupling to electromag- +netism [17]. However, our interest is in gravitationally-bounded soliton solutions for which the soliton’s +light-crossing time scale R is many orders of magnitude larger than the time scale for parametric res- +onance τ. For such solutions, it is possible that the radiation seeps out via less-intense bursts as the +merged configuration settles into a spherically-symmetric condensate [43]. This discussion motivates +further study of gravitationally-bounded vector soliton collisions. We expect that our approach, the +‘triggered’ parametric resonance model, overestimates the strength of the signal, since it allows for the +largest possible energy release and the smallest possible emission duration. +To characterize the astrophysical signature associated with such a phenomenon, we need the +signal duration τ, the central wavelength λ0, and the signal bandwidth ∆λ. The soliton lifetime τ from +eq. (4.3) sets the signal duration. For a fiducial set of parameters, we estimate +τ ∼ +� +20 µs +�� +g +10−10 GeV−1 +�2/3� +m +10−6 eV +�−1 +, +(4.5) +where the critical mass condition M = Mc has been used to eliminate µ. +The signal wavelength +λ0 = 2π/k0 is controlled by the wavenumber k0 ≈ m at the first instability band of the Floquet +chart, and the signal bandwidth ∆λ = (2π/k2 +0)∆k is controlled by the width of the Floquet band +∆k ≈ g2 ¯X2m. For the fiducial parameters we estimate the corresponding frequencies to be +ν0 ∼ +� +200 MHz +�� +m +10−6 eV +� +, +(4.6a) +∆ν ∼ +� +40 kHz +�� +g +10−10 GeV−1 +�−2/3� +m +10−6 eV +� +. +(4.6b) +These estimates imply that the radiation will be nearly monochromatic (a consequence of g2 ¯X2 ≪ 1). +For the fiducial mass parameter m = 10−6 eV, the emission is in the radio band of the electromagnetic +spectrum. +Since radio telescopes lose sensitivity below a frequency of ∼ (10 − 15) MHz, due to +absorption and scattering in the ionosphere, only models with m ≳ 5 × 10−8 eV could be probed with +ground-based radio observations.4 +The strength of the signal is parametrized by a spectral flux density SB. If the source is a distance +d away and it liberates an energy O(Mc) in a time τ, then we can estimate +SB ∼ +Mc/τ +4π∆νd2 ∼ +� +3 × 1018 Jy +�� +g +10−10 GeV−1 +�−2/3� +m +10−6 eV +�−1� +d +1 Mpc +�−2 +, +(4.7) +where 1 Jy = 10−26 W/m2/Hz. For a cosmologically-distant source, the effect of cosmological redshift +must also be included. Note that reducing the coupling g2 increases the strength of the signal, since the +suppression Mc ∼ g−2/3 is counterbalanced by the enhancements from τ −1 ∼ g2/3 and (∆ν)−1 ∼ g2/3; +for small g less energy is emitted more quickly. +4This issue also arises in axion search strategies such as that related to the axion-photon conversion during axion +ultracompact minihalo-neutron star encounters (see, for example, Sec. VII in Ref. [58]). +One solution is to consider +planned space-based facilities such as the Orbiting Low Frequency Antennas for Radio Astronomy Mission (OLFAR) [59]. +– 16 – + +Radio telescopes typically have sensitivities at the level of ∼ 100 µJy at 100 kHz with ∼ 1 kHz +resolution bandwidth [60]. Our estimate in eq. (4.7) suggests that if a vector soliton collision trig- +gers parametric resonance while the host galaxy is being observed, then the signal would easily be +detectable. However, we must remember that our model generously overestimates the energy liberated +and underestimates the duration of release. One should not interpret eq. (4.7) as a prediction for the +spectral flux density, but rather an indication from dimensional analysis that the signal may be strong +enough to detect. +Radio telescopes, such as Green Bank Telescope (GBT), measure not just the intensity but also +the polarization of incident radio waves [61]. A measurement of the polarization would prove invaluable +to discriminate among different possible soliton sources. Whereas a scalar soliton emits unpolarized +radiation, a vector soliton, such as the ones we study here, may produce polarized radiation. +In +this way, a detection of polarized emission could be interpreted as evidence of vector soliton mergers. +Moreover, the polarization strength and orientation depends on the nature of the coupling between +the dark photon field and electromagnetism, providing an additional handle on the underlying particle +physics model. +However, a realistic analysis of the expected polarization signal is non-trivial. First, depending +on the particular UV embedding, we expect that several dimension-6 operators would simultaneously +source resonance. Each may lead to a different polarization pattern for the resultant radiation. Second, +individual solitons or solitons produced from mergers may be fractionally polarized, as discussed already +above [17]. This too would complicate the resultant polarization pattern. +5 +Summary and conclusion +In this work we have studied the electromagnetic radiation that arises via parametric resonance from a +spatially-coherent dark photon field that interacts with the electromagnetic field via several dimension- +6 operators. +We study a homogeneous field and adapt these results to assess the radiation from +polarized vector solitons formed from dark photon dark matter. The calculations presented in this +article represent predictions for the electromagnetic signals arising from polarized vector solitons, and +provide an avenue for probing soliton collisions and mergers. +We identify five dimension-6 operators that couple a massive dark photon field to electromagnetism +and lead to parametric resonance. +These operators take the form XαXβFµνFρσ and ∂αXβFµνFρσ. +There also exist dimension-6 operators with one fewer factor of the photon field, which we do not +consider here, since they do not lead to parametric resonance. +We consider systems with either a +linearly-polarized or a circularly-polarized dark photon field. +In the first scenario, the orientation +of the dark photon field X(t, x) remains fixed as its magnitude oscillates, whereas in the second +scenario, the orientation oscillates while the magnitude remains fixed. For each of the five operators +and both of the polarization configurations, we perform a Floquet analysis using both analytical and +numerical methods. The electromagnetic field is exponentially amplified via parametric resonance with +|A(t)| ∝ eµmaxt. We calculate the maximal Floquet exponents µmax assuming a dark photon field with +either linear or circular polarization, and these results are summarized below. +• For a linearly-polarized vector soliton, operators of the form XαXβFµνFρσ lead to a maximum +resonance growth rate (Floquet exponent) that is parametrically ∼ g2 ¯X2m, where g2 is the +dimension-6 operator coefficient, ¯X is the amplitude of the dark photon field, and m is the dark +photon mass. This result agrees parametrically with earlier work on axion dark matter (spin-0 +particles) [42] where the interaction is φFµν ˜F µν, where φ is the scalar field amplitude. We find +– 17 – + +that the resonance band is centered at a wavenumber of |k| = m, which sets the frequency of the +resultant electromagnetic radiation. By contrast, the axion case gives |k| = m/2. For operators +XαXαFµνF µν and XαXαFµν ˜F µν, the emitted radiation does not show any preferred polarization +orientation. For operators XµXνFµρF νρ and XµXνFµρ ˜F νρ, we find that the radiation is primarily +linearly polarized along an axis that differs for each interaction operator. In this case, outgoing +radiation is peaked in the equatorial plane perpendicular to the direction of oscillation of the +dark photon field. +• For a circularly-polarized vector soliton, operators XαXαFµνF µν and XαXαFµν ˜F µν do not lead +to electromagnetic radiation via parametric resonance. This is because XαXα = −(X0)2 +X ·X +is static for a circularly-polarized dark photon field. Other operators lead to parametric resonance +with a growth rate that is parametrically ∼ g2 ¯X2m, similar to the linearly-polarized scenario. +We find that the outgoing radiation is primarily circularly polarized with the same handedness as +the dark photon field. In this case, outgoing radiation is peaked near the poles of the circularly +polarized soliton. +Since parametric resonance can occur even for an isolated vector soliton in vacuum, it provides a +channel for vector solitons to decay. We find that electromagnetic radiation by parametric resonance +exhausts the soliton’s energy very quickly as compared to the age of the Universe. Echoing earlier +studies of scalar solitons [55], we conclude that isolated vector solitons in the Universe today must +have a sufficiently small mass so as to avoid activating parametric resonance (4.4): M < Mc with +Mc ≃ (3 × 1021 kg)(m/10−6 eV)−1(g/10−10 GeV−1)−2/3. +The work presented in this article furthers the effort to model vector solitons in dark matter +halos, and assess their electromagnetic radiation as a potential channel for discovery. Although isolated +solitons would not be emitting, electromagnetic emission may occur when solitons collide and merge [44, +55]. The frequency of this radiation is controlled by the dark photon mass, ν ∼ (200 MHz)(m/10−6 eV), +falling into the radio band for typical masses. The strongest potential signal would correspond to an +O(1) fraction of the critical mass Mc being liberated in a sudden burst of electromagnetic radiation that +lasts for a time τ ∼ µ−1 +max set by the resonance growth rate. Such a strong signal would easily exceed +the sensitivity of typical radio telescopes, even for a cosmologically-distant source. To derive robust +predictions for the expected signal, a more careful study of the complex dynamics of vector soliton +collisions is warranted, including the effects of backreaction from electromagnetic radiation (similar to +[17], but for dilute vector solitons). Of particular interest is the polarization of the emitted radiation, +which carries information about the nature of the source, and could help to observationally distinguish +vector soliton mergers from other objects. While current radio telescopes routinely characterize the +polarization of incoming radio waves [61], we have not attempted to assess the feasibility of measuring +the polarization signals from solitons in a realistic setting in this paper. +It is worth reemphasizing that polarization patterns of the electromagnetic radiation depend on +the nature of the interaction (the particulars of the dimension-6 operator), as well as the polarization +state of dark photon field of the soliton. By contrast, radiation from scalar solitons do not show any +preference for polarization of the outgoing photons. The rich structure seen in the results is a direct +consequence of the assumed spin-1 nature of the dark photon field. Motivated by our results, and +taking an optimistic view, if such radiation is detected, it is a potential probe of the underlying spin +of the dark matter field that makes up the solitons. +Although we have focused on dark photon dark matter forming vector solitons, our analysis can +be extended to other field configurations as well. We briefly discuss the resonance phenomenon and its +– 18 – + +implications for fuzzy dark photon dark matter in appendix C. +Acknowledgments +We are grateful to Nathaniel Craig and Ryan Plestid for guidance in discussions of the UV embedding. +A.J.L. and E.D.S. are supported in part by the National Science Foundation under Award No. PHY- +2114024. M.A.A. is partially supported by a DOE grant DE-SC0021619. Portions of this work were +conducted in the Department of Physics at the University of Jyv¨askyl¨a, Finland, and supported in part +by the Academy of Finland grant 318319. +A +Details of the Floquet analysis +Following the general framework to compute Floquet solutions detailed in Sec. 3.2, the reader can +reproduce the maximum Floquet exponents (real part) listed in eqs. (3.9) and (3.12) for operators O1 +through O5. As an example, here we give a detailed derivation for operator O3. +A.1 +Homogeneous and linearly-polarized dark photon field for O3 +We consider a homogeneous and linearly-polarized dark photon field in the ˆz-direction as shown +eq. (3.8). We use the reduced system (3.3); however, instead of eliminating A3 we eliminate A1 from +the system using the Coulomb gauge condition. Correspondingly, the ˜Oij = Oij − Oi1kj/k1 where i +and j both take values of 2 or 3 (similarly for ˜P and ˜Q). For the case under consideration, A3 decouples +from A2, and satisfies +� +1 − g2 ¯X2(1 + cos(2mt)) sin2 θ +� ¨A3 + +� +2g2m ¯X2 sin(2mt) sin2 θ +� ˙A3 + +� +k2 − g2k2 ¯X2(1 + cos(2mt)) +� +A3 = 0 , +(A.1) +where we used k3 = k cos θ. +We solve this equation in the small amplitude regime performing an +harmonic expansion of the modes as +A3(t) = +∞ +� +l=−∞ +˜A3,l(t) eilmt , +(A.2) +where ˜A3(t) is a slowly varying function so that ¨˜A3(t) ≈ 0. There exists a spectrum of narrow resonant +bands, which are equally spaced at k2 ≈ n2m2 for n = 1, 2, 3, · · · . We replace eq. (A.2) into eq. (A.1) +and express all cosine and sine factors in their exponential form. We collect all terms proportional +to eilmt, ei(l+2)mt, and ei(l−2)mt, and change the variable of summation so that they all take the form +eilmt. We integrate over time from t = 0 to 2π/m. The resultant equation is evaluated at l = ±1, since +the first instability band dominates the resonance. Dropping ˜A3,±3, the resultant system of differential +equations to be solved is given by +� ˙˜A3,+ +˙˜A3,− +� += +� ˜M11 +˜M12 +− ˜M12 − ˜M11 +� � ˜A3,+ +˜A3,− +� +, +(A.3) +with +˜M11 = +� +2im − 2ig2m ¯X2 sin2 θ +�−1 � +−k2 + m2 + g2k2 ¯X2 − g2m2 ¯X2 sin2 θ +� +, +(A.4) +˜M12 = +� +2im − 2ig2m ¯X2 sin2 θ +�−1 +�1 +2g2k2 ¯X2 + 1 +2g2m2 ¯X2 sin2 θ +� +. +(A.5) +– 19 – + +The two Floquet exponents (associated with the A3 polarization mode function) are the complex +eigenvalues of the ˜M matrix. The eigenvalue with the larger real part is +µk,max = +�� +(2(k2 − m2) − g2 ¯X2(3k2 − m2 sin2 θ) +� � +−2(k2 − m2) + g2 ¯X2(k2 − 3m2 sin2 θ) +� +4m +� +1 − g2 ¯X2 sin2 θ +� +. +(A.6) +The edges of the first instability band are defined by the condition µk,max = 0. For a given θ, using +the expression above, we obtain the left edge kl,edge, the right edge kr,edge, the central wavenumber k0, +and the bandwidth ∆k to be +kl,edge = m +� +2 − 3g2 ¯X2sin2θ +� +2 − g2 ¯X2 += m − g2m ¯X2 +2 +� +1 − 3cos2θ +2 +� ++ O(g4) , +(A.7) +kr,edge = m +� +2 − g2 ¯X2sin2θ +� +2 − 3g2 ¯X2 += m + g2m ¯X2 +2 +� +1 + 1 +2cos2θ +� ++ O(g4) , +(A.8) +k0 = (kr,edge + kl,edge) +2 += m + 1 +2g2m ¯X2cos2θ + O(g4) , +(A.9) +∆k = (kr,edge − kl,edge) = g2m ¯X2 +� +1 − cos2θ +2 +� ++ O(g4) . +(A.10) +We evaluate eq. (A.6) at k = k0 finding +µk,max(θ) ≈ g2m ¯X2 +2 +� +1 − cos2θ +2 +� ++ O(g4) . +(A.11) +Even though µk,max(θ) was calculated using the electromagnetic field equation of motion for A3 alone, +this expression matches the largest Floquet exponent among all possible electromagnetic mode func- +tions. +A.2 +Homogeneous and circularly-polarized dark photon field for O3 +We consider a homogeneous and circularly-polarized dark photon field on the x − y plane as shown in +eq. (3.11). We use the reduced system (3.3), and we focus on radiation that propagates along k = kˆz +such that the Coulomb gauge condition imposes A3 = 0. Working in a circular-polarization basis for +the electromagnetic field, AL = (A1 + iA2)/ +√ +2 and AR = (A1 − iA2)/ +√ +2, the system of differential +equations to be solved reads as +¨AL + k2AL − i [cos(2mt) + isin(2mt)] g2 ¯X2m ˙AR = 0 , +(A.12a) +¨AR + k2AR + i [cos(2mt) − isin(2mt)] g2 ¯X2m ˙AL = 0 , +(A.12b) +We perform an harmonic expansion of the electromagnetic modes and focus on the first instability +band to obtain +� +� +� +� +� +� +˙˜AL,+ +˙˜AR,+ +˙˜AL,− +˙˜AR,− +� +� +� +� +� +� += +� +� +� +� +˜M11 +0 +0 +˜M14 +0 +˜M22 +0 +0 +0 +0 +− ˜M22 +0 +− ˜M14 +0 +0 +− ˜M11 +� +� +� +� +� +� +� +� +˜AL,+ +˜AR,+ +˜AL,− +˜AR,− +� +� +� +� +(A.13) +– 20 – + +where +˜M11 = − +� +2 +g2 ¯X2 − g2 ¯X2 +2 +�−1 � +− +ik2 +g2m ¯X2 + +im +g2 ¯X2 − ig2m ¯X2 +2 +� +, +(A.14) +˜M22 = −(2im)−1(k2 − m2) , +(A.15) +˜M14 = − +� +2 +g2 ¯X2 − g2 ¯X2 +2 +�−1 �ik2 +2m + im +2 +� +. +(A.16) +The four Floquet exponents are the four complex eigenvalues of ˜M, and the one with largest real part +is +µk,max = +� +k4 − 2k2m2 + m4 − g2m4 ¯X4 +m +� +−4 + g2 ¯X4 +(for k = k ˆz) . +(A.17) +The edges of the first instability band, its center in the k-space, and bandwidth read as +kl,edge = m +� +1 − g2 ¯X2 = m +� +1 − g2 ¯X2 +2 +� ++ O(g4) , +(A.18) +kr,edge = m +� +1 + g2 ¯X2 = m +� +1 + g2 ¯X2 +2 +� ++ O(g4) , +(A.19) +k0 = (kl,edge + kr,edge) +2 +≈ m + O(g4) , +(A.20) +∆k = (kr,edge − kl,edge) ≈ mg2 ¯X2 + O(g4) . +(A.21) +Replacing k0 into eq. (A.17), one finds the largest Floquet exponent among all possible wavenumbers +as +µk,max ≈ 1 +2g2m ¯X2 +(for k = k ˆz) +(A.22) +in complete agreement with numerical results. +B +Floquet analysis for spherical soliton profile +In the main text we observed that the unstable modes have wavenumbers k ∼ m ≫ m (µ/m)1/2 ∼ R−1 +that are large compared to the inverse of the size of the soliton. Then if the Floquet exponent is large, +µk,max ≫ R−1, such that the amplification rate exceeds the escape rate for the radiation, we argued +that the Floquet exponent can be calculated by treating the dark photon field as homogeneous. In this +appendix, we relax the assumption of a large Floquet exponent, and we extend the Floquet analysis to +account for the finite size of the polarized vector soliton. +For an electromagnetic field A(t, x) interacting with the vector soliton via operator O1, the field’s +equation of motion (in Coulomb gauge ∇ · A = 0) is given by eq. (3.1): +¨ +A − ∇2A + g2X2(r) 2ω sin(2ωt) ∇ × A = 0 . +(B.1) +As we have done in the main text, here we drop gradients of the dark photon field when compared +against gradients of the electromagnetic field, since |∇A| ≫ |∇X|. Due to the inhomogeneous term +with X(r), it is cumbersome to work directly in k-space, because the Fourier transform of eq. (B.1) +involves a convolution. +Instead, we decompose the vector potential A(t, x) onto a basis of vector +– 21 – + +spherical harmonics, and then eventually go to a one-dimensional Fourier space conjugate to the radial +component alone. A similar approach was employed previously in refs. [42, 62] to study spherically- +symmetric scalar solitons. The corresponding equation in ref. [62] is ¨ +A−∇2A−gωϕ(r) sin(ωt) ∇×A = +0. The results from that work can be carried over with the replacements: −gϕ(r) → g2X2(r) and +ω → 2ω. +The vector spherical harmonic decomposition of the vector potential reads as +A(t, x) = +∞ +� +ℓ=0 +ℓ +� +m=−ℓ +� +A(Y ) +ℓm (t, r) Yℓm(ˆx) + A(Ψ) +ℓm (t, r) Ψℓm(ˆx) + A(Φ) +ℓm (t, r) Φℓm(ˆx) +� +, +(B.2) +where Yℓm(ˆx), Ψℓm(ˆx), and Φℓm(ˆx), are the vector spherical harmonics, and where r = |x| and +ˆx = x/r. The Coulomb gauge condition, ∇ · A = 0, imposes rℓ(ℓ + 1)A(Ψ) +ℓm = ∂r(r2A(Y ) +ℓm ). For ℓ = 0 +this implies A(Y ) +ℓm = 0, and since Ψ00 = Φ00 = 0, the vector potential vanishes trivially, so only ℓ > 0 +contributes. +Using the vector spherical harmonics, the equation of motion (B.1) decomposes into three separate +equations for the three mode functions. Notice that the spherical Bessel functions of the first kind jℓ(kr) +are eigenfunctions of the Laplace operator. We discard solutions built from spherical Bessel functions +of the second kind yℓ(kr), which are singular at the origin. This observation motivates the Ansatz +A(Y ) +ℓm (t, r) = +� ∞ +0 +dk +2π +�� +ℓ(ℓ + 1) +kr +jℓ(kr) wkℓm(t) +� +(B.3a) +A(Φ) +ℓm (t, r) = +� ∞ +0 +dk +2π +� +− +i +� +ℓ(ℓ + 1) +jℓ(kr) vkℓm(t) +� +, +(B.3b) +where the complex mode functions wkℓm(t) and vkℓm(t) are labeled by k ∈ (0, ∞), ℓ ∈ {1, 2, · · · }, and +m ∈ {−ℓ, −ℓ + 1, · · · , ℓ − 1, ℓ}. Using this Ansatz and the Coulomb gauge condition lets us write +A(Y ) +ℓm (t, r) Yℓm(ˆx) + A(Ψ) +ℓm (t, r) Ψℓm(ˆx) + A(Φ) +ℓm (t, r) Φℓm(ˆx) += +� ∞ +0 +dk +2π +� +vkℓm(t) Mkℓm(x) − wkℓm(t) Nkℓm(x) +� +(B.4) +where we’ve defined the vector spherical wavefunctions +Mkℓm(x) = − +i +� +ℓ(ℓ + 1) +jℓ(kr) Φℓm(ˆx) +(B.5a) +Nkℓm(x) = − +� +ℓ(ℓ + 1) +kr +jℓ(kr) Yℓm(ˆx) +(B.5b) +− +� 1 +kr +� +ℓ + 1 +ℓ +jℓ(kr) − +1 +� +ℓ(ℓ + 1) +jℓ+1(kr) +� +Ψℓm(ˆx) . +The vector spherical wavefunctions have the following properties: +∇ × Mkℓm = −ikN , +∇ × Nkℓm = +ikM , +and +∇ · Mkℓm = ∇ · Nkℓm = 0 , +(B.6) +and they are eigenfunctions of the Laplace operator: ∇2Mkℓm = k2Mkℓm and ∇2Nkℓm = k2Nkℓm. +– 22 – + +200 +300 +400 +500 +600 +700 +0 +2 +4 +6 +8 +10 +12 +220 240 +280 300 +-1.0 +-0.5 +0.5 +1.0 +(µ(hom.) +max +� µesc)R +g mpl +µ(sol) +maxR +Figure 2: The Floquet exponent with the largest real part, µ(sol.) +max , is calculated for a linearly-polarized +vector soliton with N = m2 +pl/m2 and coupling g to electromagnetism. The red curve shows the result of +a numerical Floquet analysis applied to eq. (B.18), and the blue curve shows an analytic approximation +(4.1). We use µesc ≈ 2/R to match the numerical solution at large coupling. The numerical Floquet +analysis of the inhomogeneous soliton (red) confirms that the resonance starts shutting off when the +escape rate becomes comparable to the homogeneous Floquet exponent (ie. when the blue curve crosses +zero). In the above figure, this happens around gmpl ∼ 250. +The equations of motion are reduced to +� ∞ +0 +dk +2π +� +¨wkℓm(t) + k2 wkℓm(t) + 2ig2X2(r) ωk sin(2ωt) vkℓm(t) +� +× +�� +l(l + 1) jℓ(kr) +(kr) +� += 0 , +(B.7a) +� ∞ +0 +dk +2π +� +¨vkℓm(t) + k2 vkℓm(t) − 2ig2X2(r) ωk sin(2ωt) wkℓm(t) +� +× +� +−i +jℓ(kr) +� +ℓ(ℓ + 1) +� += 0 . +(B.7b) +To isolate the equation for the modes labeled with k, we multiply the first equation by r3jℓ(k′r) and +the second equation by r2jℓ(k′r). Then integrating over r and using the identity +� ∞ +0 +dr r2 jℓ(kr)jℓ(k′r) = +π +2k2 δ(k − k′) +(B.8) +leads to +¨wkℓm(t) + k2 wkℓm(t) + 2k2 +π 2ig2ω sin(2ωt) +� ∞ +0 +dr +� ∞ +0 +dk′X2(r) vk′ℓm(t) r2jℓ(k′r)jℓ(kr) = 0 +(B.9a) +¨vkℓm(t) + k2 vkℓm(t) − 2k2 +π 2ig2ω sin(2ωt) +� ∞ +0 +dr +� ∞ +0 +dk′X2(r) k′ wk′ℓm(t) r2jℓ(k′r)jℓ(kr) = 0 . (B.9b) +Note that the integrand contains a factor of k in the first equation and a factor of k′ in the second +equation. The soliton profile X2(r) is defined for r ≥ 0, and if we extend its domain to r < 0 by +– 23 – + +imposing X2(−r) = X2(r), then it admits a Fourier transform +X2(r) = +� ∞ +−∞ +dq +2π +� +X2(q) eiqr = 2 +� ∞ +0 +dq +2π +� +X2(q) cos(qr) +(B.10) +which lets us write +¨wkℓm(t) + k2 wkℓm(t) + 2ig2 ωk sin(2ωt) Iv = 0 , +(B.11a) +¨vkℓm(t) + k2 vkℓm(t) − 2ig2 ωk sin(2ωt) Iw = 0 , +(B.11b) +where +Iv ≡ 4k2 +π +� ∞ +0 +dr +� ∞ +0 +dk′ +� ∞ +0 +dq +2π +� +X2(q) cos(qr) vk′ℓm(t) r2jℓ(k′r)jℓ(kr) , +(B.12) +and Iw has wk′ℓm instead of vk′ℓm, and it contains an additional factor of k′/k in the integrand. In +order to simplify Iv, we use the identity [63] +jℓ(kr) jℓ(k′r) = +1 +2kk′r +� k+k′ +|k′−k| +dk′′ sin(k′′r) Pℓ +�k2 + k′2 − k′′2 +2kk′ +� +(B.13) +and +� ∞ +0 drr cos(qr) sin(k′′r) = −(π/2)∂k′′ [δ(q + k′′) + δ(q − k′′)], to obtain +Iv = − +� ∞ +0 +dk′ +2π vk′ℓm(t) k +k′ +� k+k′ +|k′−k| +dk′′ Pℓ +�k2 + k′2 − k′′2 +2kk′ +� +∂ +∂k′′ � +X2(k′′) . +(B.14) +The derivative of the one-dimensional Fourier transform � +X2(k′′) is peaked around k′′ ∼ 2π/R and +has a width order 2π/R also. To ensure that this peak is not missed by the dk′′ integration, we require +|k′ − k| ≲ 2π/R. Furthermore, for resonance, we expect k ≈ ω ≈ m, and recall that for non-relativistic +solitons mR ≫ 1. Note that this m is mass of the dark photon, not the an index of spherical harmonic. +With these considerations, the argument of the Legendre polynomial is close to unity. Expanding +the Legendre polynomial with its argument close to 1 (and for fixed ℓ) we obtain +Pℓ +�k2 + k′2 − k′′2 +2kk′ +� += 1 − ℓ(ℓ + 1) +2 +�k′′2 − (k − k′)2 +2kk′ +� ++ ... . +(B.15) +Since (k′′2 − (k − k′)2)/(2kk′) ∼ 1/(mR)2, the Legendre polynomial is well approximated by one when +ℓ ≪ mR. In this regime, +Iv = +� ∞ +0 +dk′ +2π vk′ℓm(t) k +k′ +� � +X2(k − k′) − � +X2(k + k′) +� ++ O[ℓ2/(mR)2] +(B.16) +≈ +� ∞ +0 +dk′ +2π vk′ℓm(t) � +X2(k − k′) + O[ℓ2/(mR)2]. +(B.17) +where in the second line we used k′ ∼ k ∼ m, and ignored � +X2(k + k′) using the fact that � +X2(q) is +centered around q = 0 with a width ∼ 1/R ≪ m−1. Also note that with the same approximations +Iw ≈ Iv (with v → w). +– 24 – + +Then we may write (B.11a) and (B.11b) as +¨˜vkℓm(t) + k2 ˜vkℓm(t) ± 2g2ωk sin(2ωt) +� ∞ +0 +dk′ +2π +� +X2(k − k′) ˜vk′ℓm(t) = 0 +and +˜wkℓm(t) = ±i˜vkℓm(t) +with +ℓ ≪ mR . +(B.18) +Note that � +X2(k − k′) couples modes over a k′ width of ∼ 1/R around k ≈ m. These results agree with +those derived in [42] for the case of scalar solitons, under the replacement 2ω → ω and � +X2(k − k′) → +�Φ(k−k′), where �Φ(k−k′) represents the one dimensional Fourier transform of the scalar soliton profile. +Authors in [42] only studied the particular channel (ℓ, m) = (1, 0), but due to the likeness between +the vector and scalar soliton analysis, we can conclude that their results generically holds for any pair +of spherical harmonic numbers (ℓ, m) so long as ℓ ≪ mR. We note that when ℓ ≫ mR, we have +numerically verified that Iv,w decays exponentially with ℓ, and hence we ignore that regime in what +follows. +The integro-differential eq. (B.18) can be analysed using Floquet theory since the system is coupled +in k-space, but still periodic in time. We will follow ref. [42] where a closely related system was analyzed. +We discretize the system in k-space, and solve the coupled system of different k modes numerically. +There are two physical considerations which set the resolution and size of the grid in k-space. First, +the width ∼ 1/R of � +X2(k −k′) sets the extent of the k-space grid, whereas the requirement of resolving +the resonance band near k ≈ m, sets the resolution of the k-grid (∆k < g2 ¯X2m). +By numerically solving the integro-differential equation, we study a linearly-polarized vector soli- +ton with N = m2 +pl/m2 and different values of the coupling g. We calculate the Floquet exponent with +the largest real part, µ(sol.) +max = max +i +ℜ[µi]. Our results are summarized in figure 2, which shows the +dependence of the Floquet exponent on the coupling g. These results show an excellent agreement +with the analytic approximation in eq. (4.1), i.e. the resonance phenomenon is turned on when the +maximal Floquet exponent for the corresponding homogeneous case starts becoming larger than the +soliton light-crossing time, µ(hom.) +max +≳ O(1/R). The quantity µesc. = O(1/R) can be interpreted as +the escape rate for radiation leaving the soliton. When µ(hom.) +max +≲ µesc, radiation is leaves the system +more quickly than it is being generated and the Bose enhancement required during the resonance is +suppressed. The same feature was reported in ref. [42] for the case of scalar solitons.5 We find that +µ(sol.) +max ≈ µ(hom.) +max +− µesc if we fix µesc ≈ 2/R. +We note that the zoom-in figure 2 shows a slightly disagreement between numerical results at +gmpl < 250 which are small but non-zero (at a level larger than machine precision), and the analytical +expectation that these should approach zero. +Even a small non-zero Floquet exponent is relevant +because of the exponential nature of the instability, and required further analysis to determine whether +this discrepancy is physical or numerical. Our analysis indicates that this disagreement is a result +of numerical issues. Resolving the resonance band ∆k ∝ g2 ¯X2m, and covering the width ∼ 1/R of +� +X2(k − k′) becomes exceptionally challenging at small g. We have found that for gmpl ≲ 250, the +5In ref. [42], the growth rate of photons in scalar solitons follows the analytical approximation µ(hom.) +max +− µesc, with the +escape rate defined as µesc = 1/(2Rc). These authors approximate the scalar soliton profile using a sech function, where +Rc is a characteristic scale length. This quantity is related to the radius of the power-law approximation, eq. (2.10), as +Rc ≈ R/3. In addition, the resonance calculation for the scalar case considers one power of the soliton profile, while that +for the vector case involves the square of the soliton profile. The ratio between the full width at half maximum of a sech +function and its square is about +√ +2. Thus, transforming the scalar escape rate which fits numerical data to the vector +escape rate which fits ours, we have 1/(2Rc) → 3 +√ +2/(2R) ≈ 2/R, in complete agreement with results shown in figure 2. +– 25 – + +numerically evaluated Floquet exponent continues to decrease as we increase the resolution and extent +of the k-grid, whereas for larger g the values do not change. While not quite a proof, we take this as +an indication that the Floquet rate approaches zero for small coupling as expected from theoretical +considerations. +C +Fuzzy dark photon dark matter +Although our primary interest in this work has been the phenomenon of parametric resonance in +polarized vector solitons, the calculations presented here can be carried over to other systems as well. +In this appendix, we consider fuzzy dark photon dark matter, not forming solitons, and we adapt the +results of our analysis to assess the implications of parametric resonance of electromagnetic radiation +for this system. +The inhomogeneous dark photon field admits a Fourier representation as +X(t, x) = +� d3k +(2π)3 Xk(t) eik·x , +(C.1) +where modes are labeled by a wavevector k with corresponding wavenumber k = |k| and wavelength +λ = 2π/k. We are interested in systems in which the dark photons are non-relativistic, which means +that the modes amplitudes Xk(t) only have support for modes with small wavenumbers k ≪ m. As +a fiducial parameter choice we take m = 10−20 eV, corresponding to ‘fuzzy’ dark matter, and the +non-relativistic modes have λ ≫ 2π/m ≃ (0.004 pc)(m/10−20 eV)−1. +The energy density carried by the non-relativistic dark photon field today is approximately +ρX(x) ≈ m2|X(x)|2/2. Assuming that the mode amplitude is only a function of the wavenumber, +|Xk| = |Xk|, we can write +� +d3x ρX(x) ≈ +� ∞ +0 +dk +k EX,k +with +EX,k = +1 +4π2 m2k3|Xk|2 , +(C.2) +where EX,k is the spectral energy distribution of the dark photon field today. We assume that EX,k +is peaked at a wavenumber k = k∗ such that 0 < k∗ ≪ m. +Consequently, non-relativistic modes +with wavevectors satisfying |k| ≈ k∗ carry most of the energy. For instance, the production mechanism +discussed in Refs. [24, 28, 31, 32] leads to k∗ ∼ +� +mHeq/(1+zeq) where zeq = 3300 and Heq = 10−28 eV +are the redshift and Hubble parameter at radiation-matter equality; this corresponds to a length scale +today of λ∗ ≃ (63 kpc)(m/10−20 eV)−1/2. We define ¯X = k3 +∗|Xk∗|/2π2 to be the field amplitude of the +dominant modes, and their energy density is written as ρX,∗ ≈ EX,k∗ ≈ 1 +2m2 ¯X2. +The condition µ(hom.) +max +λ∗ ≈ g2 ¯X2mλ∗/2 ≳ 1 must be satisfied in order for parametric resonance +to occur; see eq. (4.1). This places a lower bound on the field amplitude ¯X that depends upon the +coupling g, mass m, and the coherence length scale λ∗. Conversely, the requirement that the dark +photon relic abundance does not exceed the known dark matter relic abundance imposes an upper +bound on the field amplitude today ¯X ≤ +� +2ρdm/m2. Taken together, these two bounds are expressed +as +� +1 × 104 GeV +�� +g +10−10 GeV−1 +�−1� +m +10−20 eV +�−1/2� +λ∗ +1 Gpc +�−1/2 +≪ ¯X ≤ +� +4 × 105 GeV +�� +m +10−20 eV +�−1 +. +(C.3) +– 26 – + +These inequalities emphasize why we focus on such low-mass fuzzy dark matter with m ∼ 10−20 eV. +For larger values of m (at the same g, λ∗) the upper and lower bounds become incompatible. +If the condition for parametric resonance is satisfied, the dark photon field will decay into elec- +tromagnetic radiation. The time scale for this energy transfer is controlled by the maximal Floquet +exponent via τ ≈ 1/µ(hom.) +max +≈ 2/g2 ¯X2m, using the results in eqs. (3.9) and (3.12). For the same fiducial +parameters used in the estimates above, we have the lifetime +τ ≃ +� +1 × 1015 s +�� +g +10−10 GeV−1 +�−2� +¯X +105 GeV +�−2� +m +10−20 eV +�−1 +. +(C.4) +Since the age of the universe today is t0 ∼ 1017 s, these estimates imply that the dark photon field would +have been depleted long ago by the resonant amplification of electromagnetic radiation. Conversely, +the condition for parametric resonance to be inoperative today is written as +� +g +10−10 GeV−1 +� +< +� +0.025 +�� +m +10−20 eV +�1/2� +λ∗ +1 Gpc +�−1/2 +, +(C.5) +assuming that the dark photon makes up all of the dark matter. Therefore, in order to have a vi- +able model of fuzzy dark photon dark matter coupled to electromagnetism through the dimension-6 +operators that we consider, the parameters must be such that the parametric resonance instability is +inoperative today, implying an upper limit on the coupling g. +If the parameters are chosen such that the parametric resonance instability is inoperative to- +day, it is interesting to ask whether parametric resonance may have taken place in the early uni- +verse. +Specifically, we are interested in the time dependence of µ(hom.) +max +(t)λ∗(t) and how it com- +pares to 1. +In an Friedman-Robertson-Walker spacetime with scale factor a(t) at time t, we can +write the time dependence as µ(hom.) +max +(t)λ∗(t) ∝ a(t)r ¯X(t)2λ∗(t) where the additional factors of a(t)r +arise from the metrics and inverse metrics appearing in the operators O1 through O5; for exam- +ple, X · X = gµν(t)XµXν ≈ a(t)−2 ¯X(t)2. The field’s coherence length grows no more quickly than +λ∗(t) ∝ a2(t) (tracking the causal horizon during radiation domination); we can write λ∗(t) ∝ a(t)s. +Similarly, the field amplitude (for non-relativistic modes inside the horizon) oscillates under a decreas- +ing envelope ¯X(t) ∝ a(t)−1/2 [24]. Putting together these factors gives µ(hom.) +max +(t)λ∗(t) ∝ a(t)r+s−1. +Since a(t) is a growing function of time, if the condition for parametric resonance is not satisfied today, +and if r +s−1 ≥ 0 then parametric resonance was never operative (on cosmological scales) throughout +the cosmic history. Conversely, if r + s − 1 < 0 then parametric resonance may have taken place in +the early universe. 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Soc. 419 (2012) 1294 [1109.6552]. +– 30 – + diff --git a/StFJT4oBgHgl3EQfLywb/content/tmp_files/load_file.txt b/StFJT4oBgHgl3EQfLywb/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..a84cb350a21dd58bd3149b0066a156a629f2abe9 --- /dev/null +++ b/StFJT4oBgHgl3EQfLywb/content/tmp_files/load_file.txt @@ -0,0 +1,1581 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf,len=1580 +page_content='Prepared for submission to JCAP Photons from dark photon solitons via parametric resonance Mustafa A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Amin, Andrew J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Long, and Enrico D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Schiappacasse Department of Physics and Astronomy, Rice University, Houston, Texas 77005, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' E-mail: mustafa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='amin@rice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='edu, andrewjlong@rice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='edu, enrico.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='schiappacasse@rice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='edu Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Wave-like dark matter made of spin-1 particles (dark photons) is expected to form ground state clumps called “vector solitons,” which can have different polarizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' In this work, we con- sider the interaction of dark photons with photons, expressed as dimension-6 operators, and study the electromagnetic radiation that arises from an isolated vector soliton due to parametric resonant amplification of the ambient electromagnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' We characterize the directional dependence and po- larization of the outgoing radiation, which depends on the operator as well as the polarization state of the underlying vector soliton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' We discuss the implications of this radiation for the stability of solitons and as a possible channel for detecting mergers of vector solitons through astrophysical observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='11470v1 [hep-ph] 27 Jan 2023 Contents 1 Introduction 1 2 Modeling dark photon interactions with light 3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='1 Non-relativistic modes of the dark photon field 3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='2 Interactions with electromagnetism 4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='3 Ultraviolet embedding 5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='4 Polarized vector solitons 5 3 Electromagnetic radiation via parametric resonance 7 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='1 Electromagnetic equation of motion 7 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='2 Applying Floquet theory 8 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='3 Linearly polarized dark photon field 10 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='4 Circularly polarized dark photon field 11 4 Radiation from polarized vector solitons 13 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='1 Condition for parametric resonance 13 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='2 Vector soliton decay 14 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='3 Astrophysical signatures from soliton mergers 15 5 Summary and conclusion 17 A Details of the Floquet analysis 19 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='1 Homogeneous and linearly-polarized dark photon field for O3 19 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='2 Homogeneous and circularly-polarized dark photon field for O3 20 B Floquet analysis for spherical soliton profile 21 C Fuzzy dark photon dark matter 26 Contents 1 Introduction Astrophysical and cosmological observations provide strong evidence for the existence of dark matter [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' However, we do not as yet know the mass, charge, and spin of the constituent dark matter particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' What do astrophysical observations tell us about such properties, especially spin?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The electric charge of dark matter cannot be too large [3], whereas the mass cannot be lighter than O(10−19−10−18 eV) eV [4, 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' While we do not know the spin of dark matter, an important piece of information connecting the spin and mass of dark matter is known: if dark matter is sufficiently light, it cannot be fermionic since the required occupation number in phase space would be too large [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' For bosons, however, light masses are allowed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' In the regime when the dark matter mass is sufficiently light (m ≪ eV), the occupation number of the field in astrophysical settings becomes so large that dark matter is adequately described – 1 – by a classical, non-relativistic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Classical, wave dynamical effects become relevant in such settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Can such wave-effects then be used to infer the spin of bosonic dark matter?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The past decade has seen a resurgence of effort in exploring wave dynamical effects in non- relativistic, spin-0 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' scalar) dark matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' See refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' [7, 8] for recent reviews, and [9–14] for examples of numerical simulations in a structure formation context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' In the case of vector (spin-1 or dark photon) dark matter [15, 16] a similar numerical exploration is still in its nascent stage [17, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' While in a broad sense, the governing equations and the resulting gravitational clustering and growth of structure in non-relativistic vector dark matter is similar to scalars [19, 20], the additional number of components in higher spin dark matter (2s + 1 for a spin-s field) can lead to observationally relevant differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' A larger number of components leads to reduced wave interference, which reduces the variance of density fluctuations in dark matter [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Such fluctuations can, for example, be probed by dynamical heating of stars [4, 21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Such effects;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' however, can also be mimicked to an extent by n = 2s + 1 scalar fields with similar masses [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Furthermore, initial conditions in the early universe do rely on the intrinsic nature (including spin) of the field [23–33], however, the intrinsic spin (as a spatial vector) is not directly accessible to Newtonian gravity relevant for dark matter in the contemporary universe when it is characteristically non-relativistic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' To access spin more directly, one must include non-gravitational interactions within the field and/or introduce interactions with other Standard Model fields (or include relativistic corrections).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' All such effects are typically expected to be small in the case of dark matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Nevertheless, the effects of such non-gravitational interactions, even if weak, can be enhanced by the large occupation numbers, densities and coherence length of the dark matter field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' These conditions are possible in solitons — coherent field configurations that are long-lived, spatially localized and whose central amplitudes can be much larger than the background density (since the amplitudes do not decay with expansion).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' For a detailed recent discussion of non-relativistic scalar solitons, see for example ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' [34] and references therein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Such solitons have been shown to readily form in light scalar field dark matter via gravitational interactions alone [9, 35], and recently, also in vector dark matter from cosmological and astrophysical initial conditions [5, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Unlike scalar solitons, solitons in vector fields have a richer structure due to the vector nature of the field [19, 20, 36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' They can be polarized [19, 20], with no particular preference for the polarization in the case of purely gravitational interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Such vector solitons typically carry macroscopic amounts of intrinsic spin [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Non-gravitational self-interactions can lead to preference for one polarization over another, and have been explored in refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' [37–40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' This richness in structure arising from the vector nature of the field provides hope that interactions with Standard Model fields in environments with solitons might lead to interesting, and potentially large spin-dependent effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' With these considerations in mind, we consider the direct coupling of spin-1 dark matter to photons, and explore their implications in an astrophysical environment where solitons are present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' We show that such interactions, while very weak, can still lead to resonant production of photons when certain conditions are met.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' This aspect is similar to the case of resonant photon production from axion stars and miniclusters [41–44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' However, in our case, the polarization pattern of the radiation carries information about the underlying polarization state of the solitons as well as as the specific nature of the interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' With this preliminary investigation, we elucidate characteristic features of the electromagnetic radiation (frequency, polarization, spatial patterns of radiation etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' ), and the conditions under which such signals are produced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' If detected, such signals could provide insight into the underlying spin of dark matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' We study resonant photon production from dark photon (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' vector) solitons via a variety of – 2 – dimension-6 operators that couple photons and dark photons, within the framework of effective field theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' We focus on dimension-6 operators since we find that such interactions lead to significant photon production from solitons even in vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Astrophysical implications of a more natural dimension-4 operator: gauge kinetic mixing [45, 46], has been explored extensively in the literature (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' [47– 50]), albeit in non-solitonic settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Photon production from such a coupling is also of interest in the presence of solitons, and might lead to enhanced signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Furthermore, our effort here is complementary to the significant ongoing effort to detect light dark photon dark matter in terrestrial settings [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The remainder of the article is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The content of section 2 establishes the scope of the problem: we specify the model for massive dark photons interacting with electromagnetism, we discuss a possible ultraviolet embedding for the dimension-6 operators that we study, and we present the spatially-localized polarized vector soliton configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The core results of our study are presented in section 3, which includes our analysis of the electromagnetic field’s equation of motion using Floquet theory and our predictions for the Floquet exponents arising from parametric resonance of a dark photon homogeneous configuration with either linear or circular polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' In section 4, we apply previous results to study electromagnetic radiation from polarized vector solitons and discuss the possible astrophysical signatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' In section 5, we conclude and summarize key points of our work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Appendix A contains details of the homogeneous Floquet analysis, appendix B contains the modified Floquet analysis for an inhomogeneous vector soliton, and appendix C includes an extension of our work to the case of fuzzy dark photon dark matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' 2 Modeling dark photon interactions with light We are interested in the interactions of a massive spin-1 dark photon with electromagnetism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Consider a massive real vector field Xµ(x), which we call the dark photon field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The properties and interactions of these particles are encoded in the action S[Xµ(x), Aµ(x), gµν(x)] = � d4x √−g � −1 4XµνXµν − 1 2m2XµXµ − 1 4FµνF µν + 1 2m2 plR + Lint � (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='1) where Xµν = ∇µXν − ∇νXµ is the dark photon field strength tensor, Fµν = ∇µAν − ∇νAµ is the electromagnetic field strength tensor, R is the Ricci scalar, and indices are raised and lowered with the metric gµν(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' We work in natural units where ℏ = c = 1 are set to one, mpl = 1/√8πGN is the reduced Planck mass, and (- + + +) is the metric signature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' We also write Xµ = (X0, X) and ∂µf = ( ˙f, ∇f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' We consider small values of the mass parameter m ≪ 10 eV corresponding to light dark photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Extending earlier work on dark photons, we allow for interactions between Xµ(x) and the electromagnetic field Aµ(x), which is represented by Lint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' We enumerate the relevant interaction operators in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' these include Lint ⊃ FµνFρσXαXβ and FµνFρσ∂αXβ where the Lorentz indices may be contracted with various combinations of the inverse metric and Levi-Civita symbol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='1 Non-relativistic modes of the dark photon field We are interested in the dark photon as a candidate for the cold dark matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' In the systems of interest, only non-relativistic modes of the dark photon field will propagate;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' these modes have small wavenumbers k ≪ m and large de Broglie wavelengths λ ≫ 2π/m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' This observation motivates a perturbative expansion in powers of the dark photon field’s spatial gradient;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' the parametric relations are |∇Xµ| ∼ λ−1Xµ ≪ mXµ ∼ ˙Xµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' We work to leading order in this expansion, which effectively amounts – 3 – to setting ∇Xµ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='1 The temporal component of the dark photon field, X0(x), is non-dynamical in the theories that we study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Its equation of motion is an algebraic constraint equation, which has the solution X0 = � ∇2−m2�−1� ∇· ˙X), neglecting gravitational and electromagnetic interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Working to leading order in the gradient expansion, we set X0(x) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='2 Interactions with electromagnetism Since we seek to study electromagnetic radiation from vector solitons, it is necessary to introduce a coupling between the dark photon field Xµ(x) and the electromagnetic field Aµ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Working in the context of effective field theory (EFT), we consider all operators that are consistent with electromagnetic gauge invariance, and we organize the operators based on their mass dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The only such operator with mass dimension-4 is the so-called gauge-kinetic mixing [45, 46] L (4) int ⊃ FµνXαβ , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='2) where Fµν = ∂µAν − ∂νAµ is the usual electromagnetic field strength tensor and Xαβ = ∂αXβ − ∂βXα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The Lorentz indices can be contracted using any combination of the diagonal inverse Minkowski metric ηµν and the totally-antisymmetric Levi-Civita symbol ϵµνρσ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' we normalize −η00 = η11 = η22 = η33 = ϵ0123 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The gauge kinetic mixing can be exchanged for a coupling to charged matter by performing a field redefinition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' In this work we consider systems in the absence of free charges, and the gauge-kinetic mixing operators do not lead to electromagnetic radiation from a dark photon field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' At mass dimension- 5 there are no operators coupling the vector soliton to electromagnetism, since such operators would carry an odd number of Lorentz indices, which cannot be fully contracted using only the two-index metric and the four-index Levi-Civita symbol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' At dimension-6 the following operators are available: L (6) int ⊃ FµνFρσXαXβ , FµνFρσ∂αXβ , FµνXρXσ∂αXβ , Fµν∂ρXσ∂αXβ , Fµν∂ρ∂σ∂αXβ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='3) The third, fourth, and fifth operators involve only one factor of the electromagnetic field Aµ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' In the presence of a background dark photon field Xµ(x), these operators provide a source for Aµ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The radiation arising from such source terms is highly suppressed for long-wavelength background fields if plasma effects can be neglected [52], and we do not discuss these operators further here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The dimension-6 operators that we study are summarized as follows:2 O1 = − 1 2Fµν ˜F µν(X · X) ≈ 2(E · B)(X · X) (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='4a) O2 = − 1 2FµνF µν(X · X) ≈ (E · E)(X · X) − (B · B)(X · X) (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='4b) O3 = FµρF νρXµXν ≈ (B · B)(X · X) − (E · X)2 − (B · X)2 (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='4c) O4 = ˜Fµρ ˜F νρXµXν ≈ (E · E)(X · X) − (E · X)2 − (B · X)2 (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='4d) O5 = FµρF νρ∂µXν ≈ (E × B) · ˙X .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='4e) To move from the Lorentz-covariant expressions to the 3-vector expressions, we have dropped terms containing X0 and spatial gradients ∇Xµ, which is an excellent approximation for non-relativistic modes of the dark photon field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' 1We work in the zero spatial gradient approximation locally, but indirectly take spatial gradients into account by including the finite size effects of dark photon configurations in the phenomenology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' 2Some of these operators are related to one another using integration by parts (dropping total derivatives) and equa- tions of motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' For the non-relativistic dark photon field, a few other operators reduce to one of these;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' for instance Fµρ ˜F νρXµXν ≈ −O1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' – 4 – We write Lint = g2Oi and we study the effect of each operator one at a time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Validity of the effective field theory, which allows us to neglect the effects of dimension-8 (and higher-order) operators, requires the coupling g2 to remain sufficiently small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Moreover, we consider systems in which the dark photon field acquires a nonzero vacuum expectation value ⟨X⟩ ∼ ¯X, which causes these dimension-6 operators to renormalize lower-order operators;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' for instance, O2 modifies the electromagnetic kinetic term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' To ensure that these modifications are negligible, and that the EFT remains valid, we impose g2 ¯X2 ≪ 1 , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='5) where ¯X is interpreted as the typical amplitude of the dark photon field X(t, x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='3 Ultraviolet embedding Each of the operators in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='4) is used to construct an effective field theory with Lint = g2Oi, and we study the resultant electromagnetic radiation from a non-relativistic dark photon field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Our analysis is independent of the EFT’s ultraviolet (UV) embedding, except insofar as we are justified to ‘turn on’ each operator, one at a time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Nevertheless, it is interesting to remark that these operators can arise from a simple, renormalizable theory in the UV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' In the remainder of this short section, we offer a concrete UV embedding for operator O2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Consider the following theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Suppose that Xµ is the vector potential associated with a dark U(1)d gauge symmetry, and suppose that the UV theory includes a dark Higgs field φ(x) with Dµφ = ∂µφ − igdXµφ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' If the dark Higgs acquires a nonzero vacuum expectation value ⟨φ⟩ = vd/ √ 2, then operator O2 can arise from the dimension-8 operator: L8 = − 1 8 M−4 ��Dαφ ��2FµνF µν .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='6) The operator coefficients in our EFT are parametrically g2 ∼ g2 dv2/M 4 ∼ m2/M 4 where m ∼ gdv is the mass scale of the dark photon and M is the UV scale of new physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The dimension-8 operator, in turn, may arise from a renormalizable theory of charged fermions ψ and χ with a Yukawa coupling −yφ ¯ψχ + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='. A one-loop box graph generates L8 upon integrating out the fermions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Assuming that the fermions have comparable mass mχ ∼ mψ and electromagnetic charge qψe, the box graph is parametrically M−4 ∼ y2q2 ψe2/16π2m4 ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Finally we arrive at a parametric estimate for the operator coefficients in our EFT: g ∼ yqψem/4πm2 ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' In the next section, we show that operators O1 through O4 lead to resonance as long as gmpl ≫ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' For a fiducial set of parameters, we estimate gmpl ∼ (y/1)(qψ/10−14)(m/10−6 eV)(mψ/keV)−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' These parameters are chosen to reflect the constraints on millicharged particles, which place tight upper limits on qψ across a wide range of mψ values [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The strongest limits from stellar cooling plateau to qψ ≲ 10−14 for mψ below 10 keV;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' lowering mψ further does not strengthen the qψ limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' These estimates imply that a sufficiently large dimensionless coupling gmpl ≫ 1 can be achieved if the ‘UV’ embedding includes sufficiently light and weakly-charged fermions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Despite the small value of mψ compared to the Standard Model particle content, the EFT approach remains valid while the fermion mass is much larger than the dark photon mass, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' mψ ∼ keV ≫ m ∼ µeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='4 Polarized vector solitons In the nonrelativistic regime, the equations of motion for the dark photon field X(t, x) and the gravita- tional field is a Schr¨odinger-Poisson system [19, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' These equations admit spatially-localized solutions with spherically-symmetric density profiles, which correspond to gravitationally-bounded and coherent – 5 – clumps of dark photons that are ground states of the system at fixed particle number [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Such soli- tons have spatially-independent polarization of the field, with linear and circular polarization being the extremal cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' These have been called polarized vector solitons, and they typically carry macroscopic amount of spin angular momentum [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' A general polarized vector soliton field configuration takes the form X(t, x) = 1 2 � a � c(a) X(r) e−i(m−µ)t ϵ(a) + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' � , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='7) where r = |x| is the radial distance from the center of the soliton, the index a labels the three polarization modes, ϵ(a) are the corresponding polarization unit vectors that are constants, and c(a) are c-number coefficients that are normalized by � a |c(a)|2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The real and positive parameter µ, called the chemical potential, controls the field amplitude via the radial field profile X(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Note that the field amplitude oscillates in time with an angular frequency ω = m − µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Validity of the non-relativistic approximation requires µ/m ≪ 1 and ω ≈ m .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='8) For instance, vector soliton formation by the collapse of Hubble-scale inhomogeneities at radiation- matter equality [18] would give µ ∼ Heq ≈ 2 × 10−28 eV, which is far below the fiducial mass scale m ≈ 10−6 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' For solitons forming in nonlinear environments inside dark matter halos, the chemical potential is expected to be comparable to the typical kinetic energy per particle in the environment leading to µ/m ∼ v2 ∼ 10−6 [9, 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The radial field profile X(r) and the non-dynamical Newtonian potential Φ(r) are required to solve the static Schr¨odinger-Poisson system of equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' For each polarization mode, a one-parameter family of solutions are labeled by the chemical potential µ, which sets the amplitude of X(r) and thus also X(t, x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' These solutions are well-approximated by the empirical fitting formula [9, 17] X(r) ≃ ¯X (1 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='077 µmr2)4 with ¯X ≃ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='04 mpl � µ m � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='9) The localized soliton solution has a finite gravitational binding energy E, total mass M, and full width at half maximum R that are given by [20]3 E ≈ −20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='8 m2 pl m � µ m �3/2 , M ≈ 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='3 m2 pl m � µ m �1/2 , and R ≈ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='16 1 m � µ m �−1/2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='10) which have an error of ≲ 10%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Since µ/m ≪ 1 it follows that |E| ≪ M, implying that the particles in the vector soliton are cold, and that there are approximately N ≈ M/m constituent particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The average binding energy per particle is E/N ≈ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='33m(µ/m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' To ensure that the soliton is a many- particle state, N ≫ 1, the chemical potential is bounded from below as µ/m ≫ (m/mpl)4, which is easily satisfied, since m ≪ mpl for the parameters of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The three polarization unit vectors ϵ(a)(ˆx) form an orthonormal basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Two convenient basis choices are ϵ(x) = � � 1 0 0 � �, ϵ(y) = � � 0 1 0 � �, ϵ(z) = � � 0 0 1 � � and ϵ(−) = 1 √ 2 � � 1 −i 0 � �, ϵ(0) = � � 0 0 1 � �, ϵ(+) = 1 √ 2 � � 1 i 0 � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='11) 3The numerical factors are more accurate than those provided in [17, 38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' – 6 – They correspond to linear polarization along each of the three coordinate axes and circular polarization with respect to the third z axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' If non-gravitational interactions can be neglected, each of these six modes is degenerate [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' We do not consider the ‘hedgehog’ configuration ϵ = ˆx [36], since it corresponds to a state of higher energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' For example, using the circular polarization basis allows the polarized vector soliton field configuration to be written as X(t, r) = X(r) � �|c(−)| √ 2 � � cos(ωt − arg c(−)) − sin(ωt − arg c(−)) 0 � � + |c(0)| � � 0 0 cos(ωt − arg c(0)) � � + |c(+)| √ 2 � � cos(ωt − arg c(+)) sin(ωt − arg c(+)) 0 � � � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='12) where c(a) = |c(a)|ei arg c(a) and ω = m − µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' 3 Electromagnetic radiation via parametric resonance Interactions between the dark photon field and the electromagnetic field allow for electromagnetic radi- ation to arise from a dynamical dark photon field configuration, even in the absence of charged matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' We are concerned with the operators appearing in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' In the background of the oscillating dark photon field X(t, x), these operators induce a time-dependent equation of motion for the electromag- netic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' This leads to the phenomenon of parametric resonance, which can be studied using Floquet theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Fourier modes of the electromagnetic field that fall into resonance bands experience an expo- nential amplification Ak(t) ∝ eµkt, where µk are the Floquet exponents, allowing a weak seed field to be transformed into electromagnetic radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' This radiation extracts energy from the dark photon field, which impacts its lifetime while also providing a signal that would make dark photon evaporation possibly detectable from Earth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' In the remainder of this section, we apply known techniques from Floquet theory to develop an analytical formalism that allows us to study parametric resonance of the electromagnetic field coupled to a dark photon field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' We derive expressions for the Floquet exponents µk assuming different polarization configurations for the dark photon field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' As a simplifying approximation, throughout this section we treat the dark photon field as spatially homogeneous: X(t, x) = X(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' In the following sections, we discuss how our results should be adapted for the study of inhomogeneous polarized vector solitons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='1 Electromagnetic equation of motion For each of the five operators that we study, the electromagnetic field’s equation of motion is linear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Working in the Coulomb gauge ∇ · A = 0, the equation of motion admits a Fourier representation: Oij ¨Aj + Pij ˙Aj + QijAj = 0 , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='1) – 7 – where the matrix coefficients are Oij = � � � � � � � � � � � � � � � � � δij , Lint = g2O1 δij + � 2g2|X|2� δij , Lint = g2O2 δij + � −2g2� XiXj + � 2g2 k·X |k|2 � kiXj , Lint = g2O3 δij + � 2g2|X|2� δij + � 2g2 k·X |k|2 � kiXj + � −2g2� XiXj , Lint = g2O4 δij , Lint = g2O5 (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='2a) Pij = � � � � � � � � � � � � � � � � � 0 , Lint = g2O1 � 4g2X · ˙X � δij , Lint = g2O2 � −2g2� ˙XiXj + � −2g2� Xi ˙Xj + � 2g2 k·X |k|2 � ki ˙Xj + � 2g2 k· ˙X |k|2 � kiXj , Lint = g2O3 � 4g2X · ˙X � δij + � −2g2� ˙XiXj + � −2g2� Xi ˙Xj + � 2g2 k· ˙X |k|2 � kiXj + � 2g2 k·X |k|2 � ki ˙Xj , Lint = g2O4 � −2ig2k · ˙X � δij , Lint = g2O5 (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='2b) Qij = � � � � � � � � � � � � � � � |k|2 δij + � 4ig2X · ˙X � ϵijkkk , Lint = g2O1 |k|2 δij + � 2g2|k|2 |X|2� δij , Lint = g2O2 |k|2 δij + � −2g2(k · X)2� δij + � −2g2|k|2� XiXj + � 2g2k · X � kiXj , Lint = g2O3 |k|2 δij + � −2g2(k · X)2 + 2g2|k|2 |X|2� δij + � −2g2|k|2� XiXj + � 2g2k · X � kiXj , Lint = g2O4 |k|2 δij + � −ig2k · ¨ X � δij , Lint = g2O5 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='2c) Here ki = (k)i and Xi = [X(t)]i and Ai = [Ak(t)]i with A(t, x) = � d3k Ak(t) eik·x/(2π)3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' To derive these expressions we have made two simplifying assumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' First, we work to leading order in powers of the coupling g2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' If the dimensionless combination g2|X|2 were to become O(1), our EFT expansion would be invalid, and we are safe to assume g2|X|2 ≪ 1, which lets us work to leading order in g2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Second, we neglect gradients of the dark photon field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Whereas for a vector soliton, the dark photon field is inhomogeneous on a scale ∼ R, the modes that exhibit parametric resonance are inhomogeneous on a much shorter length scale λ = 2π/k ≪ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' To study electromagnetic radiation in these modes and calculate their Floquet exponent, it is a good approximation to neglect spatial gradients of X [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' At the end of the calculation, we validate this condition and thereby justify our approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='2 Applying Floquet theory To identify the growing solutions of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='1), we adapt known techniques from Floquet theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Floquet theory is well established, however, our system is somewhat non-trivial compared to the usual textbook examples because of the coupling of different components as well as constraints that must be respected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Here, we follow sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='1-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='3 in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' [54], where a general framework to compute Floquet solutions was presented and is most easily adapted to our needs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Reduced system: Before applying Floquet theory to analyse the solutions of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='1), we impose the Coulomb constraint k · A = 0 and eliminate A3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Explicitly, A3 = −k−1 3 (k2A2 + k1A1) for k3 ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' – 8 – With this substitution, eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='1) becomes ˜Oij ¨Aj + ˜Pij ˙Aj + ˜QijAj = 0, where ˜Oij ≡ Oij − Oi3kj/k3 (similarly for ˜P, ˜Q and i, j = 1, 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='3) Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='3) is a system of two, second order differential equations which can be written as four first order equations: ˙q(t) = ˜U(t) q(t) with q(t) = � A(t) ˙A(t) � and ˜U(t) = � 0 1 −˜O−1 ˜Q −˜O−1˜P � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='4) If ˜U(t + T) = ˜U(t) is periodic with period T, then Floquet’s theorem guarantees a general solution of the form q(t) = �4 s=1 cs Ps(t) eµst where Ps(t + T) = Ps(t), and µs are called the Floquet exponents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' If ℜ[µs] > 0 for any s, then the equation of motion admits exponentially growing solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Floquet Exponents: The Floquet exponents may be calculated by solving the matrix equation ˙F(t) = ˜U(t) F(t) with the initial condition F(0) = 1 (numerically if necessary).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The matrix solution F(t) with this initial condition is often referred to as the fundamental solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The fundamental so- lution evaluated at t = T is called the Monodromy matrix F(T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Let fs = |fs|eiθs, with s = 1 to 4, be the (complex) eigenvalues of the Monodromy matrix F(T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Then, the Floquet exponents are given by µs = T −1 [ln |fs| + iθs].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Since det(F) = 1, it follows that �4 s=1 µs = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Fastest growing solutions: Eigenvectors ϵs of the Monodromy matrix provide the functions Ps(t) = F(t)ϵse−µst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Since Ps(t + T) = Ps(t) is periodic, if one solves the equation numerically, a solution is only needed for one period (as is the case for calculating Floquet exponents).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' If we order the eigenvalues by the largest real part, then q1(t) = c1P1(t)eµ1t provides the fastest growing solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' So far we have suppressed the dependence of our quantities of interest on k to reduce clutter in the equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Let us re-instate this dependence to discuss the fastest growing solutions more explicitly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' For each Fourier mode, indexed by a wavevector k, there are four Floquet exponents, and four eigenvectors corresponding to particular polarizations of the outgoing electromagnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' We label the Floquet exponents by µk,s with arbitrary 3-vector k and with s = 1 − 4 (similarly for the eigenvectors ϵk,s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' If the equation of motion admits exponentially growing solutions, the dynamics will be dominated by the solution that grows most quickly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Therefore it is useful to identify µk,max = max s ℜ[µk,s] and µmax = max k, s ℜ[µk,s] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='5) The quantity µk,max gives the largest real part of the four Floquet exponents for a given wavevector k, and the quantity µmax gives the largest Floquet exponent among all possible wavevectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' In a given system, µmax parametrizes the growth rate of electromagnetic radiation, while µk,max parametrizes the radiation emitted in a particular direction and with a particular wavelength λ = 2π/|k|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' For a given k, the polarization of the radiation is determined by inspecting ϵk,max, which denotes the eigenvector corresponding to the Floquet exponent with the largest real part for fixed k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Analytical Approximations: Since ˜O−1 ˜Q and ˜O−1˜P are periodic functions with period T = 2π/ω0, they can be expanded as a Fourier series ˜O−1 ˜Q = � l[˜O−1 ˜Q]leilω0t and ˜O−1˜P = � l[˜O−1˜P]leilω0t, where l is an integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' In the small source amplitude regime, we expect a solution of the form – 9 – ˜ A(t) = ˜ A+(t)eiω0t + ˜ A−(t)e−iω0t, with a slowly varying ˜ A±(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Since interaction operators O1 through O4 are quadratic in the photon and dark photon fields, at leading order, this ansatz corresponds to the process X +X → A+A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Here, the X particles are at rest with initial energy ω0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The emitted photons have the same energy k + O(g2) = ω0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Plugging this ansatz in the reduced system of equations, and collecting terms ∝ e±iω0t, we arrive at ˙˜y(t) = ˜M˜y(t) with ˜y(t) = � ˜ A+(t) ˜ A−(t) � , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='6) where ˜M = � � � − i(ω2 0−|k|2) 2ω0 1 − (ω2 0+|k|2) 4ω2 0 [˜O−1˜P]0 + i 2ω0 � O−1Q � 0 (ω2 0+|k|2) 4ω2 0 [˜O−1˜P]2 + i 2ω0 � ˜O−1 ˜Q � 2 (ω2 0+|k|2) 4ω2 0 [˜O−1˜P]−2 − i 2ω0 � ˜O−1 ˜Q � −2 i(ω2 0−|k|2) 2ω0 1 − (ω2 0+|k|2) 4ω2 0 [˜O−1˜P]0 − i 2ω0 � O−1Q � 0 � � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='7) Here, we have only kept terms up to O(g2) and use ˜O−1˜P = O(g2), [O−1Q]0 = [˜O−1 ˜Q]0−|k|21 = O(g2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Note that these considerations mean that all entries in the above matrix are O(g2), and so are the eigenvalues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The four eigenvalues of ˜M are the Floquet exponents µs for s = 1 − 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='3 Linearly polarized dark photon field We consider a homogeneous and linearly-polarized dark photon field, which is written as X(t, x) = ¯X cos(mt) ˆz , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='8) where X has a constant orientation and varying magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' We have set the temporal oscillation frequency ω0 = m which is an excellent approximation in the non-relativistic limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' For each of the operators, O1 through O5, we perform the Floquet analysis described above, working to leading order in powers of the coupling g2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' To illustrate the details of these analytic calculations, we work through the derivation for operator O3 in appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' the calculations for other operators are similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' For each operator, the maximum Floquet exponent (real part) is found to be µmax = � � � � � � � � � � � � � � � 1 2g2 ¯X2m , for Lint = g2O1 1 2g2 ¯X2m , for Lint = g2O2 1 2g2 ¯X2m , for Lint = g2O3 1 2g2 ¯X2m , for Lint = g2O4 O(g4) , for Lint = g2O5 , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='9) where the maximization is performed over all possible wavevectors k and all possible polarizations of the outgoing radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The results are equivalent for operators O1 through O4, and we discuss these results further below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' For O5, the real part of the Floquet exponent is parametrically higher order in the coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' This is because the additional time derivative in O5, see eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='4), brings a factor of i which renders the leading-order Floquet exponent imaginary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' First we discuss operators O1 and O2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' For both of these operators, the dark photon field enters via X · X, so its indices are not ‘entangled’ with the electromagnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Consequently both O1 and O2 have the same behavior in regard to the direction and polarization of the radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' We find that – 10 – µk,max is independent of the wavevector’s orientation, and the electromagnetic radiation is emitted isotropically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Since the operators only depend on |X|, the radiation doesn’t ‘know’ about the dark photon field’s orientation, and we obtain the same radiation pattern as if the condensate had been a scalar field [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Our numerical results for operator O2 are illustrated in the top-left panel of figure 1, and the chart for O1 is indistinguishable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The dominant Floquet band is centered at k = m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The isotropic emission is reflected in the ‘vertical’ nature of the Floquet band, which is independent of the angle θ between k and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' For both operators, the emitted radiation has no preferred polarization direction as shown in the left bottom panel in figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Next we discuss operators O3 and O4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Here the indices for the dark photon field contract with the indices for the electric and magnetic fields, and this leads to a richer structure in the Floquet chart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The top-middle panel of figure 1 shows the Floquet charts for O3 and O4 which are identical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' The maximal Floquet exponent g2 ¯X2m/2 is obtained for θ = π/2, corresponding to emission that is normal to the dark photon field’s orientation, k ⊥ ˆz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Whereas for θ = 0 or π, corresponding to k = kz ˆz, the Floquet exponent is smaller by a factor of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' More generally, our analytical analysis yields an expression (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='11) for the maximal Floquet exponent (maximizing over orientations of the electromagnetic field’s polarization) with an arbitrary angle θ between k and ˆz, which is given by µk,max(θ) = 1 2g2 ¯X2m � 1 − 1 2 cos2 θ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='10) The radiation’s polarization is found to be different for the two operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' For operator O3 the outgoing radiation at θ = π/2 is polarized in the direction of the dark photon field X ∝ ˆz, and for operator O4 it is normal to the dark photon field in the azimuthal direction ˆφ, as indicated in the bottom-middle panel of figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='4 Circularly polarized dark photon field We consider a homogeneous and circularly-polarized dark photon field, which is written as X(t, x) = ¯X √ 2 � cos(mt) ˆx + sin(mt) ˆy � , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='11) where X has a constant magnitude and varying orientation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' By performing the Floquet analysis described above, we calculate the Floquet exponents µk,s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' We provide some details of this derivation for O3 in appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' Maximizing the real part over all possible directions and polarizations of the outgoing radiation yields µmax = � � � � � � � � � � � � � � � 0 , for Lint = g2O1 0 , for Lint = g2O2 1 2g2 ¯X2m , for Lint = g2O3 1 2g2 ¯X2m , for Lint = g2O4 O(g4) , for Lint = g2O5 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='12) Operators O1 and O2 do not lead to parametric resonance for a circularly polarized dark photon field, hence µmax = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' For these operators, the dark photon field enters through |X|, which remains constant in the circularly-polarized configuration (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' For operator O5, the Floquet exponent is imaginary at O(g2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' see section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='– 11 – ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='AB+3icbVC7TsMwFHXKq4RXKCOLRYXEVCUIAWMFC2OR6ENqo8pxndaqH5HtIKov8LCAEKs/Agbf4PTZoCWMx2dc6/uSdKGNXG97+dytr6xuZWdvd2d3bP/AOax0tU4VJG0smVS9CmjAqSNtQw0gvUQTxiJFuNL0t/O4jUZpK8WCyhIQcj ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} +page_content='QWNKUbGSkOvNoilMDHilGU542rm+kOv7jf8OeAqCUpSByVaQ+9rMJI45UQYzJDW/cBPTJgjZShmZOYOUk0ShKdoTPqWCsSJDvN59hk8tcoIxlLBIgicq783csS1znhkJzkyE73sFeJ/Xj818XWYU5Gkhgi8OBSnDBoJiyLgiCqCDcsQVhRmxXiCVIG1uXa0sIl9eJZ3zRnDZuLi/qDdvyjq4BicgDMQgCvQBHegBdoAgyfwDF7BmzNzXpx352MxWnHKnSPwB87nDxctlHo=0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/StFJT4oBgHgl3EQfLywb/content/2301.11470v1.pdf'} 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The asymmetry factor η = +(I+ +c −|I− +c |) +(I+c +|I−c |) is as +high as 26% at 1.6 K. This asymmetry is quite stable and the +rectification effect over one thousand repetitions is achieved, +as shown in Fig. 4(b). Figure 4(c) displays the histogram of +the measured voltages in Fig. 4(b). With an input square wave +of current jumping between 1.2 mA and -1.2 mA, the out- +put voltage is either -0.18 mV or 0 mV. Figure 4(d) further +demonstrates that the asymmetric effect persists over the en- +tire superconducting regime up to 50 K. Although a 45◦-twist +junction is used here, similar behaviors can be found at θ = 0◦ +as well (Fig. S7). We note that the results in Fig. 4 are ob- +tained without applying the magnetic field. However, we ob- +tain the peak-dip structure of η as a function of B with its +center away from B = 0 T (Fig. S7). This observation clearly +indicates that there exists a remanent field, which is approxi- +mately 1 mT. The driving mechanism for the Josephson diode +effect remains unknown at this stage [33]. Nevertheless, our +experiments suggest that a carefully designed magnetic field +shield must be applied in order to address the non-standard +temperature dependence of Ic due to intrinsic properties. +In Fig. 5(a), we provide an overview of our data points +as a function of twist angles at both OD and OP levels. In +each doping regime, we observe appreciable IcRn in multiple +samples around 45◦. These data points apparently fall out- +side the expected behavior of a pure d-wave pairing symme- +try. However, IcRn in OP and OD indeed shows a drop as +θ increases from 0◦ to 45◦, if comparing the maximal values + +5 +obtained at different angles. This decrease can be further ap- +preciated in Fig. 5(b)(c), where the averaged values at 45±1◦ +for OP or 45±2◦ for OD with those at 0◦ are compared. On +the one hand, this angular dependence can be explained by +a mixture of isotropic s-wave and anisotropic d-wave com- +ponents [4]. We show the expected angular behavior for a +mixture of 15%/20% s-wave and 85%/80% d-wave as shaded +stripes (darker colors), of which the upper and lower bounds +are set by the sampling standard deviation at 0◦. Such a mix- +ture can yield the expected value at 45◦ that is in agreement +with our data. It suggests the existence of a substantial portion +of isotropic pairing (15-20%), comparable to that in YBCO +(15%) [34]. +On the other hand, the decreasing trend can +be solely attributed to the orbital effect. To further illustrate +this point, we consider tunneling between two 100% s-wave +superconductors with tunneling coherence that is 100 times +higher than that in the s/d mixed situation [6]. The shaded +bands with lighter colors in Fig. 5(b)(c) show the calculated +behaviors, which also reproduces the suppressed IcRn at 45◦ +observed in experiment. +In reality, the two scenarios dis- +cussed above−s-wave/d-wave mixing and orbital effect−may +both participate in giving rise to the angular dependence seen +in experiment. While we cannot rule out the d-wave pairing +scenario for the time being, the estimated 15-20% of s-wave +represents at least the lower bound. +In summary, we fabricate twisted Josephson junctions at +OD and OP doping levels, and demonstrate that they are of un- +precedentedly high crystalline quality at the interfaces. Low- +temperature transport reveals strong Josephson tunneling at +the twist angle of +45◦. The conventional temperature de- +pendence of these twisted junctions speaks against the pres- +ence of d+id or d+is-wave pairing. Intriguingly, we observe +Josephson diode effect in the junctions, setting the tempera- +ture for observing such an effect to a record high value of tens +of kelvin. From the angular dependence of the Josephson cou- +pling, we conclude that there exists an indispensable isotropic +pairing component in the twisted Josephson junctions. +This work is financially supported by the National Nat- +ural Science Foundation of China (grants No. +51788104, +No. +12141402, No. +12004041, No. +11922409, No. +11790311, 5); +Ministry of Science and Technology of +China (2017YFA0302902, 2017YFA0304600); Innovation +Program for Quantum Science and Technology (Grant No. +2021ZD0302600). +∗ These authors contributed equally to this work. +† jzhu@mail.tsinghua.edu.cn +‡ dingzhang@mail.tsinghua.edu.cn +§ qkxue@mail.tsinghua.edu.cn +[1] B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, and J. 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Lett. 73, 2492 (1994). + diff --git a/TNE2T4oBgHgl3EQfWwfK/content/tmp_files/load_file.txt b/TNE2T4oBgHgl3EQfWwfK/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..de2eccea3a840cbbcfaab9976094419bbdb5118a --- /dev/null +++ b/TNE2T4oBgHgl3EQfWwfK/content/tmp_files/load_file.txt @@ -0,0 +1,727 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf,len=726 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='03838v1 [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='supr-con] 10 Jan 2023 Persistent Josephson tunneling between Bi2Sr2CaCu2O8+x flakes twisted by 45◦ across the superconducting dome Yuying Zhu,1,2, ∗ Heng Wang,3, ∗ Zechao Wang,4, 5, ∗ Shuxu Hu,3 Genda Gu,6 Jing Zhu,4,5, † Ding Zhang,1,3, 7, ‡ and Qi-Kun Xue1,3, 8, § 1Beijing Academy of Quantum Information Sciences, Beijing 100193, China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 2Hefei National laboratory, Hefei 230088, China 3State Key Laboratory of Low Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, 100084, China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 4National Center for Electron Microscopy in Beijing,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' School of Materials Science and Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Key Laboratory of Advanced Materials (MOE),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The State Key Laboratory of New Ceramics and Fine Processing,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Tsinghua University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Beijing 100084,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' China 5Ji Hua Laboratory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Foshan,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Guangdong 528200,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' China 6Condensed Matter Physics and Materials Science Department,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Brookhaven National Laboratory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Upton,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' New York 11973,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' USA 7RIKEN Center for Emergent Matter Science (CEMS),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Wako,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Saitama 351-0198,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Japan 8Southern University of Science and Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Shenzhen 518055,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' (Dated: January 11, 2023) There is a heated debate on the Josephson effect in twisted Bi2Sr2CaCu2O8+x flakes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Recent experimental results suggest the presence of either anomalously isotropic pairing or exotic d+id-wave pairing, in addition to the commonly believed d-wave one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Here, we address this controversy by fabricating ultraclean junctions with uncompromised crystalline quality and stoichiometry at the junction interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' In the optimally doped regime, we obtain prominent Josephson coupling (2-4 mV) in multiple junctions with the twist angle of 45◦, in sharp contrast to a recent report that shows two orders of magnitude suppression around 45◦ from the value at 0◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' We further extend this study to the previously unexplored overdoped regime and observe pronounced Josephson tunneling at 45◦ together with Josephson diode effect up to 50 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Our work helps establish the persistent presence of an isotropic pairing component across the entire superconducting phase diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The pairing symmetry of cuprate superconductors is of vi- tal importance for constructing a microscopic theory of high temperature superconductivity [1–5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Among the proposals for verifying the d-wave pairing, an approach is to measure the phase-sensitive Josephson coupling between two twisted cuprates along the c-axis [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 1(a)] [6–10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Based on symme- try arguments, the Josephson tunneling between two d-wave superconductors vanishes when the twist angle along c-axis is 45◦, while a strongest tunneling is expected when the twist an- gle is 0◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' In the case of s-wave superconductors, the Joseph- son current persists to flow with a constant value, indepen- dent of the twist angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Apart from the two scenarios, it was recently proposed [11–13] that co-tunneling of Cooper pairs may occur between two cuprate monolayers at the twist angle around 45◦, giving rise to an emergent d+id or d+is wave pair- ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Whether this exotic scenario, which promises topological superconductivity, is applicable to a strongly correlated sys- tem remains to be verified [14, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The intriguing proposals above call for careful ex- perimental tests, which can be carried out by using Bi2Sr2CaCu2O8+x(BSCCO) crystals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' BSCCO naturally con- sists of a series of intrinsic Josephson junctions (IJJ) along the c-axis [16, 17] and it can be mechanically cleaved [18, 19] into two parts and re-assembled after twisting one of them with a predefined angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' This re-assembling does not impose extra strain or induce changes in stoichiometry, allowing for the realization of atomically flat interface as the tunnel bar- rier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' By contrast, the in-plane Josephson junctions realized by film growth suffer from large structural distortion, tunnel- ing plane misalignment and chemical inhomogeneity at the grain boundary [2, 20, 21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Historically, the c-axis twisted BSCCO junctions were realized experimentally by using bulk bicrystals [22] and whiskers [23, 24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' These experiments fa- vored isotropic pairing instead of the d-wave pairing [6, 8– 10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' However, it remains unclear if these macroscopic junc- tions maintained the atomically sharp and uniform interface with uncompromised crystalline quality [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' There also ex- ist technical issues such as overheating in bulk samples [22] and participation of multiple intrinsic junctions [23, 24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Re- cently, micrometer-sized BSCCO junctions were realized by the van der Waals (vdW) stacking technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The atomically flat interface was revealed to extend over the complete junc- tion area [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' However, there is still a lack of consensus on the angu- lar dependence of the Josephson coupling strength, defined as the product the Josephson critical current and the normal state resistance–IcRn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Twisted junctions in the underdoped (UD) regime (p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='1) showed large IcRn at 45◦ [4], indica- tive of isotropic pairing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Yet another experiment [13] with samples in the nearly optimally doped (OP) regime reported suppression of IcRn by two orders of magnitude as the twist angle varied from 0◦ to 45◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The discrepancy requests further clarification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' One remaining technical issue is that the inter- faces often exhibit reduced signal in the atomically resolved image and expanded interlayer spacing [4, 13, 25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' More- over, the tunneling experiments so far focused on the doping regime from UD to OP [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 1(b)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The phase diagram in this regime is complicated by the charge ordering, pseudogap and strange metal phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' By contrast, the phase diagram in the OD regime is simpler and the corresponding cuprates exhibit 2 FL SM PG SC CO AF p 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='3 ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' [22] ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' [4] ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' [13] T (K) 0 200 BSCCO-t BSCCO-b s-wave ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' d-wave ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Josephson (a) (b) a b a b + + + + + + (c) BSCCO-b BSCCO-t Ti/Au 50 m μ OD1 100 I V I This work FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' (a) Schematic illustration of the twisted BSCCO junction and the theoretical expectation of the Josephson tunneling based on different pairing symmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Here the top BSCCO (BSCCO-t) is rotated against the bottom BSCCO (BSCCO-b) by 45◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' (b) Typi- cal phase diagram of high temperature cuprate superconductors in- cluding antiferromagnetism (AF), pseudo-gap (PG), charge ordering (CO), strange metal phase (SM), Fermi liquid (FL) and superconduc- tivity (SC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Solid gray curves indicate the doping and temperature range of previous studies [4, 13, 22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' (c) False-colored SEM image of a twisted junction (sample OD1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' well-established Fermi surface [26–28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' A recent theoretical study suggested a non-trivial change in the phase difference of the twisted junction as the doping level moves to the OD regime [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' It is, therefore, necessary to extend the study to the OD regime for a comprehensive understanding of the tunneling phenomena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' In this Letter, we address the Josephson effect of twisted cuprate junctions in both OP and OD regimes [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 1(b)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' We fabricate ultrathin twisted junctions of BSCCO flakes at 45◦ by an on-site cold stacking technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' By high resolu- tion transmission electron microscopy (HR-TEM), we demon- strate that our junctions meet the demanding requirement: all the atoms at the interface possess the same signal intensity as those in the bulk, attesting to the uncompromised crystalline quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Transport experiments on the same batch of junctions indicate: 1) preserved doping level at the interface as that of the bulk crystal;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 2) strong Josephson tunneling with IcRn as large as 4 mV for OP junctions and 2 mV for OD ones at the twist angle close to 45◦;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 3) conventional temperature depen- dence of Ic, in disagreement with that predicted for d+id-wave pairing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' We further unveil the asymmetric tunneling observed in some junctions, showing Josephson diode effect up to about 50 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Finally, we compare IcRn at 45◦ and 0◦ in both OP and OD regimes and observe only weak angular dependence, indicating a prominent isotropic pairing component over the (c) Cu-JJ Cu-Bulk x (nm) 5 0 3 2 1 0 2 1 3 Intensity (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' ) Intensity (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' ) z (nm) (d) 2nm OP1 θ = 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='9° OD1 θ = 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='8° (a) (b) OD1 OP1 2nm Cu-JJ Cu-JJ Bi Ca Cu Sr [001] [010] [001] [110] [001] [010] [001] [110] Bi Ca Cu Sr Bi Bi Sr Cu Sr OD1 OP1 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' (a)(b) Cross-sectional high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) images of four twisted BSCCO junctions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' (c) Intensity profile of the CuO2 plane close to the interface [dashed lines in (a)(b)] and that in the bulk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' (d) Normalized integrated intensity profiles of the TEM images along the c-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Red arrows mark the peaks from BiO layers at the inter- face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Here, z = 0 marks the twist boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Curves are horizontally offset for clarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' whole phase diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' We fabricate the Josephson junctions [an example is given in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 1(c)] out of high quality single crystals of BSCCO [29] with the cold van der Waals stacking technique [Supplemen- tary note I and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' S1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The high crystalline quality of the twisted junctions are demonstrated by TEM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Figure 2(a) shows the representative images of two samples in the OP and OD regimes (OP1 and OD1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The samples have a nominal twist angle of 45◦ such that the cross-sectional images reveal the top and bottom BSCCO structure from different crystalline orientations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' We determine the exact twist angles by using the Kikuchi patterns [4] [values are indicated in the respective TEM image].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' In particular, the deviation from perfect 45◦ for OP1 and OP2 [see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' S2] is as small as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='05-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='1◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' We de- note the twist angles of them as 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='9◦ (45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='1◦ is equivalent).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 2(a), the bottom sections of BSCCO in the im- ages show bunching of Bi atoms (brightest dots) in OP1/OD1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The artificially twisted interface is immediately discerned be- cause only one of the double BiO layers there hosts bunching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Images of equivalently superb quality are obtained from multiple samples and in horizontally displaced regions around the junction area (further examples in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' S2,S3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' From the TEM images, we observe that the atoms of Bi, Sr, Cu and Ca all show comparable intensities at the interface and in the 3 (f) I R (mV) 0 57 K IR (mV) (d) n R (Ω) 0 2 40 T (K) 80 T = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='6 K θ = 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='8° 2 2 0 0 6 2 4 6 V (mV) 2 4 OD1 n c 0 40 80 0 4 4 θ = 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='9° OP1 T = 82 K c p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='125 IR (mV) V (mV) (c) n 0 10 10 0 4 4 T = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='6 K θ = 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='9° OP1 0 40 80 T (K) R (Ω) (e) I R (mV) c n T (K) θ = 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='8° OD1 120 120 (a) 82 K 0 8 θ = 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='9° OP1 4 (b) 4 1 1 0 0 40 T (K) 80 θ = 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='8° OD1 T = 57 K c p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='227 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' (a)(b) Temperature-dependent resistance across the junctions of OP1 and OD1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The arrows mark Tc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' (c)(d) Normalized tunnel- ing characteristics at T = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='6 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Darker (lighter) color reflects data points taken in the positive (negative) sweeping direction, as indi- cated by the arrows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' (e)(f) Temperature dependence of IcRn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Solid curves are theoretical fits by using a modified Ambergaokar-Baratoff formula [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Dashed curves are the theoretical prediction based on d+id pairing [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' bulk, demonstrating the uncompromised crystalline quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' For the superconducting layer, we take a horizontal line cut along the CuO2 plane of the top BSCCO [indicated by arrows in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 2(a)(b)] next to the twist boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' We compare this line profile with that obtained from the CuO2 plane far away from the interface, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 2(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Each peak repre- sents one row of Cu atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Clearly, the two line profiles are closely matched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 2(d) shows the averaged intensity profile along the c-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' It demonstrates that the double BiO planes at the twist boundary (indicated by red arrows) exhibit intensity peaks comparable to those from the bulk (indicated by black arrows).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' In general, the artificial interface is atomi- cally flat without any reconstruction or wrinkles [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' In addi- tion, we point out that the thickness of the artificial junctions is slightly larger than that of IJJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The separation between the ver- tical dashed lines in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 2(d) represent the distance between nearest neighbored BiO layers in the bulk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' We observe that the actual peaks from the BiO plane at the twist boundary (red arrows) situate away from the dashed lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Quantitatively, the distance between the two BiO planes on average is larger (c) I (mA) 0 2 T = 24 K V (mV) 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='4 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='2 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='2 V (mV) Cycles 0 4 511 1000 I (mA) 0 1 1 I (mA) 0 30 60 T (K) Ic |I | c 0 2 1 c 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='4 2 1 (a) (b) (d) T = 24 K Counts V (mV) 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='001 40 0 + Ic Ir + + Ic Ir T = 24 K FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' (a) Current-voltage characteristics of OD-BSCCO junction with a nominal twist angle of 45◦ at T = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='6 K and 24 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Dark and light colors indicate data obtained in two opposite sweeping direc- tions, as indicated by the arrows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' I± c and I± r represent the critical current and re-trapping current in the positive/negative sweeping di- rections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The data are obtained at nominally zero magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' (b) Junction voltage (bottom) under the square wave of excitation cur- rent (±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='2 mA, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='03 Hz) (top) at T = 24 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' (c) Histograms of the measured junction voltage data in (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' (d) Temperature dependence of the critical Josephson currents in two directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Solid curves are guide to the eye.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' than the bulk value by 12% (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' S3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Apart from this slightly thicker tunnel barrier, the twisted junction has a smaller tun- neling area−the overlapping region between the top and bot- tom flakes−than the IJJ in either the top or bottom BSCCO [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 1(d)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' These features help distinguish the transport at the twisted interface from that of IJJ, as discussed below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Figure 3 shows the transport results from OP1 and OD1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Similar results from other samples are given in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' S2, S4 and S5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' For the OP samples, temperature dependent resis- tance measurements indicate a narrow superconducting tran- sition with Tc close to that of the bulk [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 3(a), Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' S2(c) and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' S4], confirming the preserved doping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' For the OD samples [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 3(b), Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' S2(d) and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' S5], however, the junc- tion resistance reaches zero at around 50 K but the onset for the superconducting transition starts at a higher temperature of about 80 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' We emphasize that the OD doping level is pre- served at the twisted interface, because the junction is formed at a cryogenic temperature (-50 ◦C) that suppresses oxygen out-diffusion and is further buried inside the relatively thick stack of BSCCO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' We attribute the higher onset temperature to the top surface of OD-BSCCO flakes, which suffers from oxygen loss in the final fabrication step at a relatively allevi- ated temperature (-30 ◦C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Further support to this argument is 4 90° 75° OP 15° 30° 45° 60° θ 0° T = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='6K 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='1 1 10 105° 120° 135° 150° 165° 180° θ + 90° OD s-wave d-wave OP1 OP2 OD1 OP3 θ (°) 0 2 4 0 4 8 12 θ (°) 0 15 30 15% s 20% s 6 OP-2212 OD-2212 (a) (b) (c) = 1 � = 1 � � 0 � 0 � 45 � 45 OP4 OD3 45 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='01 100% s � 0 15 30 45 s-wave d-wave 1 10 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='01 100% s � FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' (a) Fan-chart diagrams of IcRn as a function of twist angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Except for the filled symbols with angles determined by TEM, we use nominal twist angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Upper-left/upper-right quadrant includes data points from junctions in the OP/OD doping regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Tc for OD is in the range of 57 to 67 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='(b)(c) Comparison between the averaged IcRn at 0◦ and that at 45◦ for OP and OD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Circles represent the aver- aged values and the error bars are the corresponding sampling stan- dard deviations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The shaded bands with darker colors represent the theoretically expected behavior when the order parameter is a mix- ture of s-wave and d-wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The percentage of s-wave component is indicated in the panels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The tunneling is considered to be incoherent as represented by factor γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The upper and lower bounds of the band take into account the data scattering σ0 at 0◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The shaded bands with lighter colors are theoretically calculated angular dependence for the tunneling between two pure s-wave superconductors with enhanced coherence in tunneling (γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='01).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Details of the calculation is given in the supplementaxry note IV and in ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' given in the supplementary information (Supplementary note III and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' S6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The OP samples do not suffer from this prob- lem presumably because the out-diffusion is only prominent in the superoxygenated state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Figure 3(c)(d) show the Josephson tunneling characteris- tics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' We normalize the current by the normal state resistance (Rn) for a better comparison among samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' In each figure, the single vertical branch at zero bias reflects the Josephson effect between the two twisted cuprate layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The IJJ do not contribute here because their critical currents are much higher−due to the larger tunneling area and relatively thinner barrier−and are not reached in our measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The vertical bar essentially represents the Josephson coupling strength– IcRn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Notably, we obtain IcRn (44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='9◦) = 4 mV at OP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' This is in sharp contrast to the previous report in the same dop- ing regime, which shows that IcRn (44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='9◦) was as small as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='19 mV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' This difference may indicate that there exists sta- tistical fluctuation among samples because so far only a few samples are reported to be within 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='0±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='1◦ in OP (OP1 and OP2 in our case and one in ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' [13]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Differences in the fabri- cation steps are given in the supplementary material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Next, we show that our results are inconsistent with the d+id or d+is-wave pairing scenario [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Such an emergent pairing can give rise to Josephson tunneling of paired Cooper pairs at the twist angles where pure d-wave pairing demands strong suppression at 45◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The dashed curves in Figure 3(e)(f) indicate the predicted temperature dependence for this co- tunneling process [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' In sharp contrast to this behavior, our experimental results show quite standard behaviors sim- ilar to that prescribed by the Ambegaokar-Baratoff (A-B) for- mula [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' We also comment on the non-monotonic temper- ature dependence at twist angles away from 45◦, which was also predicted to be a manifestation of exotic pairing [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' In experiment, we indeed observe non-monotonic or non- standard temperature dependence (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' S4 and S5) but the non-monotonic behavior even appears at 0◦ [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' S5(a)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' It indicates that the temperature dependence may be influenced by other extrinsic factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' In particular, we speculate that unintentional flux trapping may be the driving mechanism, since suppression of IcRn at low temperatures was observed in the intrinsic Josephson junctions under a small magnetic field [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Interestingly, the trapped fluxes are found to give rise to an asymmetric tunneling in some devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 4, we provide a typical example of such a Josephson diode effect [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Fig- ures 4(a) show the I-V characteristics of an OD junction with θnominal = 45◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The Josephson critical current in the positive axis is obviously larger than the absolute value in the negative axis, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' I+ c > ���I− c ���.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The asymmetry factor η = (I+ c −|I− c |) (I+c +|I−c |) is as high as 26% at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='6 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' This asymmetry is quite stable and the rectification effect over one thousand repetitions is achieved, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 4(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Figure 4(c) displays the histogram of the measured voltages in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 4(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' With an input square wave of current jumping between 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='2 mA and -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='2 mA, the out- put voltage is either -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='18 mV or 0 mV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Figure 4(d) further demonstrates that the asymmetric effect persists over the en- tire superconducting regime up to 50 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Although a 45◦-twist junction is used here, similar behaviors can be found at θ = 0◦ as well (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' S7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' We note that the results in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 4 are ob- tained without applying the magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' However, we ob- tain the peak-dip structure of η as a function of B with its center away from B = 0 T (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' S7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' This observation clearly indicates that there exists a remanent field, which is approxi- mately 1 mT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The driving mechanism for the Josephson diode effect remains unknown at this stage [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Nevertheless, our experiments suggest that a carefully designed magnetic field shield must be applied in order to address the non-standard temperature dependence of Ic due to intrinsic properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 5(a), we provide an overview of our data points as a function of twist angles at both OD and OP levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' In each doping regime, we observe appreciable IcRn in multiple samples around 45◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' These data points apparently fall out- side the expected behavior of a pure d-wave pairing symme- try.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' However, IcRn in OP and OD indeed shows a drop as θ increases from 0◦ to 45◦, if comparing the maximal values 5 obtained at different angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' This decrease can be further ap- preciated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 5(b)(c), where the averaged values at 45±1◦ for OP or 45±2◦ for OD with those at 0◦ are compared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' On the one hand, this angular dependence can be explained by a mixture of isotropic s-wave and anisotropic d-wave com- ponents [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' We show the expected angular behavior for a mixture of 15%/20% s-wave and 85%/80% d-wave as shaded stripes (darker colors), of which the upper and lower bounds are set by the sampling standard deviation at 0◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Such a mix- ture can yield the expected value at 45◦ that is in agreement with our data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' It suggests the existence of a substantial portion of isotropic pairing (15-20%), comparable to that in YBCO (15%) [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' On the other hand, the decreasing trend can be solely attributed to the orbital effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' To further illustrate this point, we consider tunneling between two 100% s-wave superconductors with tunneling coherence that is 100 times higher than that in the s/d mixed situation [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The shaded bands with lighter colors in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 5(b)(c) show the calculated behaviors, which also reproduces the suppressed IcRn at 45◦ observed in experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' In reality, the two scenarios dis- cussed above−s-wave/d-wave mixing and orbital effect−may both participate in giving rise to the angular dependence seen in experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' While we cannot rule out the d-wave pairing scenario for the time being, the estimated 15-20% of s-wave represents at least the lower bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' In summary, we fabricate twisted Josephson junctions at OD and OP doping levels, and demonstrate that they are of un- precedentedly high crystalline quality at the interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Low- temperature transport reveals strong Josephson tunneling at the twist angle of 45◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' The conventional temperature de- pendence of these twisted junctions speaks against the pres- ence of d+id or d+is-wave pairing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Intriguingly, we observe Josephson diode effect in the junctions, setting the tempera- ture for observing such an effect to a record high value of tens of kelvin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' From the angular dependence of the Josephson cou- pling, we conclude that there exists an indispensable isotropic pairing component in the twisted Josephson junctions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' This work is financially supported by the National Nat- ural Science Foundation of China (grants No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 51788104, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 12141402, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 12004041, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 11922409, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 11790311, 5);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Ministry of Science and Technology of China (2017YFA0302902, 2017YFA0304600);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Innovation Program for Quantum Science and Technology (Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' 2021ZD0302600).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' ∗ These authors contributed equally to this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' † jzhu@mail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='tsinghua.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='cn ‡ dingzhang@mail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='tsinghua.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='cn § qkxue@mail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='tsinghua.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content='cn [1] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE2T4oBgHgl3EQfWwfK/content/2301.03838v1.pdf'} +page_content=' Keimer, S.' metadata={'source': 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b/TdAzT4oBgHgl3EQf0v6x/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1023a2f890e0f3d334ed73e3bb52dfde44265f42b2db75c98774c3048eba9d05 +size 2621485 diff --git a/UNE2T4oBgHgl3EQftQjd/content/tmp_files/2301.04069v1.pdf.txt b/UNE2T4oBgHgl3EQftQjd/content/tmp_files/2301.04069v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..409d884b9183b7bfe31bffb2f69beedcff9c775b --- /dev/null +++ b/UNE2T4oBgHgl3EQftQjd/content/tmp_files/2301.04069v1.pdf.txt @@ -0,0 +1,2293 @@ +The chaotic emergence of thermalization in highly +excited string decays +Maurizio Firrotta +aDipartimento di Fisica, Universit`a di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133, +Roma, Italy +bINFN sezione di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy +E-mail: maurizio.firrotta@gmail.com +Abstract: We analyse the most general process of a generic highly excited string that +decays into a less excited, yet generic, highly excited string emitting a tachyon. We provide +a simple and compact analytic description of the decay process which discriminates between +and within the structure of every single microstate of the initial and final highly excited +string. Considering the random nature of the decay process we extract the energy spectrum +of highly excited strings, microstate by microstate, finding a behavior which corresponds +to the greybody emission spectrum. In addition, by exploiting the analytic control of the +decay process, we identify the origin of thermal effects which are triggered by the chaotic +nature of the highly excited string interactions modeled by the microstates structure. +arXiv:2301.04069v1 [hep-th] 10 Jan 2023 + +Contents +1 +Chaos in highly excited string processes +3 +1.1 +Classical string vs quantum string configurations +3 +1.2 +Probing chaotic behavior of quantum strings through their interaction +5 +2 +Thermalization emergence in highly excited string decays +9 +2.1 +Chaos driven thermalization +11 +2.2 +Thermal spectrum: the greybody emission of highly excited strings +13 +3 +Results of random generated spectra +15 +4 +Conclusion and future directions +16 +A Highly excited string decay: HN ⇒ HN′ + T +19 +A.1 Decay amplitude +20 +A.2 Decay rate +22 +A.3 Thermal nature of the decay amplitude +25 +Introduction +The present paper is focused on enlightening the connection between chaos and thermal +effects within the physical systems provided by highly excited string (HES) interactions. +Motivated by the intriguing interplay between chaos, thermal effects and quantum infor- +mation [1]-[5], which are three milestones of black hole (BH) physics, we first used HES as +promising candidates of BH states [6]-[8] and then we computed the energy spectrum of +HES. The main goal was to detect a manifest connection between the chaotic behavior of +HES interactions and the thermalization of their energy spectra which emerges naturally. +In line with past studies on string decays and the produced Hawking radiation [9]-[18], we +used and improved the most general process of an HES that decays into an HES emitting a +tachyon [19][20], providing an analytic description of the decay process which discriminates +between and within the structure of every single microstate of the initial and final HES. +Considering the random nature of the decay process we extracted the spectrum of the HES, +microstate by microstate, finding a behavior which corresponds to the greybody emission +spectrum. In addition, exploiting the analytic control of the decay process, we identified +the origin of thermal effects, finding that they are triggered by the chaotic nature of HES +interactions. +The setup we adopted relies on the recent improvement of the Di Vecchia, Del Giudice +and Fubini (DDF) formalism [21][22], where its spectrum generating algebra was recasted in +a manifestly covariant form [23][24], for both bosonic string and superstring theories. The +– 1 – + +possibility of identify each state of the string spectrum with the associated physical vertex +operator gave rise to a wide range of applications: the realization of the scattering of string +coherent vertex operators1 [19], the non perturbative string footprint in the gravitational +wave (GW) signal produced in the merging phase of BHs collision [25], the non perturbative +spinning corrections to the electromagnetic wave produced in the collision of heavy sized +objects [26], such as BHs and neutron stars NSs, the two body decay of HES [20] and +finally the indications about the chaotic behavior of HES interactions [27][28]. +About the chaotic behavior of HES interactions, quite recently it was proposed a novel +measure of chaos for scattering amplitudes [29], where it was compared the behavior of HES +amplitudes with the chaotic distribution of the zeros of the Riemann zeta function and the +quantum mechanical scattering on a leaky torus, finding a common pattern between them. +The scope of the present paper was to continue the study of the physical applications +connected to the possibility of exploring the interactions of the whole tower of string exci- +tations, or string microstates, proceeding beyond the physics of light string states and also +beyond the first Regge trajectory. +The paper is organized as follows: in section 1 we explained the connection between the +shape of classical string configurations and the structure of quantum string configurations, +in particular we studied the classical string profiles as a function of the number of harmonics +and the respective coefficients and we compared their shape with the degenerate quantum +string partitions of generic mass levels. +We followed the logic that the structure of a +quantum string state can be probed through its interaction, we selected the simplest one +i.e the decay of HES into two tachyons, in order to preserve the HES structure. After a +brief review of the chaotic analysis, developed in [29], we compared the shape of classical +string configurations with the chaotic behavior of the scattering amplitudes relative to the +quantum analog of classical string configurations finding a common pattern. +In section 2 we studied the most general process of a generic HES that decays into a +less excited, yet generic, HES emitting a tachyon in the thermalization regime. Exploiting +the analytic control of the decay process, we identify the origin of thermal effects with +the chaotic structure of the process. Finally we gave a description of how to compute the +emission spectrum of HES. +In section 3 we presented the results of HES spectra, microstate by microstate. In +particular we found that a generic string excitation is characterized by a greybody emission, +while for the extreme case where only excitations of the first Regge trajectory (FRtj) are +considered, the thermal nature is such highly suppressed as to be negligible. +In the appendix 4 we reviewed the computation developed in [20], and we described +the analytical implications of the thermalization regime, or more precisely the regime in +which the ratio between the energy of the emitted state and the mass of the decaying state +is enough small in such a way that the energy loss of the decaying state is smooth. +1A very powerful application of the scattering amplitudes of coherent string states is their nature of +generating amplitudes of any desired string states, obtained by a simple derivative projection over mass +eigenstates. +– 2 – + +1 +Chaos in highly excited string processes +The aim of this section is to review recent results about the chaotic behavior of HES +interactions. +1.1 +Classical string vs quantum string configurations +Classical three dimensional2 bosonic open string profiles with Neumann boundary condi- +tions, in the temporal gauge (X0 = t), are given by [30] +Xj +{an}(σ, τ) = +n∗ +� +n=1 +xj +{n},{an}(σ, τ) +(1.1) +σ ∈ [0, π] and τ ∈ [0, ∞) are the worldsheet variables and Xj(σ, τ) is the map between +the worldsheet and the target space (R3), representing the 3-D string profile at any value +of τ. Classical string configurations can be classified by the set of harmonics {n} and the +respective set of coefficients {aj +n} which are respectively the harmonic label and the relative +weight coefficient of the classical mode xj : +xj +{n},{an}(σ, τ) = aj +n +n cos (nπσ) sin (nπτ) +(1.2) +In figure 1 there are some 3-D string profiles for different choices of the set of harmonics +and coefficients, from which one can observe how the string profile becomes more involved +if the number of harmonics is increasing. +Figure 1. Examples of 3D string profiles for different combinations of harmonics n∗ = 1, 5, 10, 50 +with uniformly distributed random parameters aj +n ∈ (0, 1). +From figure 2 one can observe the dependence of string profiles from the set of coef- +ficients {aj +n}. In the present case it was assumed that coefficients are normalized to the +identity, and they are uniformly distributed in the interval (0, 1). One can observe that the +behavior of string profiles is unchanged also for non normalized integer coefficients. The +features of string profiles are unaffected by different parametrizations of the coefficients aj +n. +At this level a trivial observation is that, if one considers a classical string profile +2In the specific case of classical string, it was chosen j = 1, 2, 3 in order to plot 3D profiles, but in general +j = 1, ..., D − 2. +– 3 – + +Xs +Xi +X2 +1 harmonic +5 harmonics +10 harmonics +50 harmonicsFigure 2. Examples of 3D string profiles for different combinations of harmonics n∗ = 10, 50, 100. +For each value of n∗ there are five choices of string profiles for different choices of uniformly dis- +tributed random parameters aj +n ∈ (0, 1). +Xj +{an}(σ, τ) = xj +{n},{an}(σ, τ) +(1.3) +with the same single generic harmonic n in the three spatial directions j = 1, 2, 3, one +obtains the smoothest profile, which is a straight line, such as the first profile of figure 1. +This is the general picture of how the classical string profiles are modeled by the +harmonic set {n} and the coefficient set {an}. +Now it is helpful to study the comparison between classical and quantum string con- +figuration. In particular, promoting the coefficients aj +n to be creation operators Aj +−n one +has the quantum analog of the string mode, and in addition to the set of harmonics {n}, +one has to include the number of excitation gn of each harmonic so much so that for a +given quantized level N of the string spectrum, one has a set of states spanned by the set +of solutions {gn}, representing all the partitions of the integer N with occupation number +J: +N = +N +� +n=1 +ngn , +J = +N +� +n=1 +gn +(1.4) +The promotion from classical to quantum string is summarized as +x{n},{an}(σ, τ) ⇒ Nn,gnAgn +−n|0⟩ ; +X{an}(σ, τ) ⇒ Π(N) +{gn} = +N +� +n=1 +Nn,gnAgn +−n|0⟩ +(1.5) +where N −1 +n,gn = √ngn gn! is the normalization constant of each mode. In particular due to +its quantum nature, the quantum string configuration for a fixed level N has a large degen- +eration3 which produces the microstate structure, so in order to identify the final quantum +string state one can take the simplest linear combination of microstates introducing the +average over microstates in the second expression of (1.5) +X(σ, τ) ⇒ +� +{gn} +Π(N) +{gn} = +� +{gn} +N +� +n=1 +Nn,gnAgn +−n|0⟩ +(1.6) +3The degeneration of states at large N grows like ∼ e +√ +N +– 4 – + +n* = 10 +n* = 50 +n* = 100Looking at the complicated classical string profiles, parametrized by {n} and {an}, a nat- +ural question is how the quantum string configurations reflect their classical characteristic +shape as a function of {n} and {gn}. +A possible way of testing the features of quantum string profiles as a function of the +microstate structure, is to probe the implications of their shapes through their interactions. +In particular one can choose the simplest string decay amplitude and study the microstate +dependence. +In the next subsection it will be reviewed the analysis of string configurations leading +to a chaotic behavior of their interactions [29]. +1.2 +Probing chaotic behavior of quantum strings through their interaction +Inspired by the systematic of classical string profiles, the logic proposed for the analysis of +quantum string configurations is the following: the main observable is the decay amplitude +provided by a level N string microstate Π(N) +{gn} decaying into two tachyons. +Following +the indications introduced in [skliros] and developed in [DDF Bianchi firrotta], the decay +amplitude AΠ(N) +{gn} for the most general HES was computed, with a remarkably simple +procedure based on coherent state techniques. The informations about the structure of +Π(N) +{gn} are translated into the decay amplitude, and they are manifested through the profile +of the decay amplitude. The choice of looking at tachyons is connected to their simple +vertex operators, in such a way that all the information inside the decay amplitude is +governed by the structure of Π(N) +{gn}. In figure 3 there is a representative picture of the +decay amplitude from which one can see that the decay amplitude profile is only a function +of the angle α. +Now comparing decay profiles of different microstates one can extract +a general behavior associated to choices of {n} and {gn}, as it was pointed out in [Gross +Rosen]. Most of the information of the decay profile can be codified in terms of its extrema, +so it is useful to introduce the logarithmic derivative F{gn}(α) and study its distribution +of zeros. A suitable parameterization of the distribution is intimately connected with the +chaotic behavior of the decay [Cobi Io Dorin B]. Before describing the chaotic analysis in +detail, a very fast presentation of the resulting decay amplitude is discussed. +Figure 3. Picture of the decay amplitude where a representative microstate Π(N) +{gn} decays into two +tachyons T. The only kinematical freedom of the decay amplitude is the emission angle α which +starts from the reference dashed line. +– 5 – + +T(p1) +T(N) +(p) +α +T(p2)The HES state of the level N with polarizations {ζn} and momentum p is described +by +Π(N) +{gn}({ζn}, p) = +N +� +n=1 +(ζn·A−n)gn +√gn! ngn |0⟩ +(1.7) +following the DDF formalism one can write the corresponding BRST vertex operator and +compute the decay amplitude of figure 3 using circular polarizations4: +AΠ(N) +{gn}(α) ≃ +� +ζ·(p1−p2) +�J +N +� +n=1 +�(1−n sin2 α)n−1 +Γ(n) +�gn +(1.8) +all the information about the microstate Π(N) +{gn} is encoded in the dressing factor of the +coupling ζ·(p1−p2) +Π(N) +{gn}−structure ⇒ +N +� +n=1 +�(1−n sin2 α)n−1 +Γ(n) +�gn +(1.9) +Using the properties of the Pochhammer factor and the explicit parametrization of the +polarizations the decay amplitude can be written as +AΠ(N) +{gn}(α) ≃ +N +� +n=1 +�sin α +Γ(n) sin +� +nπ cos2 α/2 +� +Γ +� +n cos2 α/2 +� +Γ +� +n sin2 α/2 +��gn +(1.10) +Finally the logarithmic derivative of the decay amplitude +F{gn}(α) = d +dα log AΠ(N) +{gn}(α) +(1.11) +has the following form +F{gn}(α) =J cot α − πsin α +2 +N +� +n=1 +ngn cot +� +nπ cos2 α +2 +� +−sin α +2 +N +� +n=1 +ngn +� +ψ +� +n cos2 α +2 +� +−ψ +� +n sin2 α +2 +� � +. +(1.12) +This is the final observable which will be subjected to the analysis described below. +Chaotic analysis: setup +Random Matrix Theory (RMT) provides a very powerful tool to make the bridge between +quantum chaos and universal statistical properties [31][32]. In particular a quantitative +connection between chaos and probability distributions was conjectured in [33] and sub- +sequently the link between chaos and statistical properties was widely studied in many +contexts such as quantum chromodynamics (QCD)[34], nuclear physics [35], black holes +[36] and condensed matter [37]. In what follows it will be laid out the identification strat- +egy of the target distribution used as a discriminant of the chaotic behavior. +4The general amplitude is made of contributions both linear and bilinear in ζn [19]. +The bilinear +contribution is proportional to the square of the linear contribution, so up to an irrelevant polynomial the +functional dependence on the microstate structure is preserved by the choice ζ(a) +n ·ζ(b) +m = 0. +– 6 – + +• Starting from the Hermite β-ensemble of N × N random matrices, given the set +{α} = (α1, ...., αN) of matrix eigenvalues, the associated joint probability distribution +is given by +Pβ({α}) = e− �N +j=1 +α2 +j +2 +ZN,β +� +ℓ 0 [43] and also for large asymptotic values of β +[44]. For β = 1, 2, 4 one has the standard GOE, GUE and GSE respectively, which +are the gaussian orthogonal/unitary/symplectic ensembles. +Chaotic analysis: results +Following the discussion related to figure 1 one can expect that the microstate with the +maximal number of harmonics will produce a less smooth decay amplitude. In particular +one can measure the chaotic behavior of the decay profile computing the distribution of the +index (1.16) for the zeros of (1.12), which is the study of how the unbiased r-index indicator +for the extrema of the amplitude is distributed in agreement with the target chaotic class +of β-distributions (1.17). From the results in figure 4, relative to microstates of N = 100, +one can observe the profile of the logarithmic derivative F{gn}(α) and the respective joint +probability distribution of the microstate with the maximal number of harmonics (which +are the first two plots respectively). The five small plots represent how the measured joint +– 7 – + +probability distributions deviate from the target distribution (1.17), respect the variation +of the number of harmonics. Quite similar to the case of classical string profiles where +the number of harmonics triggers the shape of the profiles, the chaotic behavior of the +decay profile is triggered by the number of harmonics. An additional check of this kind of +harmonic hierarchy is provided in figure 5, where there is the logarithmic derivative of the +decay amplitude and the joint probability distribution of the single harmonic microstate +of N = 100. In particular one can observe that the distribution totally deviates from the +chaotic jGUE, which is a hint about the connection between classical single harmonic string +profiles (straight lines) and the absence of chaos in the decay amplitude of single harmonic +microstates. +Figure 4. Microstates of N = 100. From left to right the profile of the logarithmic derivative of the +decay amplitude and the joint probability distribution both relative to the microstate with maximal +number of harmonics. +The dashed line is the joint probability distribution with β = 2, which +represents the joint GUE distribution (jGUE). Below there are five examples of joint probability +distributions for microstates with less number of harmonics. +Figure 5. The logarithmic derivative of the decay amplitude and the joint probability distribution +both relative to the microstate of N = 100 with only one harmonic. The dashed line is the jGUE. +– 8 – + +F(α) +jPDF +600 +400 +0.6 +jGUE +200 +1 +0.4 +Microstate of +0.5 +N=100 with +-200 +maximal number +0.2 +of harmonics +-400 +-600 +1 +2 +3 +4 +5 +6 +7 +jPDF +jPDF +jPDF +jPDF +jPDF +0.7 +0.7 +0.7 +0.7 +0.7 +0.6 +0.6 +0.6 +0.6 +0.6 +0.5 +0.5 +0.5 +0.5 +0.4 +0.4 +0.4 +0.3 +0.3 +0.2 +0.2 +0.1 +0.1 +0.1 +0.1 +rn +rn +rn +2 +rn +3 +2 +2 +3 +2 +3 +rn +3 +4 +4F(α) +jPDF +600 +25 +400 +20 +200 +15 +α +10 +-200 +-400 +5 +-600 +1 +2 +3 +5 +6Figure 6. Comparison between classical string profiles and decay amplitudes +2 +Thermalization emergence in highly excited string decays +In the previous section it was presented a systematic study of how the microstate structure +emerges through the profile of its decay process. +In particular it was shown how the +chaotic behavior of the decay process is triggered by the microstate structure. The aim of +this section is to describe how the chaotic behavior is related to the thermalization process +of the most general HES decay (fig.7). +Figure 7. Picture of the decay amplitude where a representative microstate Π(N) +{gn} decays into +Π(N ′) +{g′ +n′} emitting a tachyon T. +Following [20] and the appendix A the decay rate of the present process, in a d- +– 9 – + +Classical string profile +Quantum decay profile +F(α) +600 +400 +200 +NO chaos +200 +400 +600 +F(α) +3000 +2000 +1000 +chaos +1000 +-2000 +3000T(k) +(p)dimensional phase space, is given by the following expression +ΓΠN +{gn},ΠN′ +{gn′ } = +Ωs Ed−3 +k +16(N−1)(2π)d−2 +���AΠN +{gn},ΠN′ +{gn′ } +��� +2 +(2.1) +This is the decay rate of the single microstate of the level N decaying into a single microstate +of the level N′ through the emission of a tachyon of energy Ek, where the solid angle +Ωs = 2π(d−1)2/Γ((d−1)/2) is introduced. +The non trivial dependence of the decay rate is due to the square of the absolute +value of the amplitude, which is the main quantity the will be analyzed in what follows. +In particular in the region where the ratio between the energy of the emitted state and +the mass of the decaying state is enough small, in such a way that the energy loss of the +decaying state is smooth, the absolute value square of the amplitude assumes the following +form +���AΠN +{gn},ΠN′ +{gn′ } +��� +2 += � +N 2 +{gn} � +N ′2 +{g′ +n′} e−CN({gn},{g′ +n′}) Ek +TH −2µN({gn},{g′ +n′};Ek/TH) +(2.2) +where there is a weight factor CN that depends on the level N of the decaying state, and +also depends on the microstates geometry through the relation +CN({gn}, {g′ +n′}) = +2 +√ +N +� N +� +n=1 +gnn log n − +N′ +� +n′=1 +g′ +n′n′ log n′ +� +(2.3) +the additional function is given by +µN +� +{gn}, {g′ +n′}; Ek +TH +� += +N +� +n=1 +gn log Γ +� +1− n +√ +N +Ek +TH +� ++ +N′ +� +n′=1 +g′ +n′ log Γ +� +1+ n′ +√ +N +Ek +TH +� +. (2.4) +and finally the dimensional temperature TH = 1/ℓs is the Hagedorn temperature which is +the inverse of the string length ℓs = +√ +α′. +The thermal nature of the characteristic expression (2.2) is intimately related to the +chaotic behavior of the decay, in fact the non trivial dependence on the microstates is +directly related to chaos (sec.1) and it will play also a crucial role in the thermalization of +the decay, as will be explained in the next part 2.1 of the present section. +When it is considered the decay rate (see fig.8) of a state of the level N made of many +microstates +|BH⟩N = +� +{gn} +Π(N) +{gn} +(2.5) +which can be interpreted as a black hole state, the final decay rate results to be the sum +over all the possible microstate configurations of the decay rates +Γ +� +|BH⟩N ⇒ |BH⟩N′ + Ek +� += +Ωs Ed−3 +k +16(N−1)(2π)d−2 +� +{gn},{g′ +n′} +���AΠN +{gn},ΠN′ +{gn′ } +��� +2 +. +(2.6) +This is a very rich observable that is characterized by the highly non trivial functional +dependence of the microstates. +In the last part 2.2 of the present section, it will be +described the behavior of such observable and the derivation of the non trivial energy +spectrum leading to the grey-body radiation of highly excited string states. +– 10 – + +Figure 8. Qualitative picture of the decay rate |BH⟩N ⇒ |BH⟩N ′ + Ek. The microstates of the +decaying state are represented by colorful small strings, each color is associated to the possible +microstate decay. The red region represents the random superposition of all the possible decays +which is the mechanism through which the thermalization process is emerged. +2.1 +Chaos driven thermalization +In section 1 it was analyzed the chaotic behavior of a string microstate decaying into two +tachyons, where it was shown the connection between the microstate structure and the +chaotic behavior of the decay. The sensitivity of the decay to the microstate structure was +essentially encoded in the dressing factor (1.9). Now considering the direct extension of +the decay in (fig.3), which is the one of (fig.7), one has the generalization of (1.9) to the +case of two microstate structures: one for the decaying microstate ΠN +{gn} and the other for +the final microstate ΠN′ +{g′ +n′}. Using the general setup described in appendix A one finds the +decay rate represented as follows5 +���AΠN +{gn},ΠN′ +{gn′ } +��� +2 +≃ +N +� +n=1 +� +� +� +� +1−n(1−Ek/ +√ +2N) +� +n−1 +Γ(n) +� +� +� +2gn +N′ +� +n′=1 +� +� +� +� +1−n′(1+Ek/ +√ +2N) +� +n′−1 +Γ(n′) +� +� +� +2g′ +n′ +(2.7) +comparing this expression with (1.9) one can see the systematic generalization of the decay +rate due to the presence of an additional microstate. Following the expansion (A.51) and +the rest of the appendix, one recovers (2.2). This is the systematics of how the chaotic +5In the expression it was used α′ = 1/2 that means TH = +√ +2. +– 11 – + +I. +I(gn) +Microstates +Microstates +Ek +Thermalization +(BH)N +[BH)Nfactors make the decay rate thermal, giving a precise identification between chaos and the +emergence of thermalization. +Following the same logic of (fig.6), where a comparison between classical strings and +decay amplitudes was done, one can complete the scenario describing the mechanism that +originates the thermalization of the precess. +In fact one can analyze two extreme cases: the first one is to consider microstates of +the first regge trajectory. Classically their profile is just a straight line (fig.6), because of +the fact that they are single harmonic states, so they do not produce chaos. The associated +thermalization is given by the expression (2.7) with n = 1, g1 = N and n′ = 1, g′ +1 = N′, +which trivializes to the unity, so the decay is not thermal. +The second extreme case, which is less trivial, is to consider still single harmonic states +but with the maximal harmonic excited, n = N, gN = 1 and n′ = N′, g′ +N′ = 1. Classically +they are a straight lines and do not produce chaos (fig.5). From (2.7) and (2.2) one can +finds +���AΠN +{gN =1},ΠN′ +{gN′ =1} +��� +2 +≃ e−2 log( N +N′ ) +√ +NEk/TH +� +� +sin +� +π +√ +NEk/TH +� +π +√ +NEk/TH +� +� +2 +(2.8) +this behavior, at large N, is very suppressed even if N′ ∼ N, and it shows how the thermal +behavior of the decay is subdominant in the case of states with only the maximal harmonic +excited. +Beyond the two extremal cases discussed, one can have a more qualitative picture of +the microstates functional dependence of the decay looking at the explicit distributions in +(fig.9) and (fig.10). +The fluctuations of the decay reflect the connection between the geometry of mi- +crostates, which is clear in the classical picture of string profiles, and the associated chaos +which is the trigger of the thermal behavior. +Figure 9. Microstates population of the decay rate in logarithmic scale for 100 random partitions +{gn} of N = 100 and 100 random partitions {g′ +n′} of N ′ = 99. The red points are the values of the +decay rate. +– 12 – + +100 +-200 +-400 +-600 +(gn]) +100 +partitions +50 +(gn) +0 +partitionsFigure 10. Microstates population of the decay rate in logarithmic scale for 500 random partitions +{gn} of N = 100 and 500 random partitions {g′ +n′} of N ′ = 99. The red points are the values of the +decay rate. +2.2 +Thermal spectrum: the greybody emission of highly excited strings +In the previous part it was described the connection between chaos and thermal behavior of +the decay rate, where the intrinsic microscopical structure of microstates was fundamental +for the origin of such connection. Here the goal will be the analysis of the energy spectrum +radiated from HES states. The first thing to note is that the decay rate (2.2) is not a +function of the emitted energy Ek, the kinematics of the two body decay fixes the energy +Ek as a function of the masses of the present states +Ek = M2 +N − M2 +N′ + M2 +T +2MN += N − N′ − 1 +√ +2N − 2 +(2.9) +In order to extract the energy spectrum of an HES state, one has to explore the energy +range of the decay rate point by point, producing a discrete energy trajectory of the decay +process. Since the target observable is the radiation of the HES state of generic level N, +one can reproduce the energy trajectory varying the mass MN′ = 2N′ − 2 of the final +state. The energy region of interest is identified by the range in which the ratio between +the energy of the emitted state Ek and the mass of the decaying state MN = 2N − 2 is +enough small in such a way that the energy loss of the decaying state is smooth, which +is the situation where a thermal spectrum is expected [Amati-Russo][Hawking radiation]. +Given N and N′, the decay rate of a state made of microstates is given in (2.6), and even +if the energy Ek is fixed there is a non trivial microstates distribution that mediates the +decay rate (fig.10). Therefore in order to reproduce the energy spectrum of a given HES +state with +� +Π(N) +{gn} +� +microstates, one can generate an energy trajectory of random decays +for each microstate Π(N) +{gn} of the level N that can decay into a random microstate Π(N′) +{g′ +n′} of +the whole set +� +Π(N′) +{g′ +n′} +� +of the level N′. Finally the spectrum is obtained averaging over the +energy trajectories (fig.11). In general each microstate of the level N can decay into each +microstate of the level N′, and this is the reason why one has to mimic the randomness +– 13 – + +0 +200 +IN +400 +-200 +-400 +-600 +(gn'] +partitions +400 +200 +(gn] +partitionsof the decay process in order to describe the intrinsic nature of a degenerate sized object +such as the HES. +Figure 11. Picture of the random microstates energy trajectories P({Ek}). +The general behavior of the energy spectrum turns out to be described by the grey +body radiation +Σgrey +N +(Ek/Teff) = ⟨ΓN⇒N′⟩P({Ek}) = σgrey +N +(Ek/Teff) +e +Ek +Teff − 1 +(2.10) +with an effective temperature which depends on the decaying state through +Teff = TH/ +√ +N +(2.11) +and with the grey-body factor which is sensitive to the nature of the microstates of N and +N′ and also depends on the randomness of the decay process +σgrey +N +(Ek/Teff) = CN({gn}.{g′ +n′})ΩsEd−3 +k +16(N−1)(2π)d−2 +� +e +Ek +Teff − 1 +� � +Ek +Teff +�rN({gn},{g′ +n′}) +e +νN({gn},{g′ +n′}) Ek +Teff − 1 +(2.12) +The randomness of the decay process is incorporated in the coefficients +CN({gn}, {g′ +n′}) , +rN({gn}, {g′ +n′}) , +νN({gn}, {g′ +n′}) +(2.13) +that also reflect the intrinsic dependence on the chosen microstates that determine the +decaying state and the final state. +– 14 – + +(gh] +(g") +1g" +(g"] +,((E)) +Rand(IIN'=N-4) +(gn +(gh) +gr((Ek)) +EkIn the next section there will be the spectrum analysis of different states, in particular +a state with definite mass and occupation number (N, J) decaying into a generic state +of the level N′, a state (N, J) decaying into a state (N′, J′) and finally a generic state +N decaying into a state N′. For simplicity it will be considered the gray body spectrum +(2.10) without the phase space factor, which is equal for each case, therefore without loss +of generality one can redefine the final observable as +γgrey +N +(Ek/Teff) = CN({gn}.{g′ +n′}) +� +Ek +Teff +�rN({gn},{g′ +n′}) +e +νN({gn},{g′ +n′}) Ek +Teff − 1 +(2.14) +3 +Results of random generated spectra +Let’s start by considering a simple example in which only a single microstate can decay, in +particular let’s consider the specific microstate Π(100) +π1(gn) of the level N = 100 given by +π1(gn) = {g1 = 1, g2 = 1, g5 = 2, g7 = 1, g8 = 1, g9 = 1, g10 = 1, g25 = 1, g28 = 1} +(3.1) +The first energy point of the spectrum is given by the decay of Π(100) +π1(gn) into a generic +microstate of the level N′ = N − 1 and corresponds to Ek = 0. The fact that Ek = 0 is +constrained by the kinematics of the emitted tachyonic particle which make the first point +of the spectrum to be trivial. +The first non trivial energy point of the spectrum is given by the decay of Π(100) +π1(gn) into +a generic microstate of the level N′=N−2, and the consecutive points are obtained from +N′=N−3, N′=N−4 and so on. Since the HES of the level N′ is generically composed +by many degenerate microstates, one can introduce the intrinsic random nature of the +process taking the average over different sets of random microstates for each energy point +of the spectrum. In order to make clear the relation between chaos and thermalization +Figure 12. Thermal spectrum of the representative microstate Π(100) +π1(gn) computed for two different +random sample of microstates of N ′. +one can adopt the same logic of (fig.4), in particular one can compare the spectrum of the +– 15 – + +grey +grey +YN +YN +8. × 10-9 +8. × 10-9 +6. × 10-9 +6. × 10-9 +-6.5 +8.4 × 10-9 +2.3 × 10-9 +e2.38 x _ 1 +e1.7x_ 1 +: 4.×10-9 +4. × 10-9 +1000randompartitions +10000 random partitions +2. × 10-9 +2. × 10-9 +2 +4 +6 +8 +10 +12 +2 +10 +12 +14 +x = +VNE +x = VNEkmicrostate with the maximal number of harmonics and the extreme case of the first Regge +trajectory (fig.13). As expected the spectrum of a state of the FRtj is not thermal. +Figure 13. Spectra of microstates of N = 100. Comparison between the spectrum of the first Regge +trajectory (blue points) and the spectrum of the state with the maximal number of harmonics (red +points). The black dashed line represents the fitted behavior of the red spectrum. +A complementary picture of the thermal spectrum of string microstates is given in +fig.14, where many spectra are presented, classified by different microstates and values of +the occupation number J. The specific parameters of (2.14) are reported in Tab.1. +4 +Conclusion and future directions +In section 1 it was studied the interplay between classical string configurations and quan- +tum string configurations, where the latter are essentially the microstates of the mass +degeneracy of the HES. We have observed how the chaotic nature of HES interactions +has a common pattern with the shape of classical string profiles, which is provided by +the number of harmonics that characterizes the microstate. We have presented explicit +results for a representative HES of the mass level N = 100, but the same systematics +holds for different mass levels. From the point of view of the analysis of the chaotic infor- +mation present in HES interactions, one can quantitatively improve the measure of chaos +with additional parametrization of the information content based on modern techniques of +quantum information theory [45]-[50] +In section 2 we have analyzed how the thermal nature of the decay amplitude is in- +timately related to its chaotic nature, in particular we have observed that the chaotic +analytical structure, which appear as a non trivial dressing factor, originates a Boltzmann +– 16 – + +Partition with maximal +Partition of first Regge +number of harmonics +trajectory +grey +YN +4. × 10-9 +10-10x7 +FIT +3.× 10-9 +e1.5x- 1 +2.× 10-9 +10000 random partitions +1. × 10-9 +/NE +XFigure 14. Some examples of thermal spectra as a function of the occupation number J. +factor which encodes the thermal information of the decay process. Exploiting the exact +analytical result of the decay process of a generic HES that decays into a less excited, yet +generic HES, through the emission of scalar particle, such as the tachyon, we have com- +– 17 – + +J = 10 +10000 random partitions +grey +.grey +109. +109 +grey +YN +YN +109 +YN +1.0 +0.5 +INE +x = VNEkJ = 20 +10000 random partitions +101 +grey +grey +grey +N +1.5 +30 +25 +1.0 +20 +15 +0.5 +10 +10 +/NEJ = 30 +10000 random partitions +grey +.grey +1015 +YN +.grey +1015。 +YN +3.5 +3.5 +3.0 E +0.04 +3.0 +2.5 E +0.03 +2.5 +2.0 E +2.0 +1.5 E +0.02 +1.5 +1.0 E +1.0 +0.01 +0.5 +0.5 +10 +12 +14 +6 +8 +10 +12 +10 +12 +VNEJ = 40 +10000 random partitions +.grey +1022, +.grey +grey +YN +1022 +YN +0.6 +0.5 +0.6 +0.4 +0.4 +0.2 +0.2 +0.1 +10 +12 +14 +10 +12 +10 +12 +VNE +NHJ +Microstate +CN +rN +νN +{g2=3, g12=2, g3=g10=g13=g20=g24=1} +1.49 × 10−9 +4.38 +1.64 +10 +{g2=g3=g4=g5=g6=g13=g15=g16=g17=g19=1} +4.90 × 10−9 +4.70 +1.60 +{g13=2, g1=g2=g4=g6=g7=g12=g19=g23=1} +6.23 × 10−9 +3.53 +1.33 +{g2=6, g3=3, g5=g9=2, g1=g4=g6=g7=g8=g12=g13=1} +1.27 × 10−14 +9.84 +1.74 +20 +{g2=8, g7=2, g1=4, g3=g4=g11=g12=g16=g20=1} +2.08 × 10−14 +11.30 +2.64 +{g1=g2=3, g3=4, g4=3, g8=2, g5=g6=g7=g12=g21} +28.9 × 10−14 +9.52 +2.01 +{g3=g4=g6=3, g1=8, g2=6, g5=5, g7=g9=1} +1.00 × 10−23 +17.02 +1.97 +30 +{g1=8, g2=11, g3=g6=3, g8=2, g4=g5=g18=1} +7.51 × 10−24 +17.18 +2.56 +{g1=11, g2=7, g3=3, g4=g7=2, g5=g6=g8=g11=g14=1} +9.74 × 10−22 +15.63 +2.18 +{g1=15, g2=9, g3=7, g4=4, g5=3, g6=g9=1} +7.44 × 10−33 +18.35 +1.74 +40 +{g1=7, g2=10, g3=g4=4, g6=3, g5=g12=1} +6.22 × 10−32 +16.75 +1.78 +{g1=17, g2=9, g3=7, g6=3, g7=2, g4=g8=1} +6.27 × 10−32 +16.75 +1.78 +Table 1. Table of specific microstates and parameters of (2.14) relative to the spectra of fig.14. +puted the energy spectrum of HES. Starting from a definite microstate of the level N, we +computed the average over random microstates of the level N′, for many different values of +N′. In particular in section 3 we have presented numerical results of the extracted spectra +for many different microstates of the representative level N = 100, but the same holds for +higher levels. Lower levels, N < 100, have less accessible energy points of interest. We +observed a non trivial dependence of the spectra on the occupation number J that we want +to quantitatively address in future works, together with a fully quantitative computation of +the spectrum of degenerate HES, which means the computation of the linear combination +of the same spectra we computed, but for all the possible microstate of the level N. +The chaotic nature of the decay process together with the non trivial dependence of +final microstates gave rise to a greybody emission spectrum with an effective temperature +Teff = TH/ +√ +N, which is different from the temperature of the string/BH transition [7]. +In fact we recovered the characteristic behavior of the Hawking temperature which is +expected to be proportional to the inverse of the mass of the decaying state. A possible +interpretation of such result can be connected to an enhancement of the effective string +Schwarzschild radius, due to the random walk nature of HES interactions modeled by the +explicit introduction of the microstates dependence. The chaotic nature of HES interactions +[27]-[29], and also the associated thermal nature suggest a non trivial spatial distribution +of HES, which can be probed in a scattering experiment similar to the analysis in [52]. +It is well known that an HES can be described as random walk of interactions [53]-[58], +and than one can measure the precise microstates structure of the spatial distribution of +HES studying the effective horizon, for example, probed in HES Compton-like scattering +processes. +Implementing random surface techniques [59]-[63] to the HES form factors +one can obtain a complementary picture of the HES nature where chaotic and thermal +effects can be matched with the effective HES horizon governed by the superposition of +microstates. We leave this investigation for future works. +– 18 – + +Alternatively quite recently it was proposed a technique to resolve the spatial distri- +bution of strings [64] and also a connected chaotic analysis of the HES Compton scattering +[65], based on the principle of transient chaos. +The understanding of the intrinsic structure of HES along with a complete picture of +HES interactions can be very useful in studying deep microscopical connections between +thermalization and chaos. The statistical non trivial nature of HES provides a very rich +physical system which still deserves to be further explored. +Acknowledgements +I would like to thank M. Bianchi, G. Rossi, J. Sonnenschein, D. Weissman, V. Rosenhaus, +D. Gross, B. Sundborg, A. Tseytlin, G. Di Russo, A. Guerrieri and V. Niarchos for valuable +discussions and comments. I would like also to thank The Graduate Center, CUNY for the +hospitality during the completion of the manuscript. +A +Highly excited string decay: HN ⇒ HN′ + T +The present appendix concerns a fast review and new insights about the decay process +computation based on [20]. In particular it will be presented the analytical setup with the +main steps of the computation and also it will be discussed the behavior of the decay rate +in the thermalization region, which is reached when the ratio between the energy of the +emitted state and the mass of the decaying state is enough small in such a way that the +energy loss of the decaying state is smooth. Following the picture in (fig.15) the kinematics +of the process is parametrized as follows +p = +√ +2N − 2(1,⃗0) , +p′ = −(E′, ω sin θ, ω cos θ,⃗0) , +k = (−Ek, ω sin θ, ω cos θ,⃗0) +(A.1) +q = −(1, 0, 1,⃗0) +√ +2N − 2 , +λ = (0, 1, 0, ⃗Λ) +� +1 + |⃗Λ|2 +; +q′ = − (1, 0, 1,⃗0) +ω cos θ − E′ , +λ′ = (0, 1, 0, ⃗Λ′) +� +1 + |⃗Λ′|2 +(A.2) +where the momenta ˜p and ˜p′ of (fig.15) are tachyonic DDF reference momenta, while +p = ˜p − � +n ngn q and p′ = ˜p′ − � +n′ n′g′ +n′ q′ are the total momenta of the microstates +Π(N) +{gn} and Π(N′) +{g′ +n′}. The nice feature of the DDF formalism relies in the direct identification +of the final BRST vertex operator corresponding to the microstate, where its structure is +modeled by the number of DDF photon insertions with polarizations λn, λ′ +n and momenta +q and q′. The photon insertions are in exact correspondence with each harmonic and every +excitation number, exactly reproducing the action of creation operators. +– 19 – + +Figure 15. Picture of the decay amplitude where a representative microstate Π(N) +{gn} decays into +Π(N ′) +{g′ +n′} emitting a tachyon T. The DDF structure of the microstates is also depicted below the +decay process. +A.1 +Decay amplitude +Let’s start by introducing the generating amplitude of all the possible decay processes of +HN ⇒ HN′ + T discriminated by all the possible microstate Π(N) +{gn} and Π(N′) +{gn′} originated +from the partition of integers N = � +n ngn and N′ = � +n′ n′gn′ +Agen = exp +� +gn +� +n; an=1 +J(an) +n +·Vn + J +′(an) +n +·V ′ +n+ +gn,gm +� +n,m; an,bm +J(an) +n +·J(bm) +m +Wm,n + J′(an) +n +·J′(bm) +m +W ′ +m,n + J(an) +n +·J′(bm) +m +Mm,n +� +(A.3) +where all the interaction terms are classified as follows +Vµ +n = p′µVn = p′µ (−)n+1 +Γ(n) (1 + nq·p′)n−1 , +V′µ = pµV ′ +n = +pµ +Γ(n)(1 + nq′·p)n−1 +(A.4) +Wn,m = +n m +n + m(1 + q·p′) q·p′ Vn Vm , +W ′ +n,m = +n m +n + m(1 + q′·p) q′·p V ′ +n V ′ +m +(A.5) +Mn,m = −nm(1 + q·p′) +m + nq·p′ VnV ′ +m +(A.6) +Any particular decay amplitude can be obtained by operating with derivative combinations +representing the projection on the single amplitude with the desired states identified by +– 20 – + +T(k) +T +T(A +DDF +DDF +State +-p +p +0=D +n +n'the partition set {gn} and {gn′} as +AΠN +{gn},ΠN′ +{gn′ } = +� +n +gn +� +an=1 +ζ(an) +n +· +d +dJ(an) +n +� +n′ +gn′ +� +an′=1 +ζ′(an′) +n′ +· +d +dJ′(an′) +n′ +Agen +����� +J=J′=0 +(A.7) +where all the polarizations ζ(an) +n ,µ = λ(an) +n ,µ − λ(an) +n +·pqµ and ζ′(an′) +n′ ,µ = λ′(an′) +n′ ,µ − λ′(an′) +n′ +·p′q′ +µ are +independent. +By considering a kinematical setup where the decaying string is at rest [MF VR], one +can compute the relevant scalar product q·p′ that encodes the partition dependence of the +interacting states. In particular +E′ = MN − Ek , +ω = +� +E2 +k − M2 +T , +Ek = N − N′ − 1 +√ +2N − 2 +(A.8) +and using the kinematics one finds +q·p′ = +1 +q′·p = −E′ − ω cos θ +MN += −1 + Ek +MN ++ +√ +2 +MN +� +1 + E2 +k +2 cos θ +(A.9) +Without loss of generality one can chose θ = π/2, in fact the final observable will be the +decay rate, so when the modulus square of the amplitude is considered, the exact spherical +symmetry is restored. +It means that one can freely fix the value of θ without loss of +generality. With this choice one has +q·p′ = −1 + Ek +MN +(A.10) +In this framework one can easily analyze the non trivial contributions in (A.4), (A.5) and +(A.6): +Vn = (−)n+1 (1 + nq·p′)n−1 +Γ(n) += +(−)n+1Γ +� +n Ek +MN +� +Γ(n)Γ +� +1 − n(1 − Ek +MN ) +� +(A.11) +this is the oscillating function that generates chaos, in fact it can be written as +Vn = +1 +π Γ(n)Γ +� +n Ek +MN +� +Γ +� +n − n Ek +MN +� +sin +� +nπ Ek +MN +� +(A.12) +The other term to analyze is +Wn,m = +n m +n + m(1 + q·p′) q·p′ Vn Vm = +n m +n + m +Ek +MN +� Ek +MN +− 1 +� +Vn Vm +(A.13) +and also there is +V ′ +n = (1 + nq′·p)n−1 +Γ(n) += +Γ +� +−n Ek +MN +� +Γ(n)Γ +� +1 − n(1 + Ek +MN ) +� +(A.14) +where both numerator and denominator are oscillating +V ′ +n = +Γ +� +n + n Ek +MN +� +Γ(n)Γ +� +1 + n Ek +MN +� +sin +� +nπ + nπ Ek +MN +� +sin +� +nπ Ek +MN +� += (−)n +Γ +� +n + n Ek +MN +� +Γ(n)Γ +� +1 + n Ek +MN +� +(A.15) +– 21 – + +then there is +W ′ +n,m = +n m +n + m(1 + q′·p) q′·p V ′ +n V ′ +m = +n m +n + m +Ek +MN +� Ek +MN ++ 1 +� +V ′ +n V ′ +m +(A.16) +finally the mixed term +Mn,m = −nm(1 + q·p′) +m + nq·p′ VnV ′ +m = − +nm Ek +MN +m − n + n Ek +MN +VnV ′ +m +(A.17) +To sum up one has the following structures +Vµ +n = p′µVn(Ek) , +V′µ +n = pµV ′ +n(Ek) , +Mn,m = µn,m(Ek)Vn(Ek)V ′ +m(Ek) +(A.18) +Wn,m = wn,m(Ek)Vn(Ek)Vm(Ek) , +W ′ +n,m = w′ +n,m(Ek)V ′ +n(Ek)V ′ +m(Ek) +(A.19) +where +µn,m(Ek) = − +nm Ek +MN +m − n + n Ek +MN +, +wn,m(Ek) = +n m +n + m +Ek +MN +� Ek +MN +− 1 +� +(A.20) +w′ +n,m(Ek) = +n m +n + m +Ek +MN +� Ek +MN ++ 1 +� +(A.21) +Finally the general decay amplitude can be written as +AΠN +{gn},ΠN′ +{gn′ } = PΠN,ΠN′ +� +ζ(a) +n +, ζ +′(a′) +n′ +, p , p′ , wn,m , w′ +n′,m′ , µn,n′ +� � +n +� +Vn +�gn � +n′ +� +V ′ +n′ +�gn′ +(A.22) +where PΠN,ΠN′ is a polynomial that depends on the partition of N and N′ and it can be +obtained by the generating function +Pgen = exp +� +gn +� +n; an=1 +J(an) +n +·p′ + +gn +� +n; an=1 +J +′(an) +n +·p + +gn,gm +� +n,m; an,bm +J(an) +n +·J′(bm) +m +µm,n +gn,gm +� +n,m; an,bm +J(an) +n +·J(bm) +m +wm,n + +gn,gm +� +n,m; an,bm +J′(an) +n +·J′(bm) +m +w′ +m,n +� +(A.23) +the important thing to note is that the oscillating terms Vn and V ′ +n are factorized from the +polynomial. They are the same factors that produce chaos and that contain most of the +information about the microstate dependence. +A.2 +Decay rate +The general structure of the absolute value square of the amplitude is given by +���AΠN +{gn},ΠN′ +{gn′ } +��� +2 += +���PΠN,ΠN′ +� +ζn , ζ′ +n′ , p , p′ , wn,m , w′ +n′,m′ , µn,n′� ��� +2 � +n +� +V 2 +n +�gn � +n′ +� +V ′ +n′2�gn′ +(A.24) +– 22 – + +where the polynomial is generated by +PΠN,ΠN′ = +� +n +gn +� +an=1 +ζ(an) +n +· +d +dJ(an) +n +� +n′ +gn′ +� +an′=1 +ζ′(an′) +n′ +· +d +dJ′(an′) +n′ +Pgen +����� +J=J′=0 +(A.25) +Taking the absolute value square and using the completeness relations +� +pol +ζ(a)µ +n +ζ∗(a)µ +n += L(a)µν , +� +pol +ζ′(a)µ +n +ζ′∗(a)µ +n += L′(a)µν +(A.26) +where the superscript (a) refers to different independent polarizations, with the explicit +completeness structures +L(a)µν = ηµν − 2p(µqµ) + p2qµqν , +L′(a)µν = ηµν − 2p′(µq′µ) + p′2q′µq′ν +(A.27) +one can study the relevant contributions of the polynomial, in particular the first one yields +p′·L·p′ = p′2 − 2p·p′ q·p′ + p2(q·p′)2 , +with q·p′ = −1 + Ek +MN +(A.28) +that can be written as +p′·L·p′ = (p + p′)2 − 2p·p′ Ek +MN +− 2p2 Ek +MN ++ O(E2 +k) +(A.29) +using p·p′ = MNE′ = M2 +N − MNEk, p2 = −M2 +N and (p + p′)2 = k2 one has +p′·L·p′ = k2 − 2MNEk + 2E2 +k + 2MNEk = ω2 + O(E2 +k) ≃ −M2 +T = 2 +(A.30) +The second contribution is given by +p·L′·p = p2 − 2p·p′q′·p + p′2(q′·p)2 , +with q′·p = −1 − Ek +MN +(A.31) +which yields +p·L′·p = (p + p′)2 + 2p·p′ Ek +MN ++ 2p′2 Ek +MN +(A.32) +still using p·p′ = MNE′ = M2 +N − MNEk, p′2 = −M2 +N′ and (p + p′)2 = k2 one has +p·L′·p = k2 + 2MNEk − 2E2 +k − M2 +N′ +M2 +N +2MNEk +(A.33) +and finally noting that +M2 +N′ +M2 +N += 1 − Ek +MN ++ O(1/M 2 +N) +(A.34) +the expression becomes +p·L′·p = k2 = 2 +(A.35) +Using the same steps the last term can be written as +p′·L·L′·p = MNE′ + M2 +Nq·p′ + M2 +N′q′·p = 2(1 + Ek/MN) + O(E2 +k) +(A.36) +– 23 – + +This is a map from PΠN,ΠN′ and its absolute value square, where the latter can be +recasted in a new polynomial XΠN,ΠN′ +���PΠN,ΠN′ +��� +2 += XΠN,ΠN′ +� +p′·L(a)·p′, p·L′(a)·p, p′·L(a)·L′(b)·p, wn,m, w′ +n′,m′, µn,n′ +� +(A.37) +Now let’s compare the amplitude with its mod square +AΠN +{gn},ΠN′ +{gn′ } = PΠN,ΠN′ +� +n +� +Vn +�gn � +n′ +� +V ′ +n′ +�gn′ +(A.38) +���AΠN +{gn},ΠN′ +{gn′ } +��� +2 += XΠN,ΠN′ +� +n +� +V 2 +n +�gn � +n′ +� +V ′ +n′2�gn′ +(A.39) +it is clear that if one takes n, n′ = 1 and g1 = N, g′ +1 = N′ then V1 = V ′ +1 = 1, and even +if the polynomial PΠN,ΠN′ is very complicated there are no chaotic oscillations. This is a +clear information of how the polynomial PΠN,ΠN′ does not contain most of the information +about the microstate structures. When XΠN,ΠN′ is considered, there is still a complicated +structure, but there is a constant universal leading term plus many other suppressed terms. +The crucial point is that, if there is thermalization the only way to generate the process is +using the chaotic factors {Vn}, {V ′ +n′}. This is an evidence of how the chaos is a trigger for +the thermalization. +To see how the XΠN,ΠN′ contributes, let’s start by considering +���PΠN,ΠN′ +��� +2 += XΠN,ΠN′ +� +p′·L(a)·p′, p·L′(a)·p, p′·L(a)·L′(b)·p, wn,m, w′ +n′,m′, µn,n′ +� +(A.40) +where +µn,m(Ek) = − +nm Ek +MN +m − n + n Ek +MN +, +wn,m(Ek) = +n m +n + m +Ek +MN +� Ek +MN +− 1 +� +(A.41) +w′ +n,m(Ek) = +n m +n + m +Ek +MN +� Ek +MN ++ 1 +� +(A.42) +when Ek/MN is small, which is the region where the emitted radiation is expected to be +thermal, one has +w′ +n,m = −wn,m = +n m +n + m +Ek +MN ++ O +� E2 +k +M2 +N +� +(A.43) +and the other terms are given by (sopra), therefore if Ek/MN is small one has +p′·L·p′ = p·L′·p = p′·L·L′·p ≃ 2 = −2α′M2 +T +(A.44) +and the leading term of the polynomial X, included the microstates normalization is +N{gn}N ′ +{g′ +n′}XΠN,ΠN′ ≃ +(−2α′M2 +T )J+J′ +� +n ngngn! � +n′ n′gn′gn′! + O +� Ek +MN +� +(A.45) +so one can absorb the polynomial contribution into a new microstates normalization +� +N{gn} � +N ′ +{g′ +n′} = +1 +� +n(n/2)gngn! � +n′(n′/2)gn′gn′! +(A.46) +– 24 – + +Now focusing on the chaotic factors, Vn and V ′ +n′, when Ek/MN is small one can write +Vn = +Γ +� +n − n Ek +MN +� +Γ(n)Γ +� +1 − n Ek +MN +� +(A.47) +Using the Legendre duplication formula +Γ(nx) = +�n−1 +k=0 Γ +� +x + k +n +� +(2π) +n−1 +2 n +1 +2 n−nx +(A.48) +one has +Γ +� +n +� +1 − Ek +MN +�� += +�n−1 +k=0 Γ +� +1 − Ek +MN + k +n +� +(2π) +n−1 +2 n +1 +2 −n +e−n Ek +MN log n +(A.49) +since Ek/MN is very small one can approximate the function as +Γ +� +n +� +1 − Ek +MN +�� += Γ(n) e−n Ek +MN log n +(A.50) +and the final result is given by +Vn ≃ +Γ +� +n − n Ek +MN +� +Γ(n)Γ +� +1 − n Ek +MN +� ≃ +e−n Ek +MN log n +Γ +� +1 − n Ek +MN +� +(A.51) +In a similar fashion the other term can be written as +V ′ +n = (−)n +Γ +� +n + n Ek +MN +� +Γ(n)Γ +� +1 + n Ek +MN +� ≃ (−)n +en Ek +MN log n +Γ +� +1 + n Ek +MN +� +(A.52) +this is how the chaotic factors play their role in the thermalization of the decay rate. +A.3 +Thermal nature of the decay amplitude +Let’s consider the general form of the decay amplitude +AΠN +{gn},ΠN′ +{gn′ } = PΠN,ΠN′ +� +n +� +Vn +�gn � +n′ +� +V ′ +n′ +�gn′ +(A.53) +in the limit Ek/MN small, it was shown that the decay rate, which is the physical observ- +able, has a simple compact dependence on the polynomial XΠN,ΠN′ that can be absorbed +in the microstates normalization. Such simplification can be translated in the structure of +the decay amplitude when only circular polarizations are considered, for example taking +λ+ = λ′ ++ = (0, 1, i,⃗0) +(A.54) +one finds +ζn·p′ = ζ′ +n′·p ≃ −ω , +ζn·ζn = ζ′ +n′·ζ′ +n′ = ζn·ζ′ +n′ = 0 +(A.55) +– 25 – + +and the decay amplitude simplifies to +AΠN +{gn},ΠN′ +{gn′ } = N{gn}N ′ +{g′ +n′} (−ω)J+J′ � +n +� +Vn +�gn � +n′ +� +V ′ +n′ +�gn′ +(A.56) +Now using (A.51) and (A.52) one finds +AΠN +{gn},ΠN′ +{gn′ } = N{gn}N ′ +{g′ +n′} (−ω)J+J′ e−CN({gn},{g′ +n′}) Ek +2TH −µN({gn},{g′ +n′};Ek/TH) +(A.57) +and squaring the decay amplitude one recovers the formula of the decay rate (2.2). The +kinematical simplifications of the decay amplitude are just the reflection of the subleading +contributions of bilinear polarization terms of the decay rate, in the limit Ek/MN small. +The possibility of computing the most general decay amplitude, with the explicit depen- +dence on the microstates structure leads to the identification of the decay amplitude with +the Boltzmann factor, which is the thermal weight of the interaction between microstates. +References +[1] G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15 (1977), 2738-2751 inspirehep/125663. +[2] S. W. Hawking, Phys. Rev. D 14 (1976), 2460-2473 inspirehep/114952. +[3] S. W. Hawking, Phys. Rev. D 13 (1976), 191-197 inspirehep/113269. +[4] P. Hayden and J. Preskill, JHEP 09 (2007), 120 0708.4025. +[5] S. H. Shenker and D. Stanford, JHEP 03 (2014), 067 10.1007/JHEP03(2014)067. +[6] L. Susskind, [arXiv:hep-th/9309145 [hep-th]] arXiv:hep-th/9309145. +[7] G. T. Horowitz and J. Polchinski, Phys. Rev. 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Yoda, JHEP 11 (2022), 147 arXiv:2208.08380 +– 28 – + diff --git a/UNE2T4oBgHgl3EQftQjd/content/tmp_files/load_file.txt b/UNE2T4oBgHgl3EQftQjd/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..1618c1459d1427257298bae2e109a12aaa28a111 --- /dev/null +++ b/UNE2T4oBgHgl3EQftQjd/content/tmp_files/load_file.txt @@ -0,0 +1,891 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf,len=890 +page_content='The chaotic emergence of thermalization in highly excited string decays Maurizio Firrotta aDipartimento di Fisica, Universit`a di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133, Roma, Italy bINFN sezione di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy E-mail: maurizio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='firrotta@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='com Abstract: We analyse the most general process of a generic highly excited string that decays into a less excited, yet generic, highly excited string emitting a tachyon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' We provide a simple and compact analytic description of the decay process which discriminates between and within the structure of every single microstate of the initial and final highly excited string.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' Considering the random nature of the decay process we extract the energy spectrum of highly excited strings, microstate by microstate, finding a behavior which corresponds to the greybody emission spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' In addition, by exploiting the analytic control of the decay process, we identify the origin of thermal effects which are triggered by the chaotic nature of the highly excited string interactions modeled by the microstates structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='04069v1 [hep-th] 10 Jan 2023 Contents 1 Chaos in highly excited string processes 3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='1 Classical string vs quantum string configurations 3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='2 Probing chaotic behavior of quantum strings through their interaction 5 2 Thermalization emergence in highly excited string decays 9 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='1 Chaos driven thermalization 11 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='2 Thermal spectrum: the greybody emission of highly excited strings 13 3 Results of random generated spectra 15 4 Conclusion and future directions 16 A Highly excited string decay: HN ⇒ HN′ + T 19 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='1 Decay amplitude 20 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='2 Decay rate 22 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='3 Thermal nature of the decay amplitude 25 Introduction The present paper is focused on enlightening the connection between chaos and thermal effects within the physical systems provided by highly excited string (HES) interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' Motivated by the intriguing interplay between chaos, thermal effects and quantum infor- mation [1]-[5], which are three milestones of black hole (BH) physics, we first used HES as promising candidates of BH states [6]-[8] and then we computed the energy spectrum of HES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' The main goal was to detect a manifest connection between the chaotic behavior of HES interactions and the thermalization of their energy spectra which emerges naturally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' In line with past studies on string decays and the produced Hawking radiation [9]-[18], we used and improved the most general process of an HES that decays into an HES emitting a tachyon [19][20], providing an analytic description of the decay process which discriminates between and within the structure of every single microstate of the initial and final HES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' Considering the random nature of the decay process we extracted the spectrum of the HES, microstate by microstate, finding a behavior which corresponds to the greybody emission spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' In addition, exploiting the analytic control of the decay process, we identified the origin of thermal effects, finding that they are triggered by the chaotic nature of HES interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' The setup we adopted relies on the recent improvement of the Di Vecchia, Del Giudice and Fubini (DDF) formalism [21][22], where its spectrum generating algebra was recasted in a manifestly covariant form [23][24], for both bosonic string and superstring theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' The – 1 – possibility of identify each state of the string spectrum with the associated physical vertex operator gave rise to a wide range of applications: the realization of the scattering of string coherent vertex operators1 [19],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' the non perturbative string footprint in the gravitational wave (GW) signal produced in the merging phase of BHs collision [25],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' the non perturbative spinning corrections to the electromagnetic wave produced in the collision of heavy sized objects [26],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' such as BHs and neutron stars NSs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' the two body decay of HES [20] and finally the indications about the chaotic behavior of HES interactions [27][28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' About the chaotic behavior of HES interactions, quite recently it was proposed a novel measure of chaos for scattering amplitudes [29], where it was compared the behavior of HES amplitudes with the chaotic distribution of the zeros of the Riemann zeta function and the quantum mechanical scattering on a leaky torus, finding a common pattern between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' The scope of the present paper was to continue the study of the physical applications connected to the possibility of exploring the interactions of the whole tower of string exci- tations, or string microstates, proceeding beyond the physics of light string states and also beyond the first Regge trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' The paper is organized as follows: in section 1 we explained the connection between the shape of classical string configurations and the structure of quantum string configurations, in particular we studied the classical string profiles as a function of the number of harmonics and the respective coefficients and we compared their shape with the degenerate quantum string partitions of generic mass levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' We followed the logic that the structure of a quantum string state can be probed through its interaction, we selected the simplest one i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='e the decay of HES into two tachyons, in order to preserve the HES structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' After a brief review of the chaotic analysis, developed in [29], we compared the shape of classical string configurations with the chaotic behavior of the scattering amplitudes relative to the quantum analog of classical string configurations finding a common pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' In section 2 we studied the most general process of a generic HES that decays into a less excited, yet generic, HES emitting a tachyon in the thermalization regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' Exploiting the analytic control of the decay process, we identify the origin of thermal effects with the chaotic structure of the process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' Finally we gave a description of how to compute the emission spectrum of HES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' In section 3 we presented the results of HES spectra, microstate by microstate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' In particular we found that a generic string excitation is characterized by a greybody emission, while for the extreme case where only excitations of the first Regge trajectory (FRtj) are considered, the thermal nature is such highly suppressed as to be negligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' In the appendix 4 we reviewed the computation developed in [20], and we described the analytical implications of the thermalization regime, or more precisely the regime in which the ratio between the energy of the emitted state and the mass of the decaying state is enough small in such a way that the energy loss of the decaying state is smooth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' 1A very powerful application of the scattering amplitudes of coherent string states is their nature of generating amplitudes of any desired string states, obtained by a simple derivative projection over mass eigenstates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' – 2 – 1 Chaos in highly excited string processes The aim of this section is to review recent results about the chaotic behavior of HES interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='1 Classical string vs quantum string configurations Classical three dimensional2 bosonic open string profiles with Neumann boundary condi- tions, in the temporal gauge (X0 = t), are given by [30] Xj {an}(σ, τ) = n∗ � n=1 xj {n},{an}(σ, τ) (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='1) σ ∈ [0, π] and τ ∈ [0, ∞) are the worldsheet variables and Xj(σ, τ) is the map between the worldsheet and the target space (R3), representing the 3-D string profile at any value of τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' Classical string configurations can be classified by the set of harmonics {n} and the respective set of coefficients {aj n} which are respectively the harmonic label and the relative weight coefficient of the classical mode xj : xj {n},{an}(σ, τ) = aj n n cos (nπσ) sin (nπτ) (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='2) In figure 1 there are some 3-D string profiles for different choices of the set of harmonics and coefficients, from which one can observe how the string profile becomes more involved if the number of harmonics is increasing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' Examples of 3D string profiles for different combinations of harmonics n∗ = 1, 5, 10, 50 with uniformly distributed random parameters aj n ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' From figure 2 one can observe the dependence of string profiles from the set of coef- ficients {aj n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' In the present case it was assumed that coefficients are normalized to the identity, and they are uniformly distributed in the interval (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' One can observe that the behavior of string profiles is unchanged also for non normalized integer coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' The features of string profiles are unaffected by different parametrizations of the coefficients aj n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' At this level a trivial observation is that, if one considers a classical string profile 2In the specific case of classical string, it was chosen j = 1, 2, 3 in order to plot 3D profiles, but in general j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=', D − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' – 3 – Xs Xi X2 1 harmonic 5 harmonics 10 harmonics 50 harmonicsFigure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' Examples of 3D string profiles for different combinations of harmonics n∗ = 10, 50, 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' For each value of n∗ there are five choices of string profiles for different choices of uniformly dis- tributed random parameters aj n ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' Xj {an}(σ, τ) = xj {n},{an}(σ, τ) (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='3) with the same single generic harmonic n in the three spatial directions j = 1, 2, 3, one obtains the smoothest profile, which is a straight line, such as the first profile of figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' This is the general picture of how the classical string profiles are modeled by the harmonic set {n} and the coefficient set {an}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' Now it is helpful to study the comparison between classical and quantum string con- figuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' In particular, promoting the coefficients aj n to be creation operators Aj −n one has the quantum analog of the string mode, and in addition to the set of harmonics {n}, one has to include the number of excitation gn of each harmonic so much so that for a given quantized level N of the string spectrum, one has a set of states spanned by the set of solutions {gn}, representing all the partitions of the integer N with occupation number J: N = N � n=1 ngn , J = N � n=1 gn (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='4) The promotion from classical to quantum string is summarized as x{n},{an}(σ, τ) ⇒ Nn,gnAgn −n|0⟩ ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' X{an}(σ, τ) ⇒ Π(N) {gn} = N � n=1 Nn,gnAgn −n|0⟩ (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='5) where N −1 n,gn = √ngn gn!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' is the normalization constant of each mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' In particular due to its quantum nature, the quantum string configuration for a fixed level N has a large degen- eration3 which produces the microstate structure, so in order to identify the final quantum string state one can take the simplest linear combination of microstates introducing the average over microstates in the second expression of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='5) X(σ, τ) ⇒ � {gn} Π(N) {gn} = � {gn} N � n=1 Nn,gnAgn −n|0⟩ (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='6) 3The degeneration of states at large N grows like ∼ e √ N – 4 – n* = 10 n* = 50 n* = 100Looking at the complicated classical string profiles, parametrized by {n} and {an}, a nat- ural question is how the quantum string configurations reflect their classical characteristic shape as a function of {n} and {gn}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' A possible way of testing the features of quantum string profiles as a function of the microstate structure, is to probe the implications of their shapes through their interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' In particular one can choose the simplest string decay amplitude and study the microstate dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' In the next subsection it will be reviewed the analysis of string configurations leading to a chaotic behavior of their interactions [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='2 Probing chaotic behavior of quantum strings through their interaction Inspired by the systematic of classical string profiles, the logic proposed for the analysis of quantum string configurations is the following: the main observable is the decay amplitude provided by a level N string microstate Π(N) {gn} decaying into two tachyons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' Following the indications introduced in [skliros] and developed in [DDF Bianchi firrotta], the decay amplitude AΠ(N) {gn} for the most general HES was computed, with a remarkably simple procedure based on coherent state techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' The informations about the structure of Π(N) {gn} are translated into the decay amplitude, and they are manifested through the profile of the decay amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' The choice of looking at tachyons is connected to their simple vertex operators, in such a way that all the information inside the decay amplitude is governed by the structure of Π(N) {gn}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' In figure 3 there is a representative picture of the decay amplitude from which one can see that the decay amplitude profile is only a function of the angle α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' Now comparing decay profiles of different microstates one can extract a general behavior associated to choices of {n} and {gn}, as it was pointed out in [Gross Rosen].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' Most of the information of the decay profile can be codified in terms of its extrema, so it is useful to introduce the logarithmic derivative F{gn}(α) and study its distribution of zeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' A suitable parameterization of the distribution is intimately connected with the chaotic behavior of the decay [Cobi Io Dorin B].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' Before describing the chaotic analysis in detail, a very fast presentation of the resulting decay amplitude is discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' Picture of the decay amplitude where a representative microstate Π(N) {gn} decays into two tachyons T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' The only kinematical freedom of the decay amplitude is the emission angle α which starts from the reference dashed line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' – 5 – T(p1) T(N) (p) α T(p2)The HES state of the level N with polarizations {ζn} and momentum p is described by Π(N) {gn}({ζn}, p) = N � n=1 (ζn·A−n)gn √gn!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' ngn |0⟩ (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='7) following the DDF formalism one can write the corresponding BRST vertex operator and compute the decay amplitude of figure 3 using circular polarizations4: AΠ(N) {gn}(α) ≃ � ζ·(p1−p2) �J N � n=1 �(1−n sin2 α)n−1 Γ(n) �gn (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='8) all the information about the microstate Π(N) {gn} is encoded in the dressing factor of the coupling ζ·(p1−p2) Π(N) {gn}−structure ⇒ N � n=1 �(1−n sin2 α)n−1 Γ(n) �gn (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='9) Using the properties of the Pochhammer factor and the explicit parametrization of the polarizations the decay amplitude can be written as AΠ(N) {gn}(α) ≃ N � n=1 �sin α Γ(n) sin � nπ cos2 α/2 � Γ � n cos2 α/2 � Γ � n sin2 α/2 ��gn (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='10) Finally the logarithmic derivative of the decay amplitude F{gn}(α) = d dα log AΠ(N) {gn}(α) (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='11) has the following form F{gn}(α) =J cot α − πsin α 2 N � n=1 ngn cot � nπ cos2 α 2 � −sin α 2 N � n=1 ngn � ψ � n cos2 α 2 � −ψ � n sin2 α 2 � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='12) This is the final observable which will be subjected to the analysis described below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' Chaotic analysis: setup Random Matrix Theory (RMT) provides a very powerful tool to make the bridge between quantum chaos and universal statistical properties [31][32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' In particular a quantitative connection between chaos and probability distributions was conjectured in [33] and sub- sequently the link between chaos and statistical properties was widely studied in many contexts such as quantum chromodynamics (QCD)[34], nuclear physics [35], black holes [36] and condensed matter [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' In what follows it will be laid out the identification strat- egy of the target distribution used as a discriminant of the chaotic behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' 4The general amplitude is made of contributions both linear and bilinear in ζn [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' The bilinear contribution is proportional to the square of the linear contribution, so up to an irrelevant polynomial the functional dependence on the microstate structure is preserved by the choice ζ(a) n ·ζ(b) m = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content=' – 6 – Starting from the Hermite β-ensemble of N × N random matrices, given the set {α} = (α1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/UNE2T4oBgHgl3EQftQjd/content/2301.04069v1.pdf'} +page_content='., αN) of matrix eigenvalues, the associated joint probability distribution is given by Pβ({α}) = e− �N j=1 α2 j 2 ZN,β � ℓ 1/2) , +(2) +and the function U( ˆF, ˆN trash) will be specified later. +Box 1: Actual protocol +1. Alice generates a random bit ˆa ∈ {0, 1} and sends an optical pulse ˜C in a coherent +state with amplitude (−1)ˆa√µ to Bob. She repeats it for N rounds. Bob receives an +optical pulse C for each of the N rounds. +2. For the received pulse C in each round, Bob chooses a label from {signal, test, trash} +with probabilities psig, ptest, and ptrash, respectively, and announces it. According to +the label, Alice and Bob do one of the following procedures. +[signal] Bob performs a homodyne/heterodyne measurement on the received optical pulse +C and obtains an outcome ˆx ∈ R. (For the heterodyne measurement, ˆx is defined +as the real part of the outcome ˆω ∈ C.) Bob defines a sifted-key bit ˆb as ˆb = 0 with +a probability fsuc(ˆx) and ˆb = 1 with a probability fsuc(−ˆx). When Bob has defined +his sifted key bit, he announces “success”, and otherwise, he announces “failure”. In +the case of a success, Alice (resp. Bob) records a bit ˆa (ˆb). +[test] Bob performs a heterodyne measurement on the received optical pulse C and obtains +an outcome ˆω. Alice announces her bit a. Bob calculates the value of Λm,r(|ˆω − +(−1)ˆaβ|2). +[trash] Alice and Bob produce no outcomes. +3. We refer to the numbers of “success” and “failure” signal rounds, test rounds, and +trash rounds as ˆN suc, ˆN fail, ˆN test, and ˆN trash, respectively. +(N = ˆN suc + ˆN fail + +3 + +ˆN test + ˆN trash holds by definition.) Bob calculates the sum of Λm,r(|ˆω − (−1)ˆaβ|2) +obtained in the ˆN test test rounds, which is denoted by ˆF. +4. For error correction, they use HEC-bits of encrypted communication consuming a +pre-shared secret key to do the following. According to (the upper bound on) the bit +error rate eqber, Bob randomly chooses an error-correcting code and sends it with the +HEC-bits syndrome to Alice. Alice reconciles her sifted key accordingly. +5. Bob computes and announces the final key length ˆN fin according to Eq. (1). Alice +and Bob apply privacy amplification to obtain the final key. +For simplicity, we omitted the bit-error-sampling rounds in the above protocol. To satisfy the +required correctness εcor for the final key, Alice and Bob randomly insert Nsmp sampling rounds +among N rounds in which Bob performs the same measurement as that of the signal round and +estimate an upper bound eqber on the bit error rate. Let ˆN suc +smp be the number of “success” in +Nsmp sampling rounds, and let ˆEobs be the number of discrepancies between Alice’s and Bob’s bits +observed in the “success” sampling rounds. Then, Bob sets eqber to +eqber = +� +˜ +M ˆ +Nsuc+ ˆ +N suc +smp, ˆ +N suc +smp,εcor/2( ˆEobs) − ˆEobs +�� +ˆN suc, +(3) +where the function ˜ +MN,n,ϵ is defined in Eq. (101) in Appendix A. The proof that this definition +of eqber upper-bounds the actual bit error rate with probability no smaller than 1 − εcor/2 is also +shown in Appendix A. The required amount HEC of the error syndrome Bob sends to Alice in the +bit error correction depends on the error correction method; here we assume +HEC = ˆN suc (f h(˜eqber) + (1 − f)) , +˜eqber := min{eqber, 0.5}, +(4) +where f ∈ [0, 1] denotes an error correction efficiency [45, 46, 16–18, 47] for the error correction +to succeed with the probability no smaller than 1 − εcor/2. The net key gain ˆG per pulse is thus +given by +ˆG = ( ˆN fin − HEC)/(N + Nsmp). +(5) +Here, we do not use verification in the post-processing, unlike Refs. [37, 38], due to the subtleties +to incorporate it in our security proof. The acceptance probability fsuc(x) should be chosen to +post-select the rounds with larger values of x, for which the bit error probability is expected to be +lower. The definition of fsuc(x) in this article follows Ref. [38] and is slightly more general than +that of Ref. [37]. (Note that Ref. [37] can also use this definition of fsuc(x).) It is ideally a step +function with a threshold xth(> 0), but our security proof applies to any form of fsuc(x). The test +function Λm,r(ν) is the same as the one defined in Ref. [37] where it is shown to satisfy +Eρ[Λm,r(|ˆω − β|2)] ≤ ⟨β| ρ |β⟩ +(6) +for any odd integer m, positive real r, and density operator ρ (see Corollary 1 in Ref. [37]). The +parameter β is typically chosen to be √ηµ with η being a nominal transmissivity of the quantum +channel, while the security proof itself holds for any choice of β. The parameter s is related to the +overall security parameter in the security proof below. +We determine a sufficient amount of the privacy amplification according to the complementarity, +or in other words, the phase error correction [43, 48], which has been widely used for the DV-QKD +protocols. We aim at showing the secrecy of Bob’s final key against the adversary Eve. To do +so, we consider a virtual protocol in which Bob has a qubit for each success signal round such +that the outcome of the Z-basis measurement on it is equivalent to his sifted key bit b. Alice can +do arbitrary quantum operations in the virtual protocol as long as all the statistics and available +information to the adversary Eve are the same as those in the actual protocol. Then, after Bob’s +Z-basis measurement on the qubit, the reduced classical-quantum state between Bob and Eve in +the virtual protocol is the same as that in the actual protocol. +4 + +In the following, we explicitly describe the virtual protocol. For Alice, we introduce a qubit A +and assume that she entangles it with an optical pulse ˜C in a state +|Ψ⟩A ˜ +C := |0⟩A |√µ⟩ ˜ +C + |1⟩A |−√µ⟩ ˜ +C +√ +2 +, +(7) +where |ω⟩ ˜ +C with ω ∈ C denotes the coherent state with the amplitude ω, which is defined as +|ω⟩ ˜ +C := e− |ω|2 +2 +∞ +� +n=0 +ωn +√ +n! +|n⟩ ˜ +C . +(8) +Then, the optical pulse ˜C emitted by Alice is in the same state as that in the actual protocol. +For Bob, we construct a process of probabilistically converting the received optical pulse C to a +qubit B, which can be regarded as a coherent version of Bob’s signal measurement. For Homodyne +protocol, consider a map Khom +C→B defined as [37] +Khom +C→B(x)(ρC) := Khom +suc (x) ρC +� +Khom +suc (x) +�† +(9) +with +Khom +suc (x) := +� +fsuc(x) +� +|0⟩B⟨x|C + |1⟩B⟨−x|C +� +, +(10) +where ⟨x| maps a state vector to the value of its wave function at x; i.e., for a coherent state vector +|ω⟩, ⟨x| acts as +⟨x|ω⟩ = +� 2 +π +� 1 +4 +exp +� +−(x − ωr)2 + 2iωix − iωrωi +� +, +(11) +where ω = ωr + iωi with ωr, ωi ∈ R. Let Πev(od) denote a projection operator onto the subspace +of even(odd) photon numbers. Since ⟨x| (Πev − Πod) = ⟨−x| holds, we have +Khom +suc (x) = +� +2fsuc(x) +� +|+⟩B⟨x|C Πev + |−⟩B⟨x|C Πod +� +. +(12) +This defines an instrument Ihom +C→B for the process of producing the outcome ˆx and leaving C in a +post-measurement state; i.e., given a measurable set ∆ ⊆ R, the unnormalized post-measurement +state is given by +Ihom +C→B(∆)(ρC) = +� +∆ +dx Khom +C→B(x)(ρC) +(13) +with Tr[Ihom +C→B(∆)(ρC)] being a probability of “success” signal event with the outcome ˆx ∈ ∆. +Similarly, for Heterodyne protocol, consider a map Khet +C→B defined as [38] +Khet +C→B(ω)(ρC) := Khet +suc(ω) ρC +� +Khet +suc(ω) +�† +(14) +with +Khet +suc(ω) := +� +fsuc(ωr) +π +� +|0⟩B⟨ω|C + |1⟩B⟨−ω|C +� += +� +2fsuc(ωr) +π +(|+⟩B⟨ω|C Πev + |−⟩B⟨ω|C Πod) , +(15) +where |ω⟩ denotes a coherent state vector and ω = ωr + iωi with ωr, ωi ∈ R. Similarly to Homo- +dyne protocol, we can define an instrument Ihet +C→B composed of the heterodyne outcome and the +(unnormalized) post-measurement state, which is given by +Ihet +C→B(∆′)(ρC) = +� +∆′ dωrdωi Khet +C→B(ω)(ρC), +(16) +where ∆′ ⊆ R2 is a measurable set. +If Bob measures the qubit B on the Z basis after the +instrument (13) (resp. (16)), he obtains the same sifted key bit with the same probability as in the +actual protocol when ˆx ∈ ∆ (resp. ˆω ∈ ∆′) [37, 38]. +5 + +At this point, one has a degree of freedom to perform quantum operations on the system AB +for each outcome ˆx (resp. ˆω) as long as it does not change the Z-basis value of the qubit B. This +is because we aim at showing the secrecy of Bob’s final key against the adversary Eve with Alice’s +system traced out. Thus, after applying the map Khom +C→B (resp. Khet +C→B), we assume that Alice and +Bob perform a controlled isometry V hom +B;A→R(x) (resp. V het +B;A→R(ω)) of the form +V hom +B;A→R(x) := +� +|0⟩⟨0|B ⊗ V (0) +A→R(x) + |1⟩⟨1|B ⊗ V (1) +A→R(x) +� +C-XBA +(17) +V het +B;A→R(ω) := +� +|0⟩⟨0|B ⊗ V ′(0) +A→R(ω) + |1⟩⟨1|B ⊗ V ′(1) +A→R(ω) +� +C-XBA, +(18) +where C-XBA := |0⟩⟨0|B ⊗ IA + |1⟩⟨1|B ⊗ XA denotes the Controlled-NOT gate and V (j) +A→R(x) +(resp. V ′(j) +A→R(ω)) for j = 0, 1 denotes an isometry from the system A to another system R that is +no smaller than A 1. If V (j) +A→R(x) (resp. V ′(j) +A→R(ω)) is an identity, then the analysis reduces to the +previous results [37, 38]. Let Vhom +B;A→R(x) (resp. Vhet +B;A→R(ω)) be an adjoint action (i.e., a CPTP +map) for the isometry V hom +B;A→R(x) (resp. V het +B;A→R(ω)). The composition of the map Vhom +B;A→R(x) +and the map (9) (resp. the mad Vhet +B;A→R(ω) and the map (14)) with Alice’s system traced out +at the end defines a quantum operation Fhom +AC→B (resp. Fhet +AC→B) that (probabilistically) outputs +Bob’s qubits for his sifted key as +Fhom +AC→B(ρAC) = +� ∞ +−∞ +dx K′ hom +AC→B(x)(ρAC), +(19) +Fhet +AC→B(ρAC) = +�� ∞ +−∞ +dωrdωi K′ het +AC→B(x)(ρAC), +(20) +with K′ hom +AC→B(x) (resp. K′ het +AC→B(ω)) given by +K′ hom +AC→B(x)(ρAC) := TrR +� +Vhom +B;A→R(x) ◦ +� +IdA ⊗ Khom +C→B(x) +� +(ρAC) +� +, +(21) +K′ het +AC→B(ω)(ρAC) := TrR +� +Vhet +B;A→R(ω) ◦ +� +IdA ⊗ Khet +C→B(ω) +� +(ρAC) +� +, +(22) +where Id denotes the identity map. +Note that the idea of acting the isometry V hom +B;A→R(x) or +V het +B;A→R(ω) is closely related to the twisting operation on the shield system [49–53]. The difference +is that in our case it acts on the system A in a way that is incompatible with the Z-basis mea- +surement on A. This is allowed in a security proof based on complementarity since what we need +to prove in the virtual protocol is that the outcome of the Z-basis measurement on B is secret to +Eve when the system A is traced out [43]; i.e., the system A works as a shield system. +We then introduce a virtual protocol that explicitly incorporates the action of Fhom +AC→B in +Eq. (19) (resp. Fhet +AC→B in Eq. (20)) in Box 2. +Box 2: Virtual protocol +1′. Alice prepares a qubit A and an optical pulse ˜C in a state |Ψ⟩A ˜ +C defined in (7) and +sends the pulse ˜C to Bob. She repeats it for N rounds. Bob receives an optical pulse +C for each of the N rounds. +2′. For the received pulse C in each round, Bob announces a label in the same way as +that at Step 2. Alice and Bob do one of the following procedures according to the +label. +[signal] Alice and Bob perform the quantum operation on the system A and the received +pulse C specified by the map Fhom +AC→B defined in Eq. (19) (resp. Fhet +AC→B defined +1Here, a subtlety for using the verification comes in. In order to know whether verification succeeds or not, Alice +has to confirm the syndrome bits for the verification. However, this procedure may not commute with the action of +V hom +B;A→R(x) (resp. V het +B;A→R(ω)). We do not currently have a method to evaluate how much the verification affects +the secrecy condition. +6 + +in Eq. (20)) to determine success or failure of detection, obtain the qubit B upon +success, and perform the controlled isometry given in Eq. (17) (resp. Eq. (18)). Bob +announces the success or failure of the detection. +[test] Bob performs a heterodyne measurement on the received optical pulse C, and ob- +tains an outcome ˆω. Alice measures her qubit A on Z basis and announces the +outcome ˆa ∈ {0, 1}. Bob calculates the value of Λm,r(|ˆω − (−1)ˆaβ|2). +[trash] Alice measures her qubit A on X basis to obtain ˆa′ ∈ {+, −}. +3′. ˆN suc, ˆN fail, ˆN test, ˆN trash, and ˆF are defined in the same way as those at Step 3. Let +ˆQ− be the number of rounds with ˆa′ = − among the ˆN trash trash rounds. +4′. According to (the upper bound on) the bit error rate eqber, Bob performs HEC bits +of encrypted communication consuming a pre-shared secret key to send a dummy +message. +5′. Bob computes and announces the final key length ˆN fin according to Eq. (1). Bob +performs a randomly chosen unitary on his qubits (see the main text), and measures +the first ˆN fin qubits on the Z bases. +In the last line of Step 5′, the random choice of a unitary is constructed so that, along with the +subsequent ˆN fin-qubit measurement on the Z bases, it is equivalent to the privacy amplification. +This is possible because for any n × n linear transformation C on the n-bit sequence, there always +exists a corresponding unitary U(C) that satisfies U(C) |z⟩ = |Cz⟩ on the Z basis. As has already +been claimed, if Eve performs the same attacks as those in the actual protocol, the resulting +classical-quantum state between Bob and Eve is the same as that in the actual protocol. +The complementarity argument [43] in a reverse reconciliation scenario relates the amount of +privacy amplification to the so-called phase error patterns of Bob’s qubits. Suppose that, just +before the Z-basis measurement at Step 5′ of the virtual protocol, Bob’s quantum state on the +first ˆN fin qubits is arbitrarily close to |+⟩⟨+|⊗ ˆ +Nfin +. Then, the secrecy condition of the final key +is satisfied [43, 48, 54]. For this to be true, the errors on the X bases (i.e., the phase errors) on +Bob’s qubits should be corrected by the procedure at Step 5′ of the virtual protocol. To see the +correctability of the phase errors at Step 5′, suppose that Bob measured his ˆN suc qubits on the X +basis {|+⟩ , |−⟩} at the end of Step 3′, and obtained a sequence of + and −. The minuses in the +sequence are regarded as phase errors. It has already been known that, if we can find an upper +bound on the number of possible phase-error patterns, then we can prove the security [43]. To +make the argument more precise, we introduce the estimation protocol in Box 3. +Box 3: Estimation protocol +1′′. Alice prepares a qubit A and an optical pulse ˜C in a state |Ψ⟩A ˜ +C defined in (7) +and sends the pulse ˜C to Bob. She repeats it for N rounds. Bob receives an +optical pulse C for each of the N rounds. +2′′. For the received pulse C in the ith round (i = 1, . . . , N), Bob announces a label in +the same way as that at Step 2. Alice and Bob do one of the following procedures +according to the label and obtain the values of random variables ˆN suc (i) +ph +, ˆF (i), +and ˆQ(i) +− . Unless explicitly written, these random variables are set to be zeros. +[signal] Alice and Bob do the same procedure as that at “signal” of Step 2′. Upon “success”, +Bob performs the X-basis measurement on qubit B and obtains ˆb′ ∈ {+, −}. When +ˆb′ = −, ˆN suc (i) +ph +is set to be unity. +[test] Alice and Bob do the same procedure as that at “test” of Step 2′. Then ˆF (i) is set +to be Λm,r(|ˆω − (−1)ˆaβ|2). +7 + +[trash] Alice does the same procedure as that at “trash” of Step 2′. When ˆa′ = −, ˆQ(i) +− is +set to be unity. +3′′. Same as Steps 3′ of the virtual protocol. Note that ˆF = �N +i=1 ˆF (i) and ˆQ− = +�N +i=1 ˆQ(i) +− hold. +4′′. Regarding + as zero and − as unity for each ˆb′ in success signal round, define +the ˆN suc-bit sequence ˆxph. Let ˆN suc +ph be the Hamming weight of ˆxph, i.e., ˆN suc +ph = +�N +i=1 ˆN suc (i) +ph +. +The task of proving the security of the actual protocol is then reduced to constructing a function +U( ˆF, ˆN trash) that satisfies +Pr +� +ˆN suc +ph ≤ U( ˆF, ˆN trash) +� +≥ 1 − ϵ +(23) +for any attack in the estimation protocol and setting the final-key length to ˆN fin = ˆN suc −HPA −s, +where HPA is defined as +HPA := +� +ˆN such +� +U( ˆF, ˆN trash)/ ˆN suc�� +. +(24) +In fact, if the condition (23) is satisfied, then the number of possible phase-error patterns can be +bounded from above by 2HPA [55]. Therefore, by extracting the (HPA+s)-bit error syndrome of ˆxph +using the universal2 hash function, Bob could uniquely identify ˆxph with a failure probability no +smaller than 1−2−s [43, 56, 57, 44]. In the virtual protocol, the quantum operations at Step 5′ can +be made equivalent to the ( ˆN suc − ˆN fin)-bit syndrome extraction via the universal2 hash function +and the error correction on the X bases of ˆN fin qubits. Since a unitary U(C−1) that acts as the +matrix C−1 on the Z bases acts as C⊤ on the X bases, i.e., U(C−1) |xX⟩ = |C⊤xX⟩ where ·X +denotes the X basis, this procedure corresponds to the privacy amplification via the dual universal2 +hashing on the Z bases [56, 44] (i.e., in the actual protocol). Combining these, the condition (23) +implies that the actual protocol with the final key length given in Eq. (1) is ϵsec-secure with a +security parameter ϵsec = +√ +2 +√ +ϵ + 2−s + ϵcor [43, 48, 54]. From now on, we thus focus on the +estimation protocol for finding a function U( ˆF, ˆN trash) to satisfy Eq. (23). +2.2 +Phase error operator +In this section, we explain how our new security analysis can be reduced to the previous analyses +carried out in Refs. [37, 38] with a tighter operator inequality. The number of phase errors depends +on the choice of the controlled isometry V hom +B;A→R(x) (resp. V het +B;A→R(ω)) in the virtual and the +estimation protocol. We here take a suboptimal strategy; fix V hom +B;A→R(x) (resp. V het +B;A→R(ω)) so +that the probability of the phase error event ˆb′ = − in the estimation protocol is minimized for +an ideal pure-loss channel [58] with transmission η = β2/µ. When the state |Ψ⟩A ˜ +C in Eq. (7) is +put into a pure-loss channel with the channel output being |±β⟩C, the resulting state |Φ⟩ACE on +systems A, C, and an adversary’s system E (i.e., an environment of the pure-loss channel) is given +by +|Φ⟩ACE = +1 +√ +2 +� +|0⟩A |β⟩C +��� +� +µ − β2 +� +E + |1⟩A |−β⟩C +���− +� +µ − β2 +� +E +� +. +(25) +Tracing out the system E, the reduced state ΦAC is given by +ΦAC = (1 − qµ,β) |φ+⟩⟨φ+|AC + qµ,β |φ−⟩⟨φ−|AC , +(26) +where +|φ+⟩AC := +1 +√ +2(|0⟩ |β⟩ + |1⟩ |−β⟩) = |+⟩A ⊗ Πev |β⟩C + |−⟩A ⊗ Πod |β⟩C , +(27) +|φ−⟩AC := +1 +√ +2(|0⟩ |β⟩ − |1⟩ |−β⟩) = |+⟩A ⊗ Πod |β⟩C + |−⟩A ⊗ Πev |β⟩C = (ZA ⊗ IC) |φ+⟩AC , +(28) +8 + +and +qµ,β := 1 − e−2(µ−β2) +2 +(> 0). +(29) +For Homodyne protocol, we observe that +C-XBA +� +IdA ⊗ Khom +C→B(x) +� +(ΦAC) C-XBA +(30) += 2fsuc(x) C-XBA +� +(1 − qµ,β) ˆP +� +⟨x| Πev |β⟩ |++⟩AB + ⟨x| Πod |β⟩ |−−⟩AB +� ++qµ,β ˆP +� +⟨x| Πod |β⟩ |+−⟩AB + ⟨x| Πev |β⟩ |−+⟩AB +�� +C-XBA +(31) += 2fsuc(x) +� +(1 − qµ,β) ˆP +� +⟨x| Πev |β⟩ |+⟩A + ⟨x| Πod |β⟩ |−⟩A +� +⊗ |+⟩⟨+|B ++qµ,β ˆP +� +⟨x| Πod |β⟩ |+⟩A + ⟨x| Πev |β⟩ |−⟩A +� +⊗ |−⟩⟨−|B +� +(32) += fsuc(x) +� +(1 − qµ,β) ˆP +�� +gβ,1/4(x) |0⟩A + +� +g−β,1/4(x) |1⟩A +� +⊗ |+⟩⟨+|B ++qµ,β ˆP +�� +gβ,1/4(x) |0⟩A − +� +g−β,1/4(x) |1⟩A +� +⊗ |−⟩⟨−|B +� +, +(33) +where ˆP(ψ) := ψψ† (and thus ˆP(|ψ⟩) = |ψ⟩⟨ψ|), and gm,V is the normal distribution with the +mean m and the variance V , i.e., +gm,V (x) := +1 +√ +2πV +exp +� +−(x − m)2 +2V +� +. +(34) +We define τ hom +AB (x) as +τ hom +AB (x) :=(1 − qµ,β) ˆP +�� +gβ,1/4(x) |0⟩A + +� +g−β,1/4(x) |1⟩A +� +⊗ |+⟩⟨+|B ++ qµ,β ˆP +�� +gβ,1/4(x) |0⟩A − +� +g−β,1/4(x) |1⟩A +� +⊗ |−⟩⟨−|B . +(35) +From Eqs. (17), (21), (33), and (35), the probability density of an outcome x with occurrence of +the phase error is given by +Tr +� +|−⟩⟨−|B K′ hom +AC→B(x)(ΦAC) +� += fsuc(x) +2 +Tr +� +⟨0|B τ hom +AB (x) |0⟩B + ⟨1|B τ hom +AB (x) |1⟩B +− +� +V (1) +A→R(x) +�† +V (0) +A→R(x) ⟨0|B τ hom +AB (x) |1⟩B − ⟨1|B τ hom +AB (x) |0⟩B +� +V (0) +A→R(x) +�† +V (1) +A→R(x) +� (36) += fsuc(x) +�1 +2 Tr +� +τ hom +AB (x) +� +− Re +� +Tr +�� +V (1) +A→R(x) +�† +V (0) +A→R(x) ⟨0|B τ hom +AB (x) |1⟩B +��� +(37) +≥ fsuc(x) +�1 +2 Tr +� +τ hom +AB (x) +� +− +��⟨0|B τ hom +AB (x) |1⟩B +�� +1 +� +, +(38) +where the last inequality follows from the matrix Hölder inequality. If we write the polar decom- +position of ⟨0|B τ hom +AB (x) |1⟩B by W hom +A +(x) +��⟨0|B τ hom +AB (x) |1⟩B +��, the equality in (38) can be achieved +by setting +� +V (1) +A→R(x) +�† +V (0) +A→R = +� +W hom +A +(x) +�† . +(39) +From Eq. (35), ⟨0|B τ hom +AB (x) |1⟩B is given by +⟨0|B τ hom +AB (x) |1⟩B = 1 +2 +� +(1 − qµ,β) ˆP +�� +gβ,1/4(x) |0⟩A + +� +g−β,1/4(x) |1⟩A +� +−qµ,β ˆP +�� +gβ,1/4(x) |0⟩A − +� +g−β,1/4(x) |1⟩A +�� +, +(40) +9 + +which is hermitian with two eigenvalues having opposite signs. Let |uhom ++ +(x)⟩A and |uhom +− +(x)⟩A +be eigenvectors of ⟨0|B τ hom +AB (x) |1⟩B with positive and negative eigenvalues, respectively. Then, +W hom +A +(x) is given by +W hom +A +(x) = |uhom ++ +(x)⟩⟨uhom ++ +(x)|A − |uhom +− +(x)⟩⟨uhom +− +(x)|A . +(41) +The explicit form of |uhom +± +(x)⟩A is given in Eq. (151) in Appendix B. The choice of the isometry +V (j) +A→R(x) to satisfy Eq. (39) is not unique; one of the reasons is the arbitrariness of the dimension +of the system R. Here, we set R = A and set +V (0) +A→R(x) = IA, +V (1) +A→R(x) = W hom +A +(x), +(42) +which, with Eqs. (17) and (41), leads to +V hom +B;A→A(x) = +� +|uhom ++ +(x)⟩⟨uhom ++ +(x)|A ⊗ IB + |uhom +− +(x)⟩⟨uhom +− +(x)|A ⊗ ZB +� +C-XBA. +(43) +For Heterodyne protocol, the calculation similar to Eqs. (30)–(35) leads to +C-XBA +� +IdA ⊗ Khet +C→B(ω) +� +(ΦAC) C-XBA +(44) += 2fsuc(ωr) +π +C-XBA +� +(1 − qµ,β) ˆP +� +⟨ω| Πev |β⟩ |++⟩AB + ⟨ω| Πod |β⟩ |−−⟩AB +� ++qµ,β ˆP +� +⟨ω| Πod |β⟩ |+−⟩AB + ⟨ω| Πev |β⟩ |−+⟩AB +�� +C-XBA +(45) += fsuc(ωr) +π +� +(1 − qµ,β) ˆP +� +⟨ω|β⟩ |0⟩A + ⟨−ω|β⟩ |1⟩A +� +⊗ |+⟩⟨+|B ++qµ,β ˆP +� +⟨ω|β⟩ |0⟩A − ⟨−ω|β⟩ |1⟩A +� +⊗ |−⟩⟨−|B +� +, +(46) +Since ⟨ω|β⟩ = e− 1 +2 [(ωr−β)2+ω2 +i +2iωiβ] is not real in general, we insert a θ-rotation around the Z +basis +RZ +A(θ) := exp(−iθZA/2) +(47) +in order to have +� +RZ +A(2ωiβ) +�† C-XBA +� +IdA ⊗ Khet +C→B(ω) +� +(ΦAC) C-XBA RZ +A(2ωiβ) +(48) += e−ω2 +i fsuc(ωr) +√π +� +(1 − qµ,β) ˆP +�� +gβ,1/2(ωr) |0⟩A + +� +g−β,1/2(ωr) |1⟩A +� +⊗ |+⟩⟨+|B ++qµ,β ˆP +�� +gβ,1/2(ωr) |0⟩A − +� +g−β,1/2(ωr) |1⟩A +� +⊗ |−⟩⟨−|B +� +. +(49) +We define τ het +AB(ωr) as +τ het +AB(ωr) := (1 − qµ,β) ˆP +�� +gβ,1/2(ωr) |0⟩A + +� +g−β,1/2(ωr) |1⟩A +� +⊗ |+⟩⟨+|B ++ qµ,β ˆP +�� +gβ,1/2(ωr) |0⟩A − +� +g−β,1/2(ωr) |1⟩A +� +⊗ |−⟩⟨−|B . +(50) +Thus, the structure of the matrix τ het +AB(ωr) is essentially the same as τ hom +AB (x) of Homodyne protocol. +In the same way as Homodyne protocol, the probability density of outcome ω with the occurrence +of a phase error is given by +Tr +� +|−⟩⟨−|B K′ het +AC→B(ω)(ΦAC) +� += e−ω2 +i fsuc(ωr) +√π +�1 +2 Tr +� +τ het +AB(ωr) +� +(51) +−Re +� +Tr +�� +V ′(1) +A→R(ωr) +�†V ′(0) +A→R(ωr)RZ +A(2ωiβ) ⟨0|B τ het +AB(ωr) |1⟩B +� +RZ +A(2ωiβ) +�†��� +(52) +≥ e−ω2 +i fsuc(ωr) +√π +�1 +2 Tr +� +τ het +AB(ωr) +� +− +��⟨0|B τ het +AB(ωr) |1⟩B +�� +1 +� +. +(53) +10 + +If we write the polar decomposition of ⟨0|B τ het +AB(ωr) |1⟩B by W het +A (ωr) +��⟨0|B τ het +AB(ωr) |1⟩B +��, then the +equality of Eq. (53) can be achieved by setting +� +RZ +A(2ωiβ) +�† � +V ′(1) +A→R(ω) +�† +V ′(0) +A→R(ω)RZ +A(2ωiβ) = +� +W het +A (ωr) +�† . +(54) +From Eq. (50), ⟨0|B τ het +AB(ωr) |1⟩B is given by +⟨0|B τ het +AB(ωr) |1⟩B = 1 +2 +� +(1 − qµ,β) ˆP +�� +gβ,1/2(ωr) |0⟩A + +� +g−β,1/2(ωr) |1⟩A +� +−qµ,β ˆP +�� +gβ,1/2(ωr) |0⟩A − +� +g−β,1/2(ωr) |1⟩A +�� +, +(55) +which is hermitian. Let |uhet ++ (ωr)⟩A and |uhet +− (ωr)⟩A be eigenvectors of ⟨0|B τ het +AB(ωr) |1⟩B with +positive and negative eigenvalues, respectively. Then, W het +A (ωr) is given by +W het +A (ωr) = |uhet ++ (ωr)⟩⟨uhet ++ (ωr)|A − |uhet +− (ωr)⟩⟨uhet +− (ωr)|A . +(56) +We can choose V ′(j) +A→R(ω) to satisfy Eq. (54) in the same way as Homodyne protocol. We set R = A +and set +V ′(0) +A→R(ω) = +� +RZ +A(2ωiβ) +�† , +V ′(1) +A→R(ω) = W het +A (ωr) +� +RZ +A(2ωiβ) +�† , +(57) +which, with Eqs. (18) and (56), leads to +V het +B;A→A(ω) = +� +|uhet ++ (ωr)⟩⟨uhet ++ (ωr)|A ⊗ IB + |uhet +− (ωr)⟩⟨uhet +− (ωr)|A ⊗ ZB +� � +RZ +A(2ωiβ) +�† C-XBA. +(58) +As explained previously, we set V (j) +A→R(x) to the one in Eq. (42) (resp. V ′(j) +A→R(ω) to the one +in Eq. (57)) also for arbitrary channels, i.e., arbitrary coherent attacks by Eve. This choice is +suboptimal for general channels but is expected to be close to optimal for channels that are close +to the pure-loss one. Now that the controlled isometry V hom +B;A→A(x) (resp. V het +B;A→A(ω)) is fixed, we +can interpret the event that Bob announces “success” and obtains ˆb′ = − (i.e., the phase error) at +the signal round of Estimation protocol as the outcome of a generalized measurement on Alice’s +qubit A and the optical pulse C and define the corresponding POVM element M hom/het +ph +through +Eq. (19) (resp. Eq. (20)) as +M hom +ph +:= Fhom ‡ +AC→B +� +|−⟩⟨−|B +� += +� ∞ +−∞ +dx +� +K′ hom +AC→B(x) +�‡ � +|−⟩⟨−|B +� +, +(59) +M het +ph := Fhet ‡ +AC→B +� +|−⟩⟨−|B +� += +�� ∞ +−∞ +dωr dωi +� +K′ het +AC→B(ω) +�‡ � +|−⟩⟨−|B +� +, +(60) +where ‡ denotes the adjoint map. Then, for any density operator ρ on the joint system AC, M hom +ph +(resp. M het +ph ) satisfies +Eρ +� +ˆN suc (i) +ph +� += psigTr +� +ρ M hom/het +ph +� +(61) +in Homodyne (resp. Heterodyne) protocol. For Homodyne protocol, by using Eqs. (9), (21), and +(43), we have +M hom +ph += +� ∞ +−∞ +dx +� +IA ⊗ +� +Khom +suc (x) +�†� � +V hom +B;A→A(x) +�†� +IA ⊗ |−⟩⟨−|B +� +V hom +B;A→A(x) +� +IA ⊗ Khom +suc (x) +� +(62) += +� ∞ +−∞ +dx +� +ˆP +�� +IA ⊗ +� +Khom +suc (x) +�†� +C-XBA |uhom ++ +(x)⟩A ⊗ |−⟩B +� ++ ˆP +�� +IA ⊗ +� +Khom +suc (x) +�†� +C-XBA |uhom +− +(x)⟩A ⊗ |+⟩B +�� +, +(63) +11 + +where we used the fact that the adjoint map of the tracing-out TrA is taking the tensor product +with IA. Using the relation C-XBA = |+⟩⟨+|A ⊗ IB + |−⟩⟨−|A ⊗ ZB as well as Eq. (12), we have +M hom +ph += +� ∞ +−∞ +2fsuc(x)dx +� +ˆP +� +Π(+,od),(−,ev) +AC +|uhom ++ +(x)⟩A ⊗ |x⟩C +� ++ ˆP +� +Π(−,od),(+,ev) +AC +|uhom +− +(x)⟩A ⊗ |x⟩C +�� +, +(64) +where two orthogonal projections Π(+,od),(−,ev) +AC +and Π(−,od),(+,ev) +AC +are defined as +Π(+,od),(−,ev) +AC +:= |+⟩⟨+|A ⊗ Πod + |−⟩⟨−|A ⊗ Πev, +(65) +Π(−,od),(+,ev) +AC +:= |−⟩⟨−|A ⊗ Πod + |+⟩⟨+|A ⊗ Πev. +(66) +A similar relation holds for Heterodyne protocol by replacing Khom +suc (x) with Khet +suc(ω) and V hom +B;A→A(x) +with V het +B;A→A(ω) as well as using Eqs. (15), (58), (65), and (66): +M het +ph = +�� ∞ +−∞ +dωrdωi +� +ˆP +�� +IA ⊗ +� +Khet +suc(ω) +�†� +C-XBA RZ +A(2ωiβ) |uhet ++ (ωr)⟩A ⊗ |−⟩B +� ++ ˆP +�� +IA ⊗ +� +Khet +suc(ω) +�†� +C-XBA RZ +A(2ωiβ) |uhet +− (ωr)⟩A ⊗ |+⟩B +�� +(67) += +�� ∞ +−∞ +2fsuc(ωr) +π +dωrdωi +� +ˆP +� +Π(+,od),(−,ev) +AC +RZ +A(2ωiβ) |uhet ++ (ωr)⟩A ⊗ |ω⟩C +� ++ ˆP +� +Π(−,od),(+,ev) +AC +RZ +A(2ωiβ) |uhet +− (ωr)⟩A ⊗ |ω⟩C +�� +. +(68) +Using Eq. (11), we observe that +1 +π +� +dωi exp(±2iωiβ) |ω⟩⟨ω| = 1 +π +��� +dωidxdx′ +� +2 +π e±2iωiβ−(x−ωr)2+2iωix−(x′−ωr)2−2iωix′ |x⟩⟨x′| +(69) += 2 +�� +dxdx′ δ(2(x ± β − x′)) |x⟩⟨x|ωr⟩⟨ωr|x′⟩⟨x′| +(70) += +� +dx |x⟩⟨x|ωr⟩⟨ωr|x ± β⟩⟨x ± β| . +(71) +Applying this to Eq. (68) and changing the integration variable appropriately, we have +M het +ph = +�� ∞ +−∞ +2fsuc(ωr)dωrdx +� +ˆP +� +Π(+,od),(−,ev) +AC +Oβ +AC(x) |uhet ++ (ωr)⟩A ⊗ |ωr⟩C +� ++ ˆP +� +Π(−,od),(+,ev) +AC +Oβ +AC(x) |uhet +− (ωr)⟩A ⊗ |ωr⟩C +�� +, +(72) +where the operator Oβ +AC(x) is defined as +Oβ +AC(x) := |0⟩⟨0|A ⊗ |x⟩⟨x|C + |1⟩⟨1|A ⊗ |x − β⟩⟨x − β|C . +(73) +2.3 +Finite-size analysis +Since the phase error operator was defined on systems A and C, we can follow essentially the same +analysis as that in Ref. [37]. Let us define the following operators: +Πfid := |0⟩⟨0|A ⊗ |β⟩⟨β|C + |1⟩⟨1|A ⊗ |−β⟩⟨−β|C +(74) += |φ−⟩⟨φ−|AC + |φ+⟩⟨φ+|AC , +(75) +Πtrash +− +:= |−⟩⟨−|A ⊗ IC, +(76) +12 + +where |φ±⟩AC are defined in Eqs. (27) and (28). For any density operator ρ on the joint system +AC, these operators satisfy +Eρ +� +ˆF (i)� +≤ ptestTr +� +ρ Πfid� +, +(77) +Eρ +� +ˆQ(i) +− +� += ptrashTr +� +ρ Πtrash +− +� +, +(78) +where the first inequality follows from Theorem 1 in Ref. [37] as well as the definition of ˆF (i). Let +M hom/het[κ, γ] for positive numbers κ and γ determined prior to the protocol be defined as +M hom/het[κ, γ] := M hom/het +ph ++ κΠfid − γΠtrash +− +. +(79) +In Corollaries 2 and 3 in Appendix B, we show an inequality +M hom/het[κ, γ] ≤ Bhom/het(κ, γ) IAC +(80) +with a computable convex function Bhom/het(κ, γ). Let ˆT (i)[κ, γ] be a linear combination of random +variables at ith round in Estimation protocol given by +ˆT (i)[κ, γ] := p−1 +sig ˆN suc (i) +ph ++ p−1 +testκ ˆF (i) − p−1 +trashγ ˆQ(i) +− . +(81) +Furthermore, let ˆT (0)[κ, γ] be zero. +Then, by applying Azuma’s inequality [59–61] with Doob +decomposition to { ˆT (k)[κ, γ]}k=0,...,N and using Eqs. (61), (77), (78), and (80), we observe that +N +� +k=1 +ˆT (k)[κ, γ] = p−1 +sig ˆN suc +ph + p−1 +testκ ˆF − p−1 +trashγ ˆQ− ≤ NBhom/het(κ, γ) + δ1(ϵ/2), +(82) +holds with a probability no smaller than 1 − ϵ/2. (See Proposition 1 as well as Eqs. (92)–(105) in +Ref. [37].) Here, δ1(ϵ) is defined as [37] +δ1(ϵ) := +� +max +� +p−1 +sig, p−1 +testκ max +ν≥0 Λm,r(ν) +� +− min +� +p−1 +testκ min +ν≥0 Λm,r(ν), −p−1 +trashγ +�� � +N +2 ln +�1 +ϵ +� +. +(83) +Since ˆQ− is determined solely by Alice’s qubits, each in the state Tr ˜ +C(|Φ⟩⟨Φ|A ˜ +C) with |Φ⟩A ˜ +C given +in Eq. (7), it follows the same statistics as a tally of ˆN trash Bernoulli trials with a probability +q− := ∥ ⟨−|A |Ψ⟩A ˜ +C ∥2 = (1 − e−2µ)/2. Hence we observe that +ˆQ− ≤ q− ˆN trash + δ2(ϵ/2; ˆN trash) +(84) +holds with a probability no smaller than 1 − ϵ/2. (See Eq. (31) in Ref. [37].) Here, δ2(ϵ; n) is +defined as [37] +� +D(q− + δ2(ϵ; n)/n∥q−) = − 1 +n log2(ϵ) +(ϵ > qn +−) +δ2(ϵ; n) = (1 − q−)n +(ϵ ≤ qn +−) , +(85) +where +D(x∥y) := x log2 +x +y + (1 − x) log2 +1 − x +1 − y +(86) +is the Kullback-Leibler divergence. Combining Eqs. (81), (82), and (84), by setting +U( ˆF, ˆN trash) = psig +� +NBhom/het(κ, γ) + δ1(ϵ/2) +� +− psig +ptest +κ ˆF + psig +ptrash +γ +� +q− ˆN trash + δ2(ϵ/2; ˆN trash) +� +, +(87) +we observe that Eq. (23) holds from the union bound. +13 + +3 +Numerical simulations +We compute (the lower bound on) the net key gain per pulse (i.e., key rate ˆG) against the transmis- +sion distance with various values of excess noise at the channel output. In this model, Bob receives +Gaussian states ρ(ˆa) +model obtained by randomly displacing attenuated coherent states |(−1)ˆa√ηµ⟩ +with attenuation rate η to increase their variances via factor of (1 + ξ), i.e., +ρ(ˆa) +model := 2 +πξ +� +C +e−2|γ|2/ξ |(−1)ˆa√ηµ + γ⟩⟨(−1)ˆa√ηµ + γ| d2γ. +(88) +For simplicity, the number Nsmp of the sampling rounds is set to be N/100, and the bit error +correction efficiency f in Eq. (4) is to be 0.95 2. The acceptance probability fsuc(x) is assumed to +be a step function Θ(x − xth) with a threshold xth(> 0), where Θ(x) denotes the Heaviside step +function. The expected amplitude of the coherent state β is chosen to be √ηµ. We set the security +parameter ϵsec = 2−50, and set ϵcor = ϵsec/2 and ϵ = 2−s = ϵ2 +sec/16. +We assume that the number of “success” signal rounds ˆN suc is equal to its expectation, i.e., +E[ ˆN suc] = psigN +� ∞ +−∞ +(fsuc(x) + fsuc(−x)) ⟨x| 1 +2 +� +a∈{0,1} +ρ(a) +model |x⟩ dx +(89) += psigN(P + +hom + P − +hom), +(90) +where +P ± +hom := +� ∞ +−∞ +fsuc(±x) +2 +� +a∈{0,1} +⟨(−1)ax| ρ(a) +model |(−1)ax⟩ dx +(91) += 1 +2erfc +� +(xth ∓ √ηµ) +� +2 +1 + ξ +� +, +(92) +for Homodyne protocol [37]. For Heterodyne protocol [38], it is given by +E[ ˆN suc] = psigN(P + +het + P − +het), +(93) +P ± +het := +�� ∞ +−∞ +fsuc(±ωr) +2π +� +a∈{0,1} +⟨(−1)aω| ρ(a) +model |(−1)aω⟩ dωrdωi +(94) += 1 +2erfc +� +(xth ∓ √ηµ) +� +2 +2 + ξ +� +. +(95) +We also assume that the number of “success” sampling rounds is equal to (P + +hom/het+P − +hom/het)Nsmp, +the number of test rounds ˆN test is equal to ptestN, and the number of trash rounds ˆN trash is equal +to ptrashN. The test outcome ˆF is assume to be equal to its expectation given by [37] +E[ ˆF] = ptestN 1 +2 +� +a∈{0,1} +Eρ(a) +model[Λm,r(|ˆω − (−1)a√ηµ|2)] +(96) += ptestN +1 + ξ/2 +� +1 − (−1)m+1 +� +ξ/2 +1 + r(1 + ξ/2) +�m+1� +. +(97) +For the test function Λm,r in the above, we adopt m = 1 and r = 0.4120, which leads to +(maxν≥0 Λm,r(ν), minν≥0 Λm,r(ν)) = (2.824, −0.9932). We assume that the number ˆEobs of bit +errors observed in the “success” sampling rounds is equal to its expectation ˆEobs = P − +hom/hetNsmp. +The upper-bound eqber on the bit error rate is thus given by Eq. (3) with the parameters ˆN suc, +ˆN suc +smp, and ˆEobs given above. Under these assumptions, the remaining parameters to be determined +are six parameters (µ, xth, psig, ptest, κ, γ). We determined (κ, γ) via a convex optimization using +CVXPY 1.2.1 and (µ, xth, psig, ptest) via the Nelder-Mead in the scipy.minimize library in Python, +for each transmission distance L with the attenuation rate η assumed to be 10−0.02L. +2Currently, this level of efficiency may be too optimistic because the bit error correction in our protocol must +succeed with probability no smaller than 1 − εcor/2 without the use of the verification. +14 + +Figure 2: Key rates of the Homodyne protocol against transmission distance over an optical fiber. The attenu- +ation rate of the optical fiber is assumed to be 10−0.02L with transmission distance L km, an error correction +efficiency f in Eq. (4) is set to be 0.95, and the number of sampling rounds Nsmp is set to be N/100. a) Key +rates when the excess noise ξ at the channel output is zero; that is, the channel is pure loss. The bold solid +lines show the key rates with our refined analysis developed here, the broken lines show those with the previous +analysis [37], and the black thin line shows the PLOB bound, which is the ultimate limit of the key rate of +one-way QKD [58]. One can see that the logarithm of the asymptotic key rate decreases in parallel to the +PLOB bound with our refined analysis against the transmission distance (≫ 1 km) as opposed to the previous +results [37]. Improvement in the key rate is sustained in the finite-size case. b) Key rates when N = 1012 with +various values of excess noise parameter ξ. (The detail of the noise model is given in the main text.) The solid +lines show the key rates with our refined analysis, and the broken lines show those with the previous results +[37]. One can see that, although the key rate significantly improves for the pure-loss channel, the excess noise +as high as ξ = 10−3–10−2 degrades the performance to almost the same level as that of the previous results. +Figure 2 shows the key rates of Homodyne protocol for the channel model explained above. +Figures show that under the condition of low excess noise, our refined analysis results in significantly +higher key rates and longer transmission distance than that of the previous results [37] even in the +finite-key case. Furthermore, the logarithm of the asymptotic key rate in the pure-loss case (i.e., +ξ = 0) is in parallel to the PLOB bound [58] against the transmission distance; that is, it achieves a +linear scaling against the channel transmission, which is known to be optimal for one-way QKD in +the pure-loss channel. When the excess noise ξ is around 10−3.0–10−2.0, however, the improvements +in our refined analysis are lost. The result of the parameter optimization implies that our refined +analysis generates the key with relatively small intensity µ of the input coherent states compared +to the previous analyses; e.g., the optimized input intensity µ of Homodyne protocol is ∼ 0.04 in +our refined analysis compared to ∼ 0.2 in the previous analysis [37] at η = 0.1 (i.e., 50 km) for the +asymptotic pure-loss case. +The key rate of Heterodyne protocol has a similar behavior. Figure 3 shows the key rates of +Heterodyne protocol with the same noise model as above. Figures show that our refined analysis +significantly improves the key rate against the pure-loss channel, but is fragile against excess noise. +One can see, however, that, while the key rate of Heterodyne protocol is still low compared to that +of Homodyne protocol, the achievable distance (i.e., the distance with a non-zero key rate) now +becomes comparable with our refined analysis. This implies that our refined analysis based on the +reverse reconciliation is more effective for Heterodyne protocol. +4 +Discussion +We propose a refined security analysis for the protocol proposed in Ref. [37] based on the reverse +reconciliation. The motivating ideas of our refinement come from the facts that the distillability of +a secret key from a quantum state is a looser condition than the distillability of an entanglement +from it [49–51, 42, 52, 43] and the reverse reconciliation can increase the key rate for CV QKD +protocols [10]. +To exploit the ideas, we developed the procedure of “twisting” Alice’s system +with V hom +B;A→R(x) (resp. V het +B;A→R(ω)) controlled by Bob’s qubit, while the similar techniques have +already appeared in previous works [49, 42, 51, 52, 43, 53]. Our finding is that by using the twisting +15 + +a) +b) +Figure 3: Key rates of the Heterodyne protocol against transmission distance over an optical fiber. The noise +models are the same as those of Homodyne protocol. a) Key rates when the excess noise ξ at the channel +output is zero; that is, the channel is pure loss. The bold solid lines show the key rates with our refined analysis +developed here, the broken lines show those with the previous analysis [38], and the black thin line shows the +PLOB bound, which is the ultimate limit of the key rate of one-way QKD [58]. One can see that the logarithm +of the asymptotic key rate is in parallel to the PLOB bound when the transmission distance is large in the same +way as that of Homodyne protocol. The key rate is still less (about half) than that of Homodyne protocol. b) +Key rates when N = 1012 with various values of excess noise parameter ξ. The solid lines show the key rates +with our refined analysis, and the broken lines show those with the previous result [38]. +operation that minimizes the phase error probability for the pure-loss channel, the protocol has +asymptotically optimal scaling in the key rates both for Homodyne and Heterodyne protocols. +This is a clear distinction from the previous results [37, 38]; there, the asymptotic key rate non- +linearly decreases against the channel transmission. The improvement in the performance remains +in the finite-key case but is lost under the existence of excess noise as high as ξ = 10−3–10−2 at +the channel output. This may limit the feasibility of our binary-modulation protocol, but current +theoretical progress in CV QKD reveals that the discrete-modulation CV-QKD protocols with four +types of modulation have more tolerance against excess noise than those with binary modulation +[16–18]. What is important is that our security proof can be extended to the four-state protocols +with binary outcomes, such as Protocol 2 in Ref. [17] and a protocol in Ref. [18], by replacing +the bit-extracting measurements of these protocols with the qubit-extracting maps as shown in +Eq. (9) and constructing the corresponding phase error operator. This is, however, much more +complicated than the previous analysis, and we leave the problem as future work. +There are several remaining questions with our present results. +The first and foremost is +whether we can obtain higher tolerance against excess noise by extending our analysis to the four- +state protocols. As explained above, our analysis can be extended to the four-state protocols with +binary outputs [17, 18], i.e., protocols that use homodyne measurement to distinguish signals. +With the same type of argument based on the phase error estimation, we can carry out the finite- +size security proof for these protocols in principle. However, developing the analyses that preserve +the robustness against excess noise for these protocols still has non-triviality. A more challenging +problem is to apply our finite-size security proof to the four-state protocols with more than two +outputs, such as a protocol in Ref. [16] and Protocol 1 in Ref. [17]. In this case, the definition +of phase errors is already non-trivial as opposed to those with binary outputs, and we have to +develop more elaborated finite-size security proof. Whether we can extend our techniques to these +protocols or protocols with even more constellations [19] is still open. +Another important theoretical question is whether the trusted-noise model can be applied to +our security analysis. In practice, even the excess noise of ξ = 10−3 at the channel output is +difficult to realize if all the noises are untrusted. Recently, efforts have been made in the field +of CV QKD on how to incorporate noises that are intrinsic to apparatuses and thus inaccessible +to Eve into the security proof as trusted noises. This effectively eases the requirement on the +experimental apparatuses. In the present security analysis as well as ones in Refs. [37, 38], the +fidelity test measures the fidelity to a pure coherent state, which cannot be naively generalized to +16 + +the fidelity to a mixed state. Whether we can incorporate trusted noises into the fidelity test may +be crucial in this direction. +From the viewpoint of the feasibility of the protocol, the total number of 1012 of rounds to +obtain a tolerable finite-size performance may be demanding. The finite-size performance may +be improved by applying recently developed refinement [62] of the Azuma’s inequality [59] that +utilizes unconfirmed knowledge. What is non-trivial for the application of this is that the random +variable in our application of Azuma’s inequality can not directly be observed even at the end of +the protocol. Whether we can apply the refined concentration inequality [62] with the information +accessible in our protocol (in a similar fashion to Ref. [63]) may be an interesting problem. +Acknowledgments +This work was supported by the Ministry of Internal Affairs and Communications (MIC) under +the initiative Research and Development for Construction of a Global Quantum Cryptography +Network (grant number JPMI00316); Cross-ministerial Strategic Innovation Promotion Program +(SIP) (Council for Science, Technology and Innovation (CSTI)); JSPS KAKENHI Grant Number +JP22K13977. +A +Bit error sampling +In this section, we summarize how to determine an upper bound on the bit error rate from the +given sample. As explained in the main text, Nsmp sampling rounds are randomly inserted in the +actual protocol in which Alice and Bob announce their bit values if Bob’s detection succeeds (in +the same way as in the signal round). The number of “success” sampling rounds is denoted by +ˆN suc +smp, and the observed number of discrepancies between Alice and Bob is denoted by ˆEobs. +Let us first introduce a Chernoff-type bound for the hypergeometric distribution. +Lemma 1 (Tail bound for the hypergeometric distribution [64]). Let X1, . . . , XN be a binary +sequence, and M be the number of elements with Xi = 1, i.e, M := �N +i=1 Xi. Let ˆY1, . . . , ˆYn +(n ≤ N) be randomly sampled from X1, . . . , XN without replacement. Let ˆm := �n +i=1 ˆYi be the +number of ones in ˆY1, . . . , ˆYn. Then, for any δ ∈ [0, M/N], the following inequality holds: +Pr +� ˆm +n ≤ M +N − δ +� +≤ 2−nD( M +N −δ∥ M +N ), +(98) +where D(·∥·) is defined in Eq. (86). +Then, the following corollary is essential for the bit error sampling. +Corollary 1 (Estimation by the simple random sampling without replacement). Let X1, . . . , XN +be a binary sequence with M := �N +i=1 Xi. Let ˆY1, . . . , ˆYn (n ≤ N) be randomly sampled from +X1, . . . , XN without replacement, and define ˆm := �n +i=1 ˆYi. Then, for any ϵ ∈ (0, 1), the following +inequality holds: +Pr +� ˜ +MN,n,ϵ( ˆm) < M +� +≤ ϵ, +(99) +where the function ˜ +MN,n,ϵ(m) is defined to satisfy +m +n ≤ +˜ +MN,n,ϵ(m) +N +≤ 1 +(100) +and for 0 ≤ m < n, +D +� +m/n +�� ˜ +MN,n,ϵ(m)/N +� += − 1 +n log ϵ. +(101) +Proof. Let f(M) be a function of M satisfying 0 ≤ f(M)/n ≤ M/N. Then, from Lemma 1, we +have +Pr +� ˆm +n ≤ M +N − +�M +N − f(M) +n +�� +≤ 2−nD� f(M) +n +�� M +N +� +. +(102) +17 + +We set the function f(M) to the restriction of the function fN,n,ϵ( ¯ +M) of the real number ¯ +M that +satisfies +D +� +fN,n,ϵ( ¯ +M)/n∥ ¯ +M/N +� += − 1 +n log ϵ, +(103) +for ¯ +M ∈ [(1 − +n√ϵ)N, N). The function fN,n,ϵ( ¯ +M) increases monotonically with increasing ¯ +M in +[(1 − +n√ϵ)N, N), and its image lies in [0, n). Thus, from Eq. (102), we have +Pr +� +f −1 +N,n,ϵ( ˆm) ≤ M +� +≤ ϵ +(104) +for any ˆm ∈ [0, n). We define the function ˜ +MN,n,ϵ(m) := f −1 +N,n,ϵ(m) for m ∈ [0, n). To incorporate +the case ˆm = n, we use the following weaker condition that trivially follows from Eq. (104): +Pr +� ˜ +MN,n,ϵ( ˆm) < M +� +≤ ϵ, +(105) +and define ˜ +MN,n,ϵ(n) = N so that the above holds also for ˆm = n. These show that Eq. (99) holds +while ˜ +MN,n,ϵ(m) satisfies Eqs. (100) and (101) by construction in Eq. (103). +With Corollary 1, we can bound the number of total bit-error events from the sample under +the given failure probability εcor/2 by setting N = ˆN suc + ˆN suc +smp, n = ˆN suc +smp, and ϵ = εcor/2 for +˜ +MN,n,ϵ. As a result, we have the following statement; the number E of bit errors in ˆN suc-bit sifted +key is bounded from above by +Pr +� +E ≤ ˜ +M ˆ +Nsuc+ ˆ +Nsuc +smp, ˆ +N suc +smp,εcor/2( ˆEobs) − ˆEobs +� +≥ 1 − εcor/2. +(106) +Thus, we can define an upper bound eqber of the bit error rate as in Eq. (3), which holds with +probability no smaller than 1 − εcor/2. +B +Proof of the operator inequality +In this section, we prove the inequality (80) used in the security proof in the main text. We first +prove the following lemma. +Lemma 2. Let Π± be orthogonal projections that have the rank no smaller than three or infinite. +Let M be a self-adjoint operator satisfying M = (Π++Π−)M(Π++Π−) ≤ α(Π++Π−), where α is +a real constant. Let |ψ⟩ be a vector satisfying (Π++Π−) |ψ⟩ = |ψ⟩ and Π± |ψ⟩ ̸= 0. Assume Π± |ψ⟩ +are not proportional to eigenvectors of Π±MΠ+ (if they have). Define the following quantities with +respect to |ψ⟩: +C± := ⟨ψ| Π± |ψ⟩ (> 0), +(107) +λ±± := C−1 +± ⟨ψ| M±± |ψ⟩ , +(108) +λ+− := (C+C−)− 1 +2 ⟨ψ| M+− |ψ⟩ , +λ−+ := λ∗ ++−, +(109) +σ±+ := +� +C−1 ++ ∥M±+ |ψ⟩ ∥2 − |λ±+|2� 1 +2 , +(110) +σ±− := σ−1 +±+ +� +(C+C−)− 1 +2 ⟨ψ| M+±M±− |ψ⟩ − λ+−λ±± +� +, +(111) +∆±− := +� +C−1 +− ∥M±− |ψ⟩ ∥2 − |λ±−|2 − |σ±−|2� 1 +2 , +(112) +where M++, M−−, M+−, and M−+ are given respectively by +M±± := Π±MΠ±, +M+− := Π+MΠ−, +M−+ := M † ++−. +(113) +Then, for any real numbers γ±, we have +σsup(M + |ψ⟩⟨ψ| − γ+Π+ − γ−Π−) ≤ σsup(M6d), +(114) +18 + +where σsup(X) denotes the supremum of the spectrum of the operator X, and M6d is given by +M6d := +� +� +� +� +� +� +� +� +α − γ+ +0 +0 +∆+− +0 +0 +0 +α − γ+ +σ++ +σ+− +0 +0 +0 +σ++ +C+ + λ++ − γ+ +� +C+C− + λ+− +σ−+ +0 +∆+− +σ∗ ++− +� +C+C− + λ−+ +C− + λ−− − γ− +σ∗ +−− +∆−− +0 +0 +σ−+ +σ−− +α − γ− +0 +0 +0 +0 +∆−− +0 +α − γ− +� +� +� +� +� +� +� +� +. +(115) +Proof. We choose orthonormal vectors {|e(1) +± ⟩ , |e(2) +± ⟩ , |e(3) +± ⟩} in the domains of Π±, respectively, to +satisfy +� +C± +���e(1) +± +� += Π± |ψ⟩ , +(116) +M +���e(1) ++ +� += (M++ + M−+) +���e(1) ++ +� += λ++ +���e(1) ++ +� ++ σ++ +���e(2) ++ +� ++ λ−+ +���e(1) +− +� ++ σ−+ +���e(2) +− +� +, +(117) +M +���e(1) +− +� += (M+− + M−−) +���e(1) +− +� += λ+− +���e(1) ++ +� ++ σ+− +���e(2) ++ +� ++ ∆+− +���e(3) ++ +� +(118) ++ λ−− +���e(1) +− +� ++ σ−− +���e(2) +− +� ++ ∆−− +���e(3) +− +� +, +(119) +which is well-defined due to Eqs. (107)–(113) and M = (Π+ + Π−)M(Π+ + Π−). +Actually, +Eqs. (110)–(112) are derived by taking inner product of appropriate pairs among M±± |ψ⟩ and +M±∓ |ψ⟩. Overall phases of |e(2) +± ⟩ and |e(3) +± ⟩ are taken so that σ±+ and ∆±− are positive. From +(Π+ + Π−) |ψ⟩ = |ψ⟩, we have +|ψ⟩ = +� +C+ +���e(1) ++ +� ++ +� +C− +���e(1) +− +� +. +(120) +Let us now define the following projection operators: +Π(j) +± := +���e(j) +± +�� +e(j) +± +��� +(j = 1, 2, 3), +(121) +Π(≥2) +± +:= Π± − Π(1) +± , +(122) +Π(≥4) +± +:= Π(≥2) +± +− Π(2) +± − Π(3) +± . +(123) +Since Eqs. (117) and (119) imply (Π(≥4) ++ ++ Π(≥4) +− +)M(Π(1) ++ + Π(1) +− ) = 0, we have +M = (Π+ + Π−)M(Π+ + Π−) +(124) += (Π(1) ++ + Π(1) +− )M(Π(1) ++ + Π(1) +− ) + (Π(2) ++ + Π(3) ++ + Π(2) +− + Π(3) +− )M(Π(1) ++ + Π(1) +− ) ++ (Π(1) ++ + Π(1) +− )M(Π(2) ++ + Π(3) ++ + Π(2) +− + Π(3) +− ) + (Π(≥2) ++ ++ Π(≥2) +− +)M(Π(≥2) ++ ++ Π(≥2) +− +) +(125) +≤ λ++Π(1) ++ + λ−−Π(1) +− + λ+− +���e(1) ++ +�� +e(1) +− +��� + λ−+ +���e(1) +− +�� +e(1) ++ +��� ++ +� +σ++ +���e(2) ++ +�� +e(1) ++ +��� + σ−+ +���e(2) +− +�� +e(1) ++ +��� + σ+− +���e(2) ++ +�� +e(1) +− +��� ++∆+− +���e(3) ++ +�� +e(1) +− +��� + σ−− +���e(2) +− +�� +e(1) +− +��� + ∆−− +���e(3) +− +�� +e(1) +− +��� +� ++ ( +h.c. +) ++ α(Π(≥2) ++ ++ Π(≥2) +− +), +(126) +where h.c. denotes the hermitian conjugate of the terms in the preceding parenthesis. The last +inequality comes from M ≤ α(Π+ + Π−). Using Eq. (126), we have +M + |ψ⟩⟨ψ| − γ+Π+ − γ−Π− ≤ M6d ⊕ (α − γ+)Π(≥4) ++ +⊕ (α − γ−)Π(≥4) +− +, +(127) +where M6d is given in Eq. (115) with the basis {|e(3) ++ ⟩ , |e(2) ++ ⟩ , |e(1) ++ ⟩ , |e(1) +− ⟩ , |e(2) +− ⟩ , |e(3) +− ⟩}. +Since +α − γ± = ⟨e(3) +± | M6d |e(3) +± ⟩ ≤ σsup(M6d), the supremum of the spectrum of the right-hand side of +Eq. (127) is equal to the maximum eigenvalue of the six-dimensional matrix M6d. We then obtain +Eq. (114). +19 + +As a corollary of this lemma, we obtain the followings. First, we consider Homodyne protocol. +Corollary 2. Let |β⟩ be a coherent state and θhom +µ,β (x) be defined to satisfy +|θhom +µ,β (x)| ≤ π +2 , +tan θhom +µ,β (x) = e−2(µ−β2) sinh(4βx). +(128) +Let Πev(od) and M hom[κ, γ] be as defined in the main text, and let M hom +oo +, M hom +ee +, M hom +(±,o)(∓,e), and +M hom +(∓,e)(±,o) be defined as follows: +M hom +oo +:= +� ∞ +−∞ +fsuc(x)[1 + cos θhom +µ,β (x)]dx Πod |x⟩⟨x| Πod, +(129) +M hom +ee +:= +� ∞ +−∞ +fsuc(x)[1 − cos θhom +µ,β (x)]dx Πev |x⟩⟨x| Πev, +(130) +M hom +(+,o)(−,e) := +� ∞ +−∞ +fsuc(x) sin θhom +µ,β (x) dx Πod |x⟩⟨x| Πev, +(131) +M hom +(−,e)(+,o) := +� +M hom +(+,o)(−,e) +�† +, +(132) +M hom +(−,o)(+,e) := +� ∞ +−∞ +−fsuc(x) sin θhom +µ,β (x) dx Πod |x⟩⟨x| Πev = −M hom +(+,o)(−,e), +(133) +M hom +(+,e)(−,o) := +� +M hom +(−,o)(+,e) +�† += − +� +M hom +(+,o)(−,e) +�† +. +(134) +Define the following (real) parameters: +Co := ⟨β| Πod |β⟩ = e−|β|2 sinh |β|2, +Ce := ⟨β| Πev |β⟩ = e−|β|2 cosh |β|2, +(135) +λhom +oo +:= C−1 +o +⟨β| M hom +oo +|β⟩ , +λhom +ee +:= C−1 +e +⟨β| M hom +ee +|β⟩ , +(136) +λhom +(+,o)(−,e) := (CoCe)− 1 +2 ⟨β| M hom +(+,o)(−,e) |β⟩ = (λhom +(+,o)(−,e))∗, +(137) +σhom +oo +:= +� +C−1 +o ∥M hom +oo +|β⟩ ∥2 − (λhom +oo )2� 1 +2 , +(138) +σhom +eo +:= +� +C−1 +o ∥M hom +(−,e)(+,o) |β⟩ ∥2 − |λhom +(+,o)(−,e)|2� 1 +2 , +(139) +σhom +(+,o)(−,e) := (σhom +oo )−1 � +(CoCe)− 1 +2 ⟨β| M hom +oo +M hom +(+,o)(−,e) |β⟩ − λhom +oo λhom +(+,o)(−,e) +� += (σhom +(+,o)(−,e))∗, +(140) +σhom +(−,e)(−,e) := (σhom +(−,e)(+,o))−1 � +(CoCe)− 1 +2 ⟨β| M hom +(+,o)(−,e)M hom +ee +|β⟩ − λhom +(+,o)(−,e)λhom +ee +� += (σhom +(−,e)(−,e))∗, +(141) +∆hom +oe +:= +� +C−1 +e ∥M hom +(+,o)(−,e) |β⟩ ∥2 − |λhom +(+,o)(−,e)|2 − |σhom +(+,o)(−,e)|2� 1 +2 , +(142) +∆hom +ee +:= +� +C−1 +e ∥M hom +ee +|β⟩ ∥2 − (λhom +ee +)2 − |σhom +(−,e)(−,e)|2� 1 +2 . +(143) +20 + +Define the following two matrices M (0) +6d and M (1) +6d . +M (0) +6d := +� +� +� +� +� +� +� +� +� +1 +0 +0 +∆hom +oe +0 +0 +0 +1 +σhom +oo +σhom +(+,o)(−,e) +0 +0 +0 +σhom +oo +κCo + λhom +oo +κ√CoCe + λhom +(+,o)(−,e) +σhom +eo +0 +∆hom +oe +σhom +(+,o)(−,e) +κ√CoCe + λhom +(+,o)(−,e) +κCe + λhom +ee +− γ +σhom +(−,e)(−,e) +∆hom +ee +0 +0 +σhom +eo +σhom +(−,e)(−,e) +1 − γ +0 +0 +0 +0 +∆hom +ee +0 +1 − γ +� +� +� +� +� +� +� +� +� +, +(144) +M (1) +6d := +� +� +� +� +� +� +� +� +� +1 − γ +0 +0 +∆hom +oe +0 +0 +0 +1 − γ +σhom +oo +−σhom +(+,o)(−,e) +0 +0 +0 +σhom +oo +κCo + λhom +oo +− γ +κ√CoCe − λhom +(+,o)(−,e) +σhom +eo +0 +∆hom +oe +−σhom +(+,o)(−,e) +κ√CoCe − λhom +(+,o)(−,e) +κCe + λhom +ee +−σhom +(−,e)(−,e) +∆hom +ee +0 +0 +σhom +eo +−σhom +(−,e)(−,e) +1 +0 +0 +0 +0 +∆hom +ee +0 +1 +� +� +� +� +� +� +� +� +� +. +(145) +Define a convex function +Bhom(κ, γ) := max{σsup(M (0) +6d ), σsup(M (1) +6d )}. +(146) +Then, for κ, γ ≥ 0, we have +M hom[κ, γ] ≤ Bhom(κ, γ)IAC. +(147) +Proof. We first derive the explicit form of |uhom +± +(x)⟩A introduced in Eq. (41). Notice that +1 − 2qµ,β = e−2(µ−β2), +(148) +� +gβ,1/4(x) +g−β,1/4(x) = e4βx. +(149) +Let θ(x) be defined to satisfy +|θ(x)| < π +2 , +tan θ(x) = Tr +� +ZA ⟨0|B τ hom +AB (x) |1⟩B +� � +Tr +� +XA ⟨0|B τ hom +AB (x) |1⟩B +� +. +(150) +Noticing that Tr +� +YA ⟨0|B τ hom +AB (x) |1⟩B +� += 0, we have +|uhom +± +(x)⟩A = cos θ(x) +2 +|±⟩A ± sin θ(x) +2 +|∓⟩A . +(151) +From Eqs. (40), (148), (149), and (150), we can see that θ(x) coincides with θhom +µ,β (x) defined in +Eq. (128). We now observe that +| ⟨+|uhom ++ +(x)⟩ |2 = | ⟨−|uhom +− +(x)⟩ |2 = cos2 +�θhom +µ,β (x) +2 +� += +1 + cos θhom +µ,β (x) +2 +, +(152) +| ⟨−|uhom ++ +(x)⟩ |2 = | ⟨+|uhom +− +(x)⟩ |2 = sin2 +�θhom +µ,β (x) +2 +� += +1 − cos θhom +µ,β (x) +2 +, +(153) +⟨+|uhom ++ +(x)⟩⟨uhom ++ +(x)|−⟩ = ⟨−|uhom ++ +(x)⟩⟨uhom ++ +(x)|+⟩ = sin +�θhom +µ,β (x) +2 +� +cos +�θhom +µ,β (x) +2 +� += − ⟨+|uhom +− +(x)⟩⟨uhom +− +(x)|−⟩ = − ⟨−|uhom +− +(x)⟩⟨uhom +− +(x)|+⟩ = +sin θhom +µ,β (x) +2 +. +(154) +From Eq. (64) as well as Eqs. (74)–(79), it is obvious that +M hom[κ, γ] = Π(+,od),(−,ev) +AC +M hom[κ, γ] Π(+,od),(−,ev) +AC ++ Π(−,od),(+,ev) +AC +M hom[κ, γ] Π(−,od),(+,ev) +AC +, +(155) +21 + +where the two orthogonal projections Π(+,od),(−,ev) +AC +and Π(−,od),(+,ev) +AC +are defined in Eqs. (65) and +(66). Then we apply Lemma 2 respectively to the operators Π(+,od),(−,ev) +AC +M hom[κ, γ] Π(+,od),(−,ev) +AC +and Π(−,od),(+,ev) +AC +M hom[κ, γ] Π(−,od),(+,ev) +AC +. For Π(+,od),(−,ev) +AC +M hom[κ, γ] Π(+,od),(−,ev) +AC +, we set, by +using Eqs. (152)–(154), that +Π± = |±⟩⟨±|A ⊗ Πod(ev), +(156) +M = Π(+,od),(−,ev) +AC +M hom +ph Π(+,od),(−,ev) +AC +(157) += |+⟩⟨+|A ⊗ M hom +oo ++ |−⟩⟨−|A ⊗ M hom +ee ++ +� +|+⟩⟨−|A ⊗ M hom +(+,o)(−,e) + |−⟩⟨+|A ⊗ M hom +(−,e)(+,o) +� +, +(158) +|ψ⟩ = √κ |φ−⟩AC , +(159) +α = 1, +γ+ = 0, +γ− = γ, +(160) +where |φ−⟩AC is defined in Eq. (28). Since so-defined M only has continuous spectrum, we can +apply Lemma 2 and obtain +σsup +� +Π(+,od),(−,ev) +AC +M hom[κ, γ] Π(+,od),(−,ev) +AC +� +≤ σsup(M (0) +6d ). +(161) +In the same way, we apply Lemma 2 to Π(−,od),(+,ev) +AC +M hom[κ, γ] Π(−,od),(+,ev) +AC +. Using Eqs. (152)– +(154), we set +Π± = |∓⟩⟨∓|A ⊗ Πod(ev), +(162) +M = Π(−,od),(+,ev) +AC +M hom +ph Π(−,od),(+,ev) +AC +(163) += |−⟩⟨−|A ⊗ M hom +oo ++ |+⟩⟨+|A ⊗ M hom +ee ++ +� +|−⟩⟨+|A ⊗ M hom +(−,o)(+,e) + |+⟩⟨−|A ⊗ M hom +(+,e)(−,o) +� +, +(164) += |−⟩⟨−|A ⊗ M hom +oo ++ |+⟩⟨+|A ⊗ M hom +ee +− +� +|−⟩⟨+|A ⊗ M hom +(+,o)(−,e) + |+⟩⟨−|A ⊗ M hom +(−,e)(+,o) +� +, +(165) +|ψ⟩ = √κ |φ+⟩AC , +(166) +α = 1, +γ+ = γ, +γ− = 0, +(167) +where |φ+⟩AC is defined in Eq. (27). Then, we observe +σsup +� +Π(−,od),(+,ev) +AC +M hom[κ, γ] Π(−,od),(+,ev) +AC +� +≤ σsup(M (1) +6d ). +(168) +Combining inequalities (161) and (168) completes the proof. +Next, we consider Heterodyne protocol. +Corollary 3. Let |β⟩ be a coherent state and θhom +µ,β (x) be defined to satisfy +|θhet +µ,β(ωr)| ≤ π +2 , +tan θhet +µ,β(ωr) = e−2(µ−β2) sinh(2βωr). +(169) +Let Πev(od) and M het[κ, γ] be as defined in the main text, and let M het +oo , M het +ee , M het +(±,o)(∓,e), and +22 + +M het +(∓,e)(±,o) be defined as follows: +M het +oo := +�� ∞ +−∞ +fsuc(ωr)dωrdx Πod +� +|x⟩⟨x|ωr⟩⟨ωr|x⟩⟨x| ++ +cos θhet +µ,β(ωr) +2 +� +|x⟩⟨x|ωr⟩⟨ωr|x − β⟩⟨x − β| + |x − β⟩⟨x − β|ωr⟩⟨ωr|x⟩⟨x| +�� +Πod, +(170) +M het +ee +:= +�� ∞ +−∞ +fsuc(ωr)dωrdx Πev +� +|x⟩⟨x|ωr⟩⟨ωr|x⟩⟨x| +− +cos θhet +µ,β(ωr) +2 +� +|x⟩⟨x|ωr⟩⟨ωr|x − β⟩⟨x − β| + |x − β⟩⟨x − β|ωr⟩⟨ωr|x⟩⟨x| +�� +Πev, +(171) +M het +(+,o)(−,e) := +�� ∞ +−∞ +fsuc(ωr)dωrdx Πod +� +sin θhet +µ,β(ωr) |x⟩⟨x|ωr⟩⟨ωr|x⟩⟨x| +− +cos θhet +µ,β(ωr) +2 +� +|x⟩⟨x|ωr⟩⟨ωr|x − β⟩⟨x − β| − |x − β⟩⟨x − β|ωr⟩⟨ωr|x⟩⟨x| +�� +Πev, +(172) +M het +(−,e)(+,o) := +� +M het +(+,o)(−,e) +�† +, +(173) +M het +(−,o)(+,e) := +�� ∞ +−∞ +fsuc(ωr)dωrdx Πod +� +− sin θhet +µ,β(ωr) |x⟩⟨x|ωr⟩⟨ωr|x⟩⟨x| +− +cos θhet +µ,β(ωr) +2 +� +|x⟩⟨x|ωr⟩⟨ωr|x − β⟩⟨x − β| − |x − β⟩⟨x − β|ωr⟩⟨ωr|x⟩⟨x| +�� +Πev, +(174) +M het +(+,e)(−,o) := +� +M het +(−,o)(+,e) +�† +, +(175) +23 + +Define the following parameters: +Co := ⟨β| Πod |β⟩ = e−|β|2 sinh |β|2, +Ce := ⟨β| Πev |β⟩ = e−|β|2 cosh |β|2, +(176) +λhet +oo := C−1 +o +⟨β| M het +oo |β⟩ , +λhet +ee := C−1 +e +⟨β| M het +ee |β⟩ , +(177) +λhet +(+,o)(−,e) := (CoCe)− 1 +2 ⟨β| M het +(+,o)(−,e) |β⟩ = (λhet +(+,o)(−,e))∗, +(178) +λhet +(−,o)(+,e) := (CoCe)− 1 +2 ⟨β| M het +(−,o)(+,e) |β⟩ = (λhet +(−,o)(+,e))∗, +(179) +σhet +oo := +� +C−1 +o +��M het +oo |β⟩ +��2 − (λhet +oo )2� 1 +2 , +(180) +σhet +(−,e)(+,o) := +� +C−1 +o +���M het +(−,e)(+,o) |β⟩ +��� +2 +− |λhet +(+,o)(−,e)|2 +� 1 +2 +, +(181) +σhet +(+,e)(−,o) := +� +C−1 +o +���M het +(+,e)(−,o) |β⟩ +��� +2 +− |λhet +(−,o)(+,e)|2 +� 1 +2 +, +(182) +σhet +(+,o)(−,e) := σ−1 +oo +� +(CoCe)− 1 +2 ⟨β| M het +oo M het +(+,o)(−,e) |β⟩ − λhet +oo λhet +(+,o)(−,e) +� += (σhet +(+,o)(−,e))∗, +(183) +σhet +(−,o)(+,e) := σ−1 +oo +� +(CoCe)− 1 +2 ⟨β| M het +oo M het +(−,o)(+,e) |β⟩ − λhet +oo λhet +(−,o)(+,e) +� += (σhet +(−,o)(+,e))∗, +(184) +σhet +(−,e)(−,e) := [σhet +(−,e)(+,o)]−1 � +(CoCe)− 1 +2 ⟨β| M het +(+,o)(−,e)M het +ee |β⟩ − λhet +(+,o)(−,e)λhet +ee +� += (σhet +(−,e)(−,e))∗, +(185) +σhet +(+,e)(+,e) := [σhet +(+,e)(−,o)]−1 � +(CoCe)− 1 +2 ⟨β| M het +(−,o)(+,e)M het +ee |β⟩ − λhet +(−,o)(+,e)λhet +ee +� += (σhet +(+,e)(+,e))∗, +(186) +∆het +(+,o)(−,e) := +� +C−1 +e +���M het +(+,o)(−,e) |β⟩ +��� +2 +− |λhet +(+,o)(−,e)|2 − |σhet +(+,o)(−,e)|2 +� 1 +2 +, +(187) +∆het +(−,o)(+,e) := +� +C−1 +e +���M het +(−,o)(+,e) |β⟩ +��� +2 +− |λhet +(−,o)(+,e)|2 − |σhet +(−,o)(+,e)|2 +� 1 +2 +, +(188) +∆het +(−,e)(−,e) := +� +C−1 +e +��M het +ee |β⟩ +��2 − (λhet +ee )2 − |σhet +(−,e)(−,e)|2� 1 +2 , +(189) +∆het +(+,e)(+,e) := +� +C−1 +e +��M het +ee |β⟩ +��2 − (λhet +ee )2 − |σhet +(+,e)(+,e)|2� 1 +2 . +(190) +Define the following two matrices M ′(0) +6d +and M ′(1) +6d . +M ′(0) +6d +:= +� +� +� +� +� +� +� +� +� +1 +0 +0 +∆het +(+,o)(−,e) +0 +0 +0 +1 +σhet +oo +σhet +(+,o)(−,e) +0 +0 +0 +σhet +oo +κCo + λhet +oo +κ√CoCe + λhet +(+,o)(−,e) +σhet +(−,e)(+,o) +0 +∆het +(+,o)(−,e) +σhet +(+,o)(−,e) +κ√CoCe + λhet +(+,o)(−,e) +κCe + λhet +(−,e)(−,e) − γ +σhet +(−,e)(−,e) +∆het +(−,e)(−,e) +0 +0 +σhet +(−,e)(+,o) +σhet +(−,e)(−,e) +1 − γ +0 +0 +0 +0 +∆het +(−,e)(−,e) +0 +1 − γ +� +� +� +� +� +� +� +� +� +, +(191) +M ′(1) +6d +:= +� +� +� +� +� +� +� +� +� +1 − γ +0 +0 +∆het +(−,o)(+,e) +0 +0 +0 +1 − γ +σhet +oo +σhet +(−,o)(+,e) +0 +0 +0 +σhet +oo +κCo + λhet +oo − γ +κ√CoCe + λhet +(−,o)(+,e) +σhet +(+,e)(−,o) +0 +∆het +(−,o)(+,e) +σhet +(−,o)(+,e) +κ√CoCe + λhet +(−,o)(+,e) +κCe + λhet +ee +σhet +(+,e)(+,e) +∆het +(+,e)(+,e) +0 +0 +σhet +(+,e)(−,o) +σhet +(+,e)(+,e) +1 +0 +0 +0 +0 +∆het +(+,e)(+,e) +0 +1 +� +� +� +� +� +� +� +� +� +. +(192) +Define a convex function +Bhet(κ, γ) := max{σsup(M ′(0) +6d ), σsup(M ′(1) +6d )}. +(193) +24 + +Then, for κ, γ ≥ 0, we have +M het[κ, γ] ≤ Bhet(κ, γ)IAC. +(194) +Proof. In the same way as Homodyne protocol, we have from Eqs. (55) and (56) that +|uhet +± (ωr)⟩A = cos +�θhet +µ,β(ωr) +2 +� +|±⟩A ± sin +�θhet +µ,β(ωr) +2 +� +|∓⟩A . +(195) +Combining this with Eqs. (72) and (73), we observe that +(⟨+|A ⊗ Πod)M het +ph (|+⟩A ⊗ Πod) = (⟨−|A ⊗ Πod)M het +ph (|−⟩A ⊗ Πod) = M het +oo , +(196) +(⟨−|A ⊗ Πev)M het +ph (|−⟩A ⊗ Πev) = (⟨+|A ⊗ Πev)M het +ph (|+⟩A ⊗ Πev) = M het +ee +(197) +(⟨+|A ⊗ Πod)M het +ph (|−⟩A ⊗ Πev) = +� +(⟨−|A ⊗ Πev)M het +ph (|+⟩A ⊗ Πod) +�† = M het +(+,o)(−,e) +(198) +(⟨−|A ⊗ Πod)M het +ph (|+⟩A ⊗ Πev) = +� +(⟨+|A ⊗ Πev)M het +ph (|−⟩A ⊗ Πod) +�† = M het +(−,o)(+,e) +(199) +As can be seen from Eq. (72) as well as Eqs. (74)–(79), we have +M het[κ, γ] = Π(+,od),(−,ev) +AC +M het[κ, γ] Π(+,od),(−,ev) +AC ++ Π(−,od),(+,ev) +AC +M het[κ, γ] Π(−,od),(+,ev) +AC +, (200) +where Π(+,od),(−,ev) +AC +and Π(−,od),(+,ev) +AC +are defined in Eqs. (65) and (66). Then we apply Lemma +2 to the operators Π(+,od),(−,ev) +AC +M het[κ, γ] Π(+,od),(−,ev) +AC +and Π(−,od),(+,ev) +AC +M het[κ, γ] Π(−,od),(+,ev) +AC +, +respectively. For Π(+,od),(−,ev) +AC +M het[κ, γ] Π(+,od),(−,ev) +AC +, using Eqs. (196), (197), and (198), we set +Π± = |±⟩⟨±|A ⊗ Πod(ev), +(201) +M = Π(+,od),(−,ev) +AC +M het +ph Π(+,od),(−,ev) +AC +(202) += |+⟩⟨+|A ⊗ M het +oo + |−⟩⟨−|A ⊗ M het +ee + |+⟩⟨−|A ⊗ M het +(+,o)(−,e) + |−⟩⟨+|A ⊗ M het +(−,e)(+,o), +(203) +|ψ⟩ = √κ |φ−⟩AC , +(204) +α = 1, +γ+ = 0, +γ− = γ, +(205) +where |φ−⟩AC is defined in Eq. (28). Since so-defined M only has continuous spectrum, we can +apply Lemma 2 and obtain +σsup +� +Π(+,od),(−,ev) +AC +M het[κ, γ] Π(+,od),(−,ev) +AC +� +≤ σsup(M ′(0) +6d ). +(206) +We also apply Lemma 2 to Π(−,od),(+,ev) +AC +M het[κ, γ] Π(−,od),(+,ev) +AC +. +Using Eqs. 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Chvátal, Discrete Mathematics 25, 285 (1979). +27 + diff --git a/V9E1T4oBgHgl3EQfbQST/content/tmp_files/load_file.txt b/V9E1T4oBgHgl3EQfbQST/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..3c744c95c9c753487975305f37eaa6a296972974 --- /dev/null +++ b/V9E1T4oBgHgl3EQfbQST/content/tmp_files/load_file.txt @@ -0,0 +1,1584 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf,len=1583 +page_content='Refined finite-size analysis of binary-modulation continuous-variable quantum key distribution Takaya Matsuura1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Shinichiro Yamano1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Yui Kuramochi3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Toshihiko Sasaki1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' and Masato Koashi1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='4 1Department of Applied Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Graduate School of Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The University of Tokyo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 7-3-1 Hongo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Bunkyo-ku,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Tokyo 113-8656,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Japan 2Centre for Quantum Computation & Communication Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' School of Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' RMIT University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Melbourne VIC 3000,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Australia 3Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Faculty of Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Kyushu University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 744 Motooka,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Nishi-ku,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Fukuoka,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Japan 4Photon Science Center,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Graduate School of Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The University of Tokyo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 7-3-1 Hongo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Bunkyo-ku,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Tokyo 113-8656,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Japan Recent studies showed the finite-size security of binary-modulation CV-QKD pro- tocols against general attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' However, they gave poor key-rate scaling against trans- mission distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Here, we extend the security proof based on complementarity, which is used in the discrete-variable QKD, to the previously developed binary-modulation CV-QKD protocols with reverse reconciliation under the finite-size regime and obtain large improvements in the key rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Notably, the key rate in the asymptotic limit scales linearly against the attenuation rate, which is known to be optimal scaling but is not achieved in previous finite-size analyses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' This refined security approach may offer full-fledged security proofs for other discrete-modulation CV-QKD protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 1 Introduction Quantum key distribution (QKD) [1] enables two remote parties to share identical secret bits that are secure against arbitrary eavesdropping allowed in the law of quantum mechanics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' QKD combined with the one-time pad [2] can thus realize the information-theoretic security of bipartite communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Nowadays, there is increasing interest in implementing QKD in the real world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Among other things, continuous-variable (CV) QKD [3–9] has advantages over short-distance high- bit-rate QKD due to the low cost of its implementation and the affinity to the wavelength division multiplexing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' This is because homodyne and heterodyne detectors used in CV-QKD protocols do not require a low-temperature environment and have good wavelength selectivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The (single- )photon detectors used in discrete-variable (DV) QKD, on the other hand, typically require a low- temperature environment for stable operation and a high-quality frequency filter for the wavelength division multiplexing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The main problems of CV-QKD protocols are difficulties in their complete security proofs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Compared to the DV-QKD protocols, most of which have complete security proofs even in the finite-size regime, almost all the CV-QKD protocols only have asymptotic security proofs [10–19] or security proofs against collective attacks [20–25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' There are, however, some results for the com- posable finite-size security against general attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' One is for the protocol using the two-mode squeezed vacuum state [26, 27], whose security proof is based on the entropic uncertainty relation on the infinite dimension [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' This protocol, however, has difficulty in its implementation and poor key-rate scaling against the transmission distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Another is for the U(N)-symmetric protocol that uses coherent states with their complex amplitudes modulated according to a Gaussian dis- tribution [29, 21, 30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The security proof for this type of protocol utilizes the de Finetti reduction Takaya Matsuura: takaya.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='matsuura@rmit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='au 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='03171v1 [quant-ph] 9 Jan 2023 theorem [31, 32] to the i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' This methodology has proved the security of several U(N)- invariant CV-QKD protocols [33, 34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' However, in practice, ideal Gaussian modulation cannot be implemented and should be approximated by a finite number of coherent states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' It turns out that an overwhelming number of coherent states is needed to directly approximate the Gaussian ensem- ble for the security condition to be satisfied [35, 36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' If we try to mitigate the required number, additional assumptions are needed, which makes it difficult to apply it in the finite-size regime [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The other completely different approach [37, 38] is targeted at the discrete-modulation CV QKD from the beginning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [37, 38] show the finite-size security against general attacks for a binary- modulation protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' It also takes into account the discretization of the signal processing, such as binned homodyne and heterodyne measurements (see also [39] for this topic).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Although it has a nice feature, the obtained key rate has very poor scaling against transmission distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' A possible reason for this bad performance is the fact that its security proof is based on the entanglement distillation [40, 41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' It is known that the security proof based on the entanglement distillation is too stringent in general for secure key distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' There are alternative types of security proofs [42–44] that can be applied to general cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In particular, for CV-QKD protocols, the security proof based on the reverse reconciliation often provides better performance than that based on the direct reconciliation [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In this article, we develop a refined security proof based on the reverse reconciliation for the binary-modulation protocol proposed in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [37, 38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' With refined proof and no additional exper- imental requirement, we obtain a significant improvement in the key gain rate;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' in fact, it achieves near-optimal scaling against transmission distance in the asymptotic case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The article is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In Section 2, we provide the refined security proofs based on the complementarity [43] for almost the same protocols as proposed in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [37, 38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The section is further divided into three parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The first part 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='1 defines the actual protocols, which are almost the same as the ones in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [37, 38], and develops virtual protocols for the complementarity approach [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In the second part 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='2, we derive an explicit form of the phase error operator defined by the virtual procedure of the previous part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In the third part 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='3, we finish the finite-size security proof by developing operator inequalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In Section 3, we numerically demonstrate the improved performance of the protocol with our refined security proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Finally, in Section 4, we wrap up our article by discussing future work and open problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 2 Security proof 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='1 Actual, virtual, and estimation protocols In this section, we define two binary-modulation CV-QKD protocols that are closely related to the ones proposed in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [37, 38], and present their security proofs based on the reverse reconciliation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The definition of the (composable) security is the same as that in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The setups of the protocols are illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In the following, a random number is denoted with a hat such as ˆ·.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' For the places where the slash “/” is used, one can adopt either its left-hand side or right-hand side depending on which of “Homodyne protocol” or “Heterodyne protocol” defined in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 1 one chooses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Note that Homodyne protocol is the same as the protocol proposed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [37] except for the definition of fsuc(x) as well as the way of bit error correction, and Heterodyne protocol is the same as the protocol proposed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [38] except for the additional trash round as well as the way of bit error correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Prior to the protocol,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Alice and Bob determine the number N of total rounds,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' the accep- tance probability function fsuc(x) (x ∈ R) of the homodyne/heterodyne measurement satisfy- ing fsuc(x) + fsuc(−x) ≤ 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' an odd integer m and a real r for the test function Λm,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='r(ν) := e−rν(1+r)L(1) m ((1+r)ν) with L(1) m being the associated Laguerre polynomial [37],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' and the protocol parameters (µ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' psig,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' ptest,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' ptrash,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' κ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' γ) satisfying psig + ptest + ptrash = 1 and β < √µ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' where all the parameters are positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Alice and Bob then run the protocol described in Box 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Unless aborted, the protocol generates a shared final key of length ˆN fin = ˆN suc − � ˆN such � U( ˆF, ˆN trash)/ ˆN suc�� − s, (1) 2 RMIT Classifica-on: Trusted Alice Phase modulator ⟩ | 𝜇 ± 𝜇 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='𝑎 = 0, 1 Bob ー ー ー Signal Test Trash Homodyne Heterodyne Eve LO LO 𝜋 2 𝑝sig 𝑝trash 𝑝test Signal… Obtaining Test… Computing Λ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=',# "𝜔 − (−1) $%𝛽 & Trash… Discarding the pulse or the outcome 𝜇 a) b) Alice Phase modulator ⟩ | 𝜇 ± 𝜇 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='𝑎 = 0, 1 Eve 𝜇 ー ー Heterodyne LO 𝜋 2 Bob Signal Test 𝑝sig 𝑝test Trash 𝑝trash !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='𝑥 #𝜔 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content="𝑥 = Re #𝜔 #𝜔 )𝑏 ∈ 0, 1 with probability 𝑓suc( −1 '( 2𝑥) “Failure” with probability 1 − 𝑓suc 2𝑥 − 𝑓suc −2𝑥 Figure 1: Setups of the protocols." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In both protocols, the sender Alice modulates the optical phase of a laser pulse prepared in a coherent state |µ⟩ with 0 or π according to her random bit ˆa = 0 or 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (a) “Homodyne protocol”, which is similar to the protocol proposed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In this protocol, the receiver Bob randomly switches three types of measurements according to probability psig, ptest, and ptrash, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In “Signal”, Bob performs homodyne measurement and obtains the outcome ˆx ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Then he obtains ˆb ∈ {0, 1} with probability fsuc � (−1) ˆbˆx� , respectively, or announces “Failure” with probability 1 − fsuc(ˆx) − fsuc(−ˆx).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In “Test”, Bob performs heterodyne measurement and obtains the outcome ˆω ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Then he computes Λm,r � |ˆω − (−1)ˆa|2� with Alice’s bit ˆa announced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In “Trash”, Bob discards the received optical pulse and produces no outcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (b) “Heterodyne protocol”, which is similar to the protocol proposed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In this protocol, the receiver Bob performs heterodyne measurement, obtains the outcome ˆω, and randomly switches three types of post- processings according to probability psig, ptest, and ptrash, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In “Signal”, Bob defines ˆx = Re[ˆω] and follows the same procedure of obtaining the bit b or “Failure” as in Homodyne protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In “Test”, Bob follows the same procedure of computing Λm,r � |ˆω − (−1)ˆa|2� as in Homodyne protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In “Trash”, Bob discards the outcome ˆω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' where ⌈·⌉ is the ceiling function, the function h(x) is defined as h(x) := � −x log2(x) − (1 − x) log2(1 − x) (x ≤ 1/2) 1 (x > 1/2) , (2) and the function U( ˆF, ˆN trash) will be specified later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Box 1: Actual protocol 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Alice generates a random bit ˆa ∈ {0, 1} and sends an optical pulse ˜C in a coherent state with amplitude (−1)ˆa√µ to Bob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' She repeats it for N rounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Bob receives an optical pulse C for each of the N rounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' For the received pulse C in each round, Bob chooses a label from {signal, test, trash} with probabilities psig, ptest, and ptrash, respectively, and announces it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' According to the label, Alice and Bob do one of the following procedures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [signal] Bob performs a homodyne/heterodyne measurement on the received optical pulse C and obtains an outcome ˆx ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (For the heterodyne measurement, ˆx is defined as the real part of the outcome ˆω ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=') Bob defines a sifted-key bit ˆb as ˆb = 0 with a probability fsuc(ˆx) and ˆb = 1 with a probability fsuc(−ˆx).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' When Bob has defined his sifted key bit, he announces “success”, and otherwise, he announces “failure”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In the case of a success, Alice (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Bob) records a bit ˆa (ˆb).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [test] Bob performs a heterodyne measurement on the received optical pulse C and obtains an outcome ˆω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Alice announces her bit a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Bob calculates the value of Λm,r(|ˆω − (−1)ˆaβ|2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [trash] Alice and Bob produce no outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' We refer to the numbers of “success” and “failure” signal rounds, test rounds, and trash rounds as ˆN suc, ˆN fail, ˆN test, and ˆN trash, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (N = ˆN suc + ˆN fail + 3 ˆN test + ˆN trash holds by definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=') Bob calculates the sum of Λm,r(|ˆω − (−1)ˆaβ|2) obtained in the ˆN test test rounds, which is denoted by ˆF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' For error correction, they use HEC-bits of encrypted communication consuming a pre-shared secret key to do the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' According to (the upper bound on) the bit error rate eqber, Bob randomly chooses an error-correcting code and sends it with the HEC-bits syndrome to Alice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Alice reconciles her sifted key accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Bob computes and announces the final key length ˆN fin according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Alice and Bob apply privacy amplification to obtain the final key.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' For simplicity, we omitted the bit-error-sampling rounds in the above protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' To satisfy the required correctness εcor for the final key, Alice and Bob randomly insert Nsmp sampling rounds among N rounds in which Bob performs the same measurement as that of the signal round and estimate an upper bound eqber on the bit error rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let ˆN suc smp be the number of “success” in Nsmp sampling rounds, and let ˆEobs be the number of discrepancies between Alice’s and Bob’s bits observed in the “success” sampling rounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Then, Bob sets eqber to eqber = � ˜ M ˆ Nsuc+ ˆ N suc smp, ˆ N suc smp,εcor/2( ˆEobs) − ˆEobs �� ˆN suc, (3) where the function ˜ MN,n,ϵ is defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (101) in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The proof that this definition of eqber upper-bounds the actual bit error rate with probability no smaller than 1 − εcor/2 is also shown in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The required amount HEC of the error syndrome Bob sends to Alice in the bit error correction depends on the error correction method;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' here we assume HEC = ˆN suc (f h(˜eqber) + (1 − f)) , ˜eqber := min{eqber, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='5}, (4) where f ∈ [0, 1] denotes an error correction efficiency [45, 46, 16–18, 47] for the error correction to succeed with the probability no smaller than 1 − εcor/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The net key gain ˆG per pulse is thus given by ˆG = ( ˆN fin − HEC)/(N + Nsmp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (5) Here, we do not use verification in the post-processing, unlike Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [37, 38], due to the subtleties to incorporate it in our security proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The acceptance probability fsuc(x) should be chosen to post-select the rounds with larger values of x, for which the bit error probability is expected to be lower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The definition of fsuc(x) in this article follows Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [38] and is slightly more general than that of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (Note that Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [37] can also use this definition of fsuc(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=') It is ideally a step function with a threshold xth(> 0), but our security proof applies to any form of fsuc(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The test function Λm,r(ν) is the same as the one defined in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [37] where it is shown to satisfy Eρ[Λm,r(|ˆω − β|2)] ≤ ⟨β| ρ |β⟩ (6) for any odd integer m, positive real r, and density operator ρ (see Corollary 1 in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [37]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The parameter β is typically chosen to be √ηµ with η being a nominal transmissivity of the quantum channel, while the security proof itself holds for any choice of β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The parameter s is related to the overall security parameter in the security proof below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' We determine a sufficient amount of the privacy amplification according to the complementarity, or in other words, the phase error correction [43, 48], which has been widely used for the DV-QKD protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' We aim at showing the secrecy of Bob’s final key against the adversary Eve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' To do so, we consider a virtual protocol in which Bob has a qubit for each success signal round such that the outcome of the Z-basis measurement on it is equivalent to his sifted key bit b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Alice can do arbitrary quantum operations in the virtual protocol as long as all the statistics and available information to the adversary Eve are the same as those in the actual protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Then, after Bob’s Z-basis measurement on the qubit, the reduced classical-quantum state between Bob and Eve in the virtual protocol is the same as that in the actual protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 4 In the following, we explicitly describe the virtual protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' For Alice, we introduce a qubit A and assume that she entangles it with an optical pulse ˜C in a state |Ψ⟩A ˜ C := |0⟩A |√µ⟩ ˜ C + |1⟩A |−√µ⟩ ˜ C √ 2 , (7) where |ω⟩ ˜ C with ω ∈ C denotes the coherent state with the amplitude ω, which is defined as |ω⟩ ˜ C := e− |ω|2 2 ∞ � n=0 ωn √ n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' |n⟩ ˜ C .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (8) Then, the optical pulse ˜C emitted by Alice is in the same state as that in the actual protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' For Bob, we construct a process of probabilistically converting the received optical pulse C to a qubit B, which can be regarded as a coherent version of Bob’s signal measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' For Homodyne protocol, consider a map Khom C→B defined as [37] Khom C→B(x)(ρC) := Khom suc (x) ρC � Khom suc (x) �† (9) with Khom suc (x) := � fsuc(x) � |0⟩B⟨x|C + |1⟩B⟨−x|C � , (10) where ⟨x| maps a state vector to the value of its wave function at x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=', for a coherent state vector |ω⟩, ⟨x| acts as ⟨x|ω⟩ = � 2 π � 1 4 exp � −(x − ωr)2 + 2iωix − iωrωi � , (11) where ω = ωr + iωi with ωr, ωi ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let Πev(od) denote a projection operator onto the subspace of even(odd) photon numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Since ⟨x| (Πev − Πod) = ⟨−x| holds, we have Khom suc (x) = � 2fsuc(x) � |+⟩B⟨x|C Πev + |−⟩B⟨x|C Πod � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (12) This defines an instrument Ihom C→B for the process of producing the outcome ˆx and leaving C in a post-measurement state;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=', given a measurable set ∆ ⊆ R, the unnormalized post-measurement state is given by Ihom C→B(∆)(ρC) = � ∆ dx Khom C→B(x)(ρC) (13) with Tr[Ihom C→B(∆)(ρC)] being a probability of “success” signal event with the outcome ˆx ∈ ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Similarly, for Heterodyne protocol, consider a map Khet C→B defined as [38] Khet C→B(ω)(ρC) := Khet suc(ω) ρC � Khet suc(ω) �† (14) with Khet suc(ω) := � fsuc(ωr) π � |0⟩B⟨ω|C + |1⟩B⟨−ω|C � = � 2fsuc(ωr) π (|+⟩B⟨ω|C Πev + |−⟩B⟨ω|C Πod) , (15) where |ω⟩ denotes a coherent state vector and ω = ωr + iωi with ωr, ωi ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Similarly to Homo- dyne protocol, we can define an instrument Ihet C→B composed of the heterodyne outcome and the (unnormalized) post-measurement state, which is given by Ihet C→B(∆′)(ρC) = � ∆′ dωrdωi Khet C→B(ω)(ρC), (16) where ∆′ ⊆ R2 is a measurable set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' If Bob measures the qubit B on the Z basis after the instrument (13) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (16)), he obtains the same sifted key bit with the same probability as in the actual protocol when ˆx ∈ ∆ (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' ˆω ∈ ∆′) [37, 38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 5 At this point, one has a degree of freedom to perform quantum operations on the system AB for each outcome ˆx (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' ˆω) as long as it does not change the Z-basis value of the qubit B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' This is because we aim at showing the secrecy of Bob’s final key against the adversary Eve with Alice’s system traced out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Thus, after applying the map Khom C→B (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Khet C→B), we assume that Alice and Bob perform a controlled isometry V hom B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(x) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' V het B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(ω)) of the form V hom B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(x) := � |0⟩⟨0|B ⊗ V (0) A→R(x) + |1⟩⟨1|B ⊗ V (1) A→R(x) � C-XBA (17) V het B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(ω) := � |0⟩⟨0|B ⊗ V ′(0) A→R(ω) + |1⟩⟨1|B ⊗ V ′(1) A→R(ω) � C-XBA, (18) where C-XBA := |0⟩⟨0|B ⊗ IA + |1⟩⟨1|B ⊗ XA denotes the Controlled-NOT gate and V (j) A→R(x) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' V ′(j) A→R(ω)) for j = 0, 1 denotes an isometry from the system A to another system R that is no smaller than A 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' If V (j) A→R(x) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' V ′(j) A→R(ω)) is an identity, then the analysis reduces to the previous results [37, 38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let Vhom B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(x) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Vhet B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(ω)) be an adjoint action (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=', a CPTP map) for the isometry V hom B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(x) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' V het B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(ω)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The composition of the map Vhom B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(x) and the map (9) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' the mad Vhet B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(ω) and the map (14)) with Alice’s system traced out at the end defines a quantum operation Fhom AC→B (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Fhet AC→B) that (probabilistically) outputs Bob’s qubits for his sifted key as Fhom AC→B(ρAC) = � ∞ −∞ dx K′ hom AC→B(x)(ρAC), (19) Fhet AC→B(ρAC) = �� ∞ −∞ dωrdωi K′ het AC→B(x)(ρAC), (20) with K′ hom AC→B(x) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' K′ het AC→B(ω)) given by K′ hom AC→B(x)(ρAC) := TrR � Vhom B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(x) ◦ � IdA ⊗ Khom C→B(x) � (ρAC) � , (21) K′ het AC→B(ω)(ρAC) := TrR � Vhet B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(ω) ◦ � IdA ⊗ Khet C→B(ω) � (ρAC) � , (22) where Id denotes the identity map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Note that the idea of acting the isometry V hom B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(x) or V het B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(ω) is closely related to the twisting operation on the shield system [49–53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The difference is that in our case it acts on the system A in a way that is incompatible with the Z-basis mea- surement on A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' This is allowed in a security proof based on complementarity since what we need to prove in the virtual protocol is that the outcome of the Z-basis measurement on B is secret to Eve when the system A is traced out [43];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=', the system A works as a shield system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' We then introduce a virtual protocol that explicitly incorporates the action of Fhom AC→B in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (19) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Fhet AC→B in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (20)) in Box 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Box 2: Virtual protocol 1′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Alice prepares a qubit A and an optical pulse ˜C in a state |Ψ⟩A ˜ C defined in (7) and sends the pulse ˜C to Bob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' She repeats it for N rounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Bob receives an optical pulse C for each of the N rounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 2′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' For the received pulse C in each round, Bob announces a label in the same way as that at Step 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Alice and Bob do one of the following procedures according to the label.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [signal] Alice and Bob perform the quantum operation on the system A and the received pulse C specified by the map Fhom AC→B defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (19) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Fhet AC→B defined 1Here, a subtlety for using the verification comes in.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In order to know whether verification succeeds or not, Alice has to confirm the syndrome bits for the verification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' However, this procedure may not commute with the action of V hom B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(x) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' V het B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(ω)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' We do not currently have a method to evaluate how much the verification affects the secrecy condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 6 in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (20)) to determine success or failure of detection, obtain the qubit B upon success, and perform the controlled isometry given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (17) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (18)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Bob announces the success or failure of the detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [test] Bob performs a heterodyne measurement on the received optical pulse C, and ob- tains an outcome ˆω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Alice measures her qubit A on Z basis and announces the outcome ˆa ∈ {0, 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Bob calculates the value of Λm,r(|ˆω − (−1)ˆaβ|2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [trash] Alice measures her qubit A on X basis to obtain ˆa′ ∈ {+, −}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 3′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' ˆN suc, ˆN fail, ˆN test, ˆN trash, and ˆF are defined in the same way as those at Step 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let ˆQ− be the number of rounds with ˆa′ = − among the ˆN trash trash rounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 4′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' According to (the upper bound on) the bit error rate eqber, Bob performs HEC bits of encrypted communication consuming a pre-shared secret key to send a dummy message.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 5′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Bob computes and announces the final key length ˆN fin according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Bob performs a randomly chosen unitary on his qubits (see the main text), and measures the first ˆN fin qubits on the Z bases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In the last line of Step 5′, the random choice of a unitary is constructed so that, along with the subsequent ˆN fin-qubit measurement on the Z bases, it is equivalent to the privacy amplification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' This is possible because for any n × n linear transformation C on the n-bit sequence, there always exists a corresponding unitary U(C) that satisfies U(C) |z⟩ = |Cz⟩ on the Z basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' As has already been claimed, if Eve performs the same attacks as those in the actual protocol, the resulting classical-quantum state between Bob and Eve is the same as that in the actual protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The complementarity argument [43] in a reverse reconciliation scenario relates the amount of privacy amplification to the so-called phase error patterns of Bob’s qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Suppose that, just before the Z-basis measurement at Step 5′ of the virtual protocol, Bob’s quantum state on the first ˆN fin qubits is arbitrarily close to |+⟩⟨+|⊗ ˆ Nfin .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Then, the secrecy condition of the final key is satisfied [43, 48, 54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' For this to be true, the errors on the X bases (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=', the phase errors) on Bob’s qubits should be corrected by the procedure at Step 5′ of the virtual protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' To see the correctability of the phase errors at Step 5′, suppose that Bob measured his ˆN suc qubits on the X basis {|+⟩ , |−⟩} at the end of Step 3′, and obtained a sequence of + and −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The minuses in the sequence are regarded as phase errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' It has already been known that, if we can find an upper bound on the number of possible phase-error patterns, then we can prove the security [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' To make the argument more precise, we introduce the estimation protocol in Box 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Box 3: Estimation protocol 1′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Alice prepares a qubit A and an optical pulse ˜C in a state |Ψ⟩A ˜ C defined in (7) and sends the pulse ˜C to Bob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' She repeats it for N rounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Bob receives an optical pulse C for each of the N rounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 2′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' For the received pulse C in the ith round (i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' , N), Bob announces a label in the same way as that at Step 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Alice and Bob do one of the following procedures according to the label and obtain the values of random variables ˆN suc (i) ph , ˆF (i), and ˆQ(i) − .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Unless explicitly written, these random variables are set to be zeros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [signal] Alice and Bob do the same procedure as that at “signal” of Step 2′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Upon “success”, Bob performs the X-basis measurement on qubit B and obtains ˆb′ ∈ {+, −}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' When ˆb′ = −, ˆN suc (i) ph is set to be unity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [test] Alice and Bob do the same procedure as that at “test” of Step 2′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Then ˆF (i) is set to be Λm,r(|ˆω − (−1)ˆaβ|2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 7 [trash] Alice does the same procedure as that at “trash” of Step 2′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' When ˆa′ = −, ˆQ(i) − is set to be unity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 3′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Same as Steps 3′ of the virtual protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Note that ˆF = �N i=1 ˆF (i) and ˆQ− = �N i=1 ˆQ(i) − hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 4′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Regarding + as zero and − as unity for each ˆb′ in success signal round, define the ˆN suc-bit sequence ˆxph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let ˆN suc ph be the Hamming weight of ˆxph, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=', ˆN suc ph = �N i=1 ˆN suc (i) ph .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The task of proving the security of the actual protocol is then reduced to constructing a function U( ˆF, ˆN trash) that satisfies Pr � ˆN suc ph ≤ U( ˆF, ˆN trash) � ≥ 1 − ϵ (23) for any attack in the estimation protocol and setting the final-key length to ˆN fin = ˆN suc −HPA −s, where HPA is defined as HPA := � ˆN such � U( ˆF, ˆN trash)/ ˆN suc�� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (24) In fact, if the condition (23) is satisfied, then the number of possible phase-error patterns can be bounded from above by 2HPA [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Therefore, by extracting the (HPA+s)-bit error syndrome of ˆxph using the universal2 hash function, Bob could uniquely identify ˆxph with a failure probability no smaller than 1−2−s [43, 56, 57, 44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In the virtual protocol, the quantum operations at Step 5′ can be made equivalent to the ( ˆN suc − ˆN fin)-bit syndrome extraction via the universal2 hash function and the error correction on the X bases of ˆN fin qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Since a unitary U(C−1) that acts as the matrix C−1 on the Z bases acts as C⊤ on the X bases, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=', U(C−1) |xX⟩ = |C⊤xX⟩ where ·X denotes the X basis, this procedure corresponds to the privacy amplification via the dual universal2 hashing on the Z bases [56, 44] (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=', in the actual protocol).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Combining these, the condition (23) implies that the actual protocol with the final key length given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (1) is ϵsec-secure with a security parameter ϵsec = √ 2 √ ϵ + 2−s + ϵcor [43, 48, 54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' From now on, we thus focus on the estimation protocol for finding a function U( ˆF, ˆN trash) to satisfy Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='2 Phase error operator In this section, we explain how our new security analysis can be reduced to the previous analyses carried out in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [37, 38] with a tighter operator inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The number of phase errors depends on the choice of the controlled isometry V hom B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(x) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' V het B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(ω)) in the virtual and the estimation protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' We here take a suboptimal strategy;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' fix V hom B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(x) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' V het B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(ω)) so that the probability of the phase error event ˆb′ = − in the estimation protocol is minimized for an ideal pure-loss channel [58] with transmission η = β2/µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' When the state |Ψ⟩A ˜ C in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (7) is put into a pure-loss channel with the channel output being |±β⟩C, the resulting state |Φ⟩ACE on systems A, C, and an adversary’s system E (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=', an environment of the pure-loss channel) is given by |Φ⟩ACE = 1 √ 2 � |0⟩A |β⟩C ��� � µ − β2 � E + |1⟩A |−β⟩C ���− � µ − β2 � E � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (25) Tracing out the system E, the reduced state ΦAC is given by ΦAC = (1 − qµ,β) |φ+⟩⟨φ+|AC + qµ,β |φ−⟩⟨φ−|AC , (26) where |φ+⟩AC := 1 √ 2(|0⟩ |β⟩ + |1⟩ |−β⟩) = |+⟩A ⊗ Πev |β⟩C + |−⟩A ⊗ Πod |β⟩C , (27) |φ−⟩AC := 1 √ 2(|0⟩ |β⟩ − |1⟩ |−β⟩) = |+⟩A ⊗ Πod |β⟩C + |−⟩A ⊗ Πev |β⟩C = (ZA ⊗ IC) |φ+⟩AC , (28) 8 and qµ,β := 1 − e−2(µ−β2) 2 (> 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (29) For Homodyne protocol,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' we observe that C-XBA � IdA ⊗ Khom C→B(x) � (ΦAC) C-XBA (30) = 2fsuc(x) C-XBA � (1 − qµ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β) ˆP � ⟨x| Πev |β⟩ |++⟩AB + ⟨x| Πod |β⟩ |−−⟩AB � +qµ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β ˆP � ⟨x| Πod |β⟩ |+−⟩AB + ⟨x| Πev |β⟩ |−+⟩AB �� C-XBA (31) = 2fsuc(x) � (1 − qµ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β) ˆP � ⟨x| Πev |β⟩ |+⟩A + ⟨x| Πod |β⟩ |−⟩A � ⊗ |+⟩⟨+|B +qµ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β ˆP � ⟨x| Πod |β⟩ |+⟩A + ⟨x| Πev |β⟩ |−⟩A � ⊗ |−⟩⟨−|B � (32) = fsuc(x) � (1 − qµ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β) ˆP �� gβ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='1/4(x) |0⟩A + � g−β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='1/4(x) |1⟩A � ⊗ |+⟩⟨+|B +qµ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β ˆP �� gβ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='1/4(x) |0⟩A − � g−β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='1/4(x) |1⟩A � ⊗ |−⟩⟨−|B � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (33) where ˆP(ψ) := ψψ† (and thus ˆP(|ψ⟩) = |ψ⟩⟨ψ|),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' and gm,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='V is the normal distribution with the mean m and the variance V ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=', gm,V (x) := 1 √ 2πV exp � −(x − m)2 2V � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (34) We define τ hom AB (x) as τ hom AB (x) :=(1 − qµ,β) ˆP �� gβ,1/4(x) |0⟩A + � g−β,1/4(x) |1⟩A � ⊗ |+⟩⟨+|B + qµ,β ˆP �� gβ,1/4(x) |0⟩A − � g−β,1/4(x) |1⟩A � ⊗ |−⟩⟨−|B .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (35) From Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (17),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (21),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (33),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' and (35),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' the probability density of an outcome x with occurrence of ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='the phase error is given by ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='Tr ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='|−⟩⟨−|B K′ hom ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='AC→B(x)(ΦAC) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='= fsuc(x) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='Tr ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='⟨0|B τ hom ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='AB (x) |0⟩B + ⟨1|B τ hom ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='AB (x) |1⟩B ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='V (1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(x) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='�† ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='V (0) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(x) ⟨0|B τ hom ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='AB (x) |1⟩B − ⟨1|B τ hom ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='AB (x) |0⟩B ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='V (0) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(x) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='�† ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='V (1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(x) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='� (36) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='= fsuc(x) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='�1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='2 Tr ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='τ hom ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='AB (x) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− Re ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='Tr ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='V (1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(x) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='�† ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='V (0) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(x) ⟨0|B τ hom ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='AB (x) |1⟩B ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='��� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='(37) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='≥ fsuc(x) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='�1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='2 Tr ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='τ hom ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='AB (x) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='��⟨0|B τ hom ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='AB (x) |1⟩B ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=',' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (38) where the last inequality follows from the matrix Hölder inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' If we write the polar decom- position of ⟨0|B τ hom AB (x) |1⟩B by W hom A (x) ��⟨0|B τ hom AB (x) |1⟩B ��, the equality in (38) can be achieved by setting � V (1) A→R(x) �† V (0) A→R = � W hom A (x) �† .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (39) From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (35), ⟨0|B τ hom AB (x) |1⟩B is given by ⟨0|B τ hom AB (x) |1⟩B = 1 2 � (1 − qµ,β) ˆP �� gβ,1/4(x) |0⟩A + � g−β,1/4(x) |1⟩A � −qµ,β ˆP �� gβ,1/4(x) |0⟩A − � g−β,1/4(x) |1⟩A �� , (40) 9 which is hermitian with two eigenvalues having opposite signs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let |uhom + (x)⟩A and |uhom − (x)⟩A be eigenvectors of ⟨0|B τ hom AB (x) |1⟩B with positive and negative eigenvalues, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Then, W hom A (x) is given by W hom A (x) = |uhom + (x)⟩⟨uhom + (x)|A − |uhom − (x)⟩⟨uhom − (x)|A .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (41) The explicit form of |uhom ± (x)⟩A is given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (151) in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The choice of the isometry V (j) A→R(x) to satisfy Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (39) is not unique;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' one of the reasons is the arbitrariness of the dimension of the system R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Here, we set R = A and set V (0) A→R(x) = IA, V (1) A→R(x) = W hom A (x), (42) which, with Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (17) and (41), leads to V hom B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→A(x) = � |uhom + (x)⟩⟨uhom + (x)|A ⊗ IB + |uhom − (x)⟩⟨uhom − (x)|A ⊗ ZB � C-XBA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (43) For Heterodyne protocol, the calculation similar to Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (30)–(35) leads to C-XBA � IdA ⊗ Khet C→B(ω) � (ΦAC) C-XBA (44) = 2fsuc(ωr) π C-XBA � (1 − qµ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β) ˆP � ⟨ω| Πev |β⟩ |++⟩AB + ⟨ω| Πod |β⟩ |−−⟩AB � +qµ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β ˆP � ⟨ω| Πod |β⟩ |+−⟩AB + ⟨ω| Πev |β⟩ |−+⟩AB �� C-XBA (45) = fsuc(ωr) π � (1 − qµ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β) ˆP � ⟨ω|β⟩ |0⟩A + ⟨−ω|β⟩ |1⟩A � ⊗ |+⟩⟨+|B +qµ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β ˆP � ⟨ω|β⟩ |0⟩A − ⟨−ω|β⟩ |1⟩A � ⊗ |−⟩⟨−|B � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (46) Since ⟨ω|β⟩ = e− 1 2 [(ωr−β)2+ω2 i +2iωiβ] is not real in general,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' we insert a θ-rotation around the Z basis RZ A(θ) := exp(−iθZA/2) (47) in order to have � RZ A(2ωiβ) �† C-XBA � IdA ⊗ Khet C→B(ω) � (ΦAC) C-XBA RZ A(2ωiβ) (48) = e−ω2 i fsuc(ωr) √π � (1 − qµ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β) ˆP �� gβ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='1/2(ωr) |0⟩A + � g−β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='1/2(ωr) |1⟩A � ⊗ |+⟩⟨+|B +qµ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β ˆP �� gβ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='1/2(ωr) |0⟩A − � g−β,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='1/2(ωr) |1⟩A � ⊗ |−⟩⟨−|B � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (49) We define τ het AB(ωr) as τ het AB(ωr) := (1 − qµ,β) ˆP �� gβ,1/2(ωr) |0⟩A + � g−β,1/2(ωr) |1⟩A � ⊗ |+⟩⟨+|B + qµ,β ˆP �� gβ,1/2(ωr) |0⟩A − � g−β,1/2(ωr) |1⟩A � ⊗ |−⟩⟨−|B .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (50) Thus, the structure of the matrix τ het AB(ωr) is essentially the same as τ hom AB (x) of Homodyne protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In the same way as Homodyne protocol, the probability density of outcome ω with the occurrence of a phase error is given by Tr � |−⟩⟨−|B K′ het AC→B(ω)(ΦAC) � = e−ω2 i fsuc(ωr) √π �1 2 Tr � τ het AB(ωr) � (51) −Re � Tr �� V ′(1) A→R(ωr) �†V ′(0) A→R(ωr)RZ A(2ωiβ) ⟨0|B τ het AB(ωr) |1⟩B � RZ A(2ωiβ) �†��� (52) ≥ e−ω2 i fsuc(ωr) √π �1 2 Tr � τ het AB(ωr) � − ��⟨0|B τ het AB(ωr) |1⟩B �� 1 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (53) 10 If we write the polar decomposition of ⟨0|B τ het AB(ωr) |1⟩B by W het A (ωr) ��⟨0|B τ het AB(ωr) |1⟩B ��, then the equality of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (53) can be achieved by setting � RZ A(2ωiβ) �† � V ′(1) A→R(ω) �† V ′(0) A→R(ω)RZ A(2ωiβ) = � W het A (ωr) �† .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (54) From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (50), ⟨0|B τ het AB(ωr) |1⟩B is given by ⟨0|B τ het AB(ωr) |1⟩B = 1 2 � (1 − qµ,β) ˆP �� gβ,1/2(ωr) |0⟩A + � g−β,1/2(ωr) |1⟩A � −qµ,β ˆP �� gβ,1/2(ωr) |0⟩A − � g−β,1/2(ωr) |1⟩A �� , (55) which is hermitian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let |uhet + (ωr)⟩A and |uhet − (ωr)⟩A be eigenvectors of ⟨0|B τ het AB(ωr) |1⟩B with positive and negative eigenvalues, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Then, W het A (ωr) is given by W het A (ωr) = |uhet + (ωr)⟩⟨uhet + (ωr)|A − |uhet − (ωr)⟩⟨uhet − (ωr)|A .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (56) We can choose V ′(j) A→R(ω) to satisfy Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (54) in the same way as Homodyne protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' We set R = A and set V ′(0) A→R(ω) = � RZ A(2ωiβ) �† , V ′(1) A→R(ω) = W het A (ωr) � RZ A(2ωiβ) �† , (57) which, with Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (18) and (56), leads to V het B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→A(ω) = � |uhet + (ωr)⟩⟨uhet + (ωr)|A ⊗ IB + |uhet − (ωr)⟩⟨uhet − (ωr)|A ⊗ ZB � � RZ A(2ωiβ) �† C-XBA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (58) As explained previously, we set V (j) A→R(x) to the one in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (42) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' V ′(j) A→R(ω) to the one in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (57)) also for arbitrary channels, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=', arbitrary coherent attacks by Eve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' This choice is suboptimal for general channels but is expected to be close to optimal for channels that are close to the pure-loss one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Now that the controlled isometry V hom B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→A(x) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' V het B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→A(ω)) is fixed, we can interpret the event that Bob announces “success” and obtains ˆb′ = − (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=', the phase error) at the signal round of Estimation protocol as the outcome of a generalized measurement on Alice’s qubit A and the optical pulse C and define the corresponding POVM element M hom/het ph through Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (19) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (20)) as M hom ph := Fhom ‡ AC→B � |−⟩⟨−|B � = � ∞ −∞ dx � K′ hom AC→B(x) �‡ � |−⟩⟨−|B � , (59) M het ph := Fhet ‡ AC→B � |−⟩⟨−|B � = �� ∞ −∞ dωr dωi � K′ het AC→B(ω) �‡ � |−⟩⟨−|B � , (60) where ‡ denotes the adjoint map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Then, for any density operator ρ on the joint system AC, M hom ph (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' M het ph ) satisfies Eρ � ˆN suc (i) ph � = psigTr � ρ M hom/het ph � (61) in Homodyne (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Heterodyne) protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' For Homodyne protocol, by using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (9), (21), and (43), we have M hom ph = � ∞ −∞ dx � IA ⊗ � Khom suc (x) �†� � V hom B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→A(x) �†� IA ⊗ |−⟩⟨−|B � V hom B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→A(x) � IA ⊗ Khom suc (x) � (62) = � ∞ −∞ dx � ˆP �� IA ⊗ � Khom suc (x) �†� C-XBA |uhom + (x)⟩A ⊗ |−⟩B � + ˆP �� IA ⊗ � Khom suc (x) �†� C-XBA |uhom − (x)⟩A ⊗ |+⟩B �� , (63) 11 where we used the fact that the adjoint map of the tracing-out TrA is taking the tensor product with IA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Using the relation C-XBA = |+⟩⟨+|A ⊗ IB + |−⟩⟨−|A ⊗ ZB as well as Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (12), we have M hom ph = � ∞ −∞ 2fsuc(x)dx � ˆP � Π(+,od),(−,ev) AC |uhom + (x)⟩A ⊗ |x⟩C � + ˆP � Π(−,od),(+,ev) AC |uhom − (x)⟩A ⊗ |x⟩C �� , (64) where two orthogonal projections Π(+,od),(−,ev) AC and Π(−,od),(+,ev) AC are defined as Π(+,od),(−,ev) AC := |+⟩⟨+|A ⊗ Πod + |−⟩⟨−|A ⊗ Πev, (65) Π(−,od),(+,ev) AC := |−⟩⟨−|A ⊗ Πod + |+⟩⟨+|A ⊗ Πev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (66) A similar relation holds for Heterodyne protocol by replacing Khom suc (x) with Khet suc(ω) and V hom B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→A(x) with V het B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→A(ω) as well as using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (15), (58), (65), and (66): M het ph = �� ∞ −∞ dωrdωi � ˆP �� IA ⊗ � Khet suc(ω) �†� C-XBA RZ A(2ωiβ) |uhet + (ωr)⟩A ⊗ |−⟩B � + ˆP �� IA ⊗ � Khet suc(ω) �†� C-XBA RZ A(2ωiβ) |uhet − (ωr)⟩A ⊗ |+⟩B �� (67) = �� ∞ −∞ 2fsuc(ωr) π dωrdωi � ˆP � Π(+,od),(−,ev) AC RZ A(2ωiβ) |uhet + (ωr)⟩A ⊗ |ω⟩C � + ˆP � Π(−,od),(+,ev) AC RZ A(2ωiβ) |uhet − (ωr)⟩A ⊗ |ω⟩C �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (68) Using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (11), we observe that 1 π � dωi exp(±2iωiβ) |ω⟩⟨ω| = 1 π ��� dωidxdx′ � 2 π e±2iωiβ−(x−ωr)2+2iωix−(x′−ωr)2−2iωix′ |x⟩⟨x′| (69) = 2 �� dxdx′ δ(2(x ± β − x′)) |x⟩⟨x|ωr⟩⟨ωr|x′⟩⟨x′| (70) = � dx |x⟩⟨x|ωr⟩⟨ωr|x ± β⟩⟨x ± β| .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (71) Applying this to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (68) and changing the integration variable appropriately, we have M het ph = �� ∞ −∞ 2fsuc(ωr)dωrdx � ˆP � Π(+,od),(−,ev) AC Oβ AC(x) |uhet + (ωr)⟩A ⊗ |ωr⟩C � + ˆP � Π(−,od),(+,ev) AC Oβ AC(x) |uhet − (ωr)⟩A ⊗ |ωr⟩C �� , (72) where the operator Oβ AC(x) is defined as Oβ AC(x) := |0⟩⟨0|A ⊗ |x⟩⟨x|C + |1⟩⟨1|A ⊗ |x − β⟩⟨x − β|C .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (73) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='3 Finite-size analysis Since the phase error operator was defined on systems A and C, we can follow essentially the same analysis as that in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let us define the following operators: Πfid := |0⟩⟨0|A ⊗ |β⟩⟨β|C + |1⟩⟨1|A ⊗ |−β⟩⟨−β|C (74) = |φ−⟩⟨φ−|AC + |φ+⟩⟨φ+|AC , (75) Πtrash − := |−⟩⟨−|A ⊗ IC, (76) 12 where |φ±⟩AC are defined in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (27) and (28).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' For any density operator ρ on the joint system AC, these operators satisfy Eρ � ˆF (i)� ≤ ptestTr � ρ Πfid� , (77) Eρ � ˆQ(i) − � = ptrashTr � ρ Πtrash − � , (78) where the first inequality follows from Theorem 1 in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [37] as well as the definition of ˆF (i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let M hom/het[κ, γ] for positive numbers κ and γ determined prior to the protocol be defined as M hom/het[κ, γ] := M hom/het ph + κΠfid − γΠtrash − .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (79) In Corollaries 2 and 3 in Appendix B, we show an inequality M hom/het[κ, γ] ≤ Bhom/het(κ, γ) IAC (80) with a computable convex function Bhom/het(κ, γ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let ˆT (i)[κ, γ] be a linear combination of random variables at ith round in Estimation protocol given by ˆT (i)[κ, γ] := p−1 sig ˆN suc (i) ph + p−1 testκ ˆF (i) − p−1 trashγ ˆQ(i) − .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (81) Furthermore, let ˆT (0)[κ, γ] be zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Then, by applying Azuma’s inequality [59–61] with Doob decomposition to { ˆT (k)[κ, γ]}k=0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=',N and using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (61), (77), (78), and (80), we observe that N � k=1 ˆT (k)[κ, γ] = p−1 sig ˆN suc ph + p−1 testκ ˆF − p−1 trashγ ˆQ− ≤ NBhom/het(κ, γ) + δ1(ϵ/2), (82) holds with a probability no smaller than 1 − ϵ/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (See Proposition 1 as well as Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (92)–(105) in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=') Here, δ1(ϵ) is defined as [37] δ1(ϵ) := � max � p−1 sig, p−1 testκ max ν≥0 Λm,r(ν) � − min � p−1 testκ min ν≥0 Λm,r(ν), −p−1 trashγ �� � N 2 ln �1 ϵ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (83) Since ˆQ− is determined solely by Alice’s qubits, each in the state Tr ˜ C(|Φ⟩⟨Φ|A ˜ C) with |Φ⟩A ˜ C given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (7), it follows the same statistics as a tally of ˆN trash Bernoulli trials with a probability q− := ∥ ⟨−|A |Ψ⟩A ˜ C ∥2 = (1 − e−2µ)/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Hence we observe that ˆQ− ≤ q− ˆN trash + δ2(ϵ/2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' ˆN trash) (84) holds with a probability no smaller than 1 − ϵ/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (See Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (31) in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=') Here, δ2(ϵ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' n) is defined as [37] � D(q− + δ2(ϵ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' n)/n∥q−) = − 1 n log2(ϵ) (ϵ > qn −) δ2(ϵ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' n) = (1 − q−)n (ϵ ≤ qn −) , (85) where D(x∥y) := x log2 x y + (1 − x) log2 1 − x 1 − y (86) is the Kullback-Leibler divergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Combining Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (81), (82), and (84), by setting U( ˆF, ˆN trash) = psig � NBhom/het(κ, γ) + δ1(ϵ/2) � − psig ptest κ ˆF + psig ptrash γ � q− ˆN trash + δ2(ϵ/2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' ˆN trash) � , (87) we observe that Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (23) holds from the union bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 13 3 Numerical simulations We compute (the lower bound on) the net key gain per pulse (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=', key rate ˆG) against the transmis- sion distance with various values of excess noise at the channel output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In this model, Bob receives Gaussian states ρ(ˆa) model obtained by randomly displacing attenuated coherent states |(−1)ˆa√ηµ⟩ with attenuation rate η to increase their variances via factor of (1 + ξ), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=', ρ(ˆa) model := 2 πξ � C e−2|γ|2/ξ |(−1)ˆa√ηµ + γ⟩⟨(−1)ˆa√ηµ + γ| d2γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (88) For simplicity, the number Nsmp of the sampling rounds is set to be N/100, and the bit error correction efficiency f in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (4) is to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='95 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The acceptance probability fsuc(x) is assumed to be a step function Θ(x − xth) with a threshold xth(> 0), where Θ(x) denotes the Heaviside step function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The expected amplitude of the coherent state β is chosen to be √ηµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' We set the security parameter ϵsec = 2−50, and set ϵcor = ϵsec/2 and ϵ = 2−s = ϵ2 sec/16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' We assume that the number of “success” signal rounds ˆN suc is equal to its expectation, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=', E[ ˆN suc] = psigN � ∞ −∞ (fsuc(x) + fsuc(−x)) ⟨x| 1 2 � a∈{0,1} ρ(a) model |x⟩ dx (89) = psigN(P + hom + P − hom), (90) where P ± hom := � ∞ −∞ fsuc(±x) 2 � a∈{0,1} ⟨(−1)ax| ρ(a) model |(−1)ax⟩ dx (91) = 1 2erfc � (xth ∓ √ηµ) � 2 1 + ξ � , (92) for Homodyne protocol [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' For Heterodyne protocol [38], it is given by E[ ˆN suc] = psigN(P + het + P − het), (93) P ± het := �� ∞ −∞ fsuc(±ωr) 2π � a∈{0,1} ⟨(−1)aω| ρ(a) model |(−1)aω⟩ dωrdωi (94) = 1 2erfc � (xth ∓ √ηµ) � 2 2 + ξ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (95) We also assume that the number of “success” sampling rounds is equal to (P + hom/het+P − hom/het)Nsmp, the number of test rounds ˆN test is equal to ptestN, and the number of trash rounds ˆN trash is equal to ptrashN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The test outcome ˆF is assume to be equal to its expectation given by [37] E[ ˆF] = ptestN 1 2 � a∈{0,1} Eρ(a) model[Λm,r(|ˆω − (−1)a√ηµ|2)] (96) = ptestN 1 + ξ/2 � 1 − (−1)m+1 � ξ/2 1 + r(1 + ξ/2) �m+1� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (97) For the test function Λm,r in the above, we adopt m = 1 and r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='4120, which leads to (maxν≥0 Λm,r(ν), minν≥0 Λm,r(ν)) = (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='824, −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='9932).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' We assume that the number ˆEobs of bit errors observed in the “success” sampling rounds is equal to its expectation ˆEobs = P − hom/hetNsmp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The upper-bound eqber on the bit error rate is thus given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (3) with the parameters ˆN suc, ˆN suc smp, and ˆEobs given above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Under these assumptions, the remaining parameters to be determined are six parameters (µ, xth, psig, ptest, κ, γ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' We determined (κ, γ) via a convex optimization using CVXPY 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='1 and (µ, xth, psig, ptest) via the Nelder-Mead in the scipy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='minimize library in Python, for each transmission distance L with the attenuation rate η assumed to be 10−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='02L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 2Currently, this level of efficiency may be too optimistic because the bit error correction in our protocol must succeed with probability no smaller than 1 − εcor/2 without the use of the verification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 14 Figure 2: Key rates of the Homodyne protocol against transmission distance over an optical fiber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The attenu- ation rate of the optical fiber is assumed to be 10−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='02L with transmission distance L km, an error correction efficiency f in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (4) is set to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='95, and the number of sampling rounds Nsmp is set to be N/100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' a) Key rates when the excess noise ξ at the channel output is zero;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' that is, the channel is pure loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The bold solid lines show the key rates with our refined analysis developed here, the broken lines show those with the previous analysis [37], and the black thin line shows the PLOB bound, which is the ultimate limit of the key rate of one-way QKD [58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' One can see that the logarithm of the asymptotic key rate decreases in parallel to the PLOB bound with our refined analysis against the transmission distance (≫ 1 km) as opposed to the previous results [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Improvement in the key rate is sustained in the finite-size case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' b) Key rates when N = 1012 with various values of excess noise parameter ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (The detail of the noise model is given in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=') The solid lines show the key rates with our refined analysis, and the broken lines show those with the previous results [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' One can see that, although the key rate significantly improves for the pure-loss channel, the excess noise as high as ξ = 10−3–10−2 degrades the performance to almost the same level as that of the previous results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Figure 2 shows the key rates of Homodyne protocol for the channel model explained above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Figures show that under the condition of low excess noise, our refined analysis results in significantly higher key rates and longer transmission distance than that of the previous results [37] even in the finite-key case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Furthermore, the logarithm of the asymptotic key rate in the pure-loss case (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=', ξ = 0) is in parallel to the PLOB bound [58] against the transmission distance;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' that is, it achieves a linear scaling against the channel transmission, which is known to be optimal for one-way QKD in the pure-loss channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' When the excess noise ξ is around 10−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='0–10−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='0, however, the improvements in our refined analysis are lost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The result of the parameter optimization implies that our refined analysis generates the key with relatively small intensity µ of the input coherent states compared to the previous analyses;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=', the optimized input intensity µ of Homodyne protocol is ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='04 in our refined analysis compared to ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='2 in the previous analysis [37] at η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='1 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=', 50 km) for the asymptotic pure-loss case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The key rate of Heterodyne protocol has a similar behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Figure 3 shows the key rates of Heterodyne protocol with the same noise model as above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Figures show that our refined analysis significantly improves the key rate against the pure-loss channel, but is fragile against excess noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' One can see, however, that, while the key rate of Heterodyne protocol is still low compared to that of Homodyne protocol, the achievable distance (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=', the distance with a non-zero key rate) now becomes comparable with our refined analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' This implies that our refined analysis based on the reverse reconciliation is more effective for Heterodyne protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 4 Discussion We propose a refined security analysis for the protocol proposed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [37] based on the reverse reconciliation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The motivating ideas of our refinement come from the facts that the distillability of a secret key from a quantum state is a looser condition than the distillability of an entanglement from it [49–51, 42, 52, 43] and the reverse reconciliation can increase the key rate for CV QKD protocols [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' To exploit the ideas, we developed the procedure of “twisting” Alice’s system with V hom B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(x) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' V het B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='A→R(ω)) controlled by Bob’s qubit, while the similar techniques have already appeared in previous works [49, 42, 51, 52, 43, 53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Our finding is that by using the twisting 15 a) b) Figure 3: Key rates of the Heterodyne protocol against transmission distance over an optical fiber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The noise models are the same as those of Homodyne protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' a) Key rates when the excess noise ξ at the channel output is zero;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' that is, the channel is pure loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The bold solid lines show the key rates with our refined analysis developed here, the broken lines show those with the previous analysis [38], and the black thin line shows the PLOB bound, which is the ultimate limit of the key rate of one-way QKD [58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' One can see that the logarithm of the asymptotic key rate is in parallel to the PLOB bound when the transmission distance is large in the same way as that of Homodyne protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The key rate is still less (about half) than that of Homodyne protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' b) Key rates when N = 1012 with various values of excess noise parameter ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The solid lines show the key rates with our refined analysis, and the broken lines show those with the previous result [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' operation that minimizes the phase error probability for the pure-loss channel, the protocol has asymptotically optimal scaling in the key rates both for Homodyne and Heterodyne protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' This is a clear distinction from the previous results [37, 38];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' there, the asymptotic key rate non- linearly decreases against the channel transmission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The improvement in the performance remains in the finite-key case but is lost under the existence of excess noise as high as ξ = 10−3–10−2 at the channel output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' This may limit the feasibility of our binary-modulation protocol, but current theoretical progress in CV QKD reveals that the discrete-modulation CV-QKD protocols with four types of modulation have more tolerance against excess noise than those with binary modulation [16–18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' What is important is that our security proof can be extended to the four-state protocols with binary outcomes, such as Protocol 2 in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [17] and a protocol in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [18], by replacing the bit-extracting measurements of these protocols with the qubit-extracting maps as shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (9) and constructing the corresponding phase error operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' This is, however, much more complicated than the previous analysis, and we leave the problem as future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' There are several remaining questions with our present results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The first and foremost is whether we can obtain higher tolerance against excess noise by extending our analysis to the four- state protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' As explained above, our analysis can be extended to the four-state protocols with binary outputs [17, 18], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=', protocols that use homodyne measurement to distinguish signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' With the same type of argument based on the phase error estimation, we can carry out the finite- size security proof for these protocols in principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' However, developing the analyses that preserve the robustness against excess noise for these protocols still has non-triviality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' A more challenging problem is to apply our finite-size security proof to the four-state protocols with more than two outputs, such as a protocol in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [16] and Protocol 1 in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In this case, the definition of phase errors is already non-trivial as opposed to those with binary outputs, and we have to develop more elaborated finite-size security proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Whether we can extend our techniques to these protocols or protocols with even more constellations [19] is still open.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Another important theoretical question is whether the trusted-noise model can be applied to our security analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In practice, even the excess noise of ξ = 10−3 at the channel output is difficult to realize if all the noises are untrusted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Recently, efforts have been made in the field of CV QKD on how to incorporate noises that are intrinsic to apparatuses and thus inaccessible to Eve into the security proof as trusted noises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' This effectively eases the requirement on the experimental apparatuses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In the present security analysis as well as ones in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [37, 38], the fidelity test measures the fidelity to a pure coherent state, which cannot be naively generalized to 16 the fidelity to a mixed state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Whether we can incorporate trusted noises into the fidelity test may be crucial in this direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' From the viewpoint of the feasibility of the protocol, the total number of 1012 of rounds to obtain a tolerable finite-size performance may be demanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The finite-size performance may be improved by applying recently developed refinement [62] of the Azuma’s inequality [59] that utilizes unconfirmed knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' What is non-trivial for the application of this is that the random variable in our application of Azuma’s inequality can not directly be observed even at the end of the protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Whether we can apply the refined concentration inequality [62] with the information accessible in our protocol (in a similar fashion to Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' [63]) may be an interesting problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Acknowledgments This work was supported by the Ministry of Internal Affairs and Communications (MIC) under the initiative Research and Development for Construction of a Global Quantum Cryptography Network (grant number JPMI00316);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Cross-ministerial Strategic Innovation Promotion Program (SIP) (Council for Science, Technology and Innovation (CSTI));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' JSPS KAKENHI Grant Number JP22K13977.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' A Bit error sampling In this section, we summarize how to determine an upper bound on the bit error rate from the given sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' As explained in the main text, Nsmp sampling rounds are randomly inserted in the actual protocol in which Alice and Bob announce their bit values if Bob’s detection succeeds (in the same way as in the signal round).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The number of “success” sampling rounds is denoted by ˆN suc smp, and the observed number of discrepancies between Alice and Bob is denoted by ˆEobs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let us first introduce a Chernoff-type bound for the hypergeometric distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Lemma 1 (Tail bound for the hypergeometric distribution [64]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' , XN be a binary sequence, and M be the number of elements with Xi = 1, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e, M := �N i=1 Xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let ˆY1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' , ˆYn (n ≤ N) be randomly sampled from X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' , XN without replacement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let ˆm := �n i=1 ˆYi be the number of ones in ˆY1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' , ˆYn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Then, for any δ ∈ [0, M/N], the following inequality holds: Pr � ˆm n ≤ M N − δ � ≤ 2−nD( M N −δ∥ M N ), (98) where D(·∥·) is defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (86).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Then, the following corollary is essential for the bit error sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Corollary 1 (Estimation by the simple random sampling without replacement).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' , XN be a binary sequence with M := �N i=1 Xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let ˆY1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' , ˆYn (n ≤ N) be randomly sampled from X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' , XN without replacement, and define ˆm := �n i=1 ˆYi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Then, for any ϵ ∈ (0, 1), the following inequality holds: Pr � ˜ MN,n,ϵ( ˆm) < M � ≤ ϵ, (99) where the function ˜ MN,n,ϵ(m) is defined to satisfy m n ≤ ˜ MN,n,ϵ(m) N ≤ 1 (100) and for 0 ≤ m < n, D � m/n �� ˜ MN,n,ϵ(m)/N � = − 1 n log ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (101) Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let f(M) be a function of M satisfying 0 ≤ f(M)/n ≤ M/N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Then, from Lemma 1, we have Pr � ˆm n ≤ M N − �M N − f(M) n �� ≤ 2−nD� f(M) n �� M N � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (102) 17 We set the function f(M) to the restriction of the function fN,n,ϵ( ¯ M) of the real number ¯ M that satisfies D � fN,n,ϵ( ¯ M)/n∥ ¯ M/N � = − 1 n log ϵ, (103) for ¯ M ∈ [(1 − n√ϵ)N, N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The function fN,n,ϵ( ¯ M) increases monotonically with increasing ¯ M in [(1 − n√ϵ)N, N), and its image lies in [0, n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Thus, from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (102), we have Pr � f −1 N,n,ϵ( ˆm) ≤ M � ≤ ϵ (104) for any ˆm ∈ [0, n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' We define the function ˜ MN,n,ϵ(m) := f −1 N,n,ϵ(m) for m ∈ [0, n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' To incorporate the case ˆm = n, we use the following weaker condition that trivially follows from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (104): Pr � ˜ MN,n,ϵ( ˆm) < M � ≤ ϵ, (105) and define ˜ MN,n,ϵ(n) = N so that the above holds also for ˆm = n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' These show that Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (99) holds while ˜ MN,n,ϵ(m) satisfies Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (100) and (101) by construction in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (103).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' With Corollary 1, we can bound the number of total bit-error events from the sample under the given failure probability εcor/2 by setting N = ˆN suc + ˆN suc smp, n = ˆN suc smp, and ϵ = εcor/2 for ˜ MN,n,ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' As a result, we have the following statement;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' the number E of bit errors in ˆN suc-bit sifted key is bounded from above by Pr � E ≤ ˜ M ˆ Nsuc+ ˆ Nsuc smp, ˆ N suc smp,εcor/2( ˆEobs) − ˆEobs � ≥ 1 − εcor/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (106) Thus, we can define an upper bound eqber of the bit error rate as in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (3), which holds with probability no smaller than 1 − εcor/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' B Proof of the operator inequality In this section, we prove the inequality (80) used in the security proof in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' We first prove the following lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let Π± be orthogonal projections that have the rank no smaller than three or infinite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let M be a self-adjoint operator satisfying M = (Π++Π−)M(Π++Π−) ≤ α(Π++Π−), where α is a real constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let |ψ⟩ be a vector satisfying (Π++Π−) |ψ⟩ = |ψ⟩ and Π± |ψ⟩ ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Assume Π± |ψ⟩ are not proportional to eigenvectors of Π±MΠ+ (if they have).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Define the following quantities with respect to |ψ⟩: C± := ⟨ψ| Π± |ψ⟩ (> 0), (107) λ±± := C−1 ± ⟨ψ| M±± |ψ⟩ , (108) λ+− := (C+C−)− 1 2 ⟨ψ| M+− |ψ⟩ , λ−+ := λ∗ +−, (109) σ±+ := � C−1 + ∥M±+ |ψ⟩ ∥2 − |λ±+|2� 1 2 , (110) σ±− := σ−1 ±+ � (C+C−)− 1 2 ⟨ψ| M+±M±− |ψ⟩ − λ+−λ±± � , (111) ∆±− := � C−1 − ∥M±− |ψ⟩ ∥2 − |λ±−|2 − |σ±−|2� 1 2 , (112) where M++, M−−, M+−, and M−+ are given respectively by M±± := Π±MΠ±, M+− := Π+MΠ−, M−+ := M † +−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (113) Then, for any real numbers γ±, we have σsup(M + |ψ⟩⟨ψ| − γ+Π+ − γ−Π−) ≤ σsup(M6d), (114) 18 where σsup(X) denotes the supremum of the spectrum of the operator X, and M6d is given by M6d := � � � � � � � � α − γ+ 0 0 ∆+− 0 0 0 α − γ+ σ++ σ+− 0 0 0 σ++ C+ + λ++ − γ+ � C+C− + λ+− σ−+ 0 ∆+− σ∗ +− � C+C− + λ−+ C− + λ−− − γ− σ∗ −− ∆−− 0 0 σ−+ σ−− α − γ− 0 0 0 0 ∆−− 0 α − γ− � � � � � � � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (115) Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' We choose orthonormal vectors {|e(1) ± ⟩ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' |e(2) ± ⟩ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' |e(3) ± ⟩} in the domains of Π±,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' respectively,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' to satisfy � C± ���e(1) ± � = Π± |ψ⟩ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (116) M ���e(1) + � = (M++ + M−+) ���e(1) + � = λ++ ���e(1) + � + σ++ ���e(2) + � + λ−+ ���e(1) − � + σ−+ ���e(2) − � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (117) M ���e(1) − � = (M+− + M−−) ���e(1) − � = λ+− ���e(1) + � + σ+− ���e(2) + � + ∆+− ���e(3) + � (118) + λ−− ���e(1) − � + σ−− ���e(2) − � + ∆−− ���e(3) − � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (119) which is well-defined due to Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (107)–(113) and M = (Π+ + Π−)M(Π+ + Π−).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Actually, Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (110)–(112) are derived by taking inner product of appropriate pairs among M±± |ψ⟩ and M±∓ |ψ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Overall phases of |e(2) ± ⟩ and |e(3) ± ⟩ are taken so that σ±+ and ∆±− are positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' From (Π+ + Π−) |ψ⟩ = |ψ⟩, we have |ψ⟩ = � C+ ���e(1) + � + � C− ���e(1) − � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (120) Let us now define the following projection operators: Π(j) ± := ���e(j) ± �� e(j) ± ��� (j = 1, 2, 3), (121) Π(≥2) ± := Π± − Π(1) ± , (122) Π(≥4) ± := Π(≥2) ± − Π(2) ± − Π(3) ± .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (123) Since Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (117) and (119) imply (Π(≥4) + + Π(≥4) − )M(Π(1) + + Π(1) − ) = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' we have ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='M = (Π+ + Π−)M(Π+ + Π−) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='(124) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='= (Π(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ + Π(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− )M(Π(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ + Π(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− ) + (Π(2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ + Π(3) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ + Π(2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− + Π(3) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− )M(Π(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ + Π(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− ) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ (Π(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ + Π(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− )M(Π(2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ + Π(3) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ + Π(2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− + Π(3) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− ) + (Π(≥2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ Π(≥2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=')M(Π(≥2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ Π(≥2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=') ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='(125) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='≤ λ++Π(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ + λ−−Π(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− + λ+− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='���e(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='��� + λ−+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='���e(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='��� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='σ++ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='���e(2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='��� + σ−+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='���e(2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='��� + σ+− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='���e(2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='��� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+∆+− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='���e(3) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='��� + σ−− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='���e(2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='��� + ∆−− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='���e(3) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='− ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='��� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='+ ( ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' ) + α(Π(≥2) + + Π(≥2) − ), (126) where h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' denotes the hermitian conjugate of the terms in the preceding parenthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' The last inequality comes from M ≤ α(Π+ + Π−).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (126), we have M + |ψ⟩⟨ψ| − γ+Π+ − γ−Π− ≤ M6d ⊕ (α − γ+)Π(≥4) + ⊕ (α − γ−)Π(≥4) − , (127) where M6d is given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (115) with the basis {|e(3) + ⟩ , |e(2) + ⟩ , |e(1) + ⟩ , |e(1) − ⟩ , |e(2) − ⟩ , |e(3) − ⟩}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Since α − γ± = ⟨e(3) ± | M6d |e(3) ± ⟩ ≤ σsup(M6d), the supremum of the spectrum of the right-hand side of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (127) is equal to the maximum eigenvalue of the six-dimensional matrix M6d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' We then obtain Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (114).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 19 As a corollary of this lemma, we obtain the followings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' First, we consider Homodyne protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let |β⟩ be a coherent state and θhom µ,β (x) be defined to satisfy |θhom µ,β (x)| ≤ π 2 , tan θhom µ,β (x) = e−2(µ−β2) sinh(4βx).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (128) Let Πev(od) and M hom[κ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' γ] be as defined in the main text,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' and let M hom oo ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' M hom ee ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' M hom (±,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(∓,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' and M hom (∓,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(±,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o) be defined as follows: M hom oo := � ∞ −∞ fsuc(x)[1 + cos θhom µ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β (x)]dx Πod |x⟩⟨x| Πod,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (129) M hom ee := � ∞ −∞ fsuc(x)[1 − cos θhom µ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β (x)]dx Πev |x⟩⟨x| Πev,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (130) M hom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) := � ∞ −∞ fsuc(x) sin θhom µ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β (x) dx Πod |x⟩⟨x| Πev,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (131) M hom (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o) := � M hom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) �† ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (132) M hom (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) := � ∞ −∞ −fsuc(x) sin θhom µ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β (x) dx Πod |x⟩⟨x| Πev = −M hom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (133) M hom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o) := � M hom (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) �† = − � M hom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) �† .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (134) Define the following (real) parameters: Co := ⟨β| Πod |β⟩ = e−|β|2 sinh |β|2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Ce := ⟨β| Πev |β⟩ = e−|β|2 cosh |β|2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (135) λhom oo := C−1 o ⟨β| M hom oo |β⟩ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' λhom ee := C−1 e ⟨β| M hom ee |β⟩ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (136) λhom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) := (CoCe)− 1 2 ⟨β| M hom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) |β⟩ = (λhom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e))∗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (137) σhom oo := � C−1 o ∥M hom oo |β⟩ ∥2 − (λhom oo )2� 1 2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (138) σhom eo := � C−1 o ∥M hom (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o) |β⟩ ∥2 − |λhom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)|2� 1 2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (139) σhom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) := (σhom oo )−1 � (CoCe)− 1 2 ⟨β| M hom oo M hom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) |β⟩ − λhom oo λhom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) � = (σhom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e))∗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (140) σhom (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) := (σhom (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o))−1 � (CoCe)− 1 2 ⟨β| M hom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)M hom ee |β⟩ − λhom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)λhom ee � = (σhom (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e))∗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (141) ∆hom oe := � C−1 e ∥M hom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) |β⟩ ∥2 − |λhom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)|2 − |σhom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)|2� 1 2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (142) ∆hom ee := � C−1 e ∥M hom ee |β⟩ ∥2 − (λhom ee )2 − |σhom (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)|2� 1 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (143) 20 Define the following two matrices M (0) 6d and M (1) 6d .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' M (0) 6d := � � � � � � � � � 1 0 0 ∆hom oe 0 0 0 1 σhom oo σhom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) 0 0 0 σhom oo κCo + λhom oo κ√CoCe + λhom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) σhom eo 0 ∆hom oe σhom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) κ√CoCe + λhom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) κCe + λhom ee − γ σhom (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) ∆hom ee 0 0 σhom eo σhom (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) 1 − γ 0 0 0 0 ∆hom ee 0 1 − γ � � � � � � � � � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (144) M (1) 6d := � � � � � � � � � 1 − γ 0 0 ∆hom oe 0 0 0 1 − γ σhom oo −σhom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) 0 0 0 σhom oo κCo + λhom oo − γ κ√CoCe − λhom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) σhom eo 0 ∆hom oe −σhom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) κ√CoCe − λhom (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) κCe + λhom ee −σhom (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) ∆hom ee 0 0 σhom eo −σhom (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) 1 0 0 0 0 ∆hom ee 0 1 � � � � � � � � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (145) Define a convex function Bhom(κ, γ) := max{σsup(M (0) 6d ), σsup(M (1) 6d )}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (146) Then, for κ, γ ≥ 0, we have M hom[κ, γ] ≤ Bhom(κ, γ)IAC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (147) Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' We first derive the explicit form of |uhom ± (x)⟩A introduced in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (41).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Notice that 1 − 2qµ,β = e−2(µ−β2), (148) � gβ,1/4(x) g−β,1/4(x) = e4βx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (149) Let θ(x) be defined to satisfy |θ(x)| < π 2 , tan θ(x) = Tr � ZA ⟨0|B τ hom AB (x) |1⟩B � � Tr � XA ⟨0|B τ hom AB (x) |1⟩B � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (150) Noticing that Tr � YA ⟨0|B τ hom AB (x) |1⟩B � = 0, we have |uhom ± (x)⟩A = cos θ(x) 2 |±⟩A ± sin θ(x) 2 |∓⟩A .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (151) From Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (40), (148), (149), and (150), we can see that θ(x) coincides with θhom µ,β (x) defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (128).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' We now observe that | ⟨+|uhom + (x)⟩ |2 = | ⟨−|uhom − (x)⟩ |2 = cos2 �θhom µ,β (x) 2 � = 1 + cos θhom µ,β (x) 2 , (152) | ⟨−|uhom + (x)⟩ |2 = | ⟨+|uhom − (x)⟩ |2 = sin2 �θhom µ,β (x) 2 � = 1 − cos θhom µ,β (x) 2 , (153) ⟨+|uhom + (x)⟩⟨uhom + (x)|−⟩ = ⟨−|uhom + (x)⟩⟨uhom + (x)|+⟩ = sin �θhom µ,β (x) 2 � cos �θhom µ,β (x) 2 � = − ⟨+|uhom − (x)⟩⟨uhom − (x)|−⟩ = − ⟨−|uhom − (x)⟩⟨uhom − (x)|+⟩ = sin θhom µ,β (x) 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (154) From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (64) as well as Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (74)–(79), it is obvious that M hom[κ, γ] = Π(+,od),(−,ev) AC M hom[κ, γ] Π(+,od),(−,ev) AC + Π(−,od),(+,ev) AC M hom[κ, γ] Π(−,od),(+,ev) AC , (155) 21 where the two orthogonal projections Π(+,od),(−,ev) AC and Π(−,od),(+,ev) AC are defined in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (65) and (66).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Then we apply Lemma 2 respectively to the operators Π(+,od),(−,ev) AC M hom[κ, γ] Π(+,od),(−,ev) AC and Π(−,od),(+,ev) AC M hom[κ, γ] Π(−,od),(+,ev) AC .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' For Π(+,od),(−,ev) AC M hom[κ, γ] Π(+,od),(−,ev) AC , we set, by using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (152)–(154), that Π± = |±⟩⟨±|A ⊗ Πod(ev), (156) M = Π(+,od),(−,ev) AC M hom ph Π(+,od),(−,ev) AC (157) = |+⟩⟨+|A ⊗ M hom oo + |−⟩⟨−|A ⊗ M hom ee + � |+⟩⟨−|A ⊗ M hom (+,o)(−,e) + |−⟩⟨+|A ⊗ M hom (−,e)(+,o) � , (158) |ψ⟩ = √κ |φ−⟩AC , (159) α = 1, γ+ = 0, γ− = γ, (160) where |φ−⟩AC is defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (28).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Since so-defined M only has continuous spectrum, we can apply Lemma 2 and obtain σsup � Π(+,od),(−,ev) AC M hom[κ, γ] Π(+,od),(−,ev) AC � ≤ σsup(M (0) 6d ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (161) In the same way, we apply Lemma 2 to Π(−,od),(+,ev) AC M hom[κ, γ] Π(−,od),(+,ev) AC .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (152)– (154), we set Π± = |∓⟩⟨∓|A ⊗ Πod(ev), (162) M = Π(−,od),(+,ev) AC M hom ph Π(−,od),(+,ev) AC (163) = |−⟩⟨−|A ⊗ M hom oo + |+⟩⟨+|A ⊗ M hom ee + � |−⟩⟨+|A ⊗ M hom (−,o)(+,e) + |+⟩⟨−|A ⊗ M hom (+,e)(−,o) � , (164) = |−⟩⟨−|A ⊗ M hom oo + |+⟩⟨+|A ⊗ M hom ee − � |−⟩⟨+|A ⊗ M hom (+,o)(−,e) + |+⟩⟨−|A ⊗ M hom (−,e)(+,o) � , (165) |ψ⟩ = √κ |φ+⟩AC , (166) α = 1, γ+ = γ, γ− = 0, (167) where |φ+⟩AC is defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Then, we observe σsup � Π(−,od),(+,ev) AC M hom[κ, γ] Π(−,od),(+,ev) AC � ≤ σsup(M (1) 6d ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (168) Combining inequalities (161) and (168) completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Next, we consider Heterodyne protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Let |β⟩ be a coherent state and θhom µ,β (x) be defined to satisfy |θhet µ,β(ωr)| ≤ π 2 , tan θhet µ,β(ωr) = e−2(µ−β2) sinh(2βωr).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (169) Let Πev(od) and M het[κ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' γ] be as defined in the main text,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' and let M het oo ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' M het ee ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' M het (±,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(∓,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' and 22 M het (∓,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(±,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o) be defined as follows: M het oo := �� ∞ −∞ fsuc(ωr)dωrdx Πod � |x⟩⟨x|ωr⟩⟨ωr|x⟩⟨x| + cos θhet µ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β(ωr) 2 � |x⟩⟨x|ωr⟩⟨ωr|x − β⟩⟨x − β| + |x − β⟩⟨x − β|ωr⟩⟨ωr|x⟩⟨x| �� Πod,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (170) M het ee := �� ∞ −∞ fsuc(ωr)dωrdx Πev � |x⟩⟨x|ωr⟩⟨ωr|x⟩⟨x| − cos θhet µ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β(ωr) 2 � |x⟩⟨x|ωr⟩⟨ωr|x − β⟩⟨x − β| + |x − β⟩⟨x − β|ωr⟩⟨ωr|x⟩⟨x| �� Πev,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (171) M het (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) := �� ∞ −∞ fsuc(ωr)dωrdx Πod � sin θhet µ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β(ωr) |x⟩⟨x|ωr⟩⟨ωr|x⟩⟨x| − cos θhet µ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β(ωr) 2 � |x⟩⟨x|ωr⟩⟨ωr|x − β⟩⟨x − β| − |x − β⟩⟨x − β|ωr⟩⟨ωr|x⟩⟨x| �� Πev,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (172) M het (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o) := � M het (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) �† ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (173) M het (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) := �� ∞ −∞ fsuc(ωr)dωrdx Πod � − sin θhet µ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β(ωr) |x⟩⟨x|ωr⟩⟨ωr|x⟩⟨x| − cos θhet µ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='β(ωr) 2 � |x⟩⟨x|ωr⟩⟨ωr|x − β⟩⟨x − β| − |x − β⟩⟨x − β|ωr⟩⟨ωr|x⟩⟨x| �� Πev,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (174) M het (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o) := � M het (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) �† ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (175) 23 Define the following parameters: Co := ⟨β| Πod |β⟩ = e−|β|2 sinh |β|2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Ce := ⟨β| Πev |β⟩ = e−|β|2 cosh |β|2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (176) λhet oo := C−1 o ⟨β| M het oo |β⟩ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' λhet ee := C−1 e ⟨β| M het ee |β⟩ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (177) λhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) := (CoCe)− 1 2 ⟨β| M het (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) |β⟩ = (λhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e))∗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (178) λhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) := (CoCe)− 1 2 ⟨β| M het (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) |β⟩ = (λhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e))∗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (179) σhet oo := � C−1 o ��M het oo |β⟩ ��2 − (λhet oo )2� 1 2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (180) σhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o) := � C−1 o ���M het (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o) |β⟩ ��� 2 − |λhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)|2 � 1 2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (181) σhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o) := � C−1 o ���M het (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o) |β⟩ ��� 2 − |λhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)|2 � 1 2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (182) σhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) := σ−1 oo � (CoCe)− 1 2 ⟨β| M het oo M het (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) |β⟩ − λhet oo λhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) � = (σhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e))∗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (183) σhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) := σ−1 oo � (CoCe)− 1 2 ⟨β| M het oo M het (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) |β⟩ − λhet oo λhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) � = (σhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e))∗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (184) σhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) := [σhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)]−1 � (CoCe)− 1 2 ⟨β| M het (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)M het ee |β⟩ − λhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)λhet ee � = (σhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e))∗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (185) σhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) := [σhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)]−1 � (CoCe)− 1 2 ⟨β| M het (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)M het ee |β⟩ − λhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)λhet ee � = (σhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e))∗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (186) ∆het (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) := � C−1 e ���M het (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) |β⟩ ��� 2 − |λhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)|2 − |σhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)|2 � 1 2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (187) ∆het (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) := � C−1 e ���M het (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) |β⟩ ��� 2 − |λhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)|2 − |σhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)|2 � 1 2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (188) ∆het (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) := � C−1 e ��M het ee |β⟩ ��2 − (λhet ee )2 − |σhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)|2� 1 2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (189) ∆het (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) := � C−1 e ��M het ee |β⟩ ��2 − (λhet ee )2 − |σhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)|2� 1 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (190) Define the following two matrices M ′(0) 6d and M ′(1) 6d .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' M ′(0) 6d := � � � � � � � � � 1 0 0 ∆het (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) 0 0 0 1 σhet oo σhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) 0 0 0 σhet oo κCo + λhet oo κ√CoCe + λhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) σhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o) 0 ∆het (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) σhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) κ√CoCe + λhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) κCe + λhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) − γ σhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) ∆het (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) 0 0 σhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o) σhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) 1 − γ 0 0 0 0 ∆het (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) 0 1 − γ � � � � � � � � � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (191) M ′(1) 6d := � � � � � � � � � 1 − γ 0 0 ∆het (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) 0 0 0 1 − γ σhet oo σhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) 0 0 0 σhet oo κCo + λhet oo − γ κ√CoCe + λhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) σhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o) 0 ∆het (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) σhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) κ√CoCe + λhet (−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) κCe + λhet ee σhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) ∆het (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) 0 0 σhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(−,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='o) σhet (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) 1 0 0 0 0 ∆het (+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e)(+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content='e) 0 1 � � � � � � � � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (192) Define a convex function Bhet(κ, γ) := max{σsup(M ′(0) 6d ), σsup(M ′(1) 6d )}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (193) 24 Then, for κ, γ ≥ 0, we have M het[κ, γ] ≤ Bhet(κ, γ)IAC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (194) Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' In the same way as Homodyne protocol, we have from Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (55) and (56) that |uhet ± (ωr)⟩A = cos �θhet µ,β(ωr) 2 � |±⟩A ± sin �θhet µ,β(ωr) 2 � |∓⟩A .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (195) Combining this with Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (72) and (73), we observe that (⟨+|A ⊗ Πod)M het ph (|+⟩A ⊗ Πod) = (⟨−|A ⊗ Πod)M het ph (|−⟩A ⊗ Πod) = M het oo , (196) (⟨−|A ⊗ Πev)M het ph (|−⟩A ⊗ Πev) = (⟨+|A ⊗ Πev)M het ph (|+⟩A ⊗ Πev) = M het ee (197) (⟨+|A ⊗ Πod)M het ph (|−⟩A ⊗ Πev) = � (⟨−|A ⊗ Πev)M het ph (|+⟩A ⊗ Πod) �† = M het (+,o)(−,e) (198) (⟨−|A ⊗ Πod)M het ph (|+⟩A ⊗ Πev) = � (⟨+|A ⊗ Πev)M het ph (|−⟩A ⊗ Πod) �† = M het (−,o)(+,e) (199) As can be seen from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (72) as well as Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (74)–(79), we have M het[κ, γ] = Π(+,od),(−,ev) AC M het[κ, γ] Π(+,od),(−,ev) AC + Π(−,od),(+,ev) AC M het[κ, γ] Π(−,od),(+,ev) AC , (200) where Π(+,od),(−,ev) AC and Π(−,od),(+,ev) AC are defined in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (65) and (66).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Then we apply Lemma 2 to the operators Π(+,od),(−,ev) AC M het[κ, γ] Π(+,od),(−,ev) AC and Π(−,od),(+,ev) AC M het[κ, γ] Π(−,od),(+,ev) AC , respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' For Π(+,od),(−,ev) AC M het[κ, γ] Π(+,od),(−,ev) AC , using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (196), (197), and (198), we set Π± = |±⟩⟨±|A ⊗ Πod(ev), (201) M = Π(+,od),(−,ev) AC M het ph Π(+,od),(−,ev) AC (202) = |+⟩⟨+|A ⊗ M het oo + |−⟩⟨−|A ⊗ M het ee + |+⟩⟨−|A ⊗ M het (+,o)(−,e) + |−⟩⟨+|A ⊗ M het (−,e)(+,o), (203) |ψ⟩ = √κ |φ−⟩AC , (204) α = 1, γ+ = 0, γ− = γ, (205) where |φ−⟩AC is defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (28).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Since so-defined M only has continuous spectrum, we can apply Lemma 2 and obtain σsup � Π(+,od),(−,ev) AC M het[κ, γ] Π(+,od),(−,ev) AC � ≤ σsup(M ′(0) 6d ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (206) We also apply Lemma 2 to Π(−,od),(+,ev) AC M het[κ, γ] Π(−,od),(+,ev) AC .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (196), (197), and (199), we set Π± = |∓⟩⟨∓|A ⊗ Πod(ev), (207) M = Π(−,od),(+,ev) AC M het ph Π(−,od),(+,ev) AC (208) = |−⟩⟨−|A ⊗ M het oo + |+⟩⟨+|A ⊗ M het ee + |−⟩⟨+|A ⊗ M het (−,o)(+,e) + |+⟩⟨−|A ⊗ M het (+,e)(−,o), (209) |ψ⟩ = √κ |φ+⟩AC , (210) α = 1, γ+ = γ, γ− = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (211) where |φ+⟩AC is defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Then, we observe σsup � Π(−,od),(+,ev) AC M het[κ, γ] Π(−,od),(+,ev) AC � ≤ σsup(M ′(1) 6d ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' (212) Combining inequalities (206) and (212) completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' 25 References [1] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/V9E1T4oBgHgl3EQfbQST/content/2301.03171v1.pdf'} +page_content=' Bennett 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b/ZtAzT4oBgHgl3EQfm_2G/content/tmp_files/2301.01573v1.pdf.txt @@ -0,0 +1,535 @@ +arXiv:2301.01573v1 [math.AG] 20 Dec 2022 +ENDOMORPHISM ALGEBRAS AND AUTOMORPHISM +GROUPS OF CERTAIN COMPLEX TORI +YURI G. ZARHIN +Abstract. We study the endomorphism algebra and automorphism +groups of complex tori, whose second rational cohomology group enjoys +certain Hodge property introduced by F. Campana. +1. Introduction +Let X be a connected compact complex K¨ahler manifold of dimension ≥ 2, +H2(X, Q) its second rational cohomology group provided with the Hodge +decomposition +H2(X, Q) ⊗Q C = H2(X, C) = H2,0(X) ⊕ H1,1(X) ⊕ H2,0(X) +where H2,0(X) = Ω2(X) is the space of holomorphic 2-forms on X. The +following property of X was introduced and studied by F. Campana [5, Def- +inition 3.3]. Recently, it was used in the study of coisotropic and lagrangian +submanifolds of symplectic manifolds [1]. +Definition 1.1. A manifold X is irreducible in weight 2 (irr´eductible en +poids 2) if it enjoys the following property. +Let H be a rational Hodge substructure of H2(X, Q) such that +HC ∩ H2,0(T) ̸= {0} +where HC := H ⊗Q C. +Then HC contains the whole H2,0(T). +Our aim is to study complex tori T that enjoy this property. +1.2. Let T = V/Λ be a complex torus of positive dimension g where V is +a g-dimensional complex vector space, and Λ is a discrete lattice of rank 2g +in V . One may naturally identify Λ with the first integral homology group +H1(T, Z) of T and +ΛQ = Λ ⊗ Q = {v ∈ V | ∃n ∈ Z \ {0} such that nv ∈ Λ} +2010 Mathematics Subject Classification. +32M05, 32J18, 32J27, 14J50. +Key words and phrases. complex tori, Hodge structures, endomorphism algebras. +The author was partially supported by Simons Foundation Collaboration grant # +585711. Most of this work was done in January–May 2022 during his stay at the Max- +Planck Institut f¨ur Mathematik (Bonn, Germany), whose hospitality and support are +gratefully acknowledged. +1 + +2 +YURI G. ZARHIN +with the first rational homology group H1(T, Q) of T. There are also natural +isomorphisms of real vector spaces +Λ ⊗ R = ΛQ ⊗Q R → V, λ ⊗ r �→ rλ +that may be viewed as isomorphisms related to the first real cohomology +group H1(T, R) of T: +H1(T, R) = H1(T, Z) ⊗ R = H1(T, Q) ⊗Q R → V. +In particular, there is a canonical isomorphism of real vector spaces +H1(T, R) = V. +(1) +and complex vector spaces +H1(T, C) = H1(T, Q) ⊗Q C = H1(T, R) ⊗R C = V ⊗R C =: VC +(2) +where H1(T, C) is the first complex homology group of T. +There are natural isomorphisms of R-algebras +EndZ(Λ) ⊗ R ∼= EndR(V ), u ⊗ r �→ ru, +EndQ(ΛQ) ⊗ R ∼= EndR(V ), u ⊗ r �→ ru, +which give rise to the natural ring embeddings +EndZ(Λ) ⊂ EndQ(ΛQ) ⊂ EndR(V ) ⊂ EndR(V ) ⊗R C = EndC(VC). +(3) +Here the structure of a 2g-dimensional complex vector space on VC is defined +by +z(v ⊗ s) = v ⊗ zs ∀v ⊗ s ∈ V ⊗R C = VC, z ∈ C. +If u ∈ EndR(V ) then we write uC for the corresponding C-linear operator in +VC, i.e., +uC(v ⊗ z) = u(v) ⊗ z ∀u ∈ V, z ∈ C, v ⊗ z ∈ VC. +(4) +Remark 1.3. Sometimes, we will identify EndR(V ) with its image EndR(V )⊗ +1 ⊂ EndC(VC) and write u instead of uC, slightly abusing notation. +As usual, one may naturally extend the complex conjugation z �→ ¯z on C +to the C-antilinear involution +VC → VC, w �→ ¯w, v ⊗ z �→ v ⊗ z = v ⊗ ¯z, +which is usually called the complex conjugation on VC. Clearly, +uC( ¯w) = u(w) ∀u ∈ EndR(V ), w ∈ VC. +(5) +This implies easily that the set of fixed points of the involution is +V = V ⊗ 1 ⊂ VC. +Let End(T) be the endomorphism ring of the complex commutative Lie +group T and End0(T) = End(T) ⊗ Q the corresponding endomorphism +algebra, which is a finite-dimensional algebra over the field Q of rational +numbers, see [6, 4, 2]. Then it is well known that there are canonical iso- +morphisms +End(T) = EndZ(Λ) ∩ EndC(V ), End0(T) = EndQ(ΛQ) ∩ EndC(V ). + +2-SIMPLE COMPLEX TORI +3 +Let g ≥ 2 and +H2(T, Q) = ∧2 +Q(ΛQ, Q) +be the second rational cohomology group of T, which carries the natural +structure of a rational Hodge structure of weight two: +H2(T, Q) = H2(T, Q) ⊗Q C = H2,0(T) ⊕ H1,1(T) ⊕ H0,2(T) +where H2,0(T) = Ω2(T) is the g(g − 1)/2-dimensional space of holomorphic +2-forms on T. +Definition 1.4. Let g = dim(T) ≥ 2. We say that T is 2-simple if it is +irreducible of weight 2, i.e., enjoys the following property. +Let H be a rational Hodge substructure of H2(T, Q) such that +HC ∩ H2,0(T) ̸= {0} +where HC := H ⊗Q C. +Then HC contains the whole H2,0(T). +Remark 1.5. We call such complex tori 2-simple, because they are simple +in the usual meaning of this word if g > 2, see Theorem 1.7(i) below. +Example 1.6. (See [5, Example 3.4(2)].) If g = 2 then dimC(H2,0(T)) = 1. +This implies that (in the notation of Definition 1.4) if HC ∩ H2,0(T) ̸= {0} +then HC contains the whole H2,0(T). Hence, every 2-dimensional complex +torus is 2-simple. +In what follows we write Aut(T) = End(T)∗ for the automorphism group +of the complex Lie group T. +Our main result is the following assertion. +Theorem 1.7. Let T be a complex torus of dimension g ≥ 3. Suppose that +T is 2-simple. +Then T enjoys the following properties. +(i) T is simple. +(ii) If E is any subfield of End0(T) then it is a number field, whose degree +over Q is either 1 or g or 2g. +(iii) End0(T) is a number field E such that its degree [E : Q] is either 1 +(i.e., End0(T) = Q, End(T) = Z) or g or 2g. +(iv) If If End(T) = Z then Aut(T) = {±1}. +(v) If [E : Q] = 2g then E is a purely imaginary number field and +Aut(T) ∼= {±1} × Zg−1 +(vi) Suppose that [E : Q] = g. Then Aut(T) ∼= Zd × {±1} where the +integer d satisfies g +2 − 1 ≤ d ≤ g − 1. +In addition, if T is a complex abelian variety then E is a totally +real number field and d = g − 1. +Remark 1.8. +(i) It is well known (and can be easily checked) that T is +simple if and only if the rational Hodge structure on ΛQ = H1(T, Q) +is irreducible. + +4 +YURI G. ZARHIN +(ii) We may view H2(T, Q) as the Q-vector subspace H2(T, Q) ⊗ 1 of +H2(T, Q)⊗Q C = H2(T, C). Let us consider the Q-vector (sub)space +H1,1(T, Q) := H2(T, Q) ∩ H1,1(T) +of 2-dimensional Hodge cycles on T. Notice that the irreducibility of +the rational Hodge structure on ΛQ implies the complete reducibility +of the rational Hodge structure on H2(T, Q) = HomQ(∧2 +QΛQ, Q). (It +follows from the reductiveness of the Hodge group of a simple torus.) +In light of (i) and Theorem 1.7(i), a complex torus T of dimension +> 2 is 2-simple if and only if it is simple and H2(T, Q) splits into a +direct sum of H1,1(T, Q) and an irreducible rational Hodge structure. +We prove Theorem 1.7 in Section 3, using explicit constructions related +to the Hodge structure on ΛQ that will be discussed in Section 2. +This paper may be viewed as a follow up of [6] and [2]. +I am grateful to Fr´ed´eric Campana and Ekaterina Amerik for interesting +stimulating questions. +2. Hodge structures +2.1. It is well known that ΛQ = H1(T, Q) carries the natural structure of a +rational Hodge structure of weight −1. Let us recall the construction. Let +J : V → V be the multiplication by i = √−1, which is viewed as a certain +element of EndR(V ) such that +J2 = −1. +Hence, J2 +C = −1 in EndC(VC) and we define two mutually complex-conjugate +C-vector subspaces (of the same dimension) H−1,0(T) and H0,−1(T) of VC +as the eigenspaces VC(i) and VC(−i)of JC attached to eigenvalues i and −i +respectively. Clearly, +VC = VC(i) ⊕ VC(−i) = H−1,0(T) ⊕ H0,−1(T), +which defines the rational Hodge structure on ΛQ, in light of VC = ΛQ ⊗Q C. +It also follows that both H−1,0(T) and H0,−1(T) have the same dimension +2g/2 = g. +Now it’s a time to recall that V is a complex vector space. I claim that +the map +Ψ : V → VC(i) = H−1,0(T), v �→ Jv ⊗ 1 + v ⊗ i +(6) +is an isomorphism of complex vector spaces. Indeed, first, Ψ defines a ho- +momorphism of real vector spaces V → VC. Second, if v ∈ V then +JC(Jv ⊗ 1 + v ⊗ i) = J2v ⊗ 1 + Jv ⊗ i = −v ⊗ 1 + Jv ⊗ i = i(Jv ⊗ 1 + v ⊗ i), +i.e., Jv ⊗ 1 + v ⊗ i ∈ VC(i) = H0,−1(T) and therefore the map (6) is defined +correctly. Third, taking into account that J is an automorphism of V and +VC = V ⊗ 1 ⊕ V ⊗ i, we conclude that Ψ is an injective homomorphism of + +2-SIMPLE COMPLEX TORI +5 +real vector spaces and the dimension arguments imply that is is actually an +isomorphism. It remains to check that Ψ is C-linear, i.e., +Ψ(Jv) = iΨ(v). +Let us do it. We have +Ψ(Jv) = J(Jv) ⊗ 1 + Jv ⊗ i = −v ⊗ 1 + Jv ⊗ i = i(Jv ⊗ 1 + v ⊗ i) = iΨ(v). +Hence, Ψ is a C-linear isomorphism and we are done. +Now suppose that u ∈ EndR(V ) commutes with J, i.e., u ∈ EndC(V ). +Then +Ψ ◦ u = uC ◦ Ψ. +(7) +In particular, H−1,0(T) is uC-invariant. Indeed, if v ∈ V then +Ψ◦u(v) = Ju(v)⊗1+u(v)⊗i = uJ(v)⊗1+uC(v⊗i) = uC(J(v)⊗1)+uC(v⊗i) = uC◦Ψ(v), +which proves our claim. +Similarly, there is an anti-linear isomorphism of complex vector spaces +V → VC(−i) = H0,−1(T), v �→ Jv ⊗ 1 − v ⊗ i. +It is also well known that there is a canonical isomorphism of rational +Hodge structures of weight 2 +H2(T, Q) = HomQ(∧2 +QH1(T, Q), Q) +where the Hodge components Hp,q(T) (p, q ≥ 0, p + q = 2) are as follows. +H2,0(T) = HomC(∧2 +C(H−1,0(T), C), +H0,2(T) = HomC(∧2 +C(H−0,−1(T), C), +(8) +H1,1(T) = HomC(H−1,0(T), C)∧HomC(H0,−1(T), C) ∼= HomC(H−1,0(T), C)⊗HomC(H0,−1(T), C). +Clearly, +dimC(H2,0(T)) = g(g − 1) +2 +. +3. Endomorphism Fields and Automorphism Groups +Proof of Theorem 1.7. Let T be a 2-simple complex torus. +(i) Suppose that T is not simple. +This means that there is a proper +complex subtorus S = W/Γ where W is a complex vector subspace of V +with +0 < d = dimC(W) < dimC(V ) = g +such that +Γ = W ∩ Λ +is a discrete lattice of rank 2d in W. Then the quotient T/S is a complex +torus of positive dimension g − d. +Let H ⊂ H2(T, Q) be the image of the canonical injective homomor- +phism of rational Hodge structures H2(T/S, Q) ֒→ H2(T, Q) induced by the +quotient map T → T/S of complex tori. Clearly, H is a rational Hodge +substructure of H2(T, Q) and its (2, 0)-component +H2,0 ⊂ HC + +6 +YURI G. ZARHIN +has C-dimension +dimC(H2,0) = dimC(H2,0(T/S))) = (g − d)(g − d − 1) +2 +< g(g − 1) +2 += dimC(H2,0(T))). +In light of 2-simplicity of T, +dimC(H2,0) = 0, +which implies that +g − d = 1. +On the other hand, let ˜H be the kernel of the canonical surjective homo- +morphism of rational Hodge structures H2(T, Q) ։ H2(S, Q) induced by +the inclusion map S ⊂ T of complex tori. Clearly, ˜H is a rational Hodge +substructure of H2(T, Q). Notice that the induced homomorphism of (2, 0)- +components H2,0(T) → H2,0(S) is also surjective, because every holomorphic +2-form on S obviously extends to a holomorphic 2-form on T. This implies +that the (2, 0)-component +˜H2,0 ⊂ ˜HC +of ˜H has C-dimension +dimC( ˜H2,0) = dimC(H2,0(T))) − dimC(H2,0(S))) = g(g − 1) +2 +− d(d − 1) +2 +> 0. +In light of 2-simplicity of T, +dimC(H2,0) = dimC(H2,0(T))) = g(g − 1) +2 +, +which implies that d(d−1) +2 += 0, i.e., d = 1. Taking into account that g−d = 1, +we get g = 1 + 1 = 2, which is not true. The obtained contradiction proves +that T is simple and (i) is proven. +In particular, End0(T) is a division +algebra over Q. +In order to handle (ii), let us assume that E is a subfield of End0(T). The +simplicity of T implies that 1 ∈ E is the identity automorphism of T. Then +ΛQ becomes a faithful E-module. This implies that E is a number field and +ΛQ is an E-vector space of finite positive dimension +dE = +2g +[E : Q]. +This implies that VC = ΛQ⊗QC is a free E⊗QC-module of rank dE. Clearly, +both H−1,−0(T) and H0,−1(T) are E ⊗Q C-submodules of its direct sum VC. +Let +trE/Q : E → Q +bet the trace map attached to the finite field extension E/Q. Let +HomE(∧2 +EΛQ, E) +be the dE(dE−1) +2 +-dimensional E-vector space of alternating E-bilinear forms +on ΛQ that carries the natural structure of a rational Hodge structure of + +2-SIMPLE COMPLEX TORI +7 +Q-dimension [E : Q] · dE(dE−1) +2 +. There is the natural embedding of rational +Hodge structures +HomE(∧2 +EΛQ, E) ֒→ HomQ(∧2 +QΛQ, Q) = H2(T, Q), φE �→ φ := trE/Q ◦ φE, +(9) +i.e., +φ(λ1, λ2) = trE/Q +� +φE(λ1, λ2) +� +∀λ1, λ2 ∈ ΛQ. +(10) +The image of HomE(∧2 +EΛQ, E) in HomQ(∧2 +QΛQ, Q) = H2(T, Q) coincides +with the Q-vector subspace +HE := {φ ∈ HomQ(∧2 +QΛQ, Q) | φ(uλ1, λ2) = φ(λ1, uλ2) ∀u ∈ E, λ1, λ2 ∈ ΛQ}. +(11) +Indeed, it is obvious that the image lies in HE. In order to check that the +image coincide with the whole subspace HE, let us construct the inverse +map +HE → HomE(∧2 +EΛQ, E), φ �→ φE +to (9) as follows. If λ1, λ2 ∈ ΛQ then there is a Q-linear map +Φ : E �→ Q, u �→ φ(uλ1, λ2) = φ(λ1, uλ2) = −φ(uλ2, λ1) = −φ(λ2, uλ1). +(12) +The properties of trace map imply that there exists precisely one β ∈ E +such that +Φ(u) = trE/Q(uβ) ∀u ∈ E. +Let us put +φE(λ1, λ2) := β. +It follows from (12) that φE ∈ HomE(∧2 +EΛQ, E). In addition, +trE/Q(φE(λ1, λ2)) = trE/Q(β) = trE/Q(1 · β) = Φ(1) = φ(λ1, λ2), +which proves that φ �→ φE is indeed the inverse map, in light of (10). +Clearly, HE is a rational Hodge substructure of H2(T, Q). +By 2-simplicity of T, the C-dimension of the (2, 0)-component H(2,0) +E +of +HE is either 0 or g(g − 1)/2. Let us express this dimension explicitly in +terms of g and [E : Q]. +In order to do that, let us consider the [E : Q]-element set ΣE of all field +embedding σ : E ֒→ C. We have +EC := E ⊗Q C = ⊕σ∈ΣECσ where Cσ = E ⊗E,σ C = C, +(13) +which gives us the splitting of EC-modules +VC = ⊕σ∈ΣEVσ = ⊕σ∈ΣE (H−1,0(T)σ ⊕ H0,−1(T)σ) +(14) +where for all σ ∈ ΣE we define +H−1,0(T)σ := CσH−1,0(T) = {x ∈ H−1,0(T) | uCx = σ(u)x ∀u ∈ E} ⊂ H−1,0(T); +nσ := dimC(H−1,0(T)σ); + +8 +YURI G. ZARHIN +H0,−1(T)σ := CσH0,−1(T) = {x ∈ H0,−1(T) | uCx = σ(u)x ∀u ∈ E} ⊂ H0,−1(T); +mσ := dimC(H0,−1(T)σ); +Vσ = Cσ = CσVC = {x ∈ VC | uCx = σ(u)x ∀u ∈ E} = H−1,0(T)σ⊕H0,−1(T)σ +Since H−1,0(T)⊕H0,−1(T) = VC is a free EC-module of rank dE, its direct +summand Vσ is a Cσ = C-vector space of dimension dE and therefore +nσ + mσ = dE ∀σ ∈ ΣE. +(15) +Since H−1,0(T) and H0,−1(T) are mutually complex-conjugate subspaces +of VC, it follows from (5) that +mσ = n¯σ +where ¯σ : E ֒→ C, u �→ σ(u) +is the complex-conjugate of σ. Therefore, in light of (15), +nσ + n¯σ = dE ∀σ. +(16) +We have � +σ∈ΣE +nσ = +� +σ∈ΣE +dimC(H−1,0(T)σ) = dimC(H−1,0(T)) = g. +(17) +Let us consider the complexification of HE +HE,C := HE⊗QC ⊂ HomQ(∧2ΛQ, Q)⊗QC = HomC(∧2 +C(ΛQ⊗QC), C) = HomC(∧2VC, C). +In light of (11), +HE,C = {φ ∈ HomC(∧2VC, C) | φ(uCx, y) = φ(x, uCy) ∀u ∈ E, ; x, y ∈ VC} +(18) += {φ ∈ HomC(∧2VC, C) | φ(uCx, y) = φ(x, uCy) ∀u ∈ EC, ; x, y ∈ VC}. +In particular, if σ, τ ∈ ΣE are distinct field embeddings then for all φ ∈ HE,C +φ(Vσ, Vτ) = φ(Vτ, Vσ) = {0}. +This implies that +HE,C = ⊕σ∈ΣEHomC(∧2 +CVσ, C) +(19) += ⊕σ∈ΣEHomC +� +∧2 +C (H−1,0(T)σ ⊕ H0,−1(T)σ) , C +� +. +In light of (8), the (2, 0)-Hodge component of HE,C +H(2,0) +E += ⊕σ∈ΣEHomC +� +∧2 +CH−1,0(T)σ, C +� +and dimC(H(2,0) +E +) = +� +σ∈ΣE +nσ(nσ − 1) +2 +. +(20) +This implies that dimC(H(2,0) +E +) = 0 if and only if all nσ ∈ {0, 1}. If this is +the case then, in light of (16), dE ∈ {1, 2}, i.e., [E : Q] = 2g or g. +On the other hand, it follows from (17) combined with the second formula +in (20) that dimC(H(2,0) +E +) = g(g − 1)/2 if and only if there is precisely one +σ with nσ = g (and all the other multiplicities nτ are 0). This implies that + +2-SIMPLE COMPLEX TORI +9 +either dE = 2g and E = Q or dE = g and E an imaginary quadratic field +with the pair of the field embeddings +σ, ¯σ : E ֒→: C +such that +nσ = g, n¯σ = 0. +Let us assume that dE = g. Then E is an imaginary quadratic field; in +addition, +u ∈ E ⊂ EndQ(ΛQ) ⊂ EndR(V ) +then uC acts on H−1,−0(T) as multiplication by σ(u) ∈ C. In light of (5), +uC acts on the complex-conjugate subspace H0,−1(T) as multiplication by +σ(u) = ¯σ(u) ∈ C. +Since E is an imaginary quadratic field, there are a +positive integer D and α ∈ E such that α2 = −D and E = Q(α). It follows +that σ(α) = ±i +√ +D. +Replacing if necessary α by −α, we may and will +assume that +σ(α) = i +√ +D +and therefore αC acts on H−1,−0(T) as multiplication by i +√ +D. Hence, αC +acts on H0,−1(T) as multiplication by i +√ +D = −i +√ +D. Since +VC = H−1,−0(T) ⊕ H0,−1(T), +we get αC = +√ +DJC and therefore +α = +√ +DJ. +This implies that the centralizer End0(T) of J in EndQ(ΛQ) coincides with +the centralizer of α in EndQ(ΛQ), which, in turn, coincides with the central- +izer EndE(ΛQ) of E in EndQ(ΛQ), i.e., +End0(T) = EndE(ΛQ) ∼= MatdE(E). +This is the matrix algebra, which is not a division algebra, because dE = +g > 1. This contradicts to the simplicity of T. The obtained contradiction +rules out the case dE = g. This ends the proof of (ii). +In order to prove (iii), recall that End0(T) is a division algebra of Q, +thanks to the simplicity of T [6]. Hence ΛQ is a free End0(T)-module of +finite positive rank and therefore +dimQ(End0(T))|2g, +(21) +because 2g = dimQ(ΛQ). We will apply several times already proven asser- +tion (ii) to various subfields of End0(T). +Suppose that End0(T) is not a field and let Z be its center. Then Z is a +number field and there is an integer d > 1 such that dimZ(End0(T)) = d2 +and therefore +dimQ(End0(T)) = d2 · [Z : Q] + +10 +YURI G. ZARHIN +divides 2g, thanks to (21). Since Z is a subfield of End0(T), the degree +[Z : Q] is either 1 or g or 2g. If [Z : Q] > 1 then 2g is divisible by +d2 · [Z : Q] ≥ 22g = 4g, +which is nonsense. Hence, [Z : Q] = 1, i.e., Z = Q and End0(T) is a central +division Q-algebra of dimension d2 with d2|2g. Then every maximal subfield +E of the division algebra End0(T) has degree d over Q. Hence d ∈ {1, g, 2g}. +Since d > 1, we obtain that either d = g and g2|2g or d = 2g and (2g)2|2g. +This implies that d = g and g = 1 or 2. Since g ≥ 3, we get a contradiction, +which implies that End0(T) is a field. +It follows from already proven assertion (ii) that the degree dimQ(End0(T)) +of the number field End0(T) is either 1 or g or 2g. Assertion (iv) is obvious +and was included just for the sake of completeness. +In order to handle the structure of Aut(T), let us check first that the only +roots of unity in End0(T) are 1 and −1. If this is not the case then the +field End0(T) contains either √−1 or a primitive pth root of unity ζ where +p is a certain odd prime. In the former case End0(T) contains the quadratic +field Q(√−1), which contradicts (ii). In the latter case End0(T) contains +either the quadratic field Q(√−p) or the quadratic field Q(√p): each of +these outcomes contradicts to (ii) as well. +Now recall that End(T) is an order in the number field E = End0(T) and +Aut(T) = End(T)∗ is its group of units. By Theorem of Dirichlet about +units [3, Ch. II, Sect. 4, Th. 5], the group of units +Aut(T) ∼= Zd × {±1} with d = r + s − 1 +(22) +where r is the number of real field embeddings E ֒→ R and +r + 2s = [E : Q], +i.e., s = [E : Q] − r +2 +. +(23) +Let us prove (v). Assume that the number field E := End0(T) has degree +2g. The dimension arguments imply that ΛQ is a 1-dimensional E-vector +space and V = ΛQ ⊗Q R is a free ER = E ⊗Q R-module of rank 1. Hence ER +coincides with its own centralizer EndER(V ) in EndR(V ). Since J commutes +with End)(T) = E, it also commutes with ER and therefore +J ∈ EndER(V ) = ER. +Recall that the R-algebra ER is isomorphic to a product of copies of R and +C. Since J2 = −1, the only copies of C appear in ER, i.e., E is purely +imaginary, which means that r = 0 and therefore 2g = [E : Q] = 2s. This +proves the first assertion of (v); the second one follows readily from (22) +combined with (23). +Let us prove (vi). Assume that [E : Q] = g. Then the first assertion +follows readily from (22) combined with (23). +Assume now that T is a complex abelian variety. By Albert’s classification +[7], E = End0(T) is either a totally real number field or a CM field. If E is a +CM field then it contains a subfield E0 of degree [E : Q]/2 = g/2. Since E0 + +2-SIMPLE COMPLEX TORI +11 +is a subfield of End0(T) and 1 < g/2 < g (recall that g ≥ 3), the existence +of E0 contradicts to the already proven assertion (ii). This proves that E +is a totally real number field, i.e., s = 0, r = g. Now the assertion about +Aut(T) follows from (22). +□ +References +[1] E. Amerik and F. Campana, On algebraically coisotropic submanifolds of holomorphic +symplectic manifolds. arXiv:2205.07958 [math.AG]. +[2] T. Bandman and Yu. G. Zarhin, Simple Complex Tori of Algebraic Dimension 0. +In: +Proceedings of the Steklov Institute of Mathematics 320 (2023), to appear; +arXiv:2106.10308 [math.AG]. +[3] Z.I. Borevich, I.R. Shafarevich, Number Theory. Academic Press, 1986. +[4] C. Birkenhake and H. Lange, Complex Tori. Birkh¨auser, Boston Basel Stutgart, 1999. +[5] F. Campana, Isotrivialit´e de certaines familes k¨ahl´eriennes de vari´et´es non projectives. +Math. Z. 252 (2006), 147–156. +[6] F. Oort and Yu.G. Zarhin, Endomorphism algebras of complex tori. Math. Ann. +303:1 (1995), 11–30. +[7] D. Mumford, Abelian varieties, 2nd edition. Oxford University Press, London, 1974. +Pennsylvania State University, Department of Mathematics, University Park, +PA 16802, USA +Email address: zarhin@math.psu.edu + diff --git a/ZtAzT4oBgHgl3EQfm_2G/content/tmp_files/load_file.txt b/ZtAzT4oBgHgl3EQfm_2G/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..5625185d11a7afc0cbad768268338c84c7f16941 --- /dev/null +++ b/ZtAzT4oBgHgl3EQfm_2G/content/tmp_files/load_file.txt @@ -0,0 +1,304 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf,len=303 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='01573v1 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='AG] 20 Dec 2022 ENDOMORPHISM ALGEBRAS AND AUTOMORPHISM GROUPS OF CERTAIN COMPLEX TORI YURI G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' ZARHIN Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' We study the endomorphism algebra and automorphism groups of complex tori, whose second rational cohomology group enjoys certain Hodge property introduced by F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Campana.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Introduction Let X be a connected compact complex K¨ahler manifold of dimension ≥ 2, H2(X, Q) its second rational cohomology group provided with the Hodge decomposition H2(X, Q) ⊗Q C = H2(X, C) = H2,0(X) ⊕ H1,1(X) ⊕ H2,0(X) where H2,0(X) = Ω2(X) is the space of holomorphic 2-forms on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' The following property of X was introduced and studied by F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Campana [5, Def- inition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Recently, it was used in the study of coisotropic and lagrangian submanifolds of symplectic manifolds [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' A manifold X is irreducible in weight 2 (irr´eductible en poids 2) if it enjoys the following property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Let H be a rational Hodge substructure of H2(X, Q) such that HC ∩ H2,0(T) ̸= {0} where HC := H ⊗Q C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Then HC contains the whole H2,0(T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Our aim is to study complex tori T that enjoy this property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Let T = V/Λ be a complex torus of positive dimension g where V is a g-dimensional complex vector space, and Λ is a discrete lattice of rank 2g in V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' One may naturally identify Λ with the first integral homology group H1(T, Z) of T and ΛQ = Λ ⊗ Q = {v ∈ V | ∃n ∈ Z \\ {0} such that nv ∈ Λ} 2010 Mathematics Subject Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' 32M05, 32J18, 32J27, 14J50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Key words and phrases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' complex tori, Hodge structures, endomorphism algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' The author was partially supported by Simons Foundation Collaboration grant # 585711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Most of this work was done in January–May 2022 during his stay at the Max- Planck Institut f¨ur Mathematik (Bonn, Germany), whose hospitality and support are gratefully acknowledged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' 1 2 YURI G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' ZARHIN with the first rational homology group H1(T, Q) of T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' There are also natural isomorphisms of real vector spaces Λ ⊗ R = ΛQ ⊗Q R → V, λ ⊗ r �→ rλ that may be viewed as isomorphisms related to the first real cohomology group H1(T, R) of T: H1(T, R) = H1(T, Z) ⊗ R = H1(T, Q) ⊗Q R → V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' In particular, there is a canonical isomorphism of real vector spaces H1(T, R) = V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (1) and complex vector spaces H1(T, C) = H1(T, Q) ⊗Q C = H1(T, R) ⊗R C = V ⊗R C =: VC (2) where H1(T, C) is the first complex homology group of T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' There are natural isomorphisms of R-algebras EndZ(Λ) ⊗ R ∼= EndR(V ), u ⊗ r �→ ru, EndQ(ΛQ) ⊗ R ∼= EndR(V ), u ⊗ r �→ ru, which give rise to the natural ring embeddings EndZ(Λ) ⊂ EndQ(ΛQ) ⊂ EndR(V ) ⊂ EndR(V ) ⊗R C = EndC(VC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (3) Here the structure of a 2g-dimensional complex vector space on VC is defined by z(v ⊗ s) = v ⊗ zs ∀v ⊗ s ∈ V ⊗R C = VC, z ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' If u ∈ EndR(V ) then we write uC for the corresponding C-linear operator in VC, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=', uC(v ⊗ z) = u(v) ⊗ z ∀u ∈ V, z ∈ C, v ⊗ z ∈ VC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (4) Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Sometimes, we will identify EndR(V ) with its image EndR(V )⊗ 1 ⊂ EndC(VC) and write u instead of uC, slightly abusing notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' As usual, one may naturally extend the complex conjugation z �→ ¯z on C to the C-antilinear involution VC → VC, w �→ ¯w, v ⊗ z �→ v ⊗ z = v ⊗ ¯z, which is usually called the complex conjugation on VC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Clearly, uC( ¯w) = u(w) ∀u ∈ EndR(V ), w ∈ VC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (5) This implies easily that the set of fixed points of the involution is V = V ⊗ 1 ⊂ VC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Let End(T) be the endomorphism ring of the complex commutative Lie group T and End0(T) = End(T) ⊗ Q the corresponding endomorphism algebra, which is a finite-dimensional algebra over the field Q of rational numbers, see [6, 4, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Then it is well known that there are canonical iso- morphisms End(T) = EndZ(Λ) ∩ EndC(V ), End0(T) = EndQ(ΛQ) ∩ EndC(V ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' 2-SIMPLE COMPLEX TORI 3 Let g ≥ 2 and H2(T, Q) = ∧2 Q(ΛQ, Q) be the second rational cohomology group of T, which carries the natural structure of a rational Hodge structure of weight two: H2(T, Q) = H2(T, Q) ⊗Q C = H2,0(T) ⊕ H1,1(T) ⊕ H0,2(T) where H2,0(T) = Ω2(T) is the g(g − 1)/2-dimensional space of holomorphic 2-forms on T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Let g = dim(T) ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' We say that T is 2-simple if it is irreducible of weight 2, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=', enjoys the following property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Let H be a rational Hodge substructure of H2(T, Q) such that HC ∩ H2,0(T) ̸= {0} where HC := H ⊗Q C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Then HC contains the whole H2,0(T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' We call such complex tori 2-simple, because they are simple in the usual meaning of this word if g > 2, see Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='7(i) below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Example 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (See [5, Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='4(2)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=') If g = 2 then dimC(H2,0(T)) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' This implies that (in the notation of Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='4) if HC ∩ H2,0(T) ̸= {0} then HC contains the whole H2,0(T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Hence, every 2-dimensional complex torus is 2-simple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' In what follows we write Aut(T) = End(T)∗ for the automorphism group of the complex Lie group T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Our main result is the following assertion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Let T be a complex torus of dimension g ≥ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Suppose that T is 2-simple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Then T enjoys the following properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (i) T is simple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (ii) If E is any subfield of End0(T) then it is a number field, whose degree over Q is either 1 or g or 2g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (iii) End0(T) is a number field E such that its degree [E : Q] is either 1 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=', End0(T) = Q, End(T) = Z) or g or 2g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (iv) If If End(T) = Z then Aut(T) = {±1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (v) If [E : Q] = 2g then E is a purely imaginary number field and Aut(T) ∼= {±1} × Zg−1 (vi) Suppose that [E : Q] = g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Then Aut(T) ∼= Zd × {±1} where the integer d satisfies g 2 − 1 ≤ d ≤ g − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' In addition, if T is a complex abelian variety then E is a totally real number field and d = g − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (i) It is well known (and can be easily checked) that T is simple if and only if the rational Hodge structure on ΛQ = H1(T, Q) is irreducible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' 4 YURI G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' ZARHIN (ii) We may view H2(T, Q) as the Q-vector subspace H2(T, Q) ⊗ 1 of H2(T, Q)⊗Q C = H2(T, C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Let us consider the Q-vector (sub)space H1,1(T, Q) := H2(T, Q) ∩ H1,1(T) of 2-dimensional Hodge cycles on T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Notice that the irreducibility of the rational Hodge structure on ΛQ implies the complete reducibility of the rational Hodge structure on H2(T, Q) = HomQ(∧2 QΛQ, Q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (It follows from the reductiveness of the Hodge group of a simple torus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=') In light of (i) and Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='7(i), a complex torus T of dimension > 2 is 2-simple if and only if it is simple and H2(T, Q) splits into a direct sum of H1,1(T, Q) and an irreducible rational Hodge structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' We prove Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='7 in Section 3, using explicit constructions related to the Hodge structure on ΛQ that will be discussed in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' This paper may be viewed as a follow up of [6] and [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' I am grateful to Fr´ed´eric Campana and Ekaterina Amerik for interesting stimulating questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Hodge structures 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' It is well known that ΛQ = H1(T, Q) carries the natural structure of a rational Hodge structure of weight −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Let us recall the construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Let J : V → V be the multiplication by i = √−1, which is viewed as a certain element of EndR(V ) such that J2 = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Hence, J2 C = −1 in EndC(VC) and we define two mutually complex-conjugate C-vector subspaces (of the same dimension) H−1,0(T) and H0,−1(T) of VC as the eigenspaces VC(i) and VC(−i)of JC attached to eigenvalues i and −i respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Clearly, VC = VC(i) ⊕ VC(−i) = H−1,0(T) ⊕ H0,−1(T), which defines the rational Hodge structure on ΛQ, in light of VC = ΛQ ⊗Q C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' It also follows that both H−1,0(T) and H0,−1(T) have the same dimension 2g/2 = g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Now it’s a time to recall that V is a complex vector space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' I claim that the map Ψ : V → VC(i) = H−1,0(T), v �→ Jv ⊗ 1 + v ⊗ i (6) is an isomorphism of complex vector spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Indeed, first, Ψ defines a ho- momorphism of real vector spaces V → VC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Second, if v ∈ V then JC(Jv ⊗ 1 + v ⊗ i) = J2v ⊗ 1 + Jv ⊗ i = −v ⊗ 1 + Jv ⊗ i = i(Jv ⊗ 1 + v ⊗ i), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=', Jv ⊗ 1 + v ⊗ i ∈ VC(i) = H0,−1(T) and therefore the map (6) is defined correctly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Third, taking into account that J is an automorphism of V and VC = V ⊗ 1 ⊕ V ⊗ i, we conclude that Ψ is an injective homomorphism of 2-SIMPLE COMPLEX TORI 5 real vector spaces and the dimension arguments imply that is is actually an isomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' It remains to check that Ψ is C-linear, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=', Ψ(Jv) = iΨ(v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Let us do it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' We have Ψ(Jv) = J(Jv) ⊗ 1 + Jv ⊗ i = −v ⊗ 1 + Jv ⊗ i = i(Jv ⊗ 1 + v ⊗ i) = iΨ(v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Hence, Ψ is a C-linear isomorphism and we are done.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Now suppose that u ∈ EndR(V ) commutes with J, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=', u ∈ EndC(V ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Then Ψ ◦ u = uC ◦ Ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (7) In particular, H−1,0(T) is uC-invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Indeed, if v ∈ V then Ψ◦u(v) = Ju(v)⊗1+u(v)⊗i = uJ(v)⊗1+uC(v⊗i) = uC(J(v)⊗1)+uC(v⊗i) = uC◦Ψ(v), which proves our claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Similarly, there is an anti-linear isomorphism of complex vector spaces V → VC(−i) = H0,−1(T), v �→ Jv ⊗ 1 − v ⊗ i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' It is also well known that there is a canonical isomorphism of rational Hodge structures of weight 2 H2(T, Q) = HomQ(∧2 QH1(T, Q), Q) where the Hodge components Hp,q(T) (p, q ≥ 0, p + q = 2) are as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' H2,0(T) = HomC(∧2 C(H−1,0(T), C), H0,2(T) = HomC(∧2 C(H−0,−1(T), C), (8) H1,1(T) = HomC(H−1,0(T), C)∧HomC(H0,−1(T), C) ∼= HomC(H−1,0(T), C)⊗HomC(H0,−1(T), C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Clearly, dimC(H2,0(T)) = g(g − 1) 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Endomorphism Fields and Automorphism Groups Proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Let T be a 2-simple complex torus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (i) Suppose that T is not simple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' This means that there is a proper complex subtorus S = W/Γ where W is a complex vector subspace of V with 0 < d = dimC(W) < dimC(V ) = g such that Γ = W ∩ Λ is a discrete lattice of rank 2d in W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Then the quotient T/S is a complex torus of positive dimension g − d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Let H ⊂ H2(T, Q) be the image of the canonical injective homomor- phism of rational Hodge structures H2(T/S, Q) ֒→ H2(T, Q) induced by the quotient map T → T/S of complex tori.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Clearly, H is a rational Hodge substructure of H2(T, Q) and its (2, 0)-component H2,0 ⊂ HC 6 YURI G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' ZARHIN has C-dimension dimC(H2,0) = dimC(H2,0(T/S))) = (g − d)(g − d − 1) 2 < g(g − 1) 2 = dimC(H2,0(T))).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' In light of 2-simplicity of T, dimC(H2,0) = 0, which implies that g − d = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' On the other hand, let ˜H be the kernel of the canonical surjective homo- morphism of rational Hodge structures H2(T, Q) ։ H2(S, Q) induced by the inclusion map S ⊂ T of complex tori.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Clearly, ˜H is a rational Hodge substructure of H2(T, Q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Notice that the induced homomorphism of (2, 0)- components H2,0(T) → H2,0(S) is also surjective, because every holomorphic 2-form on S obviously extends to a holomorphic 2-form on T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' This implies that the (2, 0)-component ˜H2,0 ⊂ ˜HC of ˜H has C-dimension dimC( ˜H2,0) = dimC(H2,0(T))) − dimC(H2,0(S))) = g(g − 1) 2 − d(d − 1) 2 > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' In light of 2-simplicity of T, dimC(H2,0) = dimC(H2,0(T))) = g(g − 1) 2 , which implies that d(d−1) 2 = 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=', d = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Taking into account that g−d = 1, we get g = 1 + 1 = 2, which is not true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' The obtained contradiction proves that T is simple and (i) is proven.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' In particular, End0(T) is a division algebra over Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' In order to handle (ii), let us assume that E is a subfield of End0(T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' The simplicity of T implies that 1 ∈ E is the identity automorphism of T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Then ΛQ becomes a faithful E-module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' This implies that E is a number field and ΛQ is an E-vector space of finite positive dimension dE = 2g [E : Q].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' This implies that VC = ΛQ⊗QC is a free E⊗QC-module of rank dE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Clearly, both H−1,−0(T) and H0,−1(T) are E ⊗Q C-submodules of its direct sum VC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Let trE/Q : E → Q bet the trace map attached to the finite field extension E/Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Let HomE(∧2 EΛQ, E) be the dE(dE−1) 2 dimensional E-vector space of alternating E-bilinear forms on ΛQ that carries the natural structure of a rational Hodge structure of 2-SIMPLE COMPLEX TORI 7 Q-dimension [E : Q] · dE(dE−1) 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' There is the natural embedding of rational Hodge structures HomE(∧2 EΛQ, E) ֒→ HomQ(∧2 QΛQ, Q) = H2(T, Q), φE �→ φ := trE/Q ◦ φE, (9) i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=', φ(λ1, λ2) = trE/Q � φE(λ1, λ2) � ∀λ1, λ2 ∈ ΛQ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (10) The image of HomE(∧2 EΛQ, E) in HomQ(∧2 QΛQ, Q) = H2(T, Q) coincides with the Q-vector subspace HE := {φ ∈ HomQ(∧2 QΛQ, Q) | φ(uλ1, λ2) = φ(λ1, uλ2) ∀u ∈ E, λ1, λ2 ∈ ΛQ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (11) Indeed, it is obvious that the image lies in HE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' In order to check that the image coincide with the whole subspace HE, let us construct the inverse map HE → HomE(∧2 EΛQ, E), φ �→ φE to (9) as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' If λ1, λ2 ∈ ΛQ then there is a Q-linear map Φ : E �→ Q, u �→ φ(uλ1, λ2) = φ(λ1, uλ2) = −φ(uλ2, λ1) = −φ(λ2, uλ1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (12) The properties of trace map imply that there exists precisely one β ∈ E such that Φ(u) = trE/Q(uβ) ∀u ∈ E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Let us put φE(λ1, λ2) := β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' It follows from (12) that φE ∈ HomE(∧2 EΛQ, E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' In addition, trE/Q(φE(λ1, λ2)) = trE/Q(β) = trE/Q(1 · β) = Φ(1) = φ(λ1, λ2), which proves that φ �→ φE is indeed the inverse map, in light of (10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Clearly, HE is a rational Hodge substructure of H2(T, Q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' By 2-simplicity of T, the C-dimension of the (2, 0)-component H(2,0) E of HE is either 0 or g(g − 1)/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Let us express this dimension explicitly in terms of g and [E : Q].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' In order to do that, let us consider the [E : Q]-element set ΣE of all field embedding σ : E ֒→ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' We have EC := E ⊗Q C = ⊕σ∈ΣECσ where Cσ = E ⊗E,σ C = C, (13) which gives us the splitting of EC-modules VC = ⊕σ∈ΣEVσ = ⊕σ∈ΣE (H−1,0(T)σ ⊕ H0,−1(T)σ) (14) where for all σ ∈ ΣE we define H−1,0(T)σ := CσH−1,0(T) = {x ∈ H−1,0(T) | uCx = σ(u)x ∀u ∈ E} ⊂ H−1,0(T);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' nσ := dimC(H−1,0(T)σ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' 8 YURI G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' ZARHIN H0,−1(T)σ := CσH0,−1(T) = {x ∈ H0,−1(T) | uCx = σ(u)x ∀u ∈ E} ⊂ H0,−1(T);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' mσ := dimC(H0,−1(T)σ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Vσ = Cσ = CσVC = {x ∈ VC | uCx = σ(u)x ∀u ∈ E} = H−1,0(T)σ⊕H0,−1(T)σ Since H−1,0(T)⊕H0,−1(T) = VC is a free EC-module of rank dE, its direct summand Vσ is a Cσ = C-vector space of dimension dE and therefore nσ + mσ = dE ∀σ ∈ ΣE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (15) Since H−1,0(T) and H0,−1(T) are mutually complex-conjugate subspaces of VC, it follows from (5) that mσ = n¯σ where ¯σ : E ֒→ C, u �→ σ(u) is the complex-conjugate of σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Therefore, in light of (15), nσ + n¯σ = dE ∀σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (16) We have � σ∈ΣE nσ = � σ∈ΣE dimC(H−1,0(T)σ) = dimC(H−1,0(T)) = g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (17) Let us consider the complexification of HE HE,C := HE⊗QC ⊂ HomQ(∧2ΛQ, Q)⊗QC = HomC(∧2 C(ΛQ⊗QC), C) = HomC(∧2VC, C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' In light of (11), HE,C = {φ ∈ HomC(∧2VC, C) | φ(uCx, y) = φ(x, uCy) ∀u ∈ E, ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' x, y ∈ VC} (18) = {φ ∈ HomC(∧2VC, C) | φ(uCx, y) = φ(x, uCy) ∀u ∈ EC, ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' x, y ∈ VC}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' In particular, if σ, τ ∈ ΣE are distinct field embeddings then for all φ ∈ HE,C φ(Vσ, Vτ) = φ(Vτ, Vσ) = {0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' This implies that HE,C = ⊕σ∈ΣEHomC(∧2 CVσ, C) (19) = ⊕σ∈ΣEHomC � ∧2 C (H−1,0(T)σ ⊕ H0,−1(T)σ) , C � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' In light of (8), the (2, 0)-Hodge component of HE,C H(2,0) E = ⊕σ∈ΣEHomC � ∧2 CH−1,0(T)σ, C � and dimC(H(2,0) E ) = � σ∈ΣE nσ(nσ − 1) 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (20) This implies that dimC(H(2,0) E ) = 0 if and only if all nσ ∈ {0, 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' If this is the case then, in light of (16), dE ∈ {1, 2}, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=', [E : Q] = 2g or g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' On the other hand, it follows from (17) combined with the second formula in (20) that dimC(H(2,0) E ) = g(g − 1)/2 if and only if there is precisely one σ with nσ = g (and all the other multiplicities nτ are 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' This implies that 2-SIMPLE COMPLEX TORI 9 either dE = 2g and E = Q or dE = g and E an imaginary quadratic field with the pair of the field embeddings σ, ¯σ : E ֒→: C such that nσ = g, n¯σ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Let us assume that dE = g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Then E is an imaginary quadratic field;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' in addition, u ∈ E ⊂ EndQ(ΛQ) ⊂ EndR(V ) then uC acts on H−1,−0(T) as multiplication by σ(u) ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' In light of (5), uC acts on the complex-conjugate subspace H0,−1(T) as multiplication by σ(u) = ¯σ(u) ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Since E is an imaginary quadratic field, there are a positive integer D and α ∈ E such that α2 = −D and E = Q(α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' It follows that σ(α) = ±i √ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Replacing if necessary α by −α, we may and will assume that σ(α) = i √ D and therefore αC acts on H−1,−0(T) as multiplication by i √ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Hence, αC acts on H0,−1(T) as multiplication by i √ D = −i √ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Since VC = H−1,−0(T) ⊕ H0,−1(T), we get αC = √ DJC and therefore α = √ DJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' This implies that the centralizer End0(T) of J in EndQ(ΛQ) coincides with the centralizer of α in EndQ(ΛQ), which, in turn, coincides with the central- izer EndE(ΛQ) of E in EndQ(ΛQ), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=', End0(T) = EndE(ΛQ) ∼= MatdE(E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' This is the matrix algebra, which is not a division algebra, because dE = g > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' This contradicts to the simplicity of T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' The obtained contradiction rules out the case dE = g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' This ends the proof of (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' In order to prove (iii), recall that End0(T) is a division algebra of Q, thanks to the simplicity of T [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Hence ΛQ is a free End0(T)-module of finite positive rank and therefore dimQ(End0(T))|2g, (21) because 2g = dimQ(ΛQ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' We will apply several times already proven asser- tion (ii) to various subfields of End0(T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Suppose that End0(T) is not a field and let Z be its center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Then Z is a number field and there is an integer d > 1 such that dimZ(End0(T)) = d2 and therefore dimQ(End0(T)) = d2 · [Z : Q] 10 YURI G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' ZARHIN divides 2g, thanks to (21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Since Z is a subfield of End0(T), the degree [Z : Q] is either 1 or g or 2g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' If [Z : Q] > 1 then 2g is divisible by d2 · [Z : Q] ≥ 22g = 4g, which is nonsense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Hence, [Z : Q] = 1, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=', Z = Q and End0(T) is a central division Q-algebra of dimension d2 with d2|2g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Then every maximal subfield E of the division algebra End0(T) has degree d over Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Hence d ∈ {1, g, 2g}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Since d > 1, we obtain that either d = g and g2|2g or d = 2g and (2g)2|2g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' This implies that d = g and g = 1 or 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Since g ≥ 3, we get a contradiction, which implies that End0(T) is a field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' It follows from already proven assertion (ii) that the degree dimQ(End0(T)) of the number field End0(T) is either 1 or g or 2g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Assertion (iv) is obvious and was included just for the sake of completeness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' In order to handle the structure of Aut(T), let us check first that the only roots of unity in End0(T) are 1 and −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' If this is not the case then the field End0(T) contains either √−1 or a primitive pth root of unity ζ where p is a certain odd prime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' In the former case End0(T) contains the quadratic field Q(√−1), which contradicts (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' In the latter case End0(T) contains either the quadratic field Q(√−p) or the quadratic field Q(√p): each of these outcomes contradicts to (ii) as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Now recall that End(T) is an order in the number field E = End0(T) and Aut(T) = End(T)∗ is its group of units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' By Theorem of Dirichlet about units [3, Ch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' II, Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' 4, Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' 5], the group of units Aut(T) ∼= Zd × {±1} with d = r + s − 1 (22) where r is the number of real field embeddings E ֒→ R and r + 2s = [E : Q], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=', s = [E : Q] − r 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' (23) Let us prove (v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Assume that the number field E := End0(T) has degree 2g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' The dimension arguments imply that ΛQ is a 1-dimensional E-vector space and V = ΛQ ⊗Q R is a free ER = E ⊗Q R-module of rank 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Hence ER coincides with its own centralizer EndER(V ) in EndR(V ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Since J commutes with End)(T) = E, it also commutes with ER and therefore J ∈ EndER(V ) = ER.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Recall that the R-algebra ER is isomorphic to a product of copies of R and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Since J2 = −1, the only copies of C appear in ER, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=', E is purely imaginary, which means that r = 0 and therefore 2g = [E : Q] = 2s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' This proves the first assertion of (v);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' the second one follows readily from (22) combined with (23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Let us prove (vi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Assume that [E : Q] = g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Then the first assertion follows readily from (22) combined with (23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Assume now that T is a complex abelian variety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' By Albert’s classification [7], E = End0(T) is either a totally real number field or a CM field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' If E is a CM field then it contains a subfield E0 of degree [E : Q]/2 = g/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Since E0 2-SIMPLE COMPLEX TORI 11 is a subfield of End0(T) and 1 < g/2 < g (recall that g ≥ 3), the existence of E0 contradicts to the already proven assertion (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' This proves that E is a totally real number field, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=', s = 0, r = g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Now the assertion about Aut(T) follows from (22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' □ References [1] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Amerik and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' Campana, On algebraically coisotropic submanifolds of holomorphic symplectic manifolds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content=' arXiv:2205.' 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+page_content='psu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} +page_content='edu' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ZtAzT4oBgHgl3EQfm_2G/content/2301.01573v1.pdf'} diff --git a/_NAzT4oBgHgl3EQfS_tm/vector_store/index.faiss b/_NAzT4oBgHgl3EQfS_tm/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..cfa0f5e0a3cb379ef64322d3dbb8fc7b032229b4 --- /dev/null +++ b/_NAzT4oBgHgl3EQfS_tm/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:40143be9de9795ffbaca64c62cd9dc43c6ba2adffa6c8b7c44e66658d27a7ba6 +size 4194349 diff --git a/_tE1T4oBgHgl3EQfDAJg/content/tmp_files/2301.02871v1.pdf.txt b/_tE1T4oBgHgl3EQfDAJg/content/tmp_files/2301.02871v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..ed2e8fac45a14e1b4ec6520464fb611244aafddf --- /dev/null +++ b/_tE1T4oBgHgl3EQfDAJg/content/tmp_files/2301.02871v1.pdf.txt @@ -0,0 +1,1123 @@ +MODEL SELECTION FOR NETWORK DATA +BASED ON SPECTRAL INFORMATION +Jairo Ivan Pe˜na Hidalgo AND Jonathan R. Stewart +Florida State University +Abstract: We introduce a new methodology for model selection in the context of +modeling network data. The statistical network analysis literature has developed +many different classes of network data models, with notable model classes including +stochastic block models, latent position models, and exponential families of random +graph models. A persistent question in the statistical network analysis literature lies +in understanding how to compare different models for the purpose of model selection +and evaluating goodness-of-fit, especially when models have different mathematical +foundations. +In this work, we develop a novel non-parametric method for model +selection in network data settings which exploits the information contained in the +spectrum of the graph Laplacian in order to obtain a measure of goodness-of-fit for +a defined set of network data models. We explore the performance of our proposed +methodology to popular classes of network data models through numerous simulation +studies, demonstrating the practical utility of our method through two applications. +Key words and phrases: Statistical network analysis, network data, model selection, +social network analysis. +1. +Introduction +Network data have witnessed a surge of interest across a variety of fields and disciplines in recent +decades, including the study of social networks (Lusher et al., 2013), network epidemiology (involv- +ing the spread of disease through networks of contacts) (Morris, 2004), covert networks of criminal +activity and terrorism (Coutinho et al., 2020), brain networks (Obando and de Vico Fallani, 2017), +financial markets (Finger and Lux, 2017), and more. Network data, as a data structure, are typi- +cally represented as a graph (Kolaczyk, 2009), consisting of a set of nodes representing the elements +of a population of interest (e.g., researchers in a collaboration network) and a set of pairwise ob- +servations or measurements between nodes represented as edges between nodes (e.g., co-authorship +on a paper). +Many classes of models have been proposed and developed to study and model network data. +A non-exhaustive review of some of the more prominent examples include exponential families of +1 +arXiv:2301.02871v1 [stat.ME] 7 Jan 2023 + +random graph models (ERGMs) (e.g., Lusher et al., 2013; Schweinberger et al., 2020), stochastic +block models (SBMs) (e.g., Holland et al., 1983; Anderson et al., 1992; Wang and Bickel, 2017), +latent position models (LPMs) (e.g., Hoff et al., 2002; Sewell and Chen, 2015; Tang et al., 2013; +Athreya et al., 2017), and more. Each class offers a unique mathematical platform for constructing +models of networks from observed network data, with respective strengths and weaknesses. The +exponential family class provides a flexible parametric platform for building models of networks +with dependent edges. +In contrast, stochastic block models can capture network structure and +clustering of nodes through a discrete latent space, whereas latent position models capture network +structure and edge dependence through latent node positions in (e.g.) a latent Euclidean space. +A persistent challenge in statistical network analysis applications is how to compare different +models and select models for specific network data sets. At present, the literature has primarily +focused on model selection problems within each class of models, tailoring methods to specific classes +of models (SBMs: Wang and Bickel (2017); Latouche et al. (2014); ERGMs: Hunter et al. (2008); +LSMs: Ryan et al. (2017)). As a result, there is a gap in the literature which explores methods +for comparing model fit or performing model selection across models from different mathematical +platforms, e.g., comparing an ERGM to an SBM to an LPM. In this work, we introduce a novel +non-parametric methodology for model selection in network data settings that can be applied to a +broad class of models under weak assumptions, capable of facilitating comparison of models with +different mathematical foundations. Our method utilizes information in the spectrum of the graph +Laplacian in order to select a best fitting model for an observed network, and essentially only +requires the ability to simulate adjacency matrices from candidate models and compute eigenvalues +of the graph Laplacian derived from the adjacency matrices. +The rest of the paper is organized as follows. Section 2 reviews spectral properties of the graph +Laplacian for networks and motivates the use of spectral information in the model selection problem +for network data. Our proposed methodology is introduced in Section 3. We present experimental +studies and simulations in Section 4, and two applications of our methodology in Section 5. +2. +Spectral properties of the graph Laplacian +We consider simple undirected networks defined on a set of N nodes with corresponding adjacency +matrix X ∈ {0, 1}N×N, where Xi,j = 1 corresponds to the event that there is an edge between +nodes i and j and Xi,j = 0 otherwise. We adopt the standard conventions that Xi,j = Xj,i an +Xi,i = 0. Extensions of our methodology to directed networks is discussed in Section 4. Extensions +to networks with valued edges is possible, but beyond the scope of this work. Let d = deg(X) = +(�N +j=1 Xi,j : i = 1, . . . , N) ∈ RN be the vector of node degrees of the network. The Laplacian +matrix, also called the graph Laplacian, is defined as L(X) := diag(d)−X, where diag(d) is the N × +N diagonal matrix with diagonal d. Since L(X) is symmetric and positive semi-definite (Brouwer +2 + +and Haemers, 2012), the eigenvalues of L(X) will all be real and non-negative. Throughout, we +will let λ ∈ RN denote the vector of ordered eigenvalues (from smallest to largest) of the Laplacian +matrix L(X). +The vector λ will depend on the adjacency matrix X through L(X), however, +for ease of presentation, we do not make this dependence explicit notationally, as it will be clear +contextually. +Eigenvalues of Laplacian matrices encode many well known properties of a network. For ex- +ample, the multiplicity of the eigenvalue 0 corresponds to the number of connected components in +the network (Brouwer and Haemers, 2012). The second smallest eigenvalue (possibly 0) is known +as the algebraic connectivity (Fiedler, 1973), and measures the overall connectivity of a graph (de +Abreu, 2007). It is also used in stablishing Cheeger inequalities (Donetti et al., 2006), which have +applications in image segmentation (Shi and Malik, 2000), graph clustering (Kwok et al., 2013) +and expander graphs (Hoory et al., 2006). The subsequent eigenvalues of the Laplacian matrix are +related to the minimal cuts (weighted edge deleting) required to partition a network (Bollob´as and +Nikiforov, 2004). +Two undirected graphs with adjacency matrices A and B are isomorphic if there exists a +permutation matrix P such that A = P BP t, which requires that the adjacency matrices be +similar A = P BP −1, noting that a permutation matrix P satisfies P t = P −1. In such cases, the +corresponding graph Laplacian matrices will be similar as well: +L(A) = deg(P BP t) − P B P t = P deg(B)P t − P B P t = P L(B) P t. +Consequently, since L(B) is Hermitian, there exists an eigen decomposition L(B) = UD U t. +Hence, L(A) = P (UD U t) P t = (P U) D (P U)t. As a result, if λ is a vector of eigenvalues +of L(B), it is also a vector of eigenvalues of L(A). In our context, this implies one can always +differentiate two non-isomorphic networks if their eigenvalues are different. The reverse result is +not true in general. There are graphs possessing the same eigenvalue decomposition (referred to as +cospectral or isospectral) which are not isomorphic (Cvetkovi´c et al., 1980). However, numerical +evidence suggests that the fraction of (non-isomorphic) cospectral graphs tends to zero as the +number of nodes in a graph grows (Brouwer and Haemers, 2012). +Several applications of spectral decomposition of the Laplacian matrix have been proposed +in the network analysis literature. +For example, spectral clustering (Von Luxburg, 2007) is a +well known clustering algorithm based on the leading eigenvectors of the Laplacian of a similarity +matrix. Lei and Rinaldo (2015) established, under mild conditions, the consistency of the spectral +clustering method for stochastic block models. +Another example is in Newman (2006), where +a family of community detection algorithms were proposed for networks based on the spectral +decomposition of the graph Laplacian. Lastly, Shore and Lubin (2015) proposed a statistic for +evaluating goodness-of-fit for network models reminiscent of the R2 statistic in regression settings, +3 + +which compares eigenvalues of the graph Laplacian generated from a model fit to the eigenvalues +of the graph Laplacian from a pre-specified null model (typically taken to be a Bernoulli random +graph model, referred to as a density only model). +In light of these results, it is natural to regard the vector of eigenvalues λ as a signature of +a network, containing important topographical and structural information which can be exploited +for the purposes of model selection. Our proposed methodology compares the empirical distribu- +tion of the spectrum of the graph Laplacian of candidate models to that of an observed network. +Our methodology is motivated by the following considerations regarding properties of the graph +Laplacian. +First, if the true data generating process is in the list of candidate models, the observed +eigenvalues derived from an observed network are expected to fall within the spectral distribution +of the data generating process. If, in practice, none of the proposed models are the true generating +process, candidate models can still be assessed by their ability to capture the spectrum of the +observed graph Laplacian, providing a means for developing a methods for model selection. Second, +we can obtain a relative measure of fit among competing models depending on how well the spectrum +of the observed graph Laplacian is captured by candidate models, providing a means to not only +select a best fitting model, but also to compare the fit of the best fitting model to unselected +alternatives. Third, our methodology requires no parametric assumptions on the data generating +process and is able to compare models across different mathematical platforms, including models +which do not have a well-defined likelihood function or which are constructed through a stochastic +process, an example of which are agent-based models (e.g., Snijders et al., 2010; Jackson and Watts, +2002) or generative algorithms based on preferential attachment models (e.g., Barabasi and Albert, +1999; Zeng et al., 2013). +3. +Methodology +We outline a methodology for model selection in network data settings which exploits the spectral +properties of the graph Laplacian, motivated by considerations in the previous section. We assume +throughout that the network is completely observed, denoted by Xobs. The corresponding observed +vector of eigenvalues of the observed graph Laplacian L(Xobs) is denoted by λobs. Our fundamental +inferential goal is to select a best fitting model for the observed network Xobs from a set of candidate +models {M1, . . . , MM} (M ≥ 2). We frame the problem as a classification problem and aim to +construct a classifier P : RN �→ {1, . . . , M} trained on the spectrum of the graph Laplacian for +each of the candidate models in order to predict a class m⋆ ∈ {1, . . . , M} for a given vector of +eigenvalues, namely λobs. We present our model selection method algorithm in Table 1. +4 + +Model selection procedure: +1. Simulate K networks X(m,1), . . . , X(m,K) from each of the candi- +date models model Mm ∈ {M1, . . . MM}. +2. For each X(m,k), compute the Laplacian matrix L(X(m,k)) and the +corresponding vector of eigenvalues λ(m,k) ∈ RN. +3. Construct a design matrix D ∈ R(KM)×N by stacking the KM +vectors of eigenvalues λ(m,k) to form the rows of D. +4. Train a classifier P : RN �→ {1, . . . , M} to predict a model m⋆ ∈ +{1, . . . , M} using the K simulated vectors of eigenvectors λ(m,k) +for each class m ∈ {1, . . . , M} contained in the design matrix D. +Feature engineering is advised at this stage. +5. Compute the Laplacian matrix L(Xobs) for the observed network +Xobs and the corresponding vector of eigenvalues λobs. +6. Predict a class m⋆ = P(λobs) for the observed network using the +trained classifier from Step 4 and set M⋆ = Mm⋆. +Table 1: Description of the model selection algorithm. +3.1 +Selection of classifier +Real life networks can possess hundreds, thousands or even millions of nodes. As the dimension of +the vector of eigenvalues of the graph Laplacian matrices is equal to the number of nodes in the +network, classification methods based on eigenvalues of the Laplacian matrix will be prone to the +usual pitfalls of high dimensional classification problems. The literature for classification methods +is quite extensive, which makes the choice of classifier a critical step in our methodology, although +we show in Section 4 that the effect of the choice of classifier may not have a significant effect on +the results of our methodology under certain circumstances. In light of these results, we consider +practical concerns of the implementation of the choice of classifier. +Linear discriminant analysis, which requires the computation of the inverse of a covariance +matrix, has been shown in practice to suffer a decay in performance as the number of variables +increases and the sample size is fixed (Bickel and Levina, 2004). Alternative methods include sup- +port vector machines, neural networks, random forests, and boosting algorithms, which generally +perform well in high-dimensional settings (Hastie et al., 2011). Within this class is the eXtreme +Gradient Boosting (XGBoost) method, which offers both scalability and state-of-the-art perfor- +mance (Chen and Guestrin, 2016). In the rest of this paper we use exclusively XGBoost, with the +notable exception being Simulation study 5 in Section 4, in which we compare the performance of +different classifiers to establish the claim made earlier in this section. +5 + +3.2 +Relative measure of goodness-of-fit +Many classification algorithms return more than just a predicted class, often returning a vector +of propensity scores s = (s1, . . . , sM) with the property that ∥s∥1 = 1. If several models were +considered, the propensity scores for many of the models can shrink simply because of the larger +number of classes being considered, meaning that the interpretation of propensity scores s1, . . . , sM +can depend on M. To overcome this issue and facilitate the comparison of fit between models, +we propose to normalize the propensity scores to obtain a measure of goodness-of-fit which is +independent of the number of candidate models M. To this end, we define +˜si += +si +∥s∥∞ , +i = 1, . . . , M, +to be the normalized score, which is equal to 1 for the highest scoring model. For all remaining +models, the normalized score is a measure of the fit of the model relative to the highest scoring +model. By rescaling all propensity scores in this manner, the number of models M which is consid- +ered in the candidate set of models has no effect on the interpretation of the (relative) propensity +scores. +4. +Simulation studies +We conduct a number of simulation studies to demonstrate the potential of our proposed method- +ology. Specifically, we aim to examine the extent to which the signature of a network is contained +within the spectrum of the graph Laplacian. +Simulation studies permit knowledge of the true +data-generating model, which facilitates empirical studies which aim to clarify the conditions under +which our proposed methodology is able to successfully differentiate different network models and +structural properties of networks. +4.1 +Simulation study 1: curved exponential families +We study the performance of our methodology on curved exponential families, which have gained +popularity in the social network analysis community (e.g., Snijders et al., 2006; Hunter and Hand- +cock, 2006), as well as other applications (e.g., Obando and de Vico Fallani, 2017; Schweinberger +et al., 2020; Stivala and Lomi, 2021). The prominence of curved exponential family parameteriza- +tions for random graph models emerged out of a desire to solve challenges related to degeneracy +and fitting of early and ill-posed model specifications (Snijders et al., 2006). Additionally, curved +exponential family parameterizations are able to parsimoniously model complex sequences of graph +statistics, such as degree sequences and shared partner sequences, without sacrificing interpretabil- +6 + +0 +5 +10 +15 +1 +2 +3 +4 +5 +6 +7 +Degree +Count +Bernoulli Model +0 +5 +10 +15 +1 +2 +3 +4 +5 +6 +7 +Degree +Count +GWESP Model +0 +5 +10 +15 +20 +25 +1 +2 +3 +ESP +Count +0 +5 +10 +15 +20 +25 +1 +2 +3 +ESP +Count +Figure 1: We visualize the degree and ESP distributions of the Bernoulli and +GWESP model by simulating 1000 networks from (1) with data-generating +parameter vector (θ1, θ2, θ3) = (−2.5, 0, 1) (Bernoulli) and (θ1, θ2, θ3) = +(−2.5, .3, 1) (GWESP). Each column corresponds to each model and we evi- +dence the rightward shift in the degree and ESP distribution of the GWESP +model, relative to the Bernoulli model. +ity (Hunter, 2007; Stewart et al., 2019). A prototypical example used in the social network analysis +literature is the geometrically-weighted edgewise shared partner model, which models transitivity +through the shared partner sequence (Snijders et al., 2006; Hunter, 2007; Stewart et al., 2019). +We simulate networks according to the following model: +P(X = x) +∝ +exp +� +θ1 +N +� +i 5 GeV +p + p → Λ + ¯Λ + X +√ +S = 200 GeV +0 +0.5 +1 +1.5 +2 +−4 +−2 +0 +2 +4 +6 +·10−2 +η2 +CLL +Sce. I +Sce. II +Sce. III +DSV +η1 = 0 +pT 1,2 > 5 GeV +p + p → Λ + Λ + X +√ +S = 200 GeV +0 +0.5 +1 +1.5 +2 +0.00 +0.05 +0.10 +0.15 +η2 +CLL +Sce. I +Sce. II +Sce. III +DSV +p + p → Λ + ¯Λ + X +√ +S = 5.02 TeV +pT 1,2 > 20 GeV +η1 = 0 +0 +0.5 +1 +1.5 +2 +−6 +−4 +−2 +0 +2 +4 ·10−2 +η2 +CLL +Sce. I +Sce. II +Sce. III +DSV +p + p → Λ + Λ + X +√ +S = 5.02 TeV +pT 1,2 > 20 GeV +η1 = 0 +0 +0.5 +1 +1.5 +2 +0 +2 +4 +6 +8 ·10−2 +η2 +CLL +Sce. I +Sce. II +Sce. III +DSV +η1 = 0 +pT 1,2 > 20 GeV +√ +S = 1.96 TeV +p + ¯p → Λ + ¯Λ + X +−2 +−1 +0 +1 +2 +−0.05 +0.00 +0.05 +0.10 +η2 +CLL +Sce. I +Sce. II +Sce. III +DSV +η1 = 0 +pT 1,2 > 20 GeV +√ +S = 1.96 TeV +p + ¯p → Λ + Λ + X +−2 +−1 +0 +1 +2 +0 +2 +4 +6 +8 +·10−2 +η2 +CLL +Sce. I +Sce. II +Sce. III +FIG. 2. Predictions for the dihadron polarization correlation in pp/p¯p collisions at RHIC, LHC, and Tevatron energies. +to be negligible at the initial scale. Therefore, the numerical calculation underestimates the dihadron polarization +correlation in pp collisions. +The ambiguity in the gluon spin transfer can only be removed by the experimental +measurements. We expect that measuring dihadron polarization correlation in pp collisions can play an important +role on this front. It will cast new light on the fragmentation of circularly polarized gluons. +Measuring the dihadron polarization correlation in the experiment does not require polarized beams or colliding +at the Z0-pole. Therefore, it can be easily performed at Belle, RHIC, Tevatron, and the LHC. As a matter of fact, +since most of the experimental data can be used in this analysis, we expect small statistical errors. We believe this +experiment can significantly boost the quantitative study of the polarized FFs. Moreover, combining the experimental +data from e+e− and pp experiments, we can better constrain the gluon spin transfer, G1L,g. Thus, it can improve our +understanding on the hadronization mechanism. + +9 +Appendix A: Measuring dihadron polarization correlation in the experiments +In this appendix, we show how the dihadron polarization correlation can be measured in the experiment. +We +consider two almost back-to-back Λ and ¯Λ pair production. We use θ∗ +1,2 to denote the angle between the momentum +of daughter p/¯p and that of the parent Λ/¯Λ in the rest frame of Λ/¯Λ. We use P++,−−,+−,−+ to denote the probability +of the four combinations of polarization states of Λ and ¯Λ. The nomalization is given by +P++ + P−− + P+− + P−+ = 1. +(A1) +Thus, the dihadron polarization correlation is defined as +CLL = (P++ + P−−) − (P+− + P−+). +(A2) +Furthermore, the polarization of Λ hyperons is given by P Λ +L = P++ + P+− − P−+ − P−−, while that of ¯Λ hyperons +is given by P ¯Λ +L = P++ + P−+ − P+− − P−−. +The normalized angle distribution of the daughter p and ¯p is +1 +N +dN +d cos θ∗ +1d cos θ∗ +2 += P++ +1 + α cos θ∗ +1 +2 +1 + α cos θ∗ +2 +2 ++ P−− +1 − α cos θ∗ +1 +2 +1 − α cos θ∗ +2 +2 ++ P+− +1 + α cos θ∗ +1 +2 +1 − α cos θ∗ +2 +2 ++ P−+ +1 − α cos θ∗ +1 +2 +1 + α cos θ∗ +2 +2 += 1 +4 + P Λ +L +1 +4α cos θ∗ +1 + P +¯Λ +L +1 +4α cos θ∗ +2 + CLL +1 +4α2 cos θ∗ +1 cos θ∗ +2, +(A3) +where α is the decay parameter of Λ hyperons. 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D 93 (2016) no.3, 033006 doi:10.1103/PhysRevD.93.033006 [arXiv:1506.07443 [hep-ph]]. + diff --git a/a9E2T4oBgHgl3EQfwAgi/content/tmp_files/load_file.txt b/a9E2T4oBgHgl3EQfwAgi/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..ed484dcd7bd68318ed04c4e7b6349a356dc9a3ce --- /dev/null +++ b/a9E2T4oBgHgl3EQfwAgi/content/tmp_files/load_file.txt @@ -0,0 +1,1030 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf,len=1029 +page_content='Probing the longitudinal spin transfer via dihadron polarization correlations in unpolarized e+e− and pp collisions Hao-Cheng Zhang1 and Shu-Yi Wei2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' ∗ 1Taishan College,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Shandong University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Jinan,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Shandong,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' 250100,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' China 2Institute of Frontier and Interdisciplinary Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Key Laboratory of Particle Physics and Particle Irradiation (MOE),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Shandong University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Qingdao,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Shandong 266237,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' China The longitudinal spin transfer represents the probability density of producing longitudinally polar- ized hadrons from longitudinally polarized quarks or circularly polarized gluons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' It thus was usually measured in polarized reactions or high-energy collisions where weak interaction dominates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' In this work, we propose the dihadron polarization correlation as a novel probe of this quantity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Such an observable does not require the fragmenting partons to be polarized and therefore can be measured in the currently available experimental facilities, such as Belle, RHIC, Tevatron, and the LHC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' We make quantitative predictions for these experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' In light of the data already harvested, the experimental investigation of this observable provides more opportunity for the quantitative study of the longitudinal spin transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' In particular, the measurements in pp collisions can significantly constrain the fragmentation function of a circularly polarized gluon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' INTRODUCTION Fragmentation functions (FFs) are essential non-perturbative inputs in making quantitative predictions for high- energy reactions [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' While the unpolarized ones [2–20] are well constrained for several hadrons by the experimental data from e+e− annihilations, semi-inclusive deep inelastic collisions (SIDIS), and pp collisions, the quantitative study on spin dependence is still in its early stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The spin-dependent FFs are usually measured in polarized collisions or high-energy reactions where weak interaction dominates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' It is very challenging to acquire experimental data with high accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Recently, the spin-dependent FF was also investigated at Belle [21], which is neither a polarized nor a weak-interaction-dominating experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' This is possible since the Belle experiment measures the D⊥ 1T FF, which represents the probability density of producing transversely polarized hadrons from unpolarized partons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' As shown in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' [21], the experimental data is accurate enough for phenomenological studies [22–30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' On the other hand, the longitudinal spin transfer G1L(z) represents the probability density of producing longitudi- nally polarized hadrons from longitudinally polarized partons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' To measure this quantity in the experiment, one has to generate longitudinally polarized final state partons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Therefore, it is usually studied at LEP [31, 32], polarized SIDIS [33–36], NOMAD [37, 38], and RHIC [39, 40] experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' LEP is an electron-positron collider at the Z0-pole, which ensures that the fragmenting quarks are strongly polarized along the longitudinal direction [41, 42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The electron- positron annihilation process is a clean process to investigate FFs since it avoids the “contamination” from parton distribution functions (PDFs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' However, it receives little contribution from the gluon jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' This feature is double-edged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' On one hand, it makes the quark signals cleaner at LEP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' On the other, it provides little information on the gluon FF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Besides, HERMES [34, 35] and COMPASS [36] also measured the longitudinal spin transfer coefficient in SIDIS with the polarized lepton beam, which also mainly probes the longitudinal spin transfer of quarks/antiquarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Therefore, those experiments offer little constraint on the gluon longitudinal spin transfer (G1L,g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' In principle, polarized pp experiments can improve our understanding on this front [39, 40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' However, due to the large uncertainties in the ex- perimental data and the “contamination” from the longitudinal spin transfer in PDFs (g1L,g), the gluon spin transfer in FFs (G1L,g) is still largely unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' It is assumed to be negligible at the initial scale in the DSV parameterization [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Moreover, the spin correlation has also been proposed as a probe to the longitudinal spin transfer [43] in unpolarized e+e− collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The idea in that paper is intriguing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' It is established on the fact that the helicities of the two partons produced in the same hard scattering are strongly correlated, although single-inclusive partons are not polarized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' It thus proposed a genuine method to measure the longitudinal spin transfer with unpolarized final state partons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Such an idea deserves further investigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' In this work, we calculate the dihadron polarization correlation in unpolarized e+e− annihilations and pp collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' We establish the connection between experimental observables and the longitudinal spin transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' This work thus paves the way for a quantitative study of the longitudinal spin transfer at Belle, RHIC, Tevatron, and LHC experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' ∗ shuyi@sdu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='cn arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='04096v1 [hep-ph] 10 Jan 2023 2 The paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' II, we present our calculation for the dihadron polarization correlation in e+e− annihilations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' We use this simple process as an example to illustrate in detail the origin of the polarization correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Our approach is slightly different from that in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' [43], but in a more up-to-date language in QCD factorization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' We also quantitatively predict observables at the Belle and LEP energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' III, we show our corresponding results for the dihadron polarization correlation in unpolarized pp collisions and make predictions for the observables at RHIC, LHC, and Tevatron energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' A summary is given in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' DIHADRON POLARIZATION CORRELATION IN e+e− ANNIHILATIONS We consider the following process e+ + e− → Λ(λ1, z1) + ¯Λ(λ1, z2) + X, (1) with two almost back-to-back Lambda hyperons, where λ1,2 denotes the helicity of the corresponding hadron, and z1,2 represents the momentum fraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The dihadron polarization correlation, CLL, is defined as the probability for λ1 and λ2 taking the same sign minus that taking opposite signs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The technical detail on how to measure it in the experiment is presented in the appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' We use the photon exchange process as a simple example to illustrate our approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The extension to the Z0-boson exchange process and the γ∗Z0-interference term is straightforward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' At the leading order (LO) and leading twist (LT) approximation, the cross-section can be cast into [44, 45] dσγγ dydz1dz2d2P⊥ = 2πNcα2 Q4 LµνW µν, (2) where Nc = 3 is the color factor, y = (1 + cos θ)/2 with θ being the angle between incoming electron and outgoing Λ, P⊥ is the transverse momentum of ¯Λ with respect to the Λ momentum, and Q is the center-of-mass energy of the colliding leptons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The leptonic tensor reads Lµν = l1µl2ν + l1νl2µ − gµνl1 · l2, (3) with l1 and l2 being the momenta of electron and positron respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The hadronic tensor can be written as [1, 44–49] W µν = � q e2 q � d2pT 1d2pT 2δ2(z2 z1 pT 1 + pT 2 − P⊥) × Tr[2ˆΞq(z1, pT 1)γµ2ˆΞ¯q(z2, pT 2)γν + 2ˆΞq(z2, pT 2)γµ2ˆΞ¯q(z1, pT 1)γν], (4) where Ξq/¯q is the quark-quark correlator that can be decomposed in terms of Gamma matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' This is a standard procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' A full decomposition at the LT level can be found in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' [1, 44–49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Here, we only keep two terms that are relevent to this study, namely the unpolarized FF and the longitudinal spin transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Therefore, we have ˆΞq(z1, pT 1) = 1 4 /n+D1,q(z1, pT 1) + 1 4γ5/n+λ1G1L,q(z1, pT 1), (5) ˆΞ¯q(z2, pT 2) = 1 4 /n−D1,¯q(z2, pT 2) − 1 4γ5/n−λ2G1L,¯q(z2, pT 2), (6) where n± are unit vectors in the light-cone coordinate with plus direction being specified by the Λ momentum, and D1,q/¯q(z, pT ) and G1L,q/¯q(z, pT ) are transverse momentum dependent FFs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' There is a sign flip between G1L,¯q and G1L,q terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' This is in line with that in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' [44, 46, 49] due to the charge conjugation symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' As shown bellow, this sign flip can be fully appreciated in the language of helicity amplitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' It ensures that G1L,¯q and G1L,q have the same physical interpretation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Following the same convention in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' [44], we have properly chosen the normalization of G1L, so that λ1,2 = ±1 for spin-1/2 particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Since the transverse momentum dependence is not the focus of this study, we integrate over P⊥ to simplify the discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Finally, we arrive at dσγγ dydz1dz2 = 2πNcα2 Q2 � q e2 qA(y)[D1,q(z1)D1,¯q(z2) − λ1λ2G1L,q(z1)G1L,¯q(z2)] + {q ↔ ¯q}, (7) where A(y) = y2 + (1 − y)2 is the hard coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Since we cannot distinguish a quark jet from an antiquark jet in the experiment, the exchange, {q ↔ ¯q}, is implicit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Here, D1,q/¯q(z) = � d2pT D1,q/¯q(z, pT ) and G1L,q/¯q(z) = � d2pT G1L,q/¯q(z, pT ) are pT -integrated FFs (or collinear FFs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' This result agrees with that in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' [29, 44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' 3 After taking into account the Z0-exchange contribution and the γ∗Z0-interference term, we obtain the final cross section, which is given by dσ dydz1dz2 = 2πNcα2 Q2 � q � ωq(y) [D1,q(z1)D1,¯q(z2) − λ1λ2G1L,q(z1)G1L,¯q(z2)] +∆ωq(y)[λ1G1L,q(z1)D1,¯q(z2) − λ2D1,q(z1)G1L,¯q(z2)] � + {q ↔ ¯q}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (8) Here,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' the hard coefficients are given by ωq(y) = χT q 0 (y) + e2 qA(y) + χq int Iq 0(y) and ∆ωq(y) = χT q 1 (y) + χq int Iq 1(y),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' with T q 0 (y) = ce 1cq 1A(y) − ce 3cq 3B(y),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' T q 1 (y) = −ce 1cq 3A(y) + ce 3cq 1B(y),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Iq 0(y) = ce V cq V A(y) − ce Acq AB(y),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Iq 1(y) = −ce V cq AA(y) + ce Acq V B(y),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' χ = Q4/[(Q2 − M 2 Z)2 + Γ2 ZM 2 Z] sin4 2θW ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' χq int = −2eqQ2(Q2 − M 2 Z)/[(Q2 − M 2 Z)2 + Γ2 ZM 2 Z] sin2 2θW ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' B(y) = 1 − 2y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' ce 1 = (ce V )2 + (ce A)2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' ce 3 = 2ce V ce A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' cq 1 = (cq V )2 + (cq A)2 and cq 3 = 2cq V cq A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Notice that ω¯q(y) = ωq(1 − y) and ∆ω¯q = −∆ωq(1 − y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The above result has a simple physical interpretation in the parton model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' We use dˆσλqλ¯q/dy to denote the partonic cross section where λq/¯q = ±1 specifies the helicity of the fragmenting quark or antiquark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' There are in total four combinations, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=', ˆσ+−, ˆσ−+, ˆσ++, and ˆσ−−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' To bridge the partonic cross section to the hadronic one, we need to employ the probability density of producing hadrons with helicity λh from quark with helicity λq, which is denoted as Dq(z, λh;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' λq).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' It is parametrized as Dq(z, λh;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' λq) = D1,q(z) + λqλhG1L,q(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Therefore, we find that 2G1L,q(z) = Dq(z, +;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' +) − Dq(z, −;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' +) = Dq(z, −;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' −) − Dq(z, +;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' −) is just the longitudinal spin transfer and 2D1,q(z) = Dq(z, +;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' +) + Dq(z, −;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' +) = Dq(z, +;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' −) + Dq(z, −;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' −) is the unpolarized FF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' This approach is also known as the helicity amplitude approach, which has been widely used in literatures, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=', Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' [29, 50–52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The helicity amplitudes of the most commonly used partonic processes have been computed and summarized in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The above discussion also applys to the antiquark case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' At the end of the day, the cross section at the hadronic level is given by dσ dydz1dz2 = dˆσ++ dy [Dq(z1, λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' +)D¯q(z2, λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' +)] + dˆσ−− dy [Dq(z1, λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' −)D¯q(z2, λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' −)] + dˆσ+− dy [Dq(z1, λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' +)D¯q(z2, λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' −)] + dˆσ−+ dy [Dq(z1, λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' −)D¯q(z2, λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' +)] + {q ↔ ¯q}, (9) = D1,q(z1)D1,¯q(z2) �dˆσ++ dy + dˆσ−− dy + dˆσ+− dy + dˆσ−+ dy � + λ1λ2G1L,q(z1)G1L,¯q(z2) �dˆσ++ dy + dˆσ−− dy − dˆσ+− dy − dˆσ−+ dy � + λ2D1,q(z1)G1L,¯q(z2) �dˆσ++ dy − dˆσ+− dy + dˆσ−+ dy − dˆσ−− dy � + λ1G1L,q(z1)D1,¯q(z2) �dˆσ++ dy − dˆσ−+ dy + dˆσ+− dy − dˆσ−− dy � + {q ↔ ¯q}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (10) Notice that the partonic cross section should also change accordingly, while exchanging quark and antiquark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Since e+e− annihilation is an s-channel interaction, final state quark and antiquark are on the same fermionic line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' We thus have ˆσ++ = ˆσ−− = 0 for massless quarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' To put it in another way, quark and antiquark have opposite helicities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Therefore, the above cross section reduces to following simple form dσ dydz1dz2 = � D1,q(z1)D1,¯q(z2) − λ1λ2G1L,q(z1)G1L,¯q(z2) � �dˆσ+− dy + dˆσ−+ dy � + � λ1G1L,q(z1)D1,¯q(z2) − λ2D1,q(z1)G1L,¯q(z2) � �dˆσ+− dy − dˆσ−+ dy � + {q ↔ ¯q}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (11) At LO, the remaining two nonvanishing partonic cross sections are given by dˆσ+− dy = πNcα2 Q2 � q � e2 qA(y) + χq int (cq V − cq A)[ce V A(y) + ce AB(y)] + χ(cq 1 − cq 3)[ce 1A(y) + ce 3B(y)] � , (12) dˆσ−+ dy = πNcα2 Q2 � q � e2 qA(y) + χq int (cq V + cq A)[ce V A(y) − ce AB(y)] + χ(cq 1 + cq 3)[ce 1A(y) − ce 3B(y)] � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (13) Substituting Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (12-13) into 11, it is straightforward to varify that this calculation based on the probability density interpretation exactly reproduces that from the LO and LT approximation in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' This is not surprising, since 4 DSV z1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='3 Q = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='58 GeV e+e− → Λ + ¯Λ + X 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='8 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='6 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='4 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='0 z2 CLL Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' I Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' II Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' III DSV z1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='5 Q = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='58 GeV e+e− → Λ + ¯Λ + X 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='8 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='6 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='4 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='0 z2 CLL Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' I Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' II Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' III DSV z1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='3 Q = 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='2 GeV e+e− → Λ + ¯Λ + X 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='8 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='6 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='4 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='0 z2 CLL Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' I Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' II Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' III DSV z1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='5 Q = 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='2 GeV e+e− → Λ + ¯Λ + X 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='8 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='6 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='4 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='0 z2 CLL Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' I Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' II Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' III FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Predictions of dihadron polarization correlation in e+e− annihilations at Belle and LEP energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' the physical interpretations of LT PDFs and FFs coincide with the probability densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' However, this approach cannot go beyond LT, since higher twist PDFs or FFs cannot be interpreted as probability densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' As shown in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' [1, 44–49], higher twist PDFs and FFs are convoluted with different hard coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Before presenting the numerical results, we make one more comment concerning the vanishing cross sections (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=', ˆσ++ and ˆσ−−).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' They vanish because that the two final state partons are on the same trace line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' This feature maximizes the longitudinal polarization correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' As discussed in the next section, they also vanish in several similar channels (such as g + g → q + ¯q) in pp collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' However, for the other channels, such as qi + qj → qi + qj, we have nonzero ˆσ++ and ˆσ−−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Therefore, the hard coefficient of G1L(z1)G1L(z2) and that of D1(z1)D1(z2) are no longer the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' It is straightforward to obtain the dihadron polarization correlation from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (8), which reads CLL(y, z1, z2) = − � q ωq(y)G1L,q(z1)G1L,¯q(z2) + {q ↔ ¯q} � q ωq(y)D1,q(z1)D1,¯q(z2) + {q ↔ ¯q} .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (14) Integrating over y, we obtain CLL(z1, z2) = − � q(ce 1cq 1χ + e2 q + χq intce V cq V )[GΛ 1L,q(z1)G¯Λ 1L,¯q(z2) + GΛ 1L,¯q(z1)G¯Λ 1L,q(z2)] � q(ce 1cq 1χ + e2q + χq intce V cq V )[DΛ 1,q(z1)D¯Λ 1,¯q(z2) + D¯Λ 1,q(z1)DΛ 1,¯q(z2)] , (15) where the complete formula has been explicitly laid out to avoid possible confusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Since the Λ FFs in the market, such as DSV [3] and AKK08 [9], do not distinguish Λ from ¯Λ in the unpolarized FFs, we need to employ the following prescription in phenomenology DΛ 1,q(z) = D ¯Λ 1,¯q(z) = 1 + z 2 DΛ+¯Λ 1,q (z), (16) DΛ 1,¯q(z) = D ¯Λ 1,q(z) = 1 − z 2 DΛ+¯Λ 1,q (z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (17) 5 This approximation has also been employed in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' [27, 54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' We have numerically tested that such a prescription can describe the longitudinal polarization of single inclusive Λ production measured by the ALEPH [31] and OPAL [32] collaborations at LEP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Employing the DSV parametrization [3] for polarized and unpolarized FFs, we present our numerical predictions for the dihadron polarization correlation in e+e− annihilations at Belle and LEP energies with several typical kinematic values in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' It clearly shows that the polarization correlation at the Belle energy, roughly speaking, has a similar magnitude with that at the LEP energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Such a significant polarization correlation at different collisional energies makes it possible to extract the longitudinal spin transfer from the Belle experiment where the electromagnetic interaction dominates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' DIHADRON POLARIZATION CORRELATION IN pp COLLISIONS In principle, the longitudinal spin transfer can also be probed in the polarized SIDIS [33–36] and polarized pp collisions [39, 40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' RHIC is the only polarized pp collider so far.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' It has measured the longitudinal spin transfer coefficient DLL in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' [39, 40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Such an observable probes the combination of the longitudinal spin transfer in PDFs, g1L(x), and that in FFs, G1L(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Besides, RHIC, Tevatron, and LHC experiments have accumulated enormous experimental data in unpolarized pp collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' It will be interesting to analyze the longitudinal spin correlation of two almost back-to-back hadrons, which is sensitive to G1L(z1) ⊗ G1L(z2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' It is free from the contamination of the longitudinal spin transfer in PDFs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Furthermore, in light of the amount of unpolarized data that have already been collected, this analysis can shed new light on the quantitative study of longitudinal spin transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' To be more specific, we consider the following two processes p + p → Λ(λ1, η1, pT 1) + ¯Λ(λ2, η2, pT 2) + X, (18) p + p → Λ(λ1, η1, pT 1) + Λ(λ2, η2, pT 2) + X, (19) where these two final state Λ hyperons are almost back-to-back in the transverse plane (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=', pT 1/z1 ∼ −pT 2/z2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' η1,2 are the rapidities of Λ’s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Notice that in pp collisions, we usually choose the beam direction as the z axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The transverse momenta here are different from those in the TMD factorization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' We stay in the context of the collinear factorization, since the TMD factorization does not apply in this case [55, 56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Following the same strategy as that in e+e− annihilations, we can relate the hadronic cross section to the partonic ones with dσ dη1d2pT 1dη2d2pT 2 = � dz1 z2 1 dz2 z2 2 � ab→cd � λcλd 1 π dˆσab→cd λcλd dt xaf1,a(xa)xbf1,b(xb)Dc(z1, λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' λc)Dd(z2, λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' λd) × δ2 �pT 1 z1 + pT 2 z2 � + {c ↔ d}, (20) where f1,a/b(xa/b) is the collinear PDF with xa = pT 1 z1 √ S (eη1 + eη2) and xb = pT 1 z1 √ S (e−η1 + e−η2) the parton momentum fractions and √ S the center-of-mass energy of colliding protons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Again, since we cannot determine which parton fragments to the first Λ hyperon, the exchange between {c ↔ d} is implicit for non-identical final state partons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Here, � ab→cd means that we need to sum over all possible partonic scatterings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' They can be classified into eight channels, namely qi + qj → qi + qj, qi + qi → qi + qi, qi + ¯qi → qi + ¯qi, qi + ¯qi → qj + ¯qj, g + g → qi + ¯qi, qi + ¯qi → g + g, q + g → q + g, and g + g → g + g channels with qi and qj representing quarks with different flavors and g denoting a gluon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' At LO, it is direct to evaluate these helicity-dependent cross sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The helicity amplitudes of all different partonic channels can be find in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' After summing over the spin of initial state partons, we obtain the partonic cross sections used in our approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' We present the formula explicitly as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' For the g + g → qi + ¯qi and qi + ¯qi → qj + ¯qj channels, the final state q¯q pair is connected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Therefore, ˆσ++ and ˆσ−− disappear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' We find [53] dˆσg+g→qi+¯qi +− dt = dˆσg+g→qi+¯qi −+ dt = πα2 s 12s2 � t u + u t − 9 4 t2 + u2 s2 � , (21) dˆσqi+¯qi→qj+¯qj +− dt = dˆσqi+¯qi→qj+¯qj −+ dt = 2πα2 s 9s2 �t2 + u2 s2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (22) Here, we have used the partonic Mandelstam variables which are defined as s = xaxbS, t = −xa √ S pT 1 z1 e−η1 and u = −xa √ S pT 1 z1 e−η2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Summing over the helicity of final state partons, we arrive at the spin-summed cross sections which agree with those summarized in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' [57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' 6 The qi + ¯qi → qi + ¯qi, qi + qi → qi + qi, and qi + qj → qi + qj(i ̸= j) channels are more involved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' All four helicity-dependent cross sections contribute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' They are given by [53] dˆσqi+¯qi→qi+¯qi ++ dt = dˆσqi+¯qi→qi+¯qi −− dt = 2πα2 s 9s2 s2 t2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (23) dˆσqi+¯qi→qi+¯qi +− dt = dˆσqi+¯qi→qi+¯qi −+ dt = 2πα2 s 9s2 �u2 t2 + t2 + u2 s2 − 2 3 u2 st � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (24) dˆσqi+qi→qi+qi ++ dt = dˆσqi+qi→qi+qi −− dt = 2πα2 s 9s2 � s2 u2 + s2 t2 − 2 3 s2 tu � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (25) dˆσqi+qi→qi+qi +− dt = dˆσqi+qi→qi+qi −+ dt = 2πα2 s 9s2 � t2 u2 + u2 t2 � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (26) dˆσqi+qj→qi+qj ++ dt = dˆσqi+qj→qi+qj −− dt = 2πα2 s 9s2 s2 t2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (27) dˆσqi+qj→qi+qj +− dt = dˆσqi+qj→qi+qj −+ dt = 2πα2 s 9s2 u2 t2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (28) Adding ˆσ++, ˆσ−−, ˆσ+−, and ˆσ−+ together, we arrive at the spin-summed partonic cross section for each channel, which agrees with that in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' [57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Furthermore, we always have ˆσ+++ˆσ+−−ˆσ−+−ˆσ−− = 0 and ˆσ+++ˆσ−+−ˆσ+−−ˆσ−− = 0 for all the channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' This is expected since they correspond to the helicity of parton c and d respectively while averaging over the helicity of the other final state parton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Single inclusive partons are not longitudinally polarized in unpolarized pp collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Last but not least, all those helicity-dependent cross sections are positive definite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Therefore, the polarization correlations of these three channels are expected to be smaller than those of g + g → qi + ¯qi and qi + ¯qi → qj + ¯qj channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The other channels involve one or two final state gluons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The longitudinal spin transfer of g → Λ is assumed to be negligiable at the initial factorization scale in the DSV parameterization [3], since it is poorly constrained by the e+e− data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Nonetheless, it can still accumulate contributions through DGLAP evolution and becomes important at higher factorization scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' In contrast with the e+e− case, the gluon channel in pp collisions plays a crucial role in the Λ hyperon production, particularly at the LHC energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Therefore, the experimental data from pp collisions is vital on removing ambiguities in the gluon spin transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The partonic cross sections with circularly polarized gluons are given by [53] dˆσg+qi→g+qi ++ dt = dˆσg+qi→g+qi −− dt = πα2 s 2s2 �s2 t2 − 4s 9u � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (29) dˆσg+qi→g+qi +− dt = dˆσg+qi→g+qi −+ dt = πα2 s 2s2 �u2 t2 − 4u 9s � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (30) dˆσqi+ ¯qi→g+g ++ dt = dˆσqi+ ¯qi→g+g −− dt = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (31) dˆσqi+ ¯qi→g+g +− dt = dˆσqi+ ¯qi→g+g −+ dt = 4πα2 s 3s2 �4u 9t + 4t 9u − t2 + u2 s2 � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (32) dˆσg+g→g+g ++ dt = dˆσg+g→g+g −− dt = 9πα2 s 16s2 s2 t2u2 (s2 + t2 + u2),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (33) dˆσg+g→g+g +− dt = dˆσg+g→g+g −+ dt = 9πα2 s 16s2 � u2 s2t2 + t2 s2u2 � (s2 + t2 + u2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (34) Substituting the decomposition of Dc,d into Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (20), we arrive at the cross section in terms of the unpolarized FF and the longitudinal spin transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' It reads dσ dη1dη2 = � dz1dz2 1 z2 1 � d2pT 1 � ab→cd xaf1,a(xa)xbf1,b(xb) 1 π × � D1,c(z1)D1,d(z2) �dˆσab→cd ++ dt + dˆσab→cd −− dt + dˆσab→cd +− dt + dˆσab→cd −+ dt � + λ1λ2G1L,c(z1)G1L,d(z2) �dˆσab→cd ++ dt + dˆσab→cd −− dt − dˆσab→cd +− dt − dˆσab→cd −+ dt �� + {c ↔ d}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (35) 7 Thus,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' the dihadron polarization correlation in pp collisions is given by CLL(η1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' η2) = � dz1dz2 � d2pT 1 z2 1 � ab→cd xaf1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='a(xa)xbf1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='b(xb) 1 π dˆσdif dt G1L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='c(z1)G1L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='d(z2) + {c ↔ d} � dz1dz2 � d2pT 1 z2 1 � ab→cd xaf1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='a(xa)xbf1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='b(xb) 1 π dˆσsum dt D1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='c(z1)D1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='d(z2) + {c ↔ d} ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (36) where we have used the following shorthand notation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' dˆσdif dt = dˆσab→cd ++ dt + dˆσab→cd −− dt − dˆσab→cd +− dt − dˆσab→cd −+ dt ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (37) dˆσsum dt = dˆσab→cd ++ dt + dˆσab→cd −− dt + dˆσab→cd +− dt + dˆσab→cd −+ dt .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (38) In the kinematic region of interest, t ∼ u ∼ −s/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Assuming that the longitudinal spin transfers are always positive for all partons, we then find that the qi + ¯qi → qj + ¯qj, qi + ¯qi → g + g, and g + g → qi + ¯qi channels contribute to negative dihadron polarization correlations and the other channels offer positive contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Loosely speaking, s-channels lead to a negative correlation, while t-channels lead to a positive correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Therefore, there is a partial cancellation among different partonic channels, which results in a much smaller dihadron polarization correlation in pp collisions vis-a-vis that in e+e− annihilations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Notice that this assumption is not always the case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The longitudinal spin transfers of u and d quarks are assumed to be small but negative in the second scenario in the DSV parameterizations [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Utilizing CTEQ PDFs [58] and DSV FFs [3], we compute the dihadron polarization correlation in pp and p¯p collisions at different collisional energies and show the numerical results in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' For those typical kinematic configurations, we find that the dihadron polarization correlation is about a few percent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' It is much smaller than that in e+e− annihilations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The reason is twofold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' First, the final state quarks in e+e− annihilations are always connected, which maximizes the polarization correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' In contrast, in pp collisions, besides the s-channels which lead to the negative polarization correlation, there are also sizable contributions from the t-channels which give birth to the positive polarization correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' As mentioned above, the partial cancellation reduces the polarization correlation at the partonic level, which translates into smaller correlation at the hadronic level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Second, the spin transfer of a circularly polarized gluon is assumed to be negligible at the initial scale in the DSV parameterization [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The contribution only arises from the DGLAP evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Therefore, the numerical calculation underestimates the polarization correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' This work can be viewed as the lower bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' A rigorous investigation on the circularly polarized gluon FF (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' the gluon spin transfer) can be carried out once we had more experimental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Furthermore, in Scenario I of the DSV parametrization [3], the spin transfer comes almost exclusively from s → Λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Therefore, the dihadron polarization correlation in the p + p → Λ + ¯Λ + X process is mainly determined by the polarization correlation of the s¯s pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Since the production of the s¯s pair is an s-channel dominant process, we always have negative correlations in Scenario I at different collisional energies as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' However, the dihadron polarization correlation of the p + p → Λ + Λ + X process is mainly determined by that of the ss pair, which can only be produced through the t-channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Thus, the dihadron polarization correlation is then positive for this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' In Scenario III of the DSV parametrization [3], u, d, and s quarks contribute equally to the longitudinal spin transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' For the dihadron polarization correlation of Λ+ Λ production, t-channels still dominate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Therefore, the polarization correlation is always positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' However, for that of Λ + ¯Λ production, the dominant contribution varies with the kinematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Moreover, the discussion for the second scenario is more complicated, since the longitudinal spin transfer is no longer positive for u and d quarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The polarization correlation is no longer positive definite even in Λ + Λ productions where t-channel scatterings always dominate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' SUMMARY In this work, we explore the opportunity of studying the longitudinal spin transfer, G1L, through dihadron polar- ization correlations in e+e− annihilations and unpolarized pp collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Working with the LO and LT approximation, this polarization correlation can be related to the partonic helicity amplitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Thus, the physical picture of this observable is pretty clear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Employing the DSV parametrization [3] for the polarized and unpolarized FFs of Λ, we estimate that the dihadron polarization correlation is about 20% ∼ 40% in e+e− annihilations and about a few percent in pp collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' There are two reasons for the much smaller correlation in pp collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The first one is that s-channels and t-channels contribute to the dihadron polarization correlation with different signs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The partial cancellation gives birth to a weaker polarization correlation in pp collisions than that in e+e− annihilations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The second one lies in the numerical evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' In all three scenarios of the DSV parametrization [3], the longitudinal gluon spin transfer is always assumed 8 DSV η1 = 0 pT 1,2 > 5 GeV p + p → Λ + ¯Λ + X √ S = 200 GeV 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='5 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='5 2 −4 −2 0 2 4 6 10−2 η2 CLL Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' I Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' II Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' III DSV η1 = 0 pT 1,2 > 5 GeV p + p → Λ + Λ + X √ S = 200 GeV 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='5 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='5 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='15 η2 CLL Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' I Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' II Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' III DSV p + p → Λ + ¯Λ + X √ S = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='02 TeV pT 1,2 > 20 GeV η1 = 0 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='5 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='5 2 −6 −4 −2 0 2 4 ·10−2 η2 CLL Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' I Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' II Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' III DSV p + p → Λ + Λ + X √ S = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='02 TeV pT 1,2 > 20 GeV η1 = 0 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='5 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='5 2 0 2 4 6 8 ·10−2 η2 CLL Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' I Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' II Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' III DSV η1 = 0 pT 1,2 > 20 GeV √ S = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='96 TeV p + ¯p → Λ + ¯Λ + X −2 −1 0 1 2 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='10 η2 CLL Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' I Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' II Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' III DSV η1 = 0 pT 1,2 > 20 GeV √ S = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='96 TeV p + ¯p → Λ + Λ + X −2 −1 0 1 2 0 2 4 6 8 10−2 η2 CLL Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' I Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' II Sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' III FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Predictions for the dihadron polarization correlation in pp/p¯p collisions at RHIC, LHC, and Tevatron energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' to be negligible at the initial scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Therefore, the numerical calculation underestimates the dihadron polarization correlation in pp collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The ambiguity in the gluon spin transfer can only be removed by the experimental measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' We expect that measuring dihadron polarization correlation in pp collisions can play an important role on this front.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' It will cast new light on the fragmentation of circularly polarized gluons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Measuring the dihadron polarization correlation in the experiment does not require polarized beams or colliding at the Z0-pole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Therefore, it can be easily performed at Belle, RHIC, Tevatron, and the LHC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' As a matter of fact, since most of the experimental data can be used in this analysis, we expect small statistical errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' We believe this experiment can significantly boost the quantitative study of the polarized FFs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Moreover, combining the experimental data from e+e− and pp experiments, we can better constrain the gluon spin transfer, G1L,g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Thus, it can improve our understanding on the hadronization mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' 9 Appendix A: Measuring dihadron polarization correlation in the experiments In this appendix, we show how the dihadron polarization correlation can be measured in the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' We consider two almost back-to-back Λ and ¯Λ pair production.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' We use θ∗ 1,2 to denote the angle between the momentum of daughter p/¯p and that of the parent Λ/¯Λ in the rest frame of Λ/¯Λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' We use P++,−−,+−,−+ to denote the probability of the four combinations of polarization states of Λ and ¯Λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The nomalization is given by P++ + P−− + P+− + P−+ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (A1) Thus, the dihadron polarization correlation is defined as CLL = (P++ + P−−) − (P+− + P−+).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' (A2) Furthermore, the polarization of Λ hyperons is given by P Λ L = P++ + P+− − P−+ − P−−, while that of ¯Λ hyperons is given by P ¯Λ L = P++ + P−+ − P+− − P−−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' The normalized angle distribution of the daughter p and ¯p is 1 N dN d cos θ∗ 1d cos θ∗ 2 = P++ 1 + α cos θ∗ 1 2 1 + α cos θ∗ 2 2 + P−− 1 − α cos θ∗ 1 2 1 − α cos θ∗ 2 2 + P+− 1 + α cos θ∗ 1 2 1 − α cos θ∗ 2 2 + P−+ 1 − α cos θ∗ 1 2 1 + α cos θ∗ 2 2 = 1 4 + P Λ L 1 4α cos θ∗ 1 + P ¯Λ L 1 4α cos θ∗ 2 + CLL 1 4α2 cos θ∗ 1 cos θ∗ 2, (A3) where α is the decay parameter of Λ hyperons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Thus, the dihadron polarization correlation can be measured by extracting the ⟨cos θ∗ 1 cos θ∗ 2⟩ module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' ACKNOWLEDGMENTS We thank K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Liu, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Song for fruitful discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' Wei is supported by the Taishan fellowship of Shandong Province for junior scientists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/a9E2T4oBgHgl3EQfwAgi/content/2301.04096v1.pdf'} +page_content=' [1] A.' metadata={'source': 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b/atFST4oBgHgl3EQfBjj8/content/tmp_files/2301.13704v1.pdf.txt @@ -0,0 +1,1254 @@ +Implicit Linear Difference Equation over Residue Class Rings +M.V. Heneralov ∗ and A.L. Piven’† +Department of Mathematics & Computer Sciences +V. N. Karazin Kharkiv National University +Abstract +We investigate the first order implicit linear difference equation over residue class rings modulo m. We +prove an existence criterion and establish the amount of solutions for this equation. We obtain analogous +results for the initial problem of the considered equation. The examples which illustrate the developed +theory are given. +Keywords: implicit linear difference equation, ring, residue class, initial problem +2010 Mathematics Subject Classification. 39A99, 16P50 +1 +Introduction +The theory of the linear difference equations is an important branch of mathematics, having a series of +different applications (see, for example, [1]–[4]). The theory of implicit linear difference equations in vector +spaces was developed in the 80s–90s of the 20 century (see, for example, [4]–[6]). Unlike the classical theory, +the non-invertible operators have an important role in the new theory. Therefore the interesting problem +of the investigation of the implicit linear difference equation with non-invertible coefficients from the any +commutative ring appeared. +At the moment implicit difference equations over the ring of integers were +studied more detailed [7]–[9]. In [10] these equations in different classes of topological vector spaces were +investigated. +In this paper the first order implicit linear difference equations over residue classes rings is investigated. +Let Zm = Z/mZ be the residue class ring modulo m, where m ∈ N, m ≥ 2. Let A, B, Y0 ∈ Zm and let +{Fn}∞ +n=0 be a sequence of Zm. Consider the initial problem +BXn+1 = AXn + Fn, +n ∈ Z+, +(1.1) +X0 = Y0, +(1.2) +where Z+ denotes the set of non-negative integers. +The sequence {Xn}∞ +n=0 of elements of Zm is called +a solution of the initial problem (1.1), (1.2), if it satisfies Equation (1.1) and the initial condition (1.2). +Equation (1.1) is called implicit, if B is a non-invertible element of the ring Zm. If B is an invertible element +of Zm, then this equation is called explicit. Let a, b are representatives of classes A, B respectively. In the +Section 2 we prove that if the greater common divisor of numbers a, b, m is equal to 1, then Equation (1.1) +is decomposed to the explicit equation (2.5) and the implicit equation (2.6) which has a unique solution (see +lemmas 2.1, 2.2 and Theorem 2.1). Theorem 2.1 also gives the general solution for these equations. The +main results of this paper are represented in Section 3 (see theorems 3.1 and 3.2). Theorem 3.1 describes +necessary and sufficient conditions for the solvability, an amount of solutions and the general solution for the +initial problem (1.1), (1.2). This theorem gives the full description of all possible situations for the initial +problem (1.1), (1.2). The analogous results for Equation (1.1) are established in Theorem 3.2. This theorem +leads to the criteria of the existence and uniqueness of a solution for Equation (1.1) (see Corollaries 3.2, 3.3). +As in the Fredholm theory (see, for example, [11, Chapter 7]), Corollary 3.4 shows that if corresponding to +(1.1) homogeneous equation has only trivial solution then for any sequence {Fn}∞ +n=0 of Zm Equation (1.1) +has a unique solution. Section 4 of the present paper contains the examples, which illustrate the constructed +theory (see Examples 4.1–4.4). +∗me2001.com@gmail.com +†aleksei.piven@karazin.ua +1 +arXiv:2301.13704v1 [math.FA] 31 Jan 2023 + +M.V. Heneralov, A.L. Piven’ +2 +Through this paper [t]s denotes the class of the element t ∈ Z of the ring Zs, where s ∈ N. The ring Z1 +means as the null ring. For the numbers n1, n2, . . . , nN ∈ Z such that |n1| + |n2| + . . . + |nN| ̸= 0 the symbol +gcd (n1, . . . , nN) denotes their positive greater common divisor. If T is a nilpotent element of the ring Zs, +then ind(T) denotes the nilpotency index of T. +2 +Preliminary +Through this paper m ≥ 2, m ∈ N. Let A, B and Fn (n ∈ Z+) be given elements of the ring Zm. For each +of elements A, B, Y0, Fn, Xn ∈ Zm (n ∈ Z+) denote, respectively, their representatives a, b, fn, y0, xn. +By Fundamental Theorem of Arithmetic, there exists pairwise different primes p1, . . . , pr and numbers +k1, . . . , kr ∈ N such that m = +r +� +j=1 +pkj +j . +Denote +m1 = +� +j : pj∤b +pkj +j , +m2 = +� +j : pj|b +pkj +j , +where m1 = 1 in the case pj | b (j = 1, . . . , r) and m2 = 1 in the case pj ∤ b (j = 1, . . . , r). Obviously, +m1 · m2 = m, and gcd (m1, m2) = 1. +Introduce the natural projections πi : Zm → Zmi, defined as follows: +πi (T) = [t]mi, ∀T = [t]m, +i = 1, 2. +(see [12, p. 381–382]). +For each i = 1, 2, according to the [12, p. 381–382] the natural projections πi (i = 1, 2) are homomor- +phisms. +Denote +Ai = πi (A) , +Bi = πi (B) , +Yi,0 = πi (Y0) , +Fi,n = πi (Fn) , +i = 1, 2. +Let m1 ̸= 1, m2 ̸= 1. Introduce the isomorphism +ψ: Zm1 ⊕ Zm2 → Zm, +defined as follows (see, for example, [12, Section 7.6 and Exercise 5 to the Section 7.6]): +ψ (T1, T2) = [t1e1m2 + t2e2m1]m, +∀T1 = [t1]m1, ∀T2 = [t2]m2, +(2.1) +where +E1 = [e1]m1 = [m2]−1 +m1, +E2 = [e2]m2 = [m1]−1 +m2. +(2.2) +We regard that since gcd (m1, m2) = 1, the inverse elements E1 and E2 are defined. +If T1 ∈ Zm1, T2 ∈ Zm2, then definition of ψ implies +πi (ψ (T1, T2)) = Ti, +i = 1, 2. +(2.3) +Also, π−1 +1 +(T1) ∩ π−1 +2 +(T2) is a one-element set, ψ (T1, T2) is an element of this set. This means that +{ψ (T1, T2)} = π−1 +1 +(T1) ∩ π−1 +2 +(T2) . +(2.4) +Consider the following equations over rings Zm1 and Zm2 respectively: +B1X1,n+1 = A1X1,n + F1,n, +n ∈ Z+, +(2.5) +B2X2,n+1 = A2X2,n + F2,n, +n ∈ Z+. +(2.6) +The following lemma describes the connection between solutions of Equation (1.1) and equations (2.5), +(2.6). +Lemma 2.1. Let m1 ̸= 1, m2 ̸= 1. The sequence +Xn = ψ (X1,n, X2,n) , +n ∈ Z+, +(2.7) +is a solution of Equation (1.1) iff the sequences {X1,n}∞ +n=0 and {X2,n}∞ +n=0 are solutions of equations (2.5), +(2.6), respectively. Moreover, Xi,n = πi (Xn), i = 1, 2, n ∈ Z+. + +M.V. Heneralov, A.L. Piven’ +3 +Proof. The equalities (2.7) and (2.3) yield together the equality for Xi,n: πi (Xn) = Xi,n, i = 1, 2. +Since πi (i = 1, 2) are homomorphisms, by the equality (2.7), +πi (BXn+1 − AXn − Fn) = BiXi,n+1 − AiXi,n − Fi,n, +i = 1, 2, +n ∈ Z+. +By the equality (2.4), we obtain: +BXn+1 − AXn − Fn = ψ (B1X1,n+1 − A1X1,n − F1,n, B2X2,n+1 − A2X2,n − F2,n) , +n ∈ Z+. +(2.8) +We note that +π1 (0) = 0 and π2 (0) = 0. +(2.9) +Since (2.9), (2.8) hold, we obtain that the equality (1.1) is fulfilled if and only if equalities (2.5), (2.6) are +fulfilled. This ends the proof of the lemma. +Introduce the notation: +d = gcd (a, b, m) . +Consider the equations (2.5) and (2.6). The following lemma establishes important properties for coeffi- +cients of these equations. +Lemma 2.2. The following statements hold. +1. Let m1 ̸= 1, then B1 is invertible. +2. Let m2 ̸= 1, then B2 is nilpotent. If additionally d = 1, then A2 is invertible. +3. B is nilpotent if and only if m1 = 1. +Proof. Proof the statement 1. The definition of m1 and B implies the equality gcd (b, m1) = 1. Hence, the +element B1 is an invertible element of Zm1. +Proof the statement 2. Firstly prove that B2 is nilpotent. Is it evident from the definition of m2: if +k = +max +j=1,...,r{kj}, then Bk +2 = [bk]m2 = 0. +Let d = 1. We will prove that gcd (a, m2) = 1. Assuming the contrary, we obtain that there exists +j ∈ {1, . . . , r} such that pj | a. This condition yields pj | a, pj | b, pj | m. Hence pj | d. But it contradicts +d = 1. Therefore gcd (a, m2) = 1. This means that A2 is an invertible element of Zm2. +Proof the statement 3. The condition m1 = 1 is equivalent to the assertion +∀j = 1, . . . , r: pj | b. +The last condition is equivalent to the nilpotency of the element B in Zm. +Remark 2.1. Lemma 2.2 is an analogue of the spectral decomposition of a regular operator pencil in Banach +spaces (see [13, Lemma 2.1]). The analogous to (2.5), (2.6) decomposition of an implicit difference equation +in Banach spaces into two equations with regarded properties was obtained in [6, 14]. +The following theorem is a solvability theorem for Equation (2.5) and, in the case d = 1, for Equation (2.6). +Theorem 2.1. The following statements hold. +1. Let m1 ̸= 1. The general solution of Equation (2.5) is defined by the following formula: +X1,n = B−n +1 +An +1X1,0 + +n−1 +� +s=0 +As +1B−s−1 +1 +F1,n−s−1, +n ∈ N, +(2.10) +where X1,0 is an arbitrary element of Zm1. +2. Let d = 1 and m2 ̸= 1. Then Equation (2.6) has a unique solution, defined by the following formula: +X2,n = − +ind(B2)−1 +� +s=0 +A−s−1 +2 +Bs +2F2,n+s, +n ∈ Z+. +(2.11) + +M.V. Heneralov, A.L. Piven’ +4 +Remark 2.2. The corresponding inverse elements exist according to Lemma 2.2. +Proof. Prove firstly the statement 1. By the statement 1 of Lemma 2.2, B1 is invertible. The equality (2.5) +is equivalent to the equality +X1,n+1 = B−1 +1 A1X1,n + B−1 +1 F1,n, +n ∈ Z+. +(2.12) +According to [3, p. 4], the general solution of Equation (2.12) has the form (2.10). +Prove now the statement 2. By the statement 2 of Lemma 2.2, A is an invertible element, and B is +nilpotent (these are since d = 1). +The equality (2.6) is equivalent to the following: +X2,n = −A−1 +2 F2,n + A−1 +2 B2X2,n+1, +n ∈ Z+. +(2.13) +Applying (2.13) recurrently few times, obtain the equality (2.11). +Now let {Xn}∞ +n=0 be defined by the formula (2.11). Denote k = ind (B2). Substituting (2.11) to the left +part of Equation (2.6), we obtain: +B2Xn+1 = −B2A−1 +2 +k−1 +� +s=0 +A−s +2 Bs +2F2,n+1+s = − +k−1 +� +s=0 +A−s−1 +2 +Bs+1 +2 +F2,n+s+1 = − +k +� +t=1 +A−t +2 Bt +2F2,n+t = += − +k +� +t=0 +A−t +2 Bt +2F2,n+t + F2,n = −A2 · A−1 +2 +k−1 +� +t=0 +A−t +2 Bt +2F2,n+t + F2,n = A2X2,n + F2,n. +Therefore {X2,n}∞ +n=0, defined by the formula (2.11), is the unique solution of Equation (2.6). +Corollary 2.1. The following statements hold. +1. Let d = 1 and m1 = 1. Equation (1.1) has a unique solution {Xn}∞ +n=0, defined by the following formula: +Xn = − +ind(B)−1 +� +s=0 +A−s−1BsFn+s, +n ∈ Z+. +(2.14) +2. Let m2 = 1. The general solution of Equation (1.1) is defined by the following formula: +Xn = B−nAnX0 + +n−1 +� +s=0 +AsB−s−1Fn−s−1, +n ∈ N, +(2.15) +where X0 is an arbitrary element of Zm. +3 +Main results +Here we obtain the solvability theorems over Zm for Equation (1.1) and for the initial problem (1.1), (1.2). +Introduce the following notations: +m′ = m +d , Y ′ +0 = [y0]m′, A′ = [a/d]m′, B′ = [b/d]m′. +Also, when d | fn for all n ∈ Z+, denote +F ′ +n = [fn/d]m′, +n ∈ Z+. +Each a prime divisor of the number m′ is also a divisor of m. Then by Fundamental Theorem of Arithmetic, +there exist non-negative integers lj ≤ kj (j = 1, . . . , r) such that m′ = +r +� +j=1 +plj +j . +Denote also +m′ +1 = +� +j : dpj∤b +plj +j , +m′ +2 = +� +j : dpj|b +plj +j , + +M.V. Heneralov, A.L. Piven’ +5 +A′ +i = [a/d]m′ +i, +B′ +i = [b/d]m′ +i, +Y ′ +i,0 = [y0]m′ +i, +i = 1, 2. +As in the definition m1, m2, we assume m′ +1 = 1 in the case dpj | b (j = 1, . . . , r) and m′ +2 = 1 in the case +dpj ∤ b (j = 1, . . . , r). Note that if d = 1, then m′ +i = mi, i = 1, 2. +Let d | fn for all n ∈ Z+. Denote +F ′ +i,n = [fn/d]m′ +i. +and consider the initial problem +B′X′ +n+1 = A′X′ +n + F ′ +n, +n ∈ Z+, +(3.1) +X′ +0 = Y ′ +0 +(3.2) +over Zm′. +The following statement is a helpful lemma, which shows the connection between the equations (1.1) and +(3.1). +Lemma 3.1. Let d ̸= 1, d | fn (n ∈ Z+). The sequence {Xn}∞ +n=0 is a solution of Equation (1.1) iff it admits +the following representation +Xn = [x′ +n + αnm′]m, +n ∈ Z+, +(3.3) +where X′ +n = [x′ +n]m′ (n ∈ Z+) is a solution of Equation (3.1), and {αn}∞ +n=0 is a sequence of {0, 1, . . . , d − 1}. +Moreover, the sequence {αn}∞ +n=0 and the solution {X′ +n}∞ +n=0 of Equation (3.1) with x′ +n ∈ {0, . . . , m′ − 1} are +uniquely determined by the solution {Xn}∞ +n=0 of Equation (1.1). +Proof. Obviously, Equation (1.1) is equivalent to the congruence +bxn+1 ≡ axn + fn +(mod m), +n ∈ Z+. +(3.4) +The congruence (3.4) is equivalent to the following condition. +b +dxn+1 ≡ a +dxn + fn +d +(mod m′), +n ∈ Z+. +(3.5) +The congruence (3.5) means that there exists a solution X′ +n = [x′ +n]m′ (n ∈ Z+) of Equation (3.1) such that +xn ≡ x′ +n (mod m′). Therefore {Xn}∞ +n=0 is a solution of (1.1) if and only if Xn = [x′ +n + αn · m′]m (n ∈ Z+), +where {αn}∞ +n=0 is an arbitrary sequence of {0, . . . , d − 1}. +Suppose that the two following representatives for the solution of Equation (1.1) hold: +Xn = [x′ +n + αnm′]m = +� +� +x′n + � +αnm′� +m , +n ∈ Z+, +where X′ +n = [x′ +n]m′, � +X′n = +� +� +x′n +� +m′ (n ∈ Z+) are solutions of Equation (3.1), αn, � +αn (n ∈ Z+) are numbers +from {0, . . . , d − 1} and additionally xn, � +xn ∈ {0, . . . , m′ − 1}. It implies the following congruence +x′ +n + αnm′ ≡ � +x′n + � +αnm′ +(mod m), +n ∈ Z+. +(3.6) +Then x′ +n ≡ � +x′n (mod m′). According to the assumption � +x′n, x′ +n ∈ {0, . . . , m′ − 1}, we have x′ +n = � +x′n, n ∈ Z+. +Now the congruence (3.6) means αn ≡ � +αn (mod d). Since αn, � +αn ∈ {0, . . . , d − 1}, we have αn = � +αn, n ∈ +Z+. +The following theorem is a solvability theorem for the initial problem (1.1), (1.2). This theorem also +establishes the explicit form for the general solution of the considered initial problem, when a solution exists. +Theorem 3.1. The following statements hold. +1. The initial problem +(1.1), (1.2) has a unique solution iff d = 1 and one of the following conditions +holds: +(a) m2 = 1; +(b) m2 ̸= 1 and the equality +Y2,0 = − +ind(B2)−1 +� +s=0 +A−s−1 +2 +Bs +2F2,s +(3.7) +is fulfilled. + +M.V. Heneralov, A.L. Piven’ +6 +Moreover, the unique solution of the initial problem (1.1), (1.2) is defined by the formula +Xn = +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +� +B−nAnY0 + +n−1 +� +s=0 +AsB−s−1Fn−s−1, +m2 = 1, +− +ind(B)−1 +� +s=0 +A−s−1BsFn+s, +m1 = 1, +ψ +� +�B−n +1 +An +1Y1,0 + +n−1 +� +s=0 +As +1B−s−1 +1 +F1,n−s−1, − +ind(B2)−1 +� +s=0 +A−s−1 +2 +Bs +2F2,n+s +� +� , m1 ̸= 1, m2 ̸= 1. +(3.8) +2. The initial problem (1.1), (1.2) has infinitely many solutions iff d ̸= 1, d | fn for all n ∈ Z+ and one of +the following conditions holds: +(a) m′ +2 = 1; +(b) m′ +2 ̸= 1 and the equality +Y ′ +2,0 = − +ind(B′ +2)−1 +� +s=0 +(A′ +2)−s−1 (B′ +2)s F ′ +2,s +(3.9) +is fulfilled. +The general solution of the initial problem (1.1), (1.2) is defined by +Xn = [x′ +n + αn · m′]m, +n ∈ N, +(3.10) +where X′ +n = [x′ +n]m′ (n ∈ Z+) is a solution of the initial problem (3.1), (3.2) (this solution exists and is +unique), and {αn}∞ +n=1 is an arbitrary sequence of {0, 1, . . . , d − 1}. Moreover, the sequence {αn}∞ +n=1 is +uniquely determined by the solution {Xn}∞ +n=0 of the initial problem (1.1), (1.2). +3. The initial problem (1.1), (1.2) has no solutions iff one of the following conditions holds: +(a) d ∤ fn for some n ∈ Z+; +(b) d | fn (n ∈ Z+), m′ +2 ̸= 1 and the equality (3.9) is not fulfilled. +Remark 3.1. In the statement 2 of Theorem 3.1 the sequence {X′ +n}∞ +n=0, when m ̸= d, may be defined by +the formula, analogous to the formula (3.8), applied to the initial problem (3.1), (3.2). When m = d, then +evidently X′ +n = 0 for all n ∈ Z+. +Proof. The sufficient conditions of all three statements of Theorem 3.1 are mutually exclusive and they +exhaust all possibilities. Therefore it is enough to prove the sufficiency for all of three statements of this +theorem. +Prove the sufficiency of the statement 1. Let d = 1. If either m1 = 1, or m2 = 1, then the claimed +statement follows from Corollary 2.1. Further let m1 ̸= 1 and m2 ̸= 1. +Set the initial conditions: +X1,0 = Y1,0 ∈ Zm1, +(3.11) +X2,0 = Y2,0 ∈ Zm2 +(3.12) +for equations (2.5) and (2.6) respectively. +According to Lemma 2.1, the sequence {Xn}∞ +n=0 is a solution of the initial problem (1.1), (1.2) if and only +if the sequence {X1,n}∞ +n=0 is a solution of the initial problem (2.5), (3.11) and the sequence {X2,n}∞ +n=0 is a +solution of the initial problem (2.6), (3.12). By the statement 1 of Theorem 2.1, the initial problem (2.5), +(3.11) has a solution for any Y1,0 ∈ Zm1. According to the statement 2 of Theorem 2.1, the initial prob- +lem (2.6), (3.12) has a solution if and only if Y2,0 satisfies (3.7). Hence, the initial problem (1.1), (1.2) has a +solution if and only if the condition (3.7) is fulfilled, moreover this solution is unique and has the form (2.7), +where X1,n and X2,n are defined by the formulas (2.10) and (2.11) respectively. +Prove the sufficiency of the statement 2. Let d ̸= 1, d | fn for all n ∈ Z+. Additionally, let either m′ +2 = 1, +or m′ +2 ̸= 1 and (3.9) be fulfilled. Since gcd (a/d, b/d, m′) = 1, we can apply the sufficiency of the statement 1 +(which is already proved) to the initial problem (3.1), (3.2). Due to that statement, the initial problem (3.1), + +M.V. Heneralov, A.L. Piven’ +7 +(3.2) has a unique solution X′ +n = [x′ +n]m′ (n ∈ Z+). By Lemma 3.1, for any sequence {αn}∞ +n=0 of {0, . . . , d−1} +the formula (3.3) defines the solution of Equation (1.1). +We choose α0 such that (1.2) is fulfilled, i. e. [x′ +0 + α0m′]m = [y0]m. The initial condition (3.2) implies +[x′ +0]m′ = [y0]m′, and the following congruence holds x′ +0 ≡ y0 (mod m′). Then β = y0−x′ +0 +m′ +∈ Z. Divide β on d +with remainder. Then there exist q ∈ Z and α0 ∈ {0, . . . , d − 1} such that β = qd + α0. Therefore, +[x′ +0 + α0m′]m = [x′ +0 + (β − qd)m′]m = [x′ +0 + y0 − x′ +0 − qm]m = [y0]m. +Therefore for the chosen α0 and any sequence {αn}∞ +n=1 of {0, . . . , d − 1} the formula (3.10) defines a solution +of the initial problem (1.1), (1.2). By Lemma 3.1, the expression (3.10) gives infinitely many solutions of +this initial problem (see also (3.3)). +We prove that the general solution of the initial problem (1.1), (1.2) is defined by the formula (3.10). Let +{Xn}∞ +n=0 be an arbitrary solution of this initial problem. Then by Lemma 3.1, this solution has the form (3.3), +where {X′ +n}∞ +n=0 is a solution of Equation (3.1). Moreover, {X′ +n}∞ +n=0 must satisfy the initial condition (3.2). +We have proved that the initial problem (3.1), (3.2) has a unique solution. Hence the general solution of the +initial problem (1.1), (1.2) has the form (3.10). +Now prove the sufficiency of the statement 3. Assume d ∤ fn for some n ∈ Z+. The equality (1.1) for this +n is equivalent to the congruence bxn+1 − axn ≡ fn (mod m). Hence, +fn ≡ d · +� b +dxn+1 − a +dxn +� +(mod m). +(3.13) +Since d | m, the condition (3.13) means d | fn, which is a contradiction the assumption. +Therefore, if +d ∤ fn for some n ∈ Z+, then Equation (1.1) has no solutions. Now suppose that d ̸= 1, d | fn, n ∈ Z+, +m′ +2 ̸= 1 and the equality (3.9) is not fulfilled. Assume the contrary, that the initial problem (1.1), (1.2) has +a solution Xn = [xn]m (n ∈ Z+). Then the congruence (3.13) is fulfilled for all n ∈ Z+ and the sequence +X′ +n = [xn]m′ (n ∈ Z+) is a solution of the initial problem (3.1), (3.2). Since gcd (a/d, b/d, m′) = 1, we can +apply the sufficiency of the statement 1 (which is already proved) to this initial problem. Therefore, if m′ +2 ̸= 1 +and {X′ +n}∞ +n=0 is a solution of the initial problem (3.1), (3.2), then Y ′ +2,0 = [y0]m′ +2 must satisfy (3.9). This +contradicts the assumption. +The following theorem is a solvability theorem for Equation (1.1). This theorem also yields the explicit +form for the general solution of Equation (1.1). +Theorem 3.2. The following statements hold. +1. Equation (1.1) has a finite amount of solutions iff d = 1. Moreover, the amount of these solutions is +equal to m1 and in this case +(a) If m2 = 1, then the general solution of Equation (1.1) has the form +Xn = B−nAnX0 + +n−1 +� +s=0 +AsB−s−1Fn−s−1, +n ∈ N, +(3.14) +where X0 is an arbitrary element of Zm. +(b) If m1 = 1, then the unique solution of Equation (1.1) has the form +Xn = − +ind(B)−1 +� +s=0 +A−s−1BsFn+s, +n ∈ Z+. +(3.15) +(c) If m1 ̸= 1 and m2 ̸= 1, then the general solution of Equation (1.1) has the form +X0 = ψ +� +�X1,0, − +ind(B2)−1 +� +s=0 +A−s−1 +2 +Bs +2F2,s +� +� , +Xn = ψ +� +�B−n +1 +An +1X1,0 + +n−1 +� +s=0 +As +1B−s−1 +1 +F1,n−s−1, − +ind(B2)−1 +� +s=0 +A−s−1 +2 +Bs +2F2,n+s +� +� , +n ∈ N, +(3.16) +where X1,0 is an arbitrary element of Zm1. + +M.V. Heneralov, A.L. Piven’ +8 +2. Equation (1.1) has infinitely many solutions iff d ̸= 1 and d | fn for all n ∈ Z+. The general solution in +this case has the form (3.3), where X′ +n = [x′ +n]m′ (n ∈ Z+) is the general solution of Equation (3.1), and +{αn}∞ +n=0 is an arbitrary sequence of {0, . . . , d − 1}. Moreover, the sequence {αn}∞ +n=0 and the solution +{X′ +n}∞ +n=0 of Equation (3.1) with x′ +n ∈ {0, . . . , m′ −1} are uniquely determined by the solution {Xn}∞ +n=0 +of Equation (1.1). +3. Equation (1.1) has no solutions iff d ∤ fn for some n ∈ Z+. +Remark 3.2. Since gcd (a/d, b/d, m′) = 1, in the statement 2 of Theorem 3.2 the general solution of Equation +{X′ +n}∞ +n=0 may be defined by the formula, analogous to formulas (3.14)–(3.16), applied to Equation (3.1). +Proof. The sufficient conditions of all three statements of Theorem 3.2 are mutually exclusive and they +exhaust all possibilities. Therefore it is enough to prove the sufficiency for all of three statements of this +theorem. +We prove the sufficiency of the statement 1 of Theorem 3.2. Let d = 1. If either m1 = 1 or m2 = 1, +then the claimed statement implies from the corollary 2.1. Let m1 ̸= 1 and m2 ̸= 1. The statement 1 of +Theorem 3.1 implies that if there exists a solution of the initial problem (1.1), (1.2), then it is defined uniquely +by the given Y1,0, where Y1,0 is an arbitrary element of the ring Zm1. Therefore, the amount of solutions of +Equation (1.1) is equal to m1. The form (3.16) of the general solution of Equation (1.1) is obtained with +the help of the general solution (3.8) of the initial problem (1.1), (1.2). +Prove the sufficiency of the statement 2 of Theorem 3.2. Let d ̸= 1 and d | fn for all n ∈ Z+. Since +gcd +� a +d, b +d, m′� += 1, we can apply the sufficiency of the statement 1 (which is already proved) to Equation (3.1). +Due to that statement, Equation (3.1) has m′ +1 solutions. Let X′ +n = [x′ +n]m′ (n ∈ Z+) be the general solution of +this equation. By Lemma 3.1, the general solution of Equation (1.1) has the form (3.3), where {αn}∞ +n=0 is an +arbitrary sequence of {0, . . . , d − 1}. Moreover, by Lemma 3.1, Equation (1.1) has infinitely many solutions. +Prove the sufficiency of the statement 3 of Theorem 3.2. Let d ̸= 1 and d ∤ fn for some n ∈ Z+. By +the statement 3 of Theorem 3.1, for any Y0 ∈ Zm the initial problem (1.1), (1.2) has no solutions. Hence, +Equation (1.1) has no solutions. +The following corollary of Theorem 3.2 yields the solvability of Equation (1.1) in the case of an invertible +element A. +Corollary 3.1. If A is an invertible element of Zm, then Equation (1.1) always has a solution. Moreover, +the amount of solutions for Equation (1.1) is equal to m1. +Theorem 3.2 also implies the following criteria of the existence and uniqueness of a solution for Equa- +tion (1.1). +Corollary 3.2. Equation (1.1) has a unique solution iff d = 1 and m1 = 1. In particular, the homogeneous +equation +BXn+1 = AXn, +n ∈ Z+ +(3.17) +has only trivial solution iff d = 1 and m1 = 1. +Corollary 3.3. Equation (1.1) has a unique solution iff A is invertible and B is nilpotent. Moreover, this +solution has the form (3.15). +Proof. According to Corollary 3.2, Equation (1.1) has a unique solution if and only if d = 1 and m1 = 1. +Hence, it suffices to prove that the conditions B is nilpotent and A is invertible are collectively equivalent +to the conditions d = 1 and m1 = 1. +At first, prove the sufficiency of the mentioned statement: let B be nilpotent, and A be invertible. Let +us proof that d = 1, m1 = 1. By the statement 3 of Lemma 2.2, the nilpotency of B implies m1 = 1. If A is +invertible, then gcd(a, m) = 1, and hence d = 1. +Now prove the inverse statement. Let d = 1 and m1 = 1. By the statement 3 of Lemma 2.2, the condition +m1 = 1 yields B is nilpotent. By Lemma 2.2, if d = 1, then A2 is an invertible element of Zm2. Since m1 = 1, +this implies A2 = A is invertible. The representation (3.15) for the unique solution of Equation (1.1) follows +from Theorem 3.2. +Corollary 3.4. If the homogeneous equation (3.17) has only trivial solution, then for any sequence {Fn}∞ +n=0 +Equation (1.1) has a unique solution. Moreover, the unique solution of Equation (1.1) has the form (3.15). +Proof. Let Equation (3.17) has only trivial solution. +Then Corollary +3.2 implies d = 1, m1 = 1 and, +therefore, for any sequence {Fn}∞ +n=0 of Zm Equation (1.1) has a unique solution. The form (3.15) for the +unique solution of Equation (1.1) follows from Corollary 3.3. + +M.V. Heneralov, A.L. Piven’ +9 +4 +Examples +Example 4.1. Consider the following equation over Z6: +[3]6Xn+1 = [2]6Xn + Fn, +n ∈ Z+. +(4.1) +Let Fn = [fn]6. Determine the values: A = [2]6, B = [3]6, m = 6. Let b = 3, a = 2, hence d = 1. On +evidence, m1 = 2 and m2 = 3. Also determine: A2 = [2]3, B2 = [3]3, ind(B2) = 1. Let Y0 = [y0]6. By the +statement 1 of Theorem 3.1, the initial problem (4.1), (1.2) has a solution if and only if +[y0]3 = − +ind(B2)−1 +� +s=0 +A−s−1 +2 +Bs +2F2,s = −[2]−1 +3 [f0]3 = [f0]3, +i. e. +[y0]3 = [f0]3. +(4.2) +Further assume that the solution of the initial problem (4.1), (1.2) exists, i. e. the equality (4.2) is fulfilled. +This solution is unique. +The representation of this solution may be found by the formula (3.8). Evaluate: A1 = [2]2, B1 = [3]2, +E1 = [3]−1 +2 += [1]2, E2 = [2]−1 +3 += [2]3 (see also the formulas (2.2)). Choose e1 = 1, e2 = 2. According to the +formula (2.1), the isomorphism ψ: Z2 ⊕ Z3 → Z6 is defined as follows: +ψ(T1, T2) = [3t1 + 4t2]6, +∀T1 = [t1]2, ∀T2 = [t2]3. +(4.3) +Evaluate +B−n +1 +An +1X1,0 + +n−1 +� +s=0 +As +1B−s−1 +1 +F1,n−s−1 = [3]−n +2 [2]n +2X1,0 + +n−1 +� +s=0 +[2]s +2[3]−s−1 +2 +F1,n−s−1 = F1,n−1, +n ∈ N, +(4.4) +− +ind(B2)−1 +� +s=0 +A−s−1 +2 +Bs +2F2,n+s = −[2]−1 +3 F2,n = F2,n, +n ∈ Z+. +(4.5) +Substituting (4.3), (4.4) and (4.5) into (3.8), we obtain the following form for the unique solution of the +initial problem (4.1), (1.2) : +X0 = Y0, +Xn = ψ([fn−1]2, [fn]3) = [3fn−1 + 4fn]6 = 3Fn−1 + 4Fn, +n ∈ N. +(4.6) +By Theorem 3.2, Equation (4.1) has m1 = 2 solutions, and the general solution of this equation has the +form: +X0 = ψ ([β]2, [f0]3) = [3β + 4f0]6, +Xn = ψ ([fn−1]2, [fn]3) = [3fn−1 + 4fn]6 = 3Fn−1 + 4Fn, +n ∈ N, +where β may be equal to 0 or 1. +Example 4.2. Consider the following equation over Z9: +[3]9Xn+1 = [2]9Xn + Fn, +n ∈ Z+. +(4.7) +Let Y0 = [y0]9, Fn = [fn]9. Determine the values: A = [2]9, B = [3]9, m = 9. Let b = 3, a = 2, hence +d = 1. On evidence, m1 = 1 and m2 = 9. Here B is nilpotent and A is invertible elements of Z9. Evaluate: +ind(B) = 2. By Corollary 3.3, Equation (4.2) has a unique solution. This solution has the form +Xn = − +ind(B)−1 +� +s=0 +[2]−s−1 +9 +[3]s +9Fn+s = −[5]9Fn − [25]9[3]9Fn+1 = 4Fn + 6Fn+1, +n ∈ Z+. +(4.8) +The initial problem (4.7), (1.2) has a solution if and only if Y0 = 4F0 + 6F1. This solution is unique and +has the form (4.8). + +M.V. Heneralov, A.L. Piven’ +10 +Example 4.3. Consider the following equation over Z12: +[6]12Xn+1 = [2]12Xn + Fn, +n ∈ Z+. +(4.9) +Let Fn = [fn]12. Determine the values: A = [2]12, B = [6]12, m = 12, a = 2, b = 6. That implies that +d = 2. If fn is odd for some n ∈ Z+, then by the statement 3 of Theorem 3.2 Equation (4.9) has no solutions. +Further let fn be even for all n ∈ Z+. +Determine: m′ = 6, m′ +1 = 2, m′ +2 = 3, B′ = [3]6, A′ = [1]6, F ′ +n = +� +fn +2 +� +6. Let Y0 = [y0]12. Also, Y ′ +0 = [y0]6, +B′ +1 = [3]2, A′ +1 = [1]2, B′ +2 = [3]3, A′ +2 = [2]3, F ′ +1,n = +� +fn +2 +� +2, F ′ +2,n = +� +fn +2 +� +3. Here ind(B′ +2) = 1. +By the statement 2 of Theorem 3.1, the initial problem (4.9), (1.2) has a solution if and only if +[y0]3 = − +ind(B′ +2)−1 +� +s=0 +(A′ +2)−s−1(B′ +2)sF ′ +2,s = −F ′ +2,0 = 2 +�f0 +2 +� +3 += [f0]3, +i. e. +[y0]3 = [f0]3. +(4.10) +The corresponding equation (3.1) over Z6 has the form +[3]6X′ +n+1 = X′ +n + F ′ +n, +n ∈ Z+. +(4.11) +Further let (4.10) be fulfilled. +By the statement 1 of Theorem 3.1, the initial problem (4.11), (3.2) has a unique solution, which may be +obtained by the formula (3.8). +Evaluate: +(B′ +1)−n (A′ +1)n Y ′ +1,0 + +n−1 +� +s=0 +(A′ +1)s (B′ +1)−s−1 F ′ +1,n−s−1 = += ([3]2)−n Y ′ +1,0 + +n−1 +� +s=0 +([3]2)−s−1 F ′ +1,n−s−1 = Y ′ +1,0 + +n−1 +� +s=0 +F ′ +1,n−s−1, +(4.12) +− +ind(B′ +2)−1 +� +s=0 +(A′ +2)−s−1 (B′ +2)s F ′ +2,n+s = − +�fn +2 +� +3 +. +(4.13) +As in Example 4.1, the isomorphism ψ: Z2 ⊕ Z3 → Z6 is defined by the formula (4.3). Substituting (4.3), +(4.12) and (4.13) into (3.8), we obtain the unique solution of the initial problem problem (4.11), (3.2): +X′ +0 = Y ′ +0, +X′ +n = ψ +� +Y ′ +1,0 + +n−1 +� +s=0 +F ′ +1,n−s−1, − +�fn +2 +� +2 +� += += +� +3 +� +y0 + +n−1 +� +s=0 +fs +2 +� ++ 4 +� +−fn +2 +�� +6 += +� +3y0 + 3 +n−1 +� +s=0 +fs +2 + 4fn +� +6 +, +n ∈ N. +(4.14) +Hence, if fn (n ∈ Z+) is even and (4.10) is fulfilled, then by the statement 2 of Theorem 3.1 the initial +problem (4.9), (1.2) has infinitely many solutions. Moreover, the general solution of this initial problem has +the following form (see formulas (3.10) and (4.14)). +X0 = Y0, +Xn = +� +3y0 + 3 +n−1 +� +s=0 +fs +2 + 4fn + 6αn +� +12 +, +n ∈ N, +(4.15) +where {αn}∞ +n=0 is an arbitrary sequence of the elements 0 and 1. + +M.V. Heneralov, A.L. Piven’ +11 +By the statement 2 of Theorem 3.2, Equation (4.9) has infinitely many solutions. Moreover, the general +solution of Equation (4.9) has the form (see formulas (3.3) and (4.15)): +X0 = [3β + 4f0 + 6αn]12 , +Xn = +� +3β + 3 +n−1 +� +s=0 +fs +2 + 4fn + 6αn +� +12 +, +n ∈ N, +where β and αn (n ∈ Z+) are arbitrary elements of {0, 1}. +Example 4.4. Consider the following equation over Z12: +[9]12Xn+1 = [6]12Xn + Fn, +n ∈ Z+. +(4.16) +Let Y0 = [y0]12, Fn = [fn]12. Determine the values: A = [6]12, B = [9]12, m = 12. Let a = 6, b = 9. This +implies that d = 3. By the statement 2 of Theorem 3.1, if 3 ∤ fn for some n ∈ Z+, then by the statement 3 +of Theorem 3.2 Equation (4.16) has no solutions. +Further let 3 | fn for all n ∈ Z+. Determine B′ = [3]4, A′ = [2]4, m′ = 4, m′ +1 = 4, m′ +2 = 1. The +corresponding equation (3.1) over Z4 has the form: +[3]4X′ +n+1 = [2]4X′ +n + F ′ +n, +n ∈ Z+, +(4.17) +where F ′ +n = +� +fn +3 +� +4. +By the first statement of Theorem 3.1, for any Y ′ +0 ∈ Z4 the initial problem (4.17), (3.2) has a unique +solution and this solution is defined by the formula: +X′ +0 = Y ′ +0, +X′ +n = (B′)−n (A′)n Y ′ +0 + +n−1 +� +s=0 +(A′)s (B′)−s−1 F ′ +n−s−1 = += [3]−n +4 [2]n +4Y ′ +0 + +n−1 +� +s=0 +[2]s +4[3]−s−1 +4 +F ′ +n−s−1 = [2]n +4Y ′ +0 + +n−1 +� +s=0 +[2]s +4[3]−s−1 +4 +F ′ +n−s−1, +n ∈ N. +(4.18) +More precise, +X′ +0 = Y ′ +0, +X′ +1 = 2Y ′ +0 + 3F ′ +0, +X′ +n = 3F ′ +n−1 + 2F ′ +n−2, +n = 2, 3, . . . . +If 3 | fn, n ∈ Z+, then by the second statement of Theorem 3.1, for any Y0 ∈ Z12 the initial problem (4.16), +(1.2) has infinitely many solutions. Moreover, the general solution of this initial problem has the following +form (see formula (3.10)): +X0 = Y0, +Xn = [x′ +n + 4αn]12, +n ∈ N, +i. e. +X0 = Y0, +X1 = [2y0 + f0 + 4α1]12, +Xn = +� +fn−1 + 2fn−2 +3 ++ 4αn +� +12 +, +n = 2, 3, . . . . +(4.19) +Here {αn}∞ +n=0 is an arbitrary sequence of {0, 1, 2}. +If 3 | fn, n ∈ Z+, then by the statement 2 of Theorem 3.2, Equation (4.16) has infinitely many solutions. +Moreover, the general solution of this equation has the following form (see the formula (3.3)). +Xn = [x′ +n + 4αn]12, +n ∈ Z+, +(4.20) +where {αn}∞ +n=0 is an arbitrary sequence of {0, 1, 2} and the sequence X′ +n = [x′ +n]4 (n ∈ Z+) is the general +solution of Equation (4.17) which is defined as follows: +X′ +0 = [x′ +0]4, +X′ +1 = 2X′ +0 + 3F ′ +0, +X′ +n = 3F ′ +n−1 + 2F ′ +n−2, +n = 2, 3, . . . . +Now the general solution (4.20) of Equation (4.16) can be written in a more convenient form, which is similar +to (4.19): +X0 = [x0]12, +X1 = [2x0 + f0 + 4α1]12, +Xn = +� +fn−1 + 2fn−2 +3 ++ 4αn +� +12 +, +n = 2, 3, . . . , +where x0 is an arbitrary integer and {αn}∞ +n=0 is an arbitrary sequence of {0, 1, 2}. + +M.V. Heneralov, A.L. Piven’ +12 +References +[1] A. Halanay, D. Wexler, Teoria Calitativa A Sistemelor Cu Impulsuri, Academiei Republicii Socialiste +Romania, Bucuresti, 1968. +[2] W.G. Kelley, A.C. Peterson, Difference Equation: An Introduction with Applications. 2nd ed., Academic +Press, 2001. +[3] S. Elaydi, Introduction to difference equations, Springer-Verlag, New York, 2005. +[4] S.L. Campbell, Singular system of differential equations I — San Fransisco, London, Mellbourne:Pitman +Publishing, Research Notes in Mathematics, Vol. 40, 1980. +[5] M. Benabdallakh, A.G. Rutkas, A.A. Solov’ev, Application of Asymptotic Expansions to the Investi- +gation of an Infinite System of Equations Axn+1 + Bxn = fn in a Banach Space, J. Soviet Math., 48 +(1990), Iss. 2, 124–130. +[6] M.F. Bondarenko, A.G. Rutkas, On a class of implicit difference equations, Dopovidi NANU of Uktaine +(1998), No.7, 11–15. +[7] V.A. Gerasimov, S.L. Gefter, A.B. Goncharuk, Application of the p-adic Topology on Z to the Problem +of Finding Solutions in Integers of an Implicit Linear Difference Equation, J. Math. Sci., 235 (2018), No. +3. –256–261. +[8] V.V. Martseniuk, S.L. Gefter and A.L. Piven’, Uniqueness criterion and Cramer’s rule for implicit +higher order linear difference equations over Z, Progress on Difference Equations and Discrete Dynamical +Systems (eds. S. Baigent, M. Bohner, S. Elaydi), Vol. 341, Springer, 2020, 311 – 325. +[9] S.L. Gefter, A.L. Piven’, Implicit Linear Nonhomogeneous Difference Equation over Z with a Random +Right-Hand Side, J. Math. Physics, Analysis, Geometry, 18 (2022), No.1, 105–117. +[10] S.L. Gefter, A.L. Piven, Implicit Linear Nonhomogeneous Difference Equation in Banach and Locally +Convex Spaces, J. Math. Physics, Analysis, Geometry, 15 (2019), No. 3, 336 – 353. +[11] N. Dunford, J. T. Schwartz, Linear Operators. Part I: General Theory, John Wiley Sons, New & York +etc., 1988. +[12] D.S. Dummit, R.M. Foote, Abstract Algebra. 3rd ed., John Wiley and Sons, Inc., 2004. +[13] A.G. Rutkas, Spectral methods for studying degenerate differential-operator equations. I. J. Math. Sci. +144 (2007), No.4, 4246–4263. +[14] M.F. Bondarenko, L.A. Vlasenko, A linear quadratic regulator problem for descriptor lumped and dis- +tributed systems with discrete time, J. of Automation and Information Sciences 42 (2010), No.1 32–41. + diff --git a/atFST4oBgHgl3EQfBjj8/content/tmp_files/load_file.txt b/atFST4oBgHgl3EQfBjj8/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..d9c9ab8b5bea9c37ade8b0a7c399c25fb48d62b7 --- /dev/null +++ b/atFST4oBgHgl3EQfBjj8/content/tmp_files/load_file.txt @@ -0,0 +1,1006 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf,len=1005 +page_content='Implicit Linear Difference Equation over Residue Class Rings M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Heneralov ∗ and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Piven’† Department of Mathematics & Computer Sciences V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Karazin Kharkiv National University Abstract We investigate the first order implicit linear difference equation over residue class rings modulo m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' We prove an existence criterion and establish the amount of solutions for this equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' We obtain analogous results for the initial problem of the considered equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The examples which illustrate the developed theory are given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Keywords: implicit linear difference equation, ring, residue class, initial problem 2010 Mathematics Subject Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' 39A99, 16P50 1 Introduction The theory of the linear difference equations is an important branch of mathematics, having a series of different applications (see, for example, [1]–[4]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The theory of implicit linear difference equations in vector spaces was developed in the 80s–90s of the 20 century (see, for example, [4]–[6]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Unlike the classical theory, the non-invertible operators have an important role in the new theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Therefore the interesting problem of the investigation of the implicit linear difference equation with non-invertible coefficients from the any commutative ring appeared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' At the moment implicit difference equations over the ring of integers were studied more detailed [7]–[9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' In [10] these equations in different classes of topological vector spaces were investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' In this paper the first order implicit linear difference equations over residue classes rings is investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let Zm = Z/mZ be the residue class ring modulo m, where m ∈ N, m ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let A, B, Y0 ∈ Zm and let {Fn}∞ n=0 be a sequence of Zm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Consider the initial problem BXn+1 = AXn + Fn, n ∈ Z+, (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) X0 = Y0, (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) where Z+ denotes the set of non-negative integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The sequence {Xn}∞ n=0 of elements of Zm is called a solution of the initial problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2), if it satisfies Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) and the initial condition (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) is called implicit, if B is a non-invertible element of the ring Zm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' If B is an invertible element of Zm, then this equation is called explicit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let a, b are representatives of classes A, B respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' In the Section 2 we prove that if the greater common divisor of numbers a, b, m is equal to 1, then Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) is decomposed to the explicit equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='5) and the implicit equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='6) which has a unique solution (see lemmas 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2 and Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1 also gives the general solution for these equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The main results of this paper are represented in Section 3 (see theorems 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1 describes necessary and sufficient conditions for the solvability, an amount of solutions and the general solution for the initial problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' This theorem gives the full description of all possible situations for the initial problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The analogous results for Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) are established in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' This theorem leads to the criteria of the existence and uniqueness of a solution for Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) (see Corollaries 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' As in the Fredholm theory (see, for example, [11, Chapter 7]), Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='4 shows that if corresponding to (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) homogeneous equation has only trivial solution then for any sequence {Fn}∞ n=0 of Zm Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) has a unique solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Section 4 of the present paper contains the examples, which illustrate the constructed theory (see Examples 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' ∗me2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='com@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='com †aleksei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='piven@karazin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='ua 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='13704v1 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='FA] 31 Jan 2023 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Heneralov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Piven’ 2 Through this paper [t]s denotes the class of the element t ∈ Z of the ring Zs, where s ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The ring Z1 means as the null ring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' For the numbers n1, n2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , nN ∈ Z such that |n1| + |n2| + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' + |nN| ̸= 0 the symbol gcd (n1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , nN) denotes their positive greater common divisor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' If T is a nilpotent element of the ring Zs, then ind(T) denotes the nilpotency index of T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' 2 Preliminary Through this paper m ≥ 2, m ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let A, B and Fn (n ∈ Z+) be given elements of the ring Zm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' For each of elements A, B, Y0, Fn, Xn ∈ Zm (n ∈ Z+) denote, respectively, their representatives a, b, fn, y0, xn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' By Fundamental Theorem of Arithmetic, there exists pairwise different primes p1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , pr and numbers k1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , kr ∈ N such that m = r � j=1 pkj j .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Denote m1 = � j : pj∤b pkj j , m2 = � j : pj|b pkj j , where m1 = 1 in the case pj | b (j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , r) and m2 = 1 in the case pj ∤ b (j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Obviously, m1 · m2 = m, and gcd (m1, m2) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Introduce the natural projections πi : Zm → Zmi, defined as follows: πi (T) = [t]mi, ∀T = [t]m, i = 1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (see [12, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' 381–382]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' For each i = 1, 2, according to the [12, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' 381–382] the natural projections πi (i = 1, 2) are homomor- phisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Denote Ai = πi (A) , Bi = πi (B) , Yi,0 = πi (Y0) , Fi,n = πi (Fn) , i = 1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let m1 ̸= 1, m2 ̸= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Introduce the isomorphism ψ: Zm1 ⊕ Zm2 → Zm, defined as follows (see, for example, [12, Section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='6 and Exercise 5 to the Section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='6]): ψ (T1, T2) = [t1e1m2 + t2e2m1]m, ∀T1 = [t1]m1, ∀T2 = [t2]m2, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) where E1 = [e1]m1 = [m2]−1 m1, E2 = [e2]m2 = [m1]−1 m2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) We regard that since gcd (m1, m2) = 1, the inverse elements E1 and E2 are defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' If T1 ∈ Zm1, T2 ∈ Zm2, then definition of ψ implies πi (ψ (T1, T2)) = Ti, i = 1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='3) Also, π−1 1 (T1) ∩ π−1 2 (T2) is a one-element set, ψ (T1, T2) is an element of this set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' This means that {ψ (T1, T2)} = π−1 1 (T1) ∩ π−1 2 (T2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='4) Consider the following equations over rings Zm1 and Zm2 respectively: B1X1,n+1 = A1X1,n + F1,n, n ∈ Z+, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='5) B2X2,n+1 = A2X2,n + F2,n, n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='6) The following lemma describes the connection between solutions of Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) and equations (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='5), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let m1 ̸= 1, m2 ̸= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The sequence Xn = ψ (X1,n, X2,n) , n ∈ Z+, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='7) is a solution of Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) iff the sequences {X1,n}∞ n=0 and {X2,n}∞ n=0 are solutions of equations (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='5), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='6), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Moreover, Xi,n = πi (Xn), i = 1, 2, n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Heneralov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Piven’ 3 Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The equalities (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='7) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='3) yield together the equality for Xi,n: πi (Xn) = Xi,n, i = 1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Since πi (i = 1, 2) are homomorphisms, by the equality (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='7), πi (BXn+1 − AXn − Fn) = BiXi,n+1 − AiXi,n − Fi,n, i = 1, 2, n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' By the equality (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='4), we obtain: BXn+1 − AXn − Fn = ψ (B1X1,n+1 − A1X1,n − F1,n, B2X2,n+1 − A2X2,n − F2,n) , n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='8) We note that π1 (0) = 0 and π2 (0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='9) Since (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='9), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='8) hold, we obtain that the equality (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) is fulfilled if and only if equalities (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='5), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='6) are fulfilled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' This ends the proof of the lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Introduce the notation: d = gcd (a, b, m) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Consider the equations (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='5) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The following lemma establishes important properties for coeffi- cients of these equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The following statements hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let m1 ̸= 1, then B1 is invertible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let m2 ̸= 1, then B2 is nilpotent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' If additionally d = 1, then A2 is invertible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' B is nilpotent if and only if m1 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Proof the statement 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The definition of m1 and B implies the equality gcd (b, m1) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Hence, the element B1 is an invertible element of Zm1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Proof the statement 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Firstly prove that B2 is nilpotent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Is it evident from the definition of m2: if k = max j=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=',r{kj}, then Bk 2 = [bk]m2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let d = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' We will prove that gcd (a, m2) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Assuming the contrary, we obtain that there exists j ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , r} such that pj | a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' This condition yields pj | a, pj | b, pj | m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Hence pj | d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' But it contradicts d = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Therefore gcd (a, m2) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' This means that A2 is an invertible element of Zm2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Proof the statement 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The condition m1 = 1 is equivalent to the assertion ∀j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , r: pj | b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The last condition is equivalent to the nilpotency of the element B in Zm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2 is an analogue of the spectral decomposition of a regular operator pencil in Banach spaces (see [13, Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The analogous to (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='5), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='6) decomposition of an implicit difference equation in Banach spaces into two equations with regarded properties was obtained in [6, 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The following theorem is a solvability theorem for Equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='5) and, in the case d = 1, for Equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The following statements hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let m1 ̸= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The general solution of Equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='5) is defined by the following formula: X1,n = B−n 1 An 1X1,0 + n−1 � s=0 As 1B−s−1 1 F1,n−s−1, n ∈ N, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='10) where X1,0 is an arbitrary element of Zm1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let d = 1 and m2 ̸= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Then Equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='6) has a unique solution, defined by the following formula: X2,n = − ind(B2)−1 � s=0 A−s−1 2 Bs 2F2,n+s, n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='11) M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Heneralov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Piven’ 4 Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The corresponding inverse elements exist according to Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Prove firstly the statement 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' By the statement 1 of Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2, B1 is invertible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The equality (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='5) is equivalent to the equality X1,n+1 = B−1 1 A1X1,n + B−1 1 F1,n, n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='12) According to [3, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' 4], the general solution of Equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='12) has the form (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Prove now the statement 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' By the statement 2 of Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2, A is an invertible element, and B is nilpotent (these are since d = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The equality (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='6) is equivalent to the following: X2,n = −A−1 2 F2,n + A−1 2 B2X2,n+1, n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='13) Applying (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='13) recurrently few times, obtain the equality (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Now let {Xn}∞ n=0 be defined by the formula (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Denote k = ind (B2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Substituting (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='11) to the left part of Equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='6), we obtain: B2Xn+1 = −B2A−1 2 k−1 � s=0 A−s 2 Bs 2F2,n+1+s = − k−1 � s=0 A−s−1 2 Bs+1 2 F2,n+s+1 = − k � t=1 A−t 2 Bt 2F2,n+t = = − k � t=0 A−t 2 Bt 2F2,n+t + F2,n = −A2 · A−1 2 k−1 � t=0 A−t 2 Bt 2F2,n+t + F2,n = A2X2,n + F2,n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Therefore {X2,n}∞ n=0, defined by the formula (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='11), is the unique solution of Equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The following statements hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let d = 1 and m1 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) has a unique solution {Xn}∞ n=0, defined by the following formula: Xn = − ind(B)−1 � s=0 A−s−1BsFn+s, n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='14) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let m2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The general solution of Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) is defined by the following formula: Xn = B−nAnX0 + n−1 � s=0 AsB−s−1Fn−s−1, n ∈ N, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='15) where X0 is an arbitrary element of Zm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' 3 Main results Here we obtain the solvability theorems over Zm for Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) and for the initial problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Introduce the following notations: m′ = m d , Y ′ 0 = [y0]m′, A′ = [a/d]m′, B′ = [b/d]m′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Also, when d | fn for all n ∈ Z+, denote F ′ n = [fn/d]m′, n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Each a prime divisor of the number m′ is also a divisor of m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Then by Fundamental Theorem of Arithmetic, there exist non-negative integers lj ≤ kj (j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , r) such that m′ = r � j=1 plj j .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Denote also m′ 1 = � j : dpj∤b plj j , m′ 2 = � j : dpj|b plj j , M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Heneralov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Piven’ 5 A′ i = [a/d]m′ i, B′ i = [b/d]m′ i, Y ′ i,0 = [y0]m′ i, i = 1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' As in the definition m1, m2, we assume m′ 1 = 1 in the case dpj | b (j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , r) and m′ 2 = 1 in the case dpj ∤ b (j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Note that if d = 1, then m′ i = mi, i = 1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let d | fn for all n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Denote F ′ i,n = [fn/d]m′ i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' and consider the initial problem B′X′ n+1 = A′X′ n + F ′ n, n ∈ Z+, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) X′ 0 = Y ′ 0 (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) over Zm′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The following statement is a helpful lemma, which shows the connection between the equations (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let d ̸= 1, d | fn (n ∈ Z+).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The sequence {Xn}∞ n=0 is a solution of Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) iff it admits the following representation Xn = [x′ n + αnm′]m, n ∈ Z+, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='3) where X′ n = [x′ n]m′ (n ∈ Z+) is a solution of Equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), and {αn}∞ n=0 is a sequence of {0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , d − 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Moreover, the sequence {αn}∞ n=0 and the solution {X′ n}∞ n=0 of Equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) with x′ n ∈ {0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , m′ − 1} are uniquely determined by the solution {Xn}∞ n=0 of Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Obviously, Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) is equivalent to the congruence bxn+1 ≡ axn + fn (mod m), n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='4) The congruence (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='4) is equivalent to the following condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' b dxn+1 ≡ a dxn + fn d (mod m′), n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='5) The congruence (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='5) means that there exists a solution X′ n = [x′ n]m′ (n ∈ Z+) of Equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) such that xn ≡ x′ n (mod m′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Therefore {Xn}∞ n=0 is a solution of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) if and only if Xn = [x′ n + αn · m′]m (n ∈ Z+), where {αn}∞ n=0 is an arbitrary sequence of {0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , d − 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Suppose that the two following representatives for the solution of Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) hold: Xn = [x′ n + αnm′]m = � � x′n + � αnm′� m , n ∈ Z+, where X′ n = [x′ n]m′, � X′n = � � x′n � m′ (n ∈ Z+) are solutions of Equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), αn, � αn (n ∈ Z+) are numbers from {0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , d − 1} and additionally xn, � xn ∈ {0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , m′ − 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' It implies the following congruence x′ n + αnm′ ≡ � x′n + � αnm′ (mod m), n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='6) Then x′ n ≡ � x′n (mod m′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' According to the assumption � x′n, x′ n ∈ {0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , m′ − 1}, we have x′ n = � x′n, n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Now the congruence (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='6) means αn ≡ � αn (mod d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Since αn, � αn ∈ {0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , d − 1}, we have αn = � αn, n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The following theorem is a solvability theorem for the initial problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' This theorem also establishes the explicit form for the general solution of the considered initial problem, when a solution exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The following statements hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The initial problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) has a unique solution iff d = 1 and one of the following conditions holds: (a) m2 = 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (b) m2 ̸= 1 and the equality Y2,0 = − ind(B2)−1 � s=0 A−s−1 2 Bs 2F2,s (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='7) is fulfilled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Heneralov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Piven’ 6 Moreover, the unique solution of the initial problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) is defined by the formula Xn = � � � � � � � � � � � � � � � � � � � � � � � B−nAnY0 + n−1 � s=0 AsB−s−1Fn−s−1, m2 = 1, − ind(B)−1 � s=0 A−s−1BsFn+s, m1 = 1, ψ � �B−n 1 An 1Y1,0 + n−1 � s=0 As 1B−s−1 1 F1,n−s−1, − ind(B2)−1 � s=0 A−s−1 2 Bs 2F2,n+s � � , m1 ̸= 1, m2 ̸= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='8) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The initial problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) has infinitely many solutions iff d ̸= 1, d | fn for all n ∈ Z+ and one of the following conditions holds: (a) m′ 2 = 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (b) m′ 2 ̸= 1 and the equality Y ′ 2,0 = − ind(B′ 2)−1 � s=0 (A′ 2)−s−1 (B′ 2)s F ′ 2,s (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='9) is fulfilled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The general solution of the initial problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) is defined by Xn = [x′ n + αn · m′]m, n ∈ N, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='10) where X′ n = [x′ n]m′ (n ∈ Z+) is a solution of the initial problem (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) (this solution exists and is unique), and {αn}∞ n=1 is an arbitrary sequence of {0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , d − 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Moreover, the sequence {αn}∞ n=1 is uniquely determined by the solution {Xn}∞ n=0 of the initial problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The initial problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) has no solutions iff one of the following conditions holds: (a) d ∤ fn for some n ∈ Z+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (b) d | fn (n ∈ Z+), m′ 2 ̸= 1 and the equality (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='9) is not fulfilled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' In the statement 2 of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1 the sequence {X′ n}∞ n=0, when m ̸= d, may be defined by the formula, analogous to the formula (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='8), applied to the initial problem (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' When m = d, then evidently X′ n = 0 for all n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The sufficient conditions of all three statements of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1 are mutually exclusive and they exhaust all possibilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Therefore it is enough to prove the sufficiency for all of three statements of this theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Prove the sufficiency of the statement 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let d = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' If either m1 = 1, or m2 = 1, then the claimed statement follows from Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Further let m1 ̸= 1 and m2 ̸= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Set the initial conditions: X1,0 = Y1,0 ∈ Zm1, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='11) X2,0 = Y2,0 ∈ Zm2 (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='12) for equations (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='5) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='6) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' According to Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1, the sequence {Xn}∞ n=0 is a solution of the initial problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) if and only if the sequence {X1,n}∞ n=0 is a solution of the initial problem (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='5), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='11) and the sequence {X2,n}∞ n=0 is a solution of the initial problem (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='6), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' By the statement 1 of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1, the initial problem (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='5), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='11) has a solution for any Y1,0 ∈ Zm1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' According to the statement 2 of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1, the initial prob- lem (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='6), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='12) has a solution if and only if Y2,0 satisfies (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Hence, the initial problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) has a solution if and only if the condition (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='7) is fulfilled, moreover this solution is unique and has the form (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='7), where X1,n and X2,n are defined by the formulas (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='10) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='11) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Prove the sufficiency of the statement 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let d ̸= 1, d | fn for all n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Additionally, let either m′ 2 = 1, or m′ 2 ̸= 1 and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='9) be fulfilled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Since gcd (a/d, b/d, m′) = 1, we can apply the sufficiency of the statement 1 (which is already proved) to the initial problem (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Due to that statement, the initial problem (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Heneralov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Piven’ 7 (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) has a unique solution X′ n = [x′ n]m′ (n ∈ Z+).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1, for any sequence {αn}∞ n=0 of {0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , d−1} the formula (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='3) defines the solution of Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' We choose α0 such that (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) is fulfilled, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' [x′ 0 + α0m′]m = [y0]m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The initial condition (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) implies [x′ 0]m′ = [y0]m′, and the following congruence holds x′ 0 ≡ y0 (mod m′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Then β = y0−x′ 0 m′ ∈ Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Divide β on d with remainder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Then there exist q ∈ Z and α0 ∈ {0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , d − 1} such that β = qd + α0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Therefore, [x′ 0 + α0m′]m = [x′ 0 + (β − qd)m′]m = [x′ 0 + y0 − x′ 0 − qm]m = [y0]m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Therefore for the chosen α0 and any sequence {αn}∞ n=1 of {0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , d − 1} the formula (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='10) defines a solution of the initial problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1, the expression (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='10) gives infinitely many solutions of this initial problem (see also (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='3)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' We prove that the general solution of the initial problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) is defined by the formula (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let {Xn}∞ n=0 be an arbitrary solution of this initial problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Then by Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1, this solution has the form (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='3), where {X′ n}∞ n=0 is a solution of Equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Moreover, {X′ n}∞ n=0 must satisfy the initial condition (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' We have proved that the initial problem (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) has a unique solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Hence the general solution of the initial problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) has the form (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Now prove the sufficiency of the statement 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Assume d ∤ fn for some n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The equality (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) for this n is equivalent to the congruence bxn+1 − axn ≡ fn (mod m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Hence, fn ≡ d · � b dxn+1 − a dxn � (mod m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='13) Since d | m, the condition (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='13) means d | fn, which is a contradiction the assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Therefore, if d ∤ fn for some n ∈ Z+, then Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) has no solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Now suppose that d ̸= 1, d | fn, n ∈ Z+, m′ 2 ̸= 1 and the equality (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='9) is not fulfilled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Assume the contrary, that the initial problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) has a solution Xn = [xn]m (n ∈ Z+).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Then the congruence (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='13) is fulfilled for all n ∈ Z+ and the sequence X′ n = [xn]m′ (n ∈ Z+) is a solution of the initial problem (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Since gcd (a/d, b/d, m′) = 1, we can apply the sufficiency of the statement 1 (which is already proved) to this initial problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Therefore, if m′ 2 ̸= 1 and {X′ n}∞ n=0 is a solution of the initial problem (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2), then Y ′ 2,0 = [y0]m′ 2 must satisfy (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' This contradicts the assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The following theorem is a solvability theorem for Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' This theorem also yields the explicit form for the general solution of Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The following statements hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) has a finite amount of solutions iff d = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Moreover, the amount of these solutions is equal to m1 and in this case (a) If m2 = 1, then the general solution of Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) has the form Xn = B−nAnX0 + n−1 � s=0 AsB−s−1Fn−s−1, n ∈ N, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='14) where X0 is an arbitrary element of Zm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (b) If m1 = 1, then the unique solution of Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) has the form Xn = − ind(B)−1 � s=0 A−s−1BsFn+s, n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='15) (c) If m1 ̸= 1 and m2 ̸= 1, then the general solution of Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) has the form X0 = ψ � �X1,0, − ind(B2)−1 � s=0 A−s−1 2 Bs 2F2,s � � , Xn = ψ � �B−n 1 An 1X1,0 + n−1 � s=0 As 1B−s−1 1 F1,n−s−1, − ind(B2)−1 � s=0 A−s−1 2 Bs 2F2,n+s � � , n ∈ N, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='16) where X1,0 is an arbitrary element of Zm1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Heneralov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Piven’ 8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) has infinitely many solutions iff d ̸= 1 and d | fn for all n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The general solution in this case has the form (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='3), where X′ n = [x′ n]m′ (n ∈ Z+) is the general solution of Equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), and {αn}∞ n=0 is an arbitrary sequence of {0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , d − 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Moreover, the sequence {αn}∞ n=0 and the solution {X′ n}∞ n=0 of Equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) with x′ n ∈ {0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , m′ −1} are uniquely determined by the solution {Xn}∞ n=0 of Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) has no solutions iff d ∤ fn for some n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Since gcd (a/d, b/d, m′) = 1, in the statement 2 of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2 the general solution of Equation {X′ n}∞ n=0 may be defined by the formula, analogous to formulas (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='14)–(3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='16), applied to Equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The sufficient conditions of all three statements of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2 are mutually exclusive and they exhaust all possibilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Therefore it is enough to prove the sufficiency for all of three statements of this theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' We prove the sufficiency of the statement 1 of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let d = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' If either m1 = 1 or m2 = 1, then the claimed statement implies from the corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let m1 ̸= 1 and m2 ̸= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The statement 1 of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1 implies that if there exists a solution of the initial problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2), then it is defined uniquely by the given Y1,0, where Y1,0 is an arbitrary element of the ring Zm1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Therefore, the amount of solutions of Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) is equal to m1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The form (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='16) of the general solution of Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) is obtained with the help of the general solution (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='8) of the initial problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Prove the sufficiency of the statement 2 of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let d ̸= 1 and d | fn for all n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Since gcd � a d, b d, m′� = 1, we can apply the sufficiency of the statement 1 (which is already proved) to Equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Due to that statement, Equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) has m′ 1 solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let X′ n = [x′ n]m′ (n ∈ Z+) be the general solution of this equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1, the general solution of Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) has the form (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='3), where {αn}∞ n=0 is an arbitrary sequence of {0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , d − 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Moreover, by Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1, Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) has infinitely many solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Prove the sufficiency of the statement 3 of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let d ̸= 1 and d ∤ fn for some n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' By the statement 3 of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1, for any Y0 ∈ Zm the initial problem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) has no solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Hence, Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) has no solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The following corollary of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2 yields the solvability of Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) in the case of an invertible element A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' If A is an invertible element of Zm, then Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) always has a solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Moreover, the amount of solutions for Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) is equal to m1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2 also implies the following criteria of the existence and uniqueness of a solution for Equa- tion (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) has a unique solution iff d = 1 and m1 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' In particular, the homogeneous equation BXn+1 = AXn, n ∈ Z+ (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='17) has only trivial solution iff d = 1 and m1 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) has a unique solution iff A is invertible and B is nilpotent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Moreover, this solution has the form (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' According to Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2, Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) has a unique solution if and only if d = 1 and m1 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Hence, it suffices to prove that the conditions B is nilpotent and A is invertible are collectively equivalent to the conditions d = 1 and m1 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' At first, prove the sufficiency of the mentioned statement: let B be nilpotent, and A be invertible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let us proof that d = 1, m1 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' By the statement 3 of Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2, the nilpotency of B implies m1 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' If A is invertible, then gcd(a, m) = 1, and hence d = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Now prove the inverse statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let d = 1 and m1 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' By the statement 3 of Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2, the condition m1 = 1 yields B is nilpotent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2, if d = 1, then A2 is an invertible element of Zm2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Since m1 = 1, this implies A2 = A is invertible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The representation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='15) for the unique solution of Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) follows from Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' If the homogeneous equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='17) has only trivial solution, then for any sequence {Fn}∞ n=0 Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) has a unique solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Moreover, the unique solution of Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) has the form (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let Equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='17) has only trivial solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Then Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2 implies d = 1, m1 = 1 and, therefore, for any sequence {Fn}∞ n=0 of Zm Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) has a unique solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The form (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='15) for the unique solution of Equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) follows from Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Heneralov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Piven’ 9 4 Examples Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Consider the following equation over Z6: [3]6Xn+1 = [2]6Xn + Fn, n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) Let Fn = [fn]6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Determine the values: A = [2]6, B = [3]6, m = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let b = 3, a = 2, hence d = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' On evidence, m1 = 2 and m2 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Also determine: A2 = [2]3, B2 = [3]3, ind(B2) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let Y0 = [y0]6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' By the statement 1 of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1, the initial problem (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) has a solution if and only if [y0]3 = − ind(B2)−1 � s=0 A−s−1 2 Bs 2F2,s = −[2]−1 3 [f0]3 = [f0]3, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' [y0]3 = [f0]3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) Further assume that the solution of the initial problem (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) exists, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' the equality (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) is fulfilled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' This solution is unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The representation of this solution may be found by the formula (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Evaluate: A1 = [2]2, B1 = [3]2, E1 = [3]−1 2 = [1]2, E2 = [2]−1 3 = [2]3 (see also the formulas (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Choose e1 = 1, e2 = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' According to the formula (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), the isomorphism ψ: Z2 ⊕ Z3 → Z6 is defined as follows: ψ(T1, T2) = [3t1 + 4t2]6, ∀T1 = [t1]2, ∀T2 = [t2]3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='3) Evaluate B−n 1 An 1X1,0 + n−1 � s=0 As 1B−s−1 1 F1,n−s−1 = [3]−n 2 [2]n 2X1,0 + n−1 � s=0 [2]s 2[3]−s−1 2 F1,n−s−1 = F1,n−1, n ∈ N, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='4) − ind(B2)−1 � s=0 A−s−1 2 Bs 2F2,n+s = −[2]−1 3 F2,n = F2,n, n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='5) Substituting (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='3), (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='4) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='5) into (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='8), we obtain the following form for the unique solution of the initial problem (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) : X0 = Y0, Xn = ψ([fn−1]2, [fn]3) = [3fn−1 + 4fn]6 = 3Fn−1 + 4Fn, n ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='6) By Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2, Equation (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) has m1 = 2 solutions, and the general solution of this equation has the form: X0 = ψ ([β]2, [f0]3) = [3β + 4f0]6, Xn = ψ ([fn−1]2, [fn]3) = [3fn−1 + 4fn]6 = 3Fn−1 + 4Fn, n ∈ N, where β may be equal to 0 or 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Consider the following equation over Z9: [3]9Xn+1 = [2]9Xn + Fn, n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='7) Let Y0 = [y0]9, Fn = [fn]9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Determine the values: A = [2]9, B = [3]9, m = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let b = 3, a = 2, hence d = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' On evidence, m1 = 1 and m2 = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Here B is nilpotent and A is invertible elements of Z9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Evaluate: ind(B) = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' By Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='3, Equation (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) has a unique solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' This solution has the form Xn = − ind(B)−1 � s=0 [2]−s−1 9 [3]s 9Fn+s = −[5]9Fn − [25]9[3]9Fn+1 = 4Fn + 6Fn+1, n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='8) The initial problem (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='7), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) has a solution if and only if Y0 = 4F0 + 6F1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' This solution is unique and has the form (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Heneralov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Piven’ 10 Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Consider the following equation over Z12: [6]12Xn+1 = [2]12Xn + Fn, n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='9) Let Fn = [fn]12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Determine the values: A = [2]12, B = [6]12, m = 12, a = 2, b = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' That implies that d = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' If fn is odd for some n ∈ Z+, then by the statement 3 of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2 Equation (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='9) has no solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Further let fn be even for all n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Determine: m′ = 6, m′ 1 = 2, m′ 2 = 3, B′ = [3]6, A′ = [1]6, F ′ n = � fn 2 � 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let Y0 = [y0]12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Also, Y ′ 0 = [y0]6, B′ 1 = [3]2, A′ 1 = [1]2, B′ 2 = [3]3, A′ 2 = [2]3, F ′ 1,n = � fn 2 � 2, F ′ 2,n = � fn 2 � 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Here ind(B′ 2) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' By the statement 2 of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1, the initial problem (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='9), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) has a solution if and only if [y0]3 = − ind(B′ 2)−1 � s=0 (A′ 2)−s−1(B′ 2)sF ′ 2,s = −F ′ 2,0 = 2 �f0 2 � 3 = [f0]3, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' [y0]3 = [f0]3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='10) The corresponding equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) over Z6 has the form [3]6X′ n+1 = X′ n + F ′ n, n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='11) Further let (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='10) be fulfilled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' By the statement 1 of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1, the initial problem (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='11), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) has a unique solution, which may be obtained by the formula (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Evaluate: (B′ 1)−n (A′ 1)n Y ′ 1,0 + n−1 � s=0 (A′ 1)s (B′ 1)−s−1 F ′ 1,n−s−1 = = ([3]2)−n Y ′ 1,0 + n−1 � s=0 ([3]2)−s−1 F ′ 1,n−s−1 = Y ′ 1,0 + n−1 � s=0 F ′ 1,n−s−1, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='12) − ind(B′ 2)−1 � s=0 (A′ 2)−s−1 (B′ 2)s F ′ 2,n+s = − �fn 2 � 3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='13) As in Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1, the isomorphism ψ: Z2 ⊕ Z3 → Z6 is defined by the formula (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Substituting (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='3), (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='12) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='13) into (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='8), we obtain the unique solution of the initial problem problem (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='11), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2): X′ 0 = Y ′ 0, X′ n = ψ � Y ′ 1,0 + n−1 � s=0 F ′ 1,n−s−1, − �fn 2 � 2 � = = � 3 � y0 + n−1 � s=0 fs 2 � + 4 � −fn 2 �� 6 = � 3y0 + 3 n−1 � s=0 fs 2 + 4fn � 6 , n ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='14) Hence, if fn (n ∈ Z+) is even and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='10) is fulfilled, then by the statement 2 of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1 the initial problem (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='9), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) has infinitely many solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Moreover, the general solution of this initial problem has the following form (see formulas (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='10) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='14)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' X0 = Y0, Xn = � 3y0 + 3 n−1 � s=0 fs 2 + 4fn + 6αn � 12 , n ∈ N, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='15) where {αn}∞ n=0 is an arbitrary sequence of the elements 0 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Heneralov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Piven’ 11 By the statement 2 of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2, Equation (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='9) has infinitely many solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Moreover, the general solution of Equation (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='9) has the form (see formulas (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='3) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='15)): X0 = [3β + 4f0 + 6αn]12 , Xn = � 3β + 3 n−1 � s=0 fs 2 + 4fn + 6αn � 12 , n ∈ N, where β and αn (n ∈ Z+) are arbitrary elements of {0, 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Consider the following equation over Z12: [9]12Xn+1 = [6]12Xn + Fn, n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='16) Let Y0 = [y0]12, Fn = [fn]12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Determine the values: A = [6]12, B = [9]12, m = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Let a = 6, b = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' This implies that d = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' By the statement 2 of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1, if 3 ∤ fn for some n ∈ Z+, then by the statement 3 of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2 Equation (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='16) has no solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Further let 3 | fn for all n ∈ Z+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Determine B′ = [3]4, A′ = [2]4, m′ = 4, m′ 1 = 4, m′ 2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' The corresponding equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1) over Z4 has the form: [3]4X′ n+1 = [2]4X′ n + F ′ n, n ∈ Z+, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='17) where F ′ n = � fn 3 � 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' By the first statement of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1, for any Y ′ 0 ∈ Z4 the initial problem (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='17), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) has a unique solution and this solution is defined by the formula: X′ 0 = Y ′ 0, X′ n = (B′)−n (A′)n Y ′ 0 + n−1 � s=0 (A′)s (B′)−s−1 F ′ n−s−1 = = [3]−n 4 [2]n 4Y ′ 0 + n−1 � s=0 [2]s 4[3]−s−1 4 F ′ n−s−1 = [2]n 4Y ′ 0 + n−1 � s=0 [2]s 4[3]−s−1 4 F ′ n−s−1, n ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='18) More precise, X′ 0 = Y ′ 0, X′ 1 = 2Y ′ 0 + 3F ′ 0, X′ n = 3F ′ n−1 + 2F ′ n−2, n = 2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' If 3 | fn, n ∈ Z+, then by the second statement of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='1, for any Y0 ∈ Z12 the initial problem (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='16), (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2) has infinitely many solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Moreover, the general solution of this initial problem has the following form (see formula (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='10)): X0 = Y0, Xn = [x′ n + 4αn]12, n ∈ N, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' X0 = Y0, X1 = [2y0 + f0 + 4α1]12, Xn = � fn−1 + 2fn−2 3 + 4αn � 12 , n = 2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='19) Here {αn}∞ n=0 is an arbitrary sequence of {0, 1, 2}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' If 3 | fn, n ∈ Z+, then by the statement 2 of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='2, Equation (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='16) has infinitely many solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Moreover, the general solution of this equation has the following form (see the formula (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='3)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Xn = [x′ n + 4αn]12, n ∈ Z+, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='20) where {αn}∞ n=0 is an arbitrary sequence of {0, 1, 2} and the sequence X′ n = [x′ n]4 (n ∈ Z+) is the general solution of Equation (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='17) which is defined as follows: X′ 0 = [x′ 0]4, X′ 1 = 2X′ 0 + 3F ′ 0, X′ n = 3F ′ n−1 + 2F ′ n−2, n = 2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' Now the general solution (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='20) of Equation (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='16) can be written in a more convenient form, which is similar to (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='19): X0 = [x0]12, X1 = [2x0 + f0 + 4α1]12, Xn = � fn−1 + 2fn−2 3 + 4αn � 12 , n = 2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' , where x0 is an arbitrary integer and {αn}∞ n=0 is an arbitrary sequence of {0, 1, 2}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/atFST4oBgHgl3EQfBjj8/content/2301.13704v1.pdf'} +page_content='V.' metadata={'source': 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Mazziottia) +The James Franck Institute and The Department of Chemistry, The University of Chicago, Chicago, +Illinois 60637 USA +(Dated: Submitted March 5, 2022; Revised April 18, 2022) +The accurate resolution of the chemical properties of strongly correlated systems, such as biradicals, requires the use +of electronic structure theories that account for both multi-reference as well as dynamic correlation effects. A variety +of methods exist that aim to resolve the dynamic correlation in multi-reference problems, commonly relying on an ex- +ponentially scaling complete-active-space self-consistent-field (CASSCF) calculation to generate reference molecular +orbitals (MOs). However, while CASSCF orbitals provide the optimal solution for a selected set of correlated (active) +orbitals, their suitability in the quest for the resolution of the total correlation energy has not been thoroughly investi- +gated. Recent research has shown the ability of Kohn-Shan density functional theory (KS-DFT) to provide improved +orbitals for coupled cluster (CC) and Møller-Plesset perturbation theory (MP) calculations. Here we extend the search +for optimal and more cost effective MOs to post-configuration-interaction (post-CI) methods, surveying the ability of +the MOs obtained with various DFT functionals, as well as Hartree-Fock, and CC and MP calculations to accurately +capture the total electronic correlation energy. Applying the anti-Hermitian contracted Schrödinger equation (ACSE) +to the dissociation of N2, the calculation of biradical singlet-triplet gaps and the transition states of the bicylobutane +isomerization, we demonstrate DFT provides a cost-effective alternative to CASSCF in providing reference orbitals for +post-CI dynamic correlation calculations. +I. +INTRODUCTION +The computational resolution of electronic structure relies +on the accurate capture of the correlation energy, which is +defined as the difference between the full-configuration- +interaction (FCI) and Hartree-Fock (HF) energies. +The +correlation energy is generally further divided into two +components: static or strong correlation arising from a state +that may not be described by a single Slater determinant +and is hence also termed multi-reference correlation, and the +remainder which is defined as dynamic correlation1–4. While +dynamic correlation is present in all electronic systems and +may be well described by many single-reference methods +such as coupled cluster (CC), Møller-Plesset perturbation +theory (MP)5 or even density functional theory (DFT)6,7, +strong correlation only arises in systems exhibiting a de- +generacy or near-degeneracy of electronic states1. As such, +multi-reference correlation plays a particularly important role +in processes such as bond dissociation, and in the determi- +nation of properties of bi- or multi-radical systems, such as +spin state splittings and magnetic couplings in molecules +and complexes in the areas of spintronics, photonics or +catalysis8–11. +Multi-reference correlation is commonly resolved with +complete active space configuration interaction (CASCI) +or CAS self consistent field (CASSCF) calculations, which +resolve the strong correlation in a chosen active space12–15. +While +CASSCF +calculations +have proven +valuable in +the description of systems dominated by multi-reference +correlation12,13, +it has been demonstrated that even in +a)Electronic mail: damazz@uchicago.edu +such systems, experimentally relevant properties, such as +singlet-triplet (S-T) gaps or J-coupling parameters may +often not be resolved within chemical accuracy without +the additional inclusion of dynamic correlation effects16. +The historically most popular and commonly used method +to account for post-CI dynamic correlation CASSCF in +combination with second-order many-body perturbation +theory (CASPT2) suffers from a variety of shortcomings, +including poor computational scaling, +and convergence +issues arising from the fact that the MP2 correction is not +variational, often leading to nonphysical lower bounds to the +total electronic energy17–20. Consequently, the development +of electronic structure methods that account for post-CI +dynamic correlation is an area of major research interest and +recent developments include algorithms such as quantum +Monte-Carlo21–23, multi-configuration pair-density functional +theory (MC-PDFT)24–28, reduced-density-matrix functional +theory +(RDMFT)29–34, +incremental FCI +(iFCI)35–37 +or +CASCI in combination with the anti-Hermitian contracted +Schrödinger equation (ACSE)38,39 as well as related methods +that use cumulant reconstruction40,41 to solve a contracted +Schrödinger equation42–44 for dynamic correlation45,46. +While FCI yields the exact electronic energy in a chosen +basis set and hence is invariant to the molecular orbital +(MO) basis, it remains out of reach for system larger than +16 electron in 16 orbitals due to exponential computational +scaling. +As other ab-initio electronic structure methods +that aim to resolve the total electronic correlation energy +tend to rely on some approximation to truncate the exact +Hamiltonian, they exhibit a dependence on the chosen MO +basis. Recent research has been performed in the areas of CC +and MP theories with the aim of improving their predictive +properties via the use of improved molecular orbitals, rather +than the commonly used HF reference47–51. This includes + +2 +the implementation of orbital-optimized variants of CC and +second-order MP2 (OOMP2), which, while yielding im- +proved results over the HF-reference based implementations, +suffer from increased computational scaling, and in the case +of OOMP2 three major failures, namely divergence for small +MO energy gaps, artificial symmetry restoration and loss +of Coulson-Fischer points52–54. A contrary approach to the +orbital-optimization problem has recently been undertaken +by Head-Gordon and coworkers, who demonstrate significant +improvements in the prediction of chemical properties in +MP3 via the use of OOMP2 and DFT orbitals55,56, and in the +calculation of vibrational frequencies with CCSD(T) with the +use of DFT orbitals57. Additionally, natural orbitals obtained +with MR-CI-SD calculations performed after initial CASSCF +optimization may provide improved orbitals for the recovery +of additional correlation energy.58,59 +While research has been undertaken to shine light on the +orbital dependence in single-reference methods aimed at +resolving dynamic correlation, work aiming at resolving +this dependence in multi-reference and post-multi-reference +dynamic correlation calculations has been limited60–67 and +common implementations of electronic structure methods +aiming to resolve the total correlation energy such as QMC, +CASPT2 or MC-PDFT, tend to rely on CASSCF optimized +orbitals as their reference. But are orbitals that are optimized +to include multi-reference correlation necessarily the best to +account for the total correlation or is the restriction of the +orbital optimization to an active space representing a small +subset of the total molecular orbitals hindering the capture +of the complete electronic structure? +Specifically, would +CASSCF orbitals necessarily provide the best initial guess for +the orbitals in a post-CASSCF all-electron correlation SCF +method? +In this article we aim to resolve the orbital dependence +of CI and post-CI dynamic correlation calculations by using +molecular orbitals obtained from KS-DFT, HF, MP2 and +CCSD as reference orbitals in CI calculations, which are +then used to seed the anti-Hermitian contracted Schrödinger +equation (ACSE) to resolve the dynamic correlation. Orbitals +obtained from KS-DFT have previously been demonstrated +to be more suitable for the construction of electronic states in +configuration interaction (CI) calculations compared to HF +orbitals68 and may provide a viable, cost-saving alternative to +CASSCF optimization in the quest to resolve the electronic +properties of strongly correlated molecules and materials. +We apply the CASCI/ACSE algorithm seeded with the +various molecular orbitals from the surveyed single-reference +methods to three distinct chemical problems dominated by +strong correlation effects, namely the dissociation of N2, the +prediction of S-T gaps in a benchmark set of biradicals, and +the calculation of the energetic barrier of the isomerization +reaction of bicyclobutane to gauche-1,3-butadiene via both +the conrotatory and disrotatory transition states. +II. +COMPUTATIONAL DETAILS +To investigate the orbital dependence of the static and +dynamic parts of the total electronic correlation energy, +molecular orbitals were obtained via self-consistent field +(SCF) calculations using various popular single-reference, +ab-initio methods, as well as CASSCF. These methods +include Hartree Fock (HF), CASSCF, variational 2-RDM +CASSCF (V2RDM)69, DFT70, as well as, MP2 and CCSD, +in which case the natural orbitals are investigated. +For +the DFT calculations, functionals representing the various +rungs of Jacobs-Ladder of functional development were +chosen, namely simple LDA71, and the popular functionals +PBE72,73, BLYP74–76, B3LYP77, M062X78, ωB97XD79, +MN1580. Orbitals from these initial SCF calculations were +then used to perform a minimal active space complete active +space configuration interaction (CASCI) calculation using +the V2RDM method with DQGT conditions (V2-T)69,81, +obtaining the multi-reference correlation energy in the initial +orbitals, as well as the strongly correlated 1- and 2-electron +reduced density matrices (RDMs). +We then generate the 1- and 2-electron integrals, namely 1K +containing the kinetic and nuclear attraction integrals and 2V +containing the electron-electron repulsion integrals, from the +molecular orbitals obtained with the selected single-reference +method. These serve as the basis for the ACSE calculations, +which is used to calculated the dynamic, post-CI correlation in +the given molecular orbital basis. The ACSE arises from the +fact that fermions interact pairwise and hence the N-electron +Schrödinger equation may be projected onto the space of only +two-electron transitions yielding the contracted Schrödinger +equation (CSE)42–44: +⟨Ψ| ˆa† +i ˆa† +j ˆal ˆak ˆH |Ψ⟩ = E 2Di,j +k,l , +(1) +where ˆH is the Hamiltonian operator +ˆH = ∑ +ij +1Ki +j ˆa† +i ˆa j +∑ +ijkl +2V i,j +k,l ˆa† +i ˆa† +j ˆal ˆak , +(2) +and 2Di,j +k,l is the 2-RDM: +2Di,j +k,l = ⟨Ψ|a† +i a† +jalak|Ψ⟩ . +(3) +The CSE can be separated into its Hermitian and anti- +Hermitian parts, and selection of only the anti-Hermitian part +yields the ACSE: +⟨Ψ|[ ˆa† +i ˆa† +j ˆal ˆak, ˆH]|Ψ⟩ = 0, +(4) +where the square brackets indicate the commutator. Unlike +the Hermitian part of the CSE, which depends on the 2-, 3- +and 4-RDMs, the highest order terms in the ACSE, which is +expanded in more detail in ref82, depend on only the 2- and +3-RDMs. Furthermore, this dependence may be resolved by +using an cumulant reconstruction in terms of the 2-RDM40,41: +3Di,j,k +q,s,t ≈ 1Di +q ∧ 1Dj +s ∧ 1Dk +t + 32∆i,j +q,s ∧ 1Dk +t , +(5) + +3 +where +2∆i,j +q,s = 2Di,j +q,s − 1Di +q ∧ 1Dj +s , +(6) +and ∧ denotes the antisymmetric Grassmann wedge product, +which is defined as: +1Di +k ∧ 1Dj +l = 1 +2(1Di +k +1Dj +l − 1Di +l +1Dj +k). +(7) +As the 3-RDM terms appear only in the perturbative 2V +part of the Hamiltonian of the ACSE, this approximate +reconstruction of 3D neglects the cumulant 3-RDM part of +the expansion, setting 3∆ijk +qst to be zero. +Using electron integrals and initial guess 1- and 2-RDMs +obtained from a lower-level electronic structure calculation +of choice, we solve the ACSE via a system of differential +equations83: +E(λ + ε) = ⟨Ψ(λ)|e−εS(λ) ˆHeεS(λ) |Ψ(λ)⟩ += E(λ)+ ε ⟨Ψ(λ)|[ ˆH, ˆS(λ)]|Ψ(λ)⟩+ O(ε2), +(8) +dE +dλ = ⟨Ψ(λ)|[ ˆH, ˆS(λ)]|Ψ(λ)⟩ , +(9) +d2Di,j +k,l +dλ += ⟨Ψ(λ)|[ ˆa† +i ˆa† +j ˆal ˆak, ˆS(λ)]|Ψ(λ)⟩ , +(10) +where the operator ˆS is defined as: +ˆS(λ) = ∑ +ijkl +2Si,j +k,l ˆa† +i ˆa† +j ˆal ˆak(λ), +(11) +chosen at each step of λ to minimize the energy along the +gradient: +2Si,j +k,l(λ) = ⟨Ψ(λ)|[ ˆa† +i ˆa† +j ˆal ˆak, ˆH]|Ψ(λ)⟩ . +(12) +The ACSE is propagated in λ until either the energy reaches +a minimum or the norm of the residual increases. +This +algorithm is presented in more detail in Refs. 82 and 83. +Seed 1- and 2-RDMs may be obtained from single- or +multi-reference electronic structure calculations, minimizing +the total electronic energy in the chosen orbital basis of the +electron integrals. +When provided with a single-reference +guess, such as one obtained from a HF calculation, the ACSE +has been demonstrated to yield total electronic energies +of comparable accuracy to those from CCSD(T)44,84,85. +However, ACSE calculations may also be seeded with initial +RDMs from a multi-reference electronic structure calculation, +such as CASSCF or CASCI, which yields accurate results +even when strong correlation plays a major role38,39. In this +case, the ACSE resolves the dynamic correlation on top of +the static correlation recovered by the seed RDMs within the +orbital basis obtained from the multi-reference calculation. +Results have been demonstrated to outperform commonly +used CASPT286–88, and provide comparable accuracy to +MC-PDFT and AF-QMC89. All calculations were performed +with the Quantum Chemistry Package90 as implemented in +Maple91. +III. +RESULTS +A. +Nitrogen Dissociation +To investigate the orbital dependence of the single- and +multi-reference parts of the electronic correlation energy, we +first consider the dissociation of N2. Dissociation of N2 into +its two constituent nitrogen atoms provides a classic case +of transition from a system dominated by single-reference +correlation—N2 near the equilibrium bond length—to a +system dominated by multi-reference correlation as the N-N +bond is stretched and the natural occupation numbers (NON) +in the [6,6] active space formed by the 6 nitrogen-p based +orbitals become more and more fractional until they reach +full degeneracy in the dissociated regime. +For our calculations we consider eight data points of N-N +bond lengths, R = [0.8, 0.9, 1.0976, 1.2, 1.4, 1.6, 2.0, 2.5] +in Å. Calculations use the relatively small 6-31G basis92 in +order to allow comparison to full CI (FCI) data. Once orbitals +are obtained via a chosen single-reference method, CASCI +calculations in that MO basis set with [6,6] active spaces are +carried out to recover the multi-reference correlation in the +nitrogen-p-based orbitals. +Figure 1 shows the dissociation +curves obtained from the molecular orbitals of a few select +methods, with the left panel showing the CASCI results, +and the right panel displaying the ACSE results, as well as, +the FCI curve. Furthermore, results of the go-to method for +the inclusion of post-multi-reference calculations, CASPT2, +are also displayed. +It is evident that the recovery of the +multi-reference correlation is strongly orbital dependent, +with large variations in the CASCI curves across the various +methods used for orbital optimization. Differences arise not +only in terms of the correlation energy recovered across the +dissociation coordinate, i.e. in the form of a vertical shift +of the curve, but also in its general line shape. This change +in line shape is particularly evident in the cases of the HF +and CCSD orbitals, which differ significantly from those +obtained via DFT. Furthermore, inspection of the ACSE +curves shows that while near-exact in the dissociated regime, +CASSCF orbitals provide a larger deviation from the FCI +curve than any of the displayed single reference methods in +the single-reference regime around the equilibrium N-N bond +length. +To allow a more in-depth analysis of the optimality of the +molecular orbitals from a chosen method in accounting for +the different parts of the total electronic correlation energy, +we consider the errors of the energies obtained via CASCI +relative to the CASSCF results, and the energies obtained via +CASCI/ACSE relative to the FCI results. Table I shows the +mean absolute error (MAE) and mean signed error (MSE) +versus FCI over the eight N-N bond lengths, as well as, the +maximum and minimum errors. The initial results from the +orbital optimization calculations split as expected with the +wave-function based methods providing upper bounds to the +FCI energy and DFT yielding lower bounds. +The largest +positive deviation from FCI data results from HF with a MSE + +4 +0.75 +1.00 +1.25 +1.50 +1.75 +2.00 +2.25 +2.50 +R N-N in Angstrom +−109.05 +−109.00 +−108.95 +−108.90 +−108.85 +−108.80 +−108.75 +−108.70 +E in Hartree +N2 Diss ciati n CASCI +CASCI(HF) +CASCI(M062X) +CASCI(CCSD) +CASSCF +0.75 +1.00 +1.25 +1.50 +1.75 +2.00 +2.25 +2.50 +R N-N in Angstrom +−109.10 +−109.05 +−109.00 +−108.95 +−108.90 +−108.85 +E in Hartree +N2 Dissociation ACSE +ACSE(HF) +ACSE(M062X) +ACSE(CCSD) +ACSE(CASSCF) +CASPT2 +FCI +FIG. 1. Dissociation curves of N2 for (left): [6,6] CASCI calculations; (right): ACSE calculations. All calculations were performed with a 6- +31G basis set and the ACSE was seeded with the 2-RDM from the [6,6] CASCI calculations. Curves were constructed from eight points along +the N-N dissociation coordinate, [0.8, 0.9, 1.0976, 1.2, 1.4, 1.6, 2.0, 2.5] in Å.We note that the CASCI(CCSD) results yield a lower bound to +the CASSCF energy for the R = 1.4 and R = 1.6 points. This is the result from minor violation of the full N-representability conditions of +the V2RDM based CASCI procedure with the DQG and T2 N-presentability conditions, which yield a lower bound to the true ground-state +energy. For these bond lengths CCSD natural orbitals provide an essential identical solution to CASSCF. +Molecular Orbitals +Method +HF +MP2 +CCSD CASSCF CASPT2 V2-T +LDA +PBE +BLYP B3LYP M062X wB97XD MN15 +REF +MAE 225.85 +70.41 +33.26 +13.76 +947.85 +131.34 201.31 161.51 +157.01 +160.39 +115.91 +MSE 225.85 -67.80 +32.19 +13.76 +947.85 -131.33 -201.31 -161.51 -153.36 +-160.39 +-104.76 +∆EQM 148.81 +-0.95 +5.91 +13.99 +919.27 -156.14 -222.90 -196.24 -202.00 +-203.58 +-147.94 +∆DIS +462.43 -328.34 206.37 +12.68 +1041.02 -31.83 -108.37 -33.82 +14.53 +-6.76 +44.41 +∆EDIS 313.62 -327.38 200.45 +-1.31 +121.75 +124.32 114.53 162.42 +216.53 +196.82 +192.35 +CAS +MAE +94.03 +63.73 +60.82 +55.49 +54.41 +84.56 +82.99 +83.17 +83.59 +85.30 +84.23 +85.37 +MSE +94.03 +63.73 +60.82 +55.49 +54.41 +84.56 +82.99 +83.17 +83.59 +85.30 +84.23 +85.37 +∆EQM +98.88 +59.11 +109.01 +56.09 +55.47 +92.54 +91.23 +91.34 +91.90 +93.26 +92.21 +93.54 +∆DIS +76.19 +69.50 +48.21 +49.41 +49.33 +54.37 +52.38 +52.26 +53.84 +58.40 +55.89 +55.67 +∆EDIS -22.69 +10.38 +-114.82 +-6.68 +-6.13 +-38.18 +-38.85 +-39.08 +-38.06 +-34.87 +-36.32 +-37.87 +ACSE +MAE +2.00 +3.05 +2.96 +3.61 +3.02 +4.18 +4.44 +4.82 +3.80 +2.93 +3.48 +4.40 +MSE +0.44 +3.03 +1.77 +3.30 +1.79 +0.98 +3.16 +3.57 +2.59 +1.14 +2.24 +2.69 +∆EQM +1.84 +3.12 +3.45 +4.52 +3.97 +5.02 +6.62 +6.94 +5.46 +3.73 +5.11 +6.46 +∆DIS +3.84 +5.24 +0.51 +-0.14 +-0.45 +-2.73 +0.43 +0.61 +1.38 +1.73 +1.54 +-0.67 +∆EDIS +2.01 +2.12 +-2.94 +-4.66 +-4.43 +-7.76 +-6.18 +-6.33 +-4.08 +-2.00 +-3.57 +-7.13 +TABLE I. Results for the various reference calculations used for the orbital optimization, as well as [6,6] CASCI, and CASCI/ACSE calcula- +tions for the dissociation of N2, in kcal/mol. All calculations were performed with the 6-31G basis set. Errors are relative to the FCI energies +and MSE and MAE are calculated over the eight distinct points along the dissociation coordinate; ∆eqm and ∆dis are the errors at R = 1.0976 +and R = 2.5, respectively; and ∆EDIS is the error in the dissociation energy, EDIS = ER=1.0976 −ER=2.5, with respect to FCI. +of 225.85 kcal/mol, while the largest negative deviation with +DFT is obtained with the BLYP functional at an MSE of +-201.31 kcal/mol. CCSD yields the best results with an MSE +of 33.19 kcal/mol, outperforming MP2, which as expected +results in unphysical behavior in the dissociated regime and +hence large negative deviations from FCI. Use of simple LDA +gives rise to unphysical electronic energies with a MAE of +947.85 kcal/mol. +If we consider the contribution of the multi-reference cor- +relation to the total electronic energy, CASSCF calculations +using the minimal [6,6] active space give a MSE of 55.49 +kcal/mol vs FCI, and on average the correlation recovered in +the [6,6] active space accounts for 69.4% of the total corre- +lation energy in the 6-31G basis set across the 8 dissociation +points. +The CASSCF calculation provides the benchmark +result to assess the ability of a chosen method’s orbitals to +account for multi-reference correlation. As a CASSCF calcu- +lation uses orbital rotations to minimize the total energy as a +functional of the CI energy in the active space, it yields the +variational minimum to the multi-reference correlation that +may be recovered in the chosen [6,6] active space and 6-31G +basis set, and all CI calculations performed on different sets +of orbitals yield upper bounds to this energy. Of the surveyed +single-reference methods, the NOs from a CCSD calculation +provide the orbitals that best account for static correlation +across the N2 dissociation space and yield the lowest CASCI +energy, with a MAE of 60.82 kcal/mol, followed by MP2, + +5 +which even though giving rise to nonphysically low energies +in the dissociated regime gives natural molecular orbitals +that recover a correct CASCI picture with a MAE of 63.73 +kcal/mol. +DFT yields better multi-reference-ready orbitals +than HF, with variation across the different surveyed DFT +functionals being relatively small, ranging from the most +correlated orbitals at PBE, MAE of 82.99 kcal/mol, to MN15 +at MAE of 85.37 kcal/mol, recovering on average roughly +50% of the total correlation energy. +Application of the ACSE following the converged CASCI +calculation in the chosen molecular orbital basis resolves +dynamic correlation with accuracy comparable to CCSD +with perturbative triple excitations [CCSD(T)], in addition +to the multi-reference correlation recovered by the CI. +Across all surveyed orbitals the CASCI/ACSE recovers an +average of between 97.2% and 99.7% of the total corre- +lation energy, displaying relatively minor dependence on +the chosen molecular orbital basis compared to CI and +single-reference calculations. Surprisingly, while providing +the best multi-reference orbitals, CASSCF does not provide +the most optimal orbitals to resolve the total correlation +energy, recovering on average 98% of the total correlation +energy with a MAE of 3.61 kcal/mol. As such, CASSCF +orbitals are outperformed by orbitals obtained with HF, MP2, +CCSD, M062X, and wB97XD calculations. +Simple HF +provides the most optimal orbitals to account for both strong +and post-CI dynamic correlation, recovering an average of +99.7% of the FCI energy for MAE of 2.00 kcal/mol. Results +from the different DFT functionals vary from an MAE of +2.93 kcal/mol in M06-2X to 4.82 kcal/mol in BLYP. Even in +the case of the worst performing DFT functional, BLYP, the +MAE increases by only 1.21 kcal/mol over CASSCF. The +fact that MSEs are smaller than the MAEs result from the +fact that the ACSE may yield a slightly lower bound to the +FCI energy in the dissociated regime. +ACSE calculations +significantly outperform CASPT2, which only recovers an +average of 93.0% of the total correlation energy, for MAE of +13.76 kcal/mol. +Lastly, after considering recovery of the full FCI dissocia- +tion curve, we also consider the errors in the reproduction of +the FCI dissociation energy, ∆EDIS = EDIS,method − EDIS,FCI, +where EDIS = ER=1.0976 −ER=2.5. This provides a benchmark +for orbitals obtained with a certain method to accurately +recover the total energy in the dissociated multi-reference +regime and the single-reference regime around the equi- +librium bond distance. +The observed trends follow those +discussed above with large positive errors in the DFT, +HF and CCSD reference calculations, which significantly +overestimate the bonding energy as they break down as N2 is +dissociated, while MP2 diverges to large negative energies. +Considering the CASCI energies, all calculation underesti- +mate EDIS, as correlation is more accurately captured at long +bond distances. Now, accounting for mostly static correlation +with [6,6] CASCI calculations, CASSCF, and the V2RDM +implementation of CASSCF yields the optimal orbitals, +followed by MP2 NOs, then HF and finally the various DFT +functionals which display only minor variations. +CCSD +presents an outlier as the CASCI calculation with CCSD NOs +at equilibrium suffered from convergence issues. Inspection +of the individual errors at the equilibrium and dissociated +geometry, ∆EQM and ∆DIS, respectively, reveals the HF result +to arise from a favorable cancellation of error, with the +energy lying high above the CASSCF and FCI references. +Additionally, as indicated by ∆EQM and ∆DIS, the single +reference orbitals tend to yield significantly lower errors in +the multi-reference, dissociated regime than the dynamically +correlated regime around the equilibrium bond length. +Finally, accounting for all-electron correlation with the +CASCI/ACSE method, yields ∆EDISs within 10 kcal/mol +of the FCI result for all surveyed orbitals. Errors range in +magnitude from a minimum of 2.00 kcal/mol with MOs +from the M062X DFT functional and 2.01 kcal/mol with HF +orbitals to 7.76 kcal/mol with LDA DFT MOs. Only orbitals +from HF and MP2 result in an overestimation of EDIS, while +all others yield a negative deviation from FCI. Interestingly, +CASSCF does not yield the optimal orbitals to resolve the +electronic energy accurately in both the equilibrium and +dissociated regimes, with deviations from FCI of -4.66 and +-4.43 kcal/mol for its wavefunction and V2RDM implemen- +tations, respectively. Indeed, separate consideration of the +errors at equilibrium and dissociation bond lengths reveals +a relatively large ∆eqm of 4.52 kcal/mol for the CASSCF +orbitals, compared to only 1.84 kcal/mol, 3.12 kcal/mol +and 3.45 kcal/mol for those obtained with single-reference +methods HF, MP2 and CCSD, respectively. Interestingly, for +the DFT MOs, ∆eqm is larger that obtained with CASSCF +MOs for all functionals but M06-2X, with generally lower +errors in the multi-reference, dissociation regime. The result +is that CASSCF/ACSE all-electron correlation calculations +with initial CASSCF optimization of the orbitals for the +dissociation energy of N2, where energy differences between +a strongly correlated and a dynamically correlated solution +are computed, are outperformed by simple CASCI/ACSE +calculations using orbitals obtained from HF, MP2, CCSD, as +well as the DFT functionals B3LYP, M062X, and wB97XD. +B. +Singlet Triplet Gaps of Main Group Biradicaloids +Biradicals play important roles in a wide range of chemical +processes as transition states and intermediates, formed +during the breaking and forming of chemical bonds, as well +as in the development of new single-molecule magnets and +materials for spintronics or molecular qubits93–95. +Their +accurate theoretical description continues to pose a challenge +to current developments in electronic structure theory due to +the multi-reference character of their open-shell singlet states, +requiring the use of methods that account for both static and +dynamic correlation to resolve their electronic properties. +In this section we investigate the orbital dependence of the +singlet-triplet (S-T) gaps for a benchmark set of small main +group biradicals OH+, NH, NF, O2, NH+ +2 , CH2, PH+ +2 , and + +6 +SiH2 as calculated with single-reference, CI and post-CI +ACSE methods. +Singlet-triplet gaps of biradicaloids are +of particular value as they relate to experimentally relevant +properties such as the exchange coupling constant J or their +properties in photonics. +We perform calculations on the singlet and triplet states +with the cc-pVTZ basis set101,102, using a minimal [4,4] +active space chosen around the HOMO and LUMO for the +CI calculations, allowing for the inclusion of non-trivial +correlation in the triplet states and assessing the suitability +of the single-reference orbital to yield a suitable CAS guess. +The ACSE calculations use a spin-averaged implementation, +which has recently been demonstrated to yield highly accurate +singlet-triplet gaps for this benchmarking set with converged +CASSCF wave functions89. The data are presented in Table +II. Errors are calculated with respect to the experimental +reference values. As expected, none of the single-reference +methods yield accurate results, failing to capture the strong +correlation of the biradical singlets. MP2 yields extremely +inaccurate results with a MAE of 70.7 kcal/mol, while the +rest of the surveyed methods range from 6.5 kcal/mol in +CCSD (use of perturbative triples correction reduces this to +4.6 kcal/mol) to 21.4 kcal/mol in LDA. HF also yields a large +MAE of 20.3 kcal/mol. Across the surveyed DFT functionals +we observe a quite significant variation in their ability to +calculate the S-T gaps, with MN15 giving the lowest MAE of +4.7 kcal/mol and LDA and PBE giving the largest MAEs of +21.4 kcal/mol and 11.5 kcal/mol, respectively. +As with the dissociation of N2, of the surveyed methods +CCSD natural orbitals yield the most optimal basis to account +for multi-reference character in the CASCI calculations, +with a MAE of 9.39 kcal/mol, followed by the various +DFT functionals, where variation in the CASCI results is +less pronounced than in the single-reference calculations. +Furthermore, there is no correlation between the accuracy +of the CASCI calculation and the reference DFT calculation +with orbitals from the previously best performing MN15 now +yielding a MAE of 10.28 kcal/mol while the second-worst +performing PBE returns the best CASCI results with a MAE +of 9.75 kcal/mol. Apart from the unreliable MP2 calculations, +HF orbitals give the largest MAE of 15.6 kcal/mol. +No +orbital basis from any method comes close in accuracy to the +CASSCF calculation, which yields a MAE of 6.38 kcal/mol. +While the MSE is close to zero (-0.56 kcal/mol) in CASSCF, +it is of significant, positive magnitude in DFT, ranging from +3.96 kcal/mol in MN15 to 6.01 kcal/mol in M06-2X and +HF, while it is negative in MP2 and CCSD. As an additional +measure to probe the bi-radical character in the solutions, we +introduce the average distance of the 1-RDM of the CASCI +calculation from a closed-shell single-reference 1-RDM, +defined as ¯R = ∑ij ||λHF,i − λi|j/N, where i runs over all +orbitals of the system, N is the number of species in the +set, j runs over all its members, λi denotes the ith natural +occupation number and λHF,i is 2 if the orbital is occupied +and 0 if the orbital is virtual. +The inclusion of post-CI dynamic correlation with the +spin-averaged ACSE provides significant improvement over +single-reference and CASCI results in all cases. While the +[4,4] CASSCF optimization does give the best agreement +with experiment (MAE of 3.16 kcal/mol), the advantage over +the various other orbitals is relatively minor, with MP2 and +HF orbitals yielding the largest deviations with MAEs of +7.36 kcal/mol and 5.44 kcal/mol, respectively, and CCSD +again yielding the closest agreement with an MAE within 0.5 +kcal/mol of CASSCF. The CASCI/ACSE calculations per- +formed with DFT orbitals provide MAEs within 1 kcal/mol +of the CASSCF orbitals for all functionals but PBE, which +has the largest error at an MAE of 5.22 kcal/mol. Across +the surveyed functionals, variation again is minor, meaning +while S-T gaps predicted by the individual functionals differ +based on empirical fitting, the underlying molecular orbitals +obtained in the SCF procedure remain relatively unchanged. +Analogous to the N2 dissociation, the ωB97X-D functional +again performs well and provides the molecular orbitals +best suited to account for the multi-reference and dynamic +correlation in the biradicaloid set, yielding a MAE of 3.99 +kcal/mol. +In the CASCI/ACSE case the sign of the MSE +obtained for the various DFT orbitals agrees with CASSCF, +and only HF and MP2 orbitals lead to a positive MSE, +while CCSD yields a MSE of small negative magnitude. +Again considering ¯R as a measure for the recovered total +correlation, HF and MP2 which yield the largest MAEs +also result in the lowest magnitude of ¯RS, 0.533 and 0.432, +respectively. +However, surprisingly, +¯RS,CCSD = 0.835 is +significantly lower than +¯RS,CASSCF = 1.102, while DFT +orbitals, yield ¯RS values between 0.968 and 1.116, with there +being no correlation between ¯RS and MAE. To the contrary, +PBE yields greater correlation in the NOs than CASSCF +while resulting in the largest MAE of all surveyed functionals. +To resolve the origin of the minor variations across sur- +veyed methods, we plot the deviations from experimen- +tal reference values for the individually studied species for +CASSCF, HF, CCSD, and M06-2X in Figure 2. Inspection of +the individual errors in CASCI shows particularly large errors +in the calculation of O2, which has previously been demon- +strated to provide a challenge to various electronic struc- +ture methods, with AFQMC and ACSE calculations requiring +CASSCF wave functions with active spaces as large as [10,15] +and [14,14] to yield sub 2 kcal/mol accuracy for the calcula- +tion of its S-T gap89,103. The [4,4] active space successfully +resolves its diradical character; however, it significantly over- +stabilizes the singlet state leading to a large negative deviation +from experiment. We observe a particularly strong stabiliza- +tion of the singlet O2 state in the CASCI with CCSD molecu- +lar orbitals, while the remaining orbitals yield results that are +in good agreement with CASSCF, leading to the more nega- +tive MSE in the CCSD NO basis. The positive MSE in DFT +and HF arises from the fact that, while there is agreement with +CASSCF in the case of O2, the orbitals in all other species lead +a to an overestimation of the singlet triplet gap via a relatively +less pronounced stabilization of the singlet. Use of the ACSE +to include post-CI correlation leads to a significant reduction + +7 +Molecular Orbitals +Method +HF +MP2 CCSD V2-T LDA PBE BLYP B3LYP M062X wB97XD MN15 +REF +MAE 20.3 +70.7 +6.5 +21.4 +11.5 +7.12 +7.19 +6.62 +7.01 +4.7 +MSE +20.3 +70.7 +6.5 +21.4 +11.5 +6.7 +7.19 +6.62 +6.96 +3.63 +∆max +31.1 +93.5 +13.1 +35.7 +22.7 +16.7 +17.1 +13.71 +16.82 +10.9 +∆min +14.6 +26.3 +0.12 +12.4 +3.8 +0.03 +0.05 +0.77 +0.10 +1.08 +CAS +MAE 15.48 14.45 +9.39 +6.38 11.43 9.75 +10.57 +10.75 +11.85 +11.18 +10.28 +MSE 10.88 -3.16 -4.18 -0.56 5.16 +5.37 +4.06 +4.95 +6.01 +4.88 +3.96 +∆max 19.96 45.57 45.57 16.68 25.07 17.54 26.03 +23.21 +23.37 +25.17 +25.26 +∆min +9.74 +0.04 +0.12 +0.04 +7.37 +4.89 +4.88 +6.36 +8.24 +6.37 +4.51 +¯RS +0.251 0.212 0.628 0.912 0.855 0.888 0.886 +0.851 +0.720 +0.818 +0.866 +¯RT +2.005 2.027 2.037 2.036 2.013 2.013 2.013 +2.011 +2.009 +2.011 +2.013 +ACSE +MAE 5.44 +7.36 +3.64 +3.16 +4.63 +5.22 +4.37 +3.99 +4.07 +3.99 +4.48 +MSE +2.18 12.47 -0.81 -1.28 -3.27 -1.64 -2.98 +-2.87 +-1.85 +-2.43 +-3.10 +∆max +8.71 12.47 +9.44 +6.25 +9.61 12.44 10.34 +9.56 +9.62 +9.47 +10.61 +∆min +0.06 +0.05 +0.36 +0.36 +0.14 +0.51 +0.42 +0.21 +0.06 +0.45 +0.58 +¯RS +0.533 0.432 0.835 1.102 1.067 1.116 1.109 +1.084 +0.968 +1.055 +1.084 +¯RT +2.189 2.199 2.197 2.200 2.166 2.182 2.180 +2.180 +2.183 +2.183 +2.172 +TABLE II. Errors for the S-T gaps of the set of eight biradicals, OH+, NH, NF, O2, NH+ +2 , CH2, PH+ +2 , and SiH2. All calculations were carried +out using the cc-pVTZ basis set, and CASCI and ACSE calculations use a [4,4] active space. MAE and MSE, and maximum and minimum +absolute errors, ∆max and ∆min, are calculated relative to experimental reference values obtained from references96–100 and given in kcal/mol. +¯RS and ¯RT denote the average distance of the NON from the HF solution for the singlet and triplet states, respectively. +CH2 + NH + +2 +SiH2 +PH + +2 +NH +NF +O2 +OH + +−15 +−10 +−5 +0 +5 +ΔΔEΔS − T) i kcal/mol +CASSCF [4,4] S-T GAP ERRORS +CAS +ACSE +CH2 + NH + +2 +SiH2 +PH + +2 +NH +NF +O2 +OH + +−20 +−10 +0 +10 +20 +30 +ΔΔEΔS − T) i kcal/mol +HF [4,4] S-T GAP ERRORS +HF +CAS +ACSE +CH2 + NH + +2 +SiH2 +PH + +2 +NH +NF +O2 +OH + +−40 +−30 +−20 +−10 +0 +10 +ΔΔEΔS − T) in kcal/ ol +CCSD [4,4] S-T GAP ERRORS +CCSD +CAS +ACSE +CH2 + NH + +2 +SiH2 +PH + +2 +NH +NF +O2 +OH + +−25 +−20 +−15 +−10 +−5 +0 +5 +10 +15 +ΔΔEΔS − T) in cal/mol +M06-2X [4,4] S-T GAP ERRORS +M06-2X +CAS +ACSE +FIG. 2. Errors for the S-T gaps of the biradical set resolved for its individual members for four select methods used for the orbital optimization. +Bars indicate the errors of the S-T gap with respect to the experimental reference. Orange bars indicate errors of the single-reference calculation, +blue bars the CASCI results based on the single-reference orbitals, and yellow bars the CASCI/ACSE result in the respective single-reference +orbital basis. Top row: CASSCF (left), CCSD (right); bottom row: HF (left), M06-2X (right). All data were obtained with a cc-pVTZ basis +set and [4,4] active spaces for the CASCI and ACSE calculations. + +8 +Molecular Orbitals +M06-L M06 M06-2X M06-HF +Method % HF +0 +27 +54 +100 +REF +MAE +8.65 +6.92 +6.62 +4.25 +MSE +8.65 +4.73 +6.62 +4.22 +∆max +20.62 15.76 +13.71 +11.34 +∆min +0.19 +0.75 +0.77 +0.13 +CAS +MAE +10.65 10.77 +11.85 +14.41 +MSE +4.40 +5.10 +6.01 +4.55 +∆max +25.00 22.70 +23.37 +21.39 +∆min +5.45 +7.06 +8.24 +9.37 +¯RS +0.884 0.838 +0.720 +0.396 +¯RT +2.014 2.011 +2.009 +2.005 +ACSE +MAE +3.92 +4.26 +4.07 +4.55 +MSE +-2.52 +-2.95 +-1.85 +-0.27 +∆max +8.79 +10.65 +9.62 +9.72 +∆min +0.03 +0.25 +0.06 +0.52 +¯RS +1.122 1.072 +0.968 +0.662 +¯RT +2.190 2.179 +2.183 +2.177 +TABLE III. Errors for the biradical set S-T gaps resolved with or- +bitals from the members of the MN06 suite of functionals. All cal- +culations were carried out using the cc-pVTZ basis set, and CASCI +and ACSE calculations use a [4,4] active space. MAE and MSE, +and maximum and minimum absolute errors, ∆max and ∆min, are +calculated relative to experimental reference values obtained from +references96–100 and given in kcal/mol. +¯RS and ¯RT denote the av- +erage distance of the NON from the HF solution for the singlet and +triplet states, respectively. +in the variation of the errors across the different species and +methods, with only HF orbitals showing deviations in signifi- +cant magnitude from the CASSCF/ACSE results, particularly +in the cases of NF and OH+. +Lastly, to provide insight into the effect of exact HF +exchange in a chosen DFT functional on the molecular +orbitals obtained from the SCF procedure, we compare the +results from four M06 functionals with varying degrees of HF +exchange: M06-L (0%), M06 (27%), M06-2X (54%), and +M06-HF (100%), shown in Table III. Interestingly, the MAE +and MSE of the DFT S-T gaps decreases as the HF exchange +contribution to the functional increases. While this is contrary +to results from large-scale functional benchmarks, which +suggest functionals with larger HF exchange contributions +yield worse performance on multi-reference interactions104, +the expected trend is observed in the CASCI errors. These +consistently increase with the HF exchange fraction, sug- +gesting the inclusion of more exact HF exchange leads to +worse multi-reference orbitals in the KS-SCF optimization. +Inclusion of post-CI dynamic correlation again results in +reduced variation across the functionals, however, showing +a trend of increasing MAE with increasing HF exchange in +the functional used for the orbital optimization. In fact, the +molecular orbitals obtained from a SCF optimization with +the 0% HF exchange containing M06L functional yields the +lowest MAE, as well as, maximum and minimum errors +across the data set of all surveyed functionals. Additionally, +the decrease in the ability of the functional’s orbitals to +account for multi-reference character of the singlet state is +clearly reflected in the trend observed in the ¯RS values with a +ΔEǂ +dis +ΔEǂ +con +FIG. 3. Reaction coordinate of the isomerization reaction of bicy- +clobutane to 1,3-butadiene with the con- and dis-rotatory transition +states shown. The conversion to the 1,3-butadiene is not considered. +steady decrease from a maximum of 1.122 in M06-L to just +0.662 in M06-HF. +While the results obtained from the [4,4] spin-averaged +CASSCF/ACSE calculation are comparable to those from +CASSCF/MC-PDFT, which yields a MAE of 3.5 kcal/mol105, +the computationally less expensive CASCI/ACSE calcula- +tions based on a DFT orbital optimization yield results in +line with various methods reported across the literature, such +as (V)FS-PBE (MAE = 4.3 kcal/mol)106, pp-B3LYP (4.8 +kcal/mol)107, W2X (3.7 kcal/mol)105, or tPBE/MC-PDFT +(4.3 kcal/mol)105. +C. +Transition States of the Bicyclobutane Isomerization +Reaction to gauche-1,3-Butadiene +As a final example, we consider the orbital dependence +in the use of CI and post-CI methods to model a simple +chemical reaction, calculating the energy barrier, ∆H‡, to +the isomerization reaction of bicyclobutane to gauche-1,3- +butadiene. This isomerization process may proceed via two +different transition states arising from conrotatory (CON) +and disrotatory (DIS) pathways. +The reaction coordinate +diagram displaying these is shown in Figure 3. Optimized +geometries and zero-point and vibrational corrections to the +electronic energy were obtained from reference108, using +the MCSCF/6-31G*109 level of theory, and amounting to +0.0911, 0.0862, and 0.0844 hartrees for bicyclobutane, and +the CON and DIS transition states, respectively. Calculations +were performed with the previously surveyed methods, CAS +orbitals were selected around the HOMO and LUMO, and +the results are compared to those obtained from [14,14] +CASSCF/ACSE calculations, as well as previously reported +ACSE108, CC(P;Q)110, and DMC111 data. The barrier for the +CON transition pathway has been experimentally determined +to be 40.6 ± 2.5 kcal/mol. The data are shown in Table IV. + +9 +CASSCF +Molecular Orbitals +Pathway +[4,4] [14,14] +HF +MP2 CCSD V2-T LDA PBE BLYP B3LYP M062X wB97XD MN15 +CON +∆H‡ +57.59 48.60 47.53 +41.92 42.25 36.75 +43.50 +53.42 +50.30 +50.89 +∆H‡ +CAS +37.68 33.70 +42.86 39.49 31.16 37.85 45.92 45.23 44.51 +43.07 +43.25 +42.91 +42.80 +∆H‡ +ACSE +40.56 40.78 +46.56 46.71 43.43 40.74 39.54 42.14 42.49 +43.38 +43.63 +44.01 +42.95 +λHONO,CAS 1.701 1.734 +1.816 1.846 1.755 1.701 1.782 1.776 1.770 +1.776 +1.794 +1.787 +1.785 +λLUNO,CAS 0.299 0.271 +0.187 0.155 0.247 0.299 0.220 0.224 0.230 +0.225 +0.209 +0.216 +0.218 +λHONO,ACSE 1.669 1.703 +1.763 1.800 1.720 1.669 1.722 1.723 1.719 +1.726 +1.741 +1.737 +1.732 +λLUNO,ACSE 0.319 0.286 +0.228 0.188 0.270 0.319 0.281 0.277 0.280 +0.271 +0.256 +0.261 +0.267 +DIS +∆H‡ +92.38 68.98 67.51 +64.45 64.46 58.18 +67.69 +80.78 +76.36 +76.95 +∆H‡ +CAS +46.49 47.25 +53.30 53.91 40.07 46.69 51.63 50.21 50.10 +49.75 +50.62 +50.03 +49.31 +∆H‡ +ACSE +52.11 51.79 +55.93 59.59 54.32 52.33 49.35 51.76 52.43 +53.53 +53.15 +53.53 +51.72 +λHONO,CAS 1.364 1.413 +1.462 1.612 1.438 1.364 1.434 1.428 1.418 +1.420 +1.433 +1.429 +1.428 +λLUNO,CAS 0.636 0.589 +0.547 0.398 0.566 0.636 0.573 0.580 0.590 +0.588 +0.576 +0.580 +0.581 +λHONO,ACSE 1.345 1.393 +1.423 1.574 1.416 1.345 1.399 1.396 1.387 +1.390 +1.400 +1.398 +1.395 +λLUNO,ACSE 0.641 0.594 +0.567 0.419 0.574 0.641 0.602 0.605 0.612 +0.608 +0.598 +0.601 +0.603 +TABLE IV. Data for the con- and disrotatory pathways of the isomerization reaction of bicyclobutane. Calculations were carried out with +the 6-31G* basis set and CASCI and ACSE calculations utilize a [4,4] active space. Geometries and free energy corrections calculated at the +MCSCF/6-31G* level of theory and were obtained from reference108. ∆H‡ denotes the transition state barrier in kcal/mol including zero point +and vibrational corrections amount to -3.087 kcal/mol and -4.221 kcal/mol for the CON and DIS pathways, respectively. λHONO and λLUNO +denote the occupations of the highest and lowest natural orbitals (HONO and LUNO), respectively. +First considering the conrotatory pathway, variation across +the barriers predicted by the single reference methods is +significant, ranging from ∆H‡ = 36.75 kcal/mol with BYLP +to ∆H‡ = 57.59 kcal/mol with HF. Within the DFT realm, the +obtained results are very sensitive to the choice of functional +and lack consistency, with BLYP underestimating ∆H‡ while +the remaining functionals overestimate it and variations +far exceeding chemical accuracy. +Nonetheless, the LDA +and PBE functionals predict ∆H‡ values that lie within the +experimental bounds of error. It is noteworthy that the MN15 +functional which is fitted to perform well in multi-reference +problems, gives a large overestimation of ∆H‡ with the +predicted 50.89 kcal/mol being far outside the realms of +chemical accuracy. +Using a [14,14] active space CASSCF yields ∆H‡ = 33.70 +kcal/mol, with highest occupied natural orbital (HONO) +and lowest unoccupied natural orbital (LUNO) occupation +numbers of 1.734 and 0.271, respectively, making the CON +transition state the less correlated one. The static correlation +from the CASSCF calculation overstabilizes the TS compared +to bicyclobutane, resulting in underestimation of ∆H‡,CAS. +For our CASCI calculations we use a smaller [4,4] active +space (∆H‡ +CAS = 37.68), which reduces the magnitude of +this underestimation and is sufficient to resolve the biradical +character of the TS, yielding HONO and LUNO occupation +numbers of 1.701 and 0.299, respectively. For the CASCI +calculations, CCSD again provides the orbitals most optimal +to resolve the multireference correlation of the methods +surveyed, underestimating the CON barrier, and yielding +the smallest deviation from the [14,14] CASSCF result and +with ∆H‡ = 31.16 kcal/mol—a lower barrier than both [4,4] +and [14,14] CASSCF. All other orbitals provide a CASCI +energy with a positive deviation from the CASSCF ∆H‡, +with MP2 NOs yielding the least correlated solution but the +smallest error, followed by HF and finally the various DFT +functionals, which yield large ∆H‡s but more correlated +solutions than MP2 and HF, showing HONO and LUNO +occupations numbers comparable to [4,4] CASSCF. +Using the ACSE to resolve the full correlation energy, +both [4,4] and [14,14] CASSCF resolve the CON barrier +to near-exact accuracy providing near-identical results of +40.74 kcal/mol and 40.78 kcal/mol, respectively. MP2 NOs +provides both the least correlated solution, as well as the +largest deviation from the experimental range of ∆H‡, lying +3.61 kcal/mol above this interval. It is closely followed in +both error and correlation by HF. Contrary to the results +from the S-T gaps and N2 dissociation, CCSD NOs are now +outperformed by the majority of DFT functionals, with only +M06-2X, and ωB97XD deviating by more than CCSD’s 0.33 +kcal/mol from the experimental confidence interval. +The +LDA, PBE, BLYP and MN15 orbitals all yield ∆H‡ values +obtained by the CASCI/ACSE algorithm that lie within the +experimental error bound. +The disrotatory TS provides for the more correlated +and higher energy isomerization pathway, with [14,14] +CASSCF/ACSE yielding a barrier of ∆H‡ = 51.79 kcal/mol +and LUNO and LUNO occupation numbers of 1.393 and +0.594, respectively. There is no experimental reference data +for the DIS pathway, but DMC calculations have yielded +a barrier of 58.6 kcal/mol111, while CR-CC(2,3) predicts a +barrier height of 67.5 kcal/mol110. Across the various single- +reference methods and the CASCI calculations, the trends +remain unchanged from the CON pathway, however, with +increased errors in the single-reference calculations as the +degree of multi-reference correlation in the TS is increased. +All CASCI/ACSE calculations with DFT orbitals fall within +the ± 2.5 kcal/mol range of the CASSCF[14,14]/ACSE +reference, with MN15 and PBE yielding the closest, and +near-identical, results. In this more strongly correlated TS, + +10 +Molecular Orbitals +M06-L M06 M06-2X M06-HF +Pathway +% HF +0 +27 +54 +100 +CON +∆H‡ +46.72 48.46 +53.42 +57.46 +∆H‡ +CAS +44.87 43.16 +43.25 +42.66 +∆H‡ +ACSE +42.14 43.03 +43.63 +45.15 +λHONO,CAS +1.785 1.787 +1.794 +1.806 +λLUNO,CAS +0.215 0.214 +0.209 +0.198 +λHONO,ACSE +1.732 1.735 +1.741 +1.755 +λLUNO,ACSE +0.269 0.264 +0.256 +0.240 +DIS +∆H‡ +72.43 74.69 +80.78 +85.41 +∆H‡ +CAS +49.29 49.60 +50.62 +52.26 +∆H‡ +ACSE +51.76 52.57 +53.15 +53.87 +λHONO,CAS +1.426 1.427 +1.433 +1.449 +λLUNO,CAS +0.582 0.582 +0.576 +0.560 +λHONO,ACSE +1.395 1.395 +1.400 +1.413 +λLUNO,ACSE +0.606 0.604 +0.598 +0.580 +TABLE V. Data for the con- and disrotatory pathways of the bicy- +lobutane isomerization resolved for the members of the MN06 suite +of functionals with their varying degrees of exact HF-exchange. Cal- +culations were carried out with the 6-31G* basis set and CASCI and +ACSE calculations utilize a [4,4] active space. Geometries and free +energy corrections calculated at the MCSCF/6-31G* level of the- +ory and were obtained from reference108. ∆H‡ denotes the tran- +sition state barrier in kcal/mol including zero point and vibrational +corrections amount to -3.087 kcal/mol and -4.221 kcal/mol for the +CON and DIS pathways, respectively. λHONO and λLUNO denote the +occupations of the highest and lowest natural orbitals (HONO and +LUNO), respectively. +CCSD NOs yield a larger error of 2.53 kcal/mol. As in the +CON TS, DFT orbitals yields more fractional NON than +those from HF, MP2, and comparable values to CCSD NOs. +Lastly, we again look at the M06 suite of functionals to +resolve the influence of HF exchange in the DFT functional. +While there is no obvious trend in the barrier height predicted +by CASCI based on the various orbitals, ∆H‡ predicted by +the functional and the CASCI/ACSE calculation, as well as, +the NONs follow the expected trend with a lower fraction +of HF exchange better accounting for the multi-reference +correlation in the studied transition states. +Consequently, +errors in ∆H‡ and the value of the NON increase across the +series from M06-L to M06-HF. The M06-L functional MOs +provide a barrier height within the experimental range of +error for the CON pathway, yielding identical results to PBE +and an only slightly larger error than LDA, while in the DIS +pathway M06-L orbitals yield near-exact agreement with +[14,14] in both NON and ∆H‡, providing the best orbitals +from any method surveyed. +IV. +DISCUSSION & CONCLUSIONS +We have employed CASCI calculations in combination +with the ACSE to resolve the orbital dependence on the +dynamic and multi-reference parts of the total electronic +correlation energy. +Considering problems dominated by +multi-reference correlation, we show that CASCI calculations +display significant dependence on the chosen molecular +orbital basis, with coupled cluster natural orbitals yielding +the most optimal orbitals to account for multi-reference +correlation of the single-reference methods surveyed, and HF +yielding the least suitable orbitals, while DFT functionals +lie between the two methods. Nonetheless, for the accurate +prediction of multi-reference dependent properties through +the means of CI calculations only, CASSCF orbital opti- +mization is prudent. +Use of a post-CI method to account +for dynamic correlation, in this case the ACSE, reduces the +orbital dependence of the accuracy in the predicted properties. +Using the ACSE to resolve post-CI dynamic correlation, we +survey orbitals from wave-function based single-reference, +as well as, various popular DFT functionals. +While HF +orbitals yield good results for the N2 dissociation, they +tend to fail to capture accurately multi-reference character +and deliver lackluster results in the CASCI/ACSE scheme +for the prediction of biradical S-T gaps and TS barriers. +MP2 is plagued by inconsistencies and convergence issues. +Natural orbitals obtained from CCSD calculations, however, +allow CASCI/ACSE to resolve both dynamic and strong +correlation effects in the three case studies accurately, out- +performing CASSCF orbitals in the N2 dissociation, where +molecular geometries not dominated by static correlation +are considered, most closely mirroring the FCI dissociation +curve, and yielding biradical S-T gaps and bicyclobutane +isomerization barriers with accuracies close to those achieved +with CASSCF orbitals. +The various DFT functionals, which are known to yield +widely varying results for different systems and properties +based on their parametric fitting, produce orbitals that com- +pared to the results predicted by the functionals themselves, +such as S-T gaps or dissociation energies, show much greater +consistency. Of the tested functionals, the M06 suite and the +ωB97XD functionals provide the best suited orbitals for the +CASCI/ACSE calculations, yielding only marginally worse +performance than CASSCF and CCSD orbitals. Furthermore, +resolving the S-T gaps and bicyclobutane isomerization +barriers obtained with the M06 suite functionals shows the +most optimal orbitals to account for both multi-reference +and dynamic correlation are obtained with the lowest HF- +exchange fraction, i.e. the M06-L functional, which yields +the best orbitals for the treatment of multi-reference problems +of any tested functional. As DFT presents the most ubiq- +uitous electronic structure method across many disciplines +in chemistry, physics and materials science, implemented in +any commonly used software package, offering inexpensive +computational scaling compared to CASSCF or CC methods, +it provides a good compromise between computational costs, +ease-of-use, and accuracy. Especially, considering the fact +that DFT molecular orbitals are already available in most +cases through prior geometry optimizations or frequency +calculations, they provide a viable option for further ab-initio +calculations aimed at resolving electron correlation in many + +11 +applications, significantly reducing further computational +expense while retaining viable accuracy. +This work provides valuable insight into the orbital +dependence in the ability of CASCI and post-CI methods +to resolve multi-reference and dynamic correlation. +We +demonstrate that contrary to popular implementations that +rely on CASSCF orbital optimizations for the resolution of +the total correlation energy, CASSCF may not always provide +the optimal molecular orbital basis set to account for the com- +bination of static and dynamic contributions to the electronic +energy. Furthermore, improved computational scaling may be +obtained through the use of widely available single-reference +methods for the optimization of the molecular orbitals. Addi- +tionally, if a post-CI method to resolve all-electron correlation +were to be implemented in a SCF fashion, undergoing further +orbital optimization after the initial CAS seed calculation, +performance of an initial CASSCF calculation may be of +limited value as compared to a seed with orbitals obtained +from the surveyed single-reference methods. Throughout the +studied systems we show that the CASCI/ACSE method is a +valuable tool in the accurate resolution of the properties of a +multi-reference system, and may be used in combination with +any single-reference calculation, in particular with DFT, not +requiring further CASSCF calculations. +ACKNOWLEDGMENTS +D.A.M. gratefully acknowledges the U.S. National Science +Foundation Grant CHE-1565638. +1C. J. Stein, V. von Burg, and M. 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A +114, 13222–13227 (2010). + diff --git a/hNAyT4oBgHgl3EQfxfmy/content/tmp_files/load_file.txt b/hNAyT4oBgHgl3EQfxfmy/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..0250f06f05d5bd5890c417e72f5889a6721f60aa --- /dev/null +++ b/hNAyT4oBgHgl3EQfxfmy/content/tmp_files/load_file.txt @@ -0,0 +1,1945 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf,len=1944 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='00668v1 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='chem-ph] 29 Dec 2022 Elucidating the Molecular Orbital Dependence of the Total Electronic Energy in Multireference Problems Jan-Niklas Boyn and David A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Mazziottia) The James Franck Institute and The Department of Chemistry, The University of Chicago, Chicago, Illinois 60637 USA (Dated: Submitted March 5, 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Revised April 18, 2022) The accurate resolution of the chemical properties of strongly correlated systems, such as biradicals, requires the use of electronic structure theories that account for both multi-reference as well as dynamic correlation effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' A variety of methods exist that aim to resolve the dynamic correlation in multi-reference problems, commonly relying on an ex- ponentially scaling complete-active-space self-consistent-field (CASSCF) calculation to generate reference molecular orbitals (MOs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' However, while CASSCF orbitals provide the optimal solution for a selected set of correlated (active) orbitals, their suitability in the quest for the resolution of the total correlation energy has not been thoroughly investi- gated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Recent research has shown the ability of Kohn-Shan density functional theory (KS-DFT) to provide improved orbitals for coupled cluster (CC) and Møller-Plesset perturbation theory (MP) calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Here we extend the search for optimal and more cost effective MOs to post-configuration-interaction (post-CI) methods, surveying the ability of the MOs obtained with various DFT functionals, as well as Hartree-Fock, and CC and MP calculations to accurately capture the total electronic correlation energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Applying the anti-Hermitian contracted Schrödinger equation (ACSE) to the dissociation of N2, the calculation of biradical singlet-triplet gaps and the transition states of the bicylobutane isomerization, we demonstrate DFT provides a cost-effective alternative to CASSCF in providing reference orbitals for post-CI dynamic correlation calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' INTRODUCTION The computational resolution of electronic structure relies on the accurate capture of the correlation energy, which is defined as the difference between the full-configuration- interaction (FCI) and Hartree-Fock (HF) energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The correlation energy is generally further divided into two components: static or strong correlation arising from a state that may not be described by a single Slater determinant and is hence also termed multi-reference correlation, and the remainder which is defined as dynamic correlation1–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' While dynamic correlation is present in all electronic systems and may be well described by many single-reference methods such as coupled cluster (CC), Møller-Plesset perturbation theory (MP)5 or even density functional theory (DFT)6,7, strong correlation only arises in systems exhibiting a de- generacy or near-degeneracy of electronic states1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' As such, multi-reference correlation plays a particularly important role in processes such as bond dissociation, and in the determi- nation of properties of bi- or multi-radical systems, such as spin state splittings and magnetic couplings in molecules and complexes in the areas of spintronics, photonics or catalysis8–11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Multi-reference correlation is commonly resolved with complete active space configuration interaction (CASCI) or CAS self consistent field (CASSCF) calculations, which resolve the strong correlation in a chosen active space12–15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' While CASSCF calculations have proven valuable in the description of systems dominated by multi-reference correlation12,13, it has been demonstrated that even in a)Electronic mail: damazz@uchicago.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='edu such systems, experimentally relevant properties, such as singlet-triplet (S-T) gaps or J-coupling parameters may often not be resolved within chemical accuracy without the additional inclusion of dynamic correlation effects16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The historically most popular and commonly used method to account for post-CI dynamic correlation CASSCF in combination with second-order many-body perturbation theory (CASPT2) suffers from a variety of shortcomings, including poor computational scaling, and convergence issues arising from the fact that the MP2 correction is not variational, often leading to nonphysical lower bounds to the total electronic energy17–20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Consequently,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' the development of electronic structure methods that account for post-CI dynamic correlation is an area of major research interest and recent developments include algorithms such as quantum Monte-Carlo21–23,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' multi-configuration pair-density functional theory (MC-PDFT)24–28,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' reduced-density-matrix functional theory (RDMFT)29–34,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' incremental FCI (iFCI)35–37 or CASCI in combination with the anti-Hermitian contracted Schrödinger equation (ACSE)38,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='39 as well as related methods that use cumulant reconstruction40,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='41 to solve a contracted Schrödinger equation42–44 for dynamic correlation45,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' While FCI yields the exact electronic energy in a chosen basis set and hence is invariant to the molecular orbital (MO) basis, it remains out of reach for system larger than 16 electron in 16 orbitals due to exponential computational scaling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' As other ab-initio electronic structure methods that aim to resolve the total electronic correlation energy tend to rely on some approximation to truncate the exact Hamiltonian, they exhibit a dependence on the chosen MO basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Recent research has been performed in the areas of CC and MP theories with the aim of improving their predictive properties via the use of improved molecular orbitals, rather than the commonly used HF reference47–51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' This includes 2 the implementation of orbital-optimized variants of CC and second-order MP2 (OOMP2), which, while yielding im- proved results over the HF-reference based implementations, suffer from increased computational scaling, and in the case of OOMP2 three major failures, namely divergence for small MO energy gaps, artificial symmetry restoration and loss of Coulson-Fischer points52–54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' A contrary approach to the orbital-optimization problem has recently been undertaken by Head-Gordon and coworkers, who demonstrate significant improvements in the prediction of chemical properties in MP3 via the use of OOMP2 and DFT orbitals55,56, and in the calculation of vibrational frequencies with CCSD(T) with the use of DFT orbitals57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Additionally, natural orbitals obtained with MR-CI-SD calculations performed after initial CASSCF optimization may provide improved orbitals for the recovery of additional correlation energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='58,59 While research has been undertaken to shine light on the orbital dependence in single-reference methods aimed at resolving dynamic correlation, work aiming at resolving this dependence in multi-reference and post-multi-reference dynamic correlation calculations has been limited60–67 and common implementations of electronic structure methods aiming to resolve the total correlation energy such as QMC, CASPT2 or MC-PDFT, tend to rely on CASSCF optimized orbitals as their reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' But are orbitals that are optimized to include multi-reference correlation necessarily the best to account for the total correlation or is the restriction of the orbital optimization to an active space representing a small subset of the total molecular orbitals hindering the capture of the complete electronic structure?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Specifically, would CASSCF orbitals necessarily provide the best initial guess for the orbitals in a post-CASSCF all-electron correlation SCF method?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' In this article we aim to resolve the orbital dependence of CI and post-CI dynamic correlation calculations by using molecular orbitals obtained from KS-DFT, HF, MP2 and CCSD as reference orbitals in CI calculations, which are then used to seed the anti-Hermitian contracted Schrödinger equation (ACSE) to resolve the dynamic correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Orbitals obtained from KS-DFT have previously been demonstrated to be more suitable for the construction of electronic states in configuration interaction (CI) calculations compared to HF orbitals68 and may provide a viable, cost-saving alternative to CASSCF optimization in the quest to resolve the electronic properties of strongly correlated molecules and materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' We apply the CASCI/ACSE algorithm seeded with the various molecular orbitals from the surveyed single-reference methods to three distinct chemical problems dominated by strong correlation effects, namely the dissociation of N2, the prediction of S-T gaps in a benchmark set of biradicals, and the calculation of the energetic barrier of the isomerization reaction of bicyclobutane to gauche-1,3-butadiene via both the conrotatory and disrotatory transition states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' COMPUTATIONAL DETAILS To investigate the orbital dependence of the static and dynamic parts of the total electronic correlation energy, molecular orbitals were obtained via self-consistent field (SCF) calculations using various popular single-reference, ab-initio methods, as well as CASSCF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' These methods include Hartree Fock (HF), CASSCF, variational 2-RDM CASSCF (V2RDM)69, DFT70, as well as, MP2 and CCSD, in which case the natural orbitals are investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' For the DFT calculations, functionals representing the various rungs of Jacobs-Ladder of functional development were chosen, namely simple LDA71, and the popular functionals PBE72,73, BLYP74–76, B3LYP77, M062X78, ωB97XD79, MN1580.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Orbitals from these initial SCF calculations were then used to perform a minimal active space complete active space configuration interaction (CASCI) calculation using the V2RDM method with DQGT conditions (V2-T)69,81, obtaining the multi-reference correlation energy in the initial orbitals, as well as the strongly correlated 1- and 2-electron reduced density matrices (RDMs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' We then generate the 1- and 2-electron integrals, namely 1K containing the kinetic and nuclear attraction integrals and 2V containing the electron-electron repulsion integrals, from the molecular orbitals obtained with the selected single-reference method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' These serve as the basis for the ACSE calculations, which is used to calculated the dynamic, post-CI correlation in the given molecular orbital basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The ACSE arises from the fact that fermions interact pairwise and hence the N-electron Schrödinger equation may be projected onto the space of only two-electron transitions yielding the contracted Schrödinger equation (CSE)42–44: ⟨Ψ| ˆa† i ˆa† j ˆal ˆak ˆH |Ψ⟩ = E 2Di,j k,l , (1) where ˆH is the Hamiltonian operator ˆH = ∑ ij 1Ki j ˆa† i ˆa j +∑ ijkl 2V i,j k,l ˆa† i ˆa† j ˆal ˆak , (2) and 2Di,j k,l is the 2-RDM: 2Di,j k,l = ⟨Ψ|a† i a† jalak|Ψ⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' (3) The CSE can be separated into its Hermitian and anti- Hermitian parts, and selection of only the anti-Hermitian part yields the ACSE: ⟨Ψ|[ ˆa† i ˆa† j ˆal ˆak, ˆH]|Ψ⟩ = 0, (4) where the square brackets indicate the commutator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Unlike the Hermitian part of the CSE, which depends on the 2-, 3- and 4-RDMs, the highest order terms in the ACSE, which is expanded in more detail in ref82, depend on only the 2- and 3-RDMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Furthermore, this dependence may be resolved by using an cumulant reconstruction in terms of the 2-RDM40,41: 3Di,j,k q,s,t ≈ 1Di q ∧ 1Dj s ∧ 1Dk t + 32∆i,j q,s ∧ 1Dk t , (5) 3 where 2∆i,j q,s = 2Di,j q,s − 1Di q ∧ 1Dj s , (6) and ∧ denotes the antisymmetric Grassmann wedge product, which is defined as: 1Di k ∧ 1Dj l = 1 2(1Di k 1Dj l − 1Di l 1Dj k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' (7) As the 3-RDM terms appear only in the perturbative 2V part of the Hamiltonian of the ACSE, this approximate reconstruction of 3D neglects the cumulant 3-RDM part of the expansion, setting 3∆ijk qst to be zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Using electron integrals and initial guess 1- and 2-RDMs obtained from a lower-level electronic structure calculation of choice,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' we solve the ACSE via a system of differential equations83: E(λ + ε) = ⟨Ψ(λ)|e−εS(λ) ˆHeεS(λ) |Ψ(λ)⟩ = E(λ)+ ε ⟨Ψ(λ)|[ ˆH,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' ˆS(λ)]|Ψ(λ)⟩+ O(ε2),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' (8) dE dλ = ⟨Ψ(λ)|[ ˆH,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' ˆS(λ)]|Ψ(λ)⟩ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' (9) d2Di,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='j k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='l dλ = ⟨Ψ(λ)|[ ˆa† i ˆa† j ˆal ˆak,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' ˆS(λ)]|Ψ(λ)⟩ ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' (10) where the operator ˆS is defined as: ˆS(λ) = ∑ ijkl 2Si,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='j k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='l ˆa† i ˆa† j ˆal ˆak(λ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' (11) chosen at each step of λ to minimize the energy along the gradient: 2Si,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='j k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='l(λ) = ⟨Ψ(λ)|[ ˆa† i ˆa† j ˆal ˆak,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' ˆH]|Ψ(λ)⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' (12) The ACSE is propagated in λ until either the energy reaches a minimum or the norm of the residual increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' This algorithm is presented in more detail in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' 82 and 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Seed 1- and 2-RDMs may be obtained from single- or multi-reference electronic structure calculations, minimizing the total electronic energy in the chosen orbital basis of the electron integrals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' When provided with a single-reference guess, such as one obtained from a HF calculation, the ACSE has been demonstrated to yield total electronic energies of comparable accuracy to those from CCSD(T)44,84,85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' However, ACSE calculations may also be seeded with initial RDMs from a multi-reference electronic structure calculation, such as CASSCF or CASCI, which yields accurate results even when strong correlation plays a major role38,39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' In this case, the ACSE resolves the dynamic correlation on top of the static correlation recovered by the seed RDMs within the orbital basis obtained from the multi-reference calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Results have been demonstrated to outperform commonly used CASPT286–88, and provide comparable accuracy to MC-PDFT and AF-QMC89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' All calculations were performed with the Quantum Chemistry Package90 as implemented in Maple91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' RESULTS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Nitrogen Dissociation To investigate the orbital dependence of the single- and multi-reference parts of the electronic correlation energy, we first consider the dissociation of N2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Dissociation of N2 into its two constituent nitrogen atoms provides a classic case of transition from a system dominated by single-reference correlation—N2 near the equilibrium bond length—to a system dominated by multi-reference correlation as the N-N bond is stretched and the natural occupation numbers (NON) in the [6,6] active space formed by the 6 nitrogen-p based orbitals become more and more fractional until they reach full degeneracy in the dissociated regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' For our calculations we consider eight data points of N-N bond lengths, R = [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='8, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='9, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='0976, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='2, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='4, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='6, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='5] in Å.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Calculations use the relatively small 6-31G basis92 in order to allow comparison to full CI (FCI) data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Once orbitals are obtained via a chosen single-reference method, CASCI calculations in that MO basis set with [6,6] active spaces are carried out to recover the multi-reference correlation in the nitrogen-p-based orbitals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Figure 1 shows the dissociation curves obtained from the molecular orbitals of a few select methods, with the left panel showing the CASCI results, and the right panel displaying the ACSE results, as well as, the FCI curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Furthermore, results of the go-to method for the inclusion of post-multi-reference calculations, CASPT2, are also displayed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' It is evident that the recovery of the multi-reference correlation is strongly orbital dependent, with large variations in the CASCI curves across the various methods used for orbital optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Differences arise not only in terms of the correlation energy recovered across the dissociation coordinate, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' in the form of a vertical shift of the curve, but also in its general line shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' This change in line shape is particularly evident in the cases of the HF and CCSD orbitals, which differ significantly from those obtained via DFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Furthermore, inspection of the ACSE curves shows that while near-exact in the dissociated regime, CASSCF orbitals provide a larger deviation from the FCI curve than any of the displayed single reference methods in the single-reference regime around the equilibrium N-N bond length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' To allow a more in-depth analysis of the optimality of the molecular orbitals from a chosen method in accounting for the different parts of the total electronic correlation energy, we consider the errors of the energies obtained via CASCI relative to the CASSCF results, and the energies obtained via CASCI/ACSE relative to the FCI results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Table I shows the mean absolute error (MAE) and mean signed error (MSE) versus FCI over the eight N-N bond lengths, as well as, the maximum and minimum errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The initial results from the orbital optimization calculations split as expected with the wave-function based methods providing upper bounds to the FCI energy and DFT yielding lower bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The largest positive deviation from FCI data results from HF with a MSE 4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='50 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='75 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='00 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='25 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='50 R N-N in Angstrom −109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='05 −109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='00 −108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='95 −108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='90 −108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='85 −108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='80 −108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='75 −108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='70 E in Hartree N2 Diss ciati n CASCI CASCI(HF) CASCI(M062X) CASCI(CCSD) CASSCF 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='50 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='75 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='00 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='25 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='50 R N-N in Angstrom −109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='10 −109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='05 −109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='00 −108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='95 −108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='90 −108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='85 E in Hartree N2 Dissociation ACSE ACSE(HF) ACSE(M062X) ACSE(CCSD) ACSE(CASSCF) CASPT2 FCI FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Dissociation curves of N2 for (left): [6,6] CASCI calculations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' (right): ACSE calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' All calculations were performed with a 6- 31G basis set and the ACSE was seeded with the 2-RDM from the [6,6] CASCI calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Curves were constructed from eight points along the N-N dissociation coordinate, [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='8, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='9, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='0976, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='2, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='4, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='6, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='5] in Å.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='We note that the CASCI(CCSD) results yield a lower bound to the CASSCF energy for the R = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='4 and R = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='6 points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' This is the result from minor violation of the full N-representability conditions of the V2RDM based CASCI procedure with the DQG and T2 N-presentability conditions, which yield a lower bound to the true ground-state energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' For these bond lengths CCSD natural orbitals provide an essential identical solution to CASSCF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Molecular Orbitals Method HF MP2 CCSD CASSCF CASPT2 V2-T LDA PBE BLYP B3LYP M062X wB97XD MN15 REF MAE 225.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='85 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='41 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='26 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='76 947.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='85 131.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='34 201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='31 161.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='51 157.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='01 160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='39 115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='91 MSE 225.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='85 -67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='80 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='19 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='76 947.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='85 -131.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='33 -201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='31 -161.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='51 -153.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='36 160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='39 104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='76 ∆EQM 148.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='81 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='95 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='91 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='99 919.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='27 -156.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='14 -222.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='90 -196.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='24 -202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='00 203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='58 147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='94 ∆DIS 462.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='43 -328.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='34 206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='37 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='68 1041.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='02 -31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='83 -108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='37 -33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='82 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='53 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='76 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='41 ∆EDIS 313.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='62 -327.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='38 200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='45 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='31 121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='75 124.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='32 114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='53 162.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='42 216.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='53 196.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='82 192.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='35 CAS MAE 94.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='43 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='76 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='18 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='33 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='08 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='00 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='57 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='13 TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Results for the various reference calculations used for the orbital optimization, as well as [6,6] CASCI, and CASCI/ACSE calcula- tions for the dissociation of N2, in kcal/mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' All calculations were performed with the 6-31G basis set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Errors are relative to the FCI energies and MSE and MAE are calculated over the eight distinct points along the dissociation coordinate;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' ∆eqm and ∆dis are the errors at R = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='0976 and R = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='5, respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' and ∆EDIS is the error in the dissociation energy, EDIS = ER=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='0976 −ER=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='5, with respect to FCI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' of 225.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='85 kcal/mol, while the largest negative deviation with DFT is obtained with the BLYP functional at an MSE of 201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='31 kcal/mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' CCSD yields the best results with an MSE of 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='19 kcal/mol, outperforming MP2, which as expected results in unphysical behavior in the dissociated regime and hence large negative deviations from FCI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Use of simple LDA gives rise to unphysical electronic energies with a MAE of 947.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='85 kcal/mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' If we consider the contribution of the multi-reference cor- relation to the total electronic energy, CASSCF calculations using the minimal [6,6] active space give a MSE of 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='49 kcal/mol vs FCI, and on average the correlation recovered in the [6,6] active space accounts for 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='4% of the total corre- lation energy in the 6-31G basis set across the 8 dissociation points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The CASSCF calculation provides the benchmark result to assess the ability of a chosen method’s orbitals to account for multi-reference correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' As a CASSCF calcu- lation uses orbital rotations to minimize the total energy as a functional of the CI energy in the active space, it yields the variational minimum to the multi-reference correlation that may be recovered in the chosen [6,6] active space and 6-31G basis set, and all CI calculations performed on different sets of orbitals yield upper bounds to this energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Of the surveyed single-reference methods, the NOs from a CCSD calculation provide the orbitals that best account for static correlation across the N2 dissociation space and yield the lowest CASCI energy, with a MAE of 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='82 kcal/mol, followed by MP2, 5 which even though giving rise to nonphysically low energies in the dissociated regime gives natural molecular orbitals that recover a correct CASCI picture with a MAE of 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='73 kcal/mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' DFT yields better multi-reference-ready orbitals than HF, with variation across the different surveyed DFT functionals being relatively small, ranging from the most correlated orbitals at PBE, MAE of 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='99 kcal/mol, to MN15 at MAE of 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='37 kcal/mol, recovering on average roughly 50% of the total correlation energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Application of the ACSE following the converged CASCI calculation in the chosen molecular orbital basis resolves dynamic correlation with accuracy comparable to CCSD with perturbative triple excitations [CCSD(T)], in addition to the multi-reference correlation recovered by the CI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Across all surveyed orbitals the CASCI/ACSE recovers an average of between 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='2% and 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='7% of the total corre- lation energy, displaying relatively minor dependence on the chosen molecular orbital basis compared to CI and single-reference calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Surprisingly, while providing the best multi-reference orbitals, CASSCF does not provide the most optimal orbitals to resolve the total correlation energy, recovering on average 98% of the total correlation energy with a MAE of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='61 kcal/mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' As such, CASSCF orbitals are outperformed by orbitals obtained with HF, MP2, CCSD, M062X, and wB97XD calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Simple HF provides the most optimal orbitals to account for both strong and post-CI dynamic correlation, recovering an average of 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='7% of the FCI energy for MAE of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='00 kcal/mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Results from the different DFT functionals vary from an MAE of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='93 kcal/mol in M06-2X to 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='82 kcal/mol in BLYP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Even in the case of the worst performing DFT functional, BLYP, the MAE increases by only 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='21 kcal/mol over CASSCF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The fact that MSEs are smaller than the MAEs result from the fact that the ACSE may yield a slightly lower bound to the FCI energy in the dissociated regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' ACSE calculations significantly outperform CASPT2, which only recovers an average of 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='0% of the total correlation energy, for MAE of 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='76 kcal/mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Lastly, after considering recovery of the full FCI dissocia- tion curve, we also consider the errors in the reproduction of the FCI dissociation energy, ∆EDIS = EDIS,method − EDIS,FCI, where EDIS = ER=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='0976 −ER=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' This provides a benchmark for orbitals obtained with a certain method to accurately recover the total energy in the dissociated multi-reference regime and the single-reference regime around the equi- librium bond distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The observed trends follow those discussed above with large positive errors in the DFT, HF and CCSD reference calculations, which significantly overestimate the bonding energy as they break down as N2 is dissociated, while MP2 diverges to large negative energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Considering the CASCI energies, all calculation underesti- mate EDIS, as correlation is more accurately captured at long bond distances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Now, accounting for mostly static correlation with [6,6] CASCI calculations, CASSCF, and the V2RDM implementation of CASSCF yields the optimal orbitals, followed by MP2 NOs, then HF and finally the various DFT functionals which display only minor variations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' CCSD presents an outlier as the CASCI calculation with CCSD NOs at equilibrium suffered from convergence issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Inspection of the individual errors at the equilibrium and dissociated geometry, ∆EQM and ∆DIS, respectively, reveals the HF result to arise from a favorable cancellation of error, with the energy lying high above the CASSCF and FCI references.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Additionally, as indicated by ∆EQM and ∆DIS, the single reference orbitals tend to yield significantly lower errors in the multi-reference, dissociated regime than the dynamically correlated regime around the equilibrium bond length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Finally, accounting for all-electron correlation with the CASCI/ACSE method, yields ∆EDISs within 10 kcal/mol of the FCI result for all surveyed orbitals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Errors range in magnitude from a minimum of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='00 kcal/mol with MOs from the M062X DFT functional and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='01 kcal/mol with HF orbitals to 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='76 kcal/mol with LDA DFT MOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Only orbitals from HF and MP2 result in an overestimation of EDIS, while all others yield a negative deviation from FCI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Interestingly, CASSCF does not yield the optimal orbitals to resolve the electronic energy accurately in both the equilibrium and dissociated regimes, with deviations from FCI of -4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='66 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='43 kcal/mol for its wavefunction and V2RDM implemen- tations, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Indeed, separate consideration of the errors at equilibrium and dissociation bond lengths reveals a relatively large ∆eqm of 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='52 kcal/mol for the CASSCF orbitals, compared to only 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='84 kcal/mol, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='12 kcal/mol and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='45 kcal/mol for those obtained with single-reference methods HF, MP2 and CCSD, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Interestingly, for the DFT MOs, ∆eqm is larger that obtained with CASSCF MOs for all functionals but M06-2X, with generally lower errors in the multi-reference, dissociation regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The result is that CASSCF/ACSE all-electron correlation calculations with initial CASSCF optimization of the orbitals for the dissociation energy of N2, where energy differences between a strongly correlated and a dynamically correlated solution are computed, are outperformed by simple CASCI/ACSE calculations using orbitals obtained from HF, MP2, CCSD, as well as the DFT functionals B3LYP, M062X, and wB97XD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Singlet Triplet Gaps of Main Group Biradicaloids Biradicals play important roles in a wide range of chemical processes as transition states and intermediates, formed during the breaking and forming of chemical bonds, as well as in the development of new single-molecule magnets and materials for spintronics or molecular qubits93–95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Their accurate theoretical description continues to pose a challenge to current developments in electronic structure theory due to the multi-reference character of their open-shell singlet states, requiring the use of methods that account for both static and dynamic correlation to resolve their electronic properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' In this section we investigate the orbital dependence of the singlet-triplet (S-T) gaps for a benchmark set of small main group biradicals OH+, NH, NF, O2, NH+ 2 , CH2, PH+ 2 , and 6 SiH2 as calculated with single-reference, CI and post-CI ACSE methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Singlet-triplet gaps of biradicaloids are of particular value as they relate to experimentally relevant properties such as the exchange coupling constant J or their properties in photonics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' We perform calculations on the singlet and triplet states with the cc-pVTZ basis set101,102, using a minimal [4,4] active space chosen around the HOMO and LUMO for the CI calculations, allowing for the inclusion of non-trivial correlation in the triplet states and assessing the suitability of the single-reference orbital to yield a suitable CAS guess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The ACSE calculations use a spin-averaged implementation, which has recently been demonstrated to yield highly accurate singlet-triplet gaps for this benchmarking set with converged CASSCF wave functions89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The data are presented in Table II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Errors are calculated with respect to the experimental reference values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' As expected, none of the single-reference methods yield accurate results, failing to capture the strong correlation of the biradical singlets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' MP2 yields extremely inaccurate results with a MAE of 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='7 kcal/mol, while the rest of the surveyed methods range from 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='5 kcal/mol in CCSD (use of perturbative triples correction reduces this to 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='6 kcal/mol) to 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='4 kcal/mol in LDA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' HF also yields a large MAE of 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='3 kcal/mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Across the surveyed DFT functionals we observe a quite significant variation in their ability to calculate the S-T gaps, with MN15 giving the lowest MAE of 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='7 kcal/mol and LDA and PBE giving the largest MAEs of 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='4 kcal/mol and 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='5 kcal/mol, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' As with the dissociation of N2, of the surveyed methods CCSD natural orbitals yield the most optimal basis to account for multi-reference character in the CASCI calculations, with a MAE of 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='39 kcal/mol, followed by the various DFT functionals, where variation in the CASCI results is less pronounced than in the single-reference calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Furthermore, there is no correlation between the accuracy of the CASCI calculation and the reference DFT calculation with orbitals from the previously best performing MN15 now yielding a MAE of 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='28 kcal/mol while the second-worst performing PBE returns the best CASCI results with a MAE of 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='75 kcal/mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Apart from the unreliable MP2 calculations, HF orbitals give the largest MAE of 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='6 kcal/mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' No orbital basis from any method comes close in accuracy to the CASSCF calculation, which yields a MAE of 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='38 kcal/mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' While the MSE is close to zero (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='56 kcal/mol) in CASSCF, it is of significant, positive magnitude in DFT, ranging from 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='96 kcal/mol in MN15 to 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='01 kcal/mol in M06-2X and HF, while it is negative in MP2 and CCSD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' As an additional measure to probe the bi-radical character in the solutions, we introduce the average distance of the 1-RDM of the CASCI calculation from a closed-shell single-reference 1-RDM, defined as ¯R = ∑ij ||λHF,i − λi|j/N, where i runs over all orbitals of the system, N is the number of species in the set, j runs over all its members, λi denotes the ith natural occupation number and λHF,i is 2 if the orbital is occupied and 0 if the orbital is virtual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The inclusion of post-CI dynamic correlation with the spin-averaged ACSE provides significant improvement over single-reference and CASCI results in all cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' While the [4,4] CASSCF optimization does give the best agreement with experiment (MAE of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='16 kcal/mol), the advantage over the various other orbitals is relatively minor, with MP2 and HF orbitals yielding the largest deviations with MAEs of 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='36 kcal/mol and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='44 kcal/mol, respectively, and CCSD again yielding the closest agreement with an MAE within 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='5 kcal/mol of CASSCF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The CASCI/ACSE calculations per- formed with DFT orbitals provide MAEs within 1 kcal/mol of the CASSCF orbitals for all functionals but PBE, which has the largest error at an MAE of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='22 kcal/mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Across the surveyed functionals, variation again is minor, meaning while S-T gaps predicted by the individual functionals differ based on empirical fitting, the underlying molecular orbitals obtained in the SCF procedure remain relatively unchanged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Analogous to the N2 dissociation, the ωB97X-D functional again performs well and provides the molecular orbitals best suited to account for the multi-reference and dynamic correlation in the biradicaloid set, yielding a MAE of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='99 kcal/mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' In the CASCI/ACSE case the sign of the MSE obtained for the various DFT orbitals agrees with CASSCF, and only HF and MP2 orbitals lead to a positive MSE, while CCSD yields a MSE of small negative magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Again considering ¯R as a measure for the recovered total correlation, HF and MP2 which yield the largest MAEs also result in the lowest magnitude of ¯RS, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='533 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='432, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' However, surprisingly, ¯RS,CCSD = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='835 is significantly lower than ¯RS,CASSCF = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='102, while DFT orbitals, yield ¯RS values between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='968 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='116, with there being no correlation between ¯RS and MAE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' To the contrary, PBE yields greater correlation in the NOs than CASSCF while resulting in the largest MAE of all surveyed functionals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' To resolve the origin of the minor variations across sur- veyed methods, we plot the deviations from experimen- tal reference values for the individually studied species for CASSCF, HF, CCSD, and M06-2X in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Inspection of the individual errors in CASCI shows particularly large errors in the calculation of O2, which has previously been demon- strated to provide a challenge to various electronic struc- ture methods, with AFQMC and ACSE calculations requiring CASSCF wave functions with active spaces as large as [10,15] and [14,14] to yield sub 2 kcal/mol accuracy for the calcula- tion of its S-T gap89,103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The [4,4] active space successfully resolves its diradical character;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' however, it significantly over- stabilizes the singlet state leading to a large negative deviation from experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' We observe a particularly strong stabiliza- tion of the singlet O2 state in the CASCI with CCSD molecu- lar orbitals, while the remaining orbitals yield results that are in good agreement with CASSCF, leading to the more nega- tive MSE in the CCSD NO basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The positive MSE in DFT and HF arises from the fact that, while there is agreement with CASSCF in the case of O2, the orbitals in all other species lead a to an overestimation of the singlet triplet gap via a relatively less pronounced stabilization of the singlet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Use of the ACSE to include post-CI correlation leads to a significant reduction 7 Molecular Orbitals Method HF MP2 CCSD V2-T LDA PBE BLYP B3LYP M062X wB97XD MN15 REF MAE 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='3 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='7 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='5 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='4 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='5 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='12 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='19 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='62 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='01 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='7 MSE 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='3 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='7 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='5 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='4 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='5 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='7 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='19 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='62 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='96 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='63 ∆max 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='1 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='5 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='1 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='7 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='7 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='7 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='1 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='71 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='82 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='9 ∆min 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='6 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='12 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='4 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='77 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='10 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='08 CAS MAE 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='48 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='45 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='39 6.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='183 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='183 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='172 TABLE II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Errors for the S-T gaps of the set of eight biradicals, OH+, NH, NF, O2, NH+ 2 , CH2, PH+ 2 , and SiH2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' All calculations were carried out using the cc-pVTZ basis set, and CASCI and ACSE calculations use a [4,4] active space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' MAE and MSE, and maximum and minimum absolute errors, ∆max and ∆min, are calculated relative to experimental reference values obtained from references96–100 and given in kcal/mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' ¯RS and ¯RT denote the average distance of the NON from the HF solution for the singlet and triplet states, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' CH2 NH + 2 SiH2 PH + 2 NH NF O2 OH + −15 −10 −5 0 5 ΔΔEΔS − T) i kcal/mol CASSCF [4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='4] S-T GAP ERRORS CAS ACSE CH2 NH + 2 SiH2 PH + 2 NH NF O2 OH + −20 −10 0 10 20 30 ΔΔEΔS − T) i kcal/mol HF [4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='4] S-T GAP ERRORS HF CAS ACSE CH2 NH + 2 SiH2 PH + 2 NH NF O2 OH + −40 −30 −20 −10 0 10 ΔΔEΔS − T) in kcal/ ol CCSD [4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='4] S-T GAP ERRORS CCSD CAS ACSE CH2 NH + 2 SiH2 PH + 2 NH NF O2 OH + −25 −20 −15 −10 −5 0 5 10 15 ΔΔEΔS − T) in cal/mol M06-2X [4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='4] S-T GAP ERRORS M06-2X CAS ACSE FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Errors for the S-T gaps of the biradical set resolved for its individual members for four select methods used for the orbital optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Bars indicate the errors of the S-T gap with respect to the experimental reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Orange bars indicate errors of the single-reference calculation, blue bars the CASCI results based on the single-reference orbitals, and yellow bars the CASCI/ACSE result in the respective single-reference orbital basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Top row: CASSCF (left), CCSD (right);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' bottom row: HF (left), M06-2X (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' All data were obtained with a cc-pVTZ basis set and [4,4] active spaces for the CASCI and ACSE calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' 8 Molecular Orbitals M06-L M06 M06-2X M06-HF Method % HF 0 27 54 100 REF MAE 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='65 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='92 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='62 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='25 MSE 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='65 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='73 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='62 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='22 ∆max 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='62 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='76 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='71 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='34 ∆min 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='19 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='75 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='77 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='13 CAS MAE 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='65 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='77 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='85 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='41 MSE 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='40 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='10 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='01 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='55 ∆max 25.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='37 ¯RS 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='884 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='838 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='720 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='396 ¯RT 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='014 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='011 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='009 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='005 ACSE MAE 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='92 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='26 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='07 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='55 MSE 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='52 2.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='662 ¯RT 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='190 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='179 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='183 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='177 TABLE III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Errors for the biradical set S-T gaps resolved with or- bitals from the members of the MN06 suite of functionals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' All cal- culations were carried out using the cc-pVTZ basis set, and CASCI and ACSE calculations use a [4,4] active space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' MAE and MSE, and maximum and minimum absolute errors, ∆max and ∆min, are calculated relative to experimental reference values obtained from references96–100 and given in kcal/mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' ¯RS and ¯RT denote the av- erage distance of the NON from the HF solution for the singlet and triplet states, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' in the variation of the errors across the different species and methods, with only HF orbitals showing deviations in signifi- cant magnitude from the CASSCF/ACSE results, particularly in the cases of NF and OH+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Lastly, to provide insight into the effect of exact HF exchange in a chosen DFT functional on the molecular orbitals obtained from the SCF procedure, we compare the results from four M06 functionals with varying degrees of HF exchange: M06-L (0%), M06 (27%), M06-2X (54%), and M06-HF (100%), shown in Table III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Interestingly, the MAE and MSE of the DFT S-T gaps decreases as the HF exchange contribution to the functional increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' While this is contrary to results from large-scale functional benchmarks, which suggest functionals with larger HF exchange contributions yield worse performance on multi-reference interactions104, the expected trend is observed in the CASCI errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' These consistently increase with the HF exchange fraction, sug- gesting the inclusion of more exact HF exchange leads to worse multi-reference orbitals in the KS-SCF optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Inclusion of post-CI dynamic correlation again results in reduced variation across the functionals, however, showing a trend of increasing MAE with increasing HF exchange in the functional used for the orbital optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' In fact, the molecular orbitals obtained from a SCF optimization with the 0% HF exchange containing M06L functional yields the lowest MAE, as well as, maximum and minimum errors across the data set of all surveyed functionals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Additionally, the decrease in the ability of the functional’s orbitals to account for multi-reference character of the singlet state is clearly reflected in the trend observed in the ¯RS values with a ΔEǂ dis ΔEǂ con FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Reaction coordinate of the isomerization reaction of bicy- clobutane to 1,3-butadiene with the con- and dis-rotatory transition states shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The conversion to the 1,3-butadiene is not considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' steady decrease from a maximum of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='122 in M06-L to just 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='662 in M06-HF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' While the results obtained from the [4,4] spin-averaged CASSCF/ACSE calculation are comparable to those from CASSCF/MC-PDFT, which yields a MAE of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='5 kcal/mol105, the computationally less expensive CASCI/ACSE calcula- tions based on a DFT orbital optimization yield results in line with various methods reported across the literature, such as (V)FS-PBE (MAE = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='3 kcal/mol)106, pp-B3LYP (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='8 kcal/mol)107, W2X (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='7 kcal/mol)105, or tPBE/MC-PDFT (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='3 kcal/mol)105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Transition States of the Bicyclobutane Isomerization Reaction to gauche-1,3-Butadiene As a final example, we consider the orbital dependence in the use of CI and post-CI methods to model a simple chemical reaction, calculating the energy barrier, ∆H‡, to the isomerization reaction of bicyclobutane to gauche-1,3- butadiene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' This isomerization process may proceed via two different transition states arising from conrotatory (CON) and disrotatory (DIS) pathways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The reaction coordinate diagram displaying these is shown in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Optimized geometries and zero-point and vibrational corrections to the electronic energy were obtained from reference108, using the MCSCF/6-31G*109 level of theory, and amounting to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='0911, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='0862, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='0844 hartrees for bicyclobutane, and the CON and DIS transition states, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Calculations were performed with the previously surveyed methods, CAS orbitals were selected around the HOMO and LUMO, and the results are compared to those obtained from [14,14] CASSCF/ACSE calculations, as well as previously reported ACSE108, CC(P;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='Q)110, and DMC111 data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The barrier for the CON transition pathway has been experimentally determined to be 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='6 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='5 kcal/mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The data are shown in Table IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' 9 CASSCF Molecular Orbitals Pathway [4,4] [14,14] HF MP2 CCSD V2-T LDA PBE BLYP B3LYP M062X wB97XD MN15 CON ∆H‡ 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='59 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='60 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='53 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='92 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='25 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='75 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='50 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='42 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='30 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='89 ∆H‡ CAS 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='68 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='70 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='86 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='49 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='16 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='85 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='92 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='23 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='51 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='07 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='25 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='91 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='80 ∆H‡ ACSE 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='56 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='78 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='56 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='71 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='43 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='74 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='54 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='14 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='49 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='38 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='63 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='01 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='95 λHONO,CAS 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='701 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='734 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='816 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='846 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='755 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='701 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='782 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='776 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='770 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='776 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='794 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='787 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='785 λLUNO,CAS 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='299 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='271 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='187 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='155 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='247 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='299 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='220 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='224 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='230 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='225 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='209 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='216 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='218 λHONO,ACSE 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='669 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='703 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='763 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='800 1.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='267 DIS ∆H‡ 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='38 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='98 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='51 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='45 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='46 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='18 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='69 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='78 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='36 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='95 ∆H‡ CAS 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='49 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='25 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='30 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='91 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='07 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='69 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='63 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='21 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='10 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='75 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='62 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='03 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='31 ∆H‡ ACSE 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='11 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='79 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='93 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='59 54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='32 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='33 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='35 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='76 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='43 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='53 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='15 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='53 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='72 λHONO,CAS 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='364 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='413 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='462 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='612 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='438 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='364 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='434 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='428 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='418 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='420 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='433 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='429 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='428 λLUNO,CAS 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='636 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='589 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='547 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='398 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='566 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='636 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='573 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='580 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='590 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='588 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='576 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='580 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='581 λHONO,ACSE 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='345 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='393 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='423 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='574 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='416 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='345 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='399 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='396 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='387 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='390 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='400 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='398 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='395 λLUNO,ACSE 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='641 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='594 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='567 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='419 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='574 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='641 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='602 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='605 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='612 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='608 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='598 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='601 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='603 TABLE IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Data for the con- and disrotatory pathways of the isomerization reaction of bicyclobutane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Calculations were carried out with the 6-31G* basis set and CASCI and ACSE calculations utilize a [4,4] active space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Geometries and free energy corrections calculated at the MCSCF/6-31G* level of theory and were obtained from reference108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' ∆H‡ denotes the transition state barrier in kcal/mol including zero point and vibrational corrections amount to -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='087 kcal/mol and -4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='221 kcal/mol for the CON and DIS pathways, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' λHONO and λLUNO denote the occupations of the highest and lowest natural orbitals (HONO and LUNO), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' First considering the conrotatory pathway, variation across the barriers predicted by the single reference methods is significant, ranging from ∆H‡ = 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='75 kcal/mol with BYLP to ∆H‡ = 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='59 kcal/mol with HF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Within the DFT realm, the obtained results are very sensitive to the choice of functional and lack consistency, with BLYP underestimating ∆H‡ while the remaining functionals overestimate it and variations far exceeding chemical accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Nonetheless, the LDA and PBE functionals predict ∆H‡ values that lie within the experimental bounds of error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' It is noteworthy that the MN15 functional which is fitted to perform well in multi-reference problems, gives a large overestimation of ∆H‡ with the predicted 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='89 kcal/mol being far outside the realms of chemical accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Using a [14,14] active space CASSCF yields ∆H‡ = 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='70 kcal/mol, with highest occupied natural orbital (HONO) and lowest unoccupied natural orbital (LUNO) occupation numbers of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='734 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='271, respectively, making the CON transition state the less correlated one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The static correlation from the CASSCF calculation overstabilizes the TS compared to bicyclobutane, resulting in underestimation of ∆H‡,CAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' For our CASCI calculations we use a smaller [4,4] active space (∆H‡ CAS = 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='68), which reduces the magnitude of this underestimation and is sufficient to resolve the biradical character of the TS, yielding HONO and LUNO occupation numbers of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='701 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='299, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' For the CASCI calculations, CCSD again provides the orbitals most optimal to resolve the multireference correlation of the methods surveyed, underestimating the CON barrier, and yielding the smallest deviation from the [14,14] CASSCF result and with ∆H‡ = 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='16 kcal/mol—a lower barrier than both [4,4] and [14,14] CASSCF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' All other orbitals provide a CASCI energy with a positive deviation from the CASSCF ∆H‡, with MP2 NOs yielding the least correlated solution but the smallest error, followed by HF and finally the various DFT functionals, which yield large ∆H‡s but more correlated solutions than MP2 and HF, showing HONO and LUNO occupations numbers comparable to [4,4] CASSCF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Using the ACSE to resolve the full correlation energy, both [4,4] and [14,14] CASSCF resolve the CON barrier to near-exact accuracy providing near-identical results of 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='74 kcal/mol and 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='78 kcal/mol, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' MP2 NOs provides both the least correlated solution, as well as the largest deviation from the experimental range of ∆H‡, lying 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='61 kcal/mol above this interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' It is closely followed in both error and correlation by HF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Contrary to the results from the S-T gaps and N2 dissociation, CCSD NOs are now outperformed by the majority of DFT functionals, with only M06-2X, and ωB97XD deviating by more than CCSD’s 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='33 kcal/mol from the experimental confidence interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The LDA, PBE, BLYP and MN15 orbitals all yield ∆H‡ values obtained by the CASCI/ACSE algorithm that lie within the experimental error bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The disrotatory TS provides for the more correlated and higher energy isomerization pathway, with [14,14] CASSCF/ACSE yielding a barrier of ∆H‡ = 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='79 kcal/mol and LUNO and LUNO occupation numbers of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='393 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='594, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' There is no experimental reference data for the DIS pathway, but DMC calculations have yielded a barrier of 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='6 kcal/mol111, while CR-CC(2,3) predicts a barrier height of 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='5 kcal/mol110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Across the various single- reference methods and the CASCI calculations, the trends remain unchanged from the CON pathway, however, with increased errors in the single-reference calculations as the degree of multi-reference correlation in the TS is increased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' All CASCI/ACSE calculations with DFT orbitals fall within the ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='5 kcal/mol range of the CASSCF[14,14]/ACSE reference, with MN15 and PBE yielding the closest, and near-identical, results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' In this more strongly correlated TS, 10 Molecular Orbitals M06-L M06 M06-2X M06-HF Pathway % HF 0 27 54 100 CON ∆H‡ 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='72 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='46 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='42 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='46 ∆H‡ CAS 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='87 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='16 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='25 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='66 ∆H‡ ACSE 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='14 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='03 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='63 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='15 λHONO,CAS 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='785 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='787 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='794 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='806 λLUNO,CAS 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='215 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='214 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='209 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='198 λHONO,ACSE 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='732 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='735 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='741 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='755 λLUNO,ACSE 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='269 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='264 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='256 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='240 DIS ∆H‡ 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='43 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='69 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='78 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='41 ∆H‡ CAS 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='29 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='60 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='62 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='26 ∆H‡ ACSE 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='76 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='57 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='15 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='87 λHONO,CAS 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='426 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='427 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='433 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='449 λLUNO,CAS 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='582 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='582 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='576 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='560 λHONO,ACSE 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='395 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='395 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='400 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='413 λLUNO,ACSE 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='606 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='604 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='598 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='580 TABLE V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Data for the con- and disrotatory pathways of the bicy- lobutane isomerization resolved for the members of the MN06 suite of functionals with their varying degrees of exact HF-exchange.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Cal- culations were carried out with the 6-31G* basis set and CASCI and ACSE calculations utilize a [4,4] active space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Geometries and free energy corrections calculated at the MCSCF/6-31G* level of the- ory and were obtained from reference108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' ∆H‡ denotes the tran- sition state barrier in kcal/mol including zero point and vibrational corrections amount to -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='087 kcal/mol and -4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='221 kcal/mol for the CON and DIS pathways, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' λHONO and λLUNO denote the occupations of the highest and lowest natural orbitals (HONO and LUNO), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' CCSD NOs yield a larger error of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='53 kcal/mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' As in the CON TS, DFT orbitals yields more fractional NON than those from HF, MP2, and comparable values to CCSD NOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Lastly, we again look at the M06 suite of functionals to resolve the influence of HF exchange in the DFT functional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' While there is no obvious trend in the barrier height predicted by CASCI based on the various orbitals, ∆H‡ predicted by the functional and the CASCI/ACSE calculation, as well as, the NONs follow the expected trend with a lower fraction of HF exchange better accounting for the multi-reference correlation in the studied transition states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Consequently, errors in ∆H‡ and the value of the NON increase across the series from M06-L to M06-HF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The M06-L functional MOs provide a barrier height within the experimental range of error for the CON pathway, yielding identical results to PBE and an only slightly larger error than LDA, while in the DIS pathway M06-L orbitals yield near-exact agreement with [14,14] in both NON and ∆H‡, providing the best orbitals from any method surveyed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' DISCUSSION & CONCLUSIONS We have employed CASCI calculations in combination with the ACSE to resolve the orbital dependence on the dynamic and multi-reference parts of the total electronic correlation energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Considering problems dominated by multi-reference correlation, we show that CASCI calculations display significant dependence on the chosen molecular orbital basis, with coupled cluster natural orbitals yielding the most optimal orbitals to account for multi-reference correlation of the single-reference methods surveyed, and HF yielding the least suitable orbitals, while DFT functionals lie between the two methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Nonetheless, for the accurate prediction of multi-reference dependent properties through the means of CI calculations only, CASSCF orbital opti- mization is prudent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Use of a post-CI method to account for dynamic correlation, in this case the ACSE, reduces the orbital dependence of the accuracy in the predicted properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Using the ACSE to resolve post-CI dynamic correlation, we survey orbitals from wave-function based single-reference, as well as, various popular DFT functionals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' While HF orbitals yield good results for the N2 dissociation, they tend to fail to capture accurately multi-reference character and deliver lackluster results in the CASCI/ACSE scheme for the prediction of biradical S-T gaps and TS barriers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' MP2 is plagued by inconsistencies and convergence issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Natural orbitals obtained from CCSD calculations, however, allow CASCI/ACSE to resolve both dynamic and strong correlation effects in the three case studies accurately, out- performing CASSCF orbitals in the N2 dissociation, where molecular geometries not dominated by static correlation are considered, most closely mirroring the FCI dissociation curve, and yielding biradical S-T gaps and bicyclobutane isomerization barriers with accuracies close to those achieved with CASSCF orbitals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' The various DFT functionals, which are known to yield widely varying results for different systems and properties based on their parametric fitting, produce orbitals that com- pared to the results predicted by the functionals themselves, such as S-T gaps or dissociation energies, show much greater consistency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Of the tested functionals, the M06 suite and the ωB97XD functionals provide the best suited orbitals for the CASCI/ACSE calculations, yielding only marginally worse performance than CASSCF and CCSD orbitals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Furthermore, resolving the S-T gaps and bicyclobutane isomerization barriers obtained with the M06 suite functionals shows the most optimal orbitals to account for both multi-reference and dynamic correlation are obtained with the lowest HF- exchange fraction, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' the M06-L functional, which yields the best orbitals for the treatment of multi-reference problems of any tested functional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' As DFT presents the most ubiq- uitous electronic structure method across many disciplines in chemistry, physics and materials science, implemented in any commonly used software package, offering inexpensive computational scaling compared to CASSCF or CC methods, it provides a good compromise between computational costs, ease-of-use, and accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Especially, considering the fact that DFT molecular orbitals are already available in most cases through prior geometry optimizations or frequency calculations, they provide a viable option for further ab-initio calculations aimed at resolving electron correlation in many 11 applications, significantly reducing further computational expense while retaining viable accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' This work provides valuable insight into the orbital dependence in the ability of CASCI and post-CI methods to resolve multi-reference and dynamic correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' We demonstrate that contrary to popular implementations that rely on CASSCF orbital optimizations for the resolution of the total correlation energy, CASSCF may not always provide the optimal molecular orbital basis set to account for the com- bination of static and dynamic contributions to the electronic energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Furthermore, improved computational scaling may be obtained through the use of widely available single-reference methods for the optimization of the molecular orbitals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Addi- tionally, if a post-CI method to resolve all-electron correlation were to be implemented in a SCF fashion, undergoing further orbital optimization after the initial CAS seed calculation, performance of an initial CASSCF calculation may be of limited value as compared to a seed with orbitals obtained from the surveyed single-reference methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' Throughout the studied systems we show that the CASCI/ACSE method is a valuable tool in the accurate resolution of the properties of a multi-reference system, and may be used in combination with any single-reference calculation, in particular with DFT, not requiring further CASSCF calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' ACKNOWLEDGMENTS D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content=' gratefully acknowledges the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfxfmy/content/2301.00668v1.pdf'} +page_content='S.' metadata={'source': 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b/i9E3T4oBgHgl3EQfJAlP/content/tmp_files/2301.04339v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..781c041b9256898f9667b6ac662860696bcf45e2 --- /dev/null +++ b/i9E3T4oBgHgl3EQfJAlP/content/tmp_files/2301.04339v1.pdf.txt @@ -0,0 +1,1098 @@ +Topics in Contextualised Attention Embeddings +Mozhgan Talebpour1, Alba Garcia Seco de Herrera1, Shoaib Jameel2 +1 Computer Science and Electronic Engineering, University of Essex, United +Kingdom. +2 Electronics and Computer Science, University of Southampton, United Kingdom. +{mozhgan.talebpour, alba.garcia}@essex.ac.uk, +M.S.Jameel@southampton.ac.uk +Abstract. Contextualised word vectors obtained via pre-trained lan- +guage models encode a variety of knowledge that has already been ex- +ploited in applications. Complementary to these language models are +probabilistic topic models that learn thematic patterns from the text. +Recent work has demonstrated that conducting clustering on the word- +level contextual representations from a language model emulates word +clusters that are discovered in latent topics of words from Latent Dirichlet +Allocation. The important question is how such topical word clusters are +automatically formed, through clustering, in the language model when +it has not been explicitly designed to model latent topics. To address +this question, we design different probe experiments. Using BERT and +DistilBERT, we find that the attention framework plays a key role in +modelling such word topic clusters. We strongly believe that our work +paves way for further research into the relationships between probabilis- +tic topic models and pre-trained language models. +1 +Introduction +Pre-trained language models (PLMs), e.g., ELMo [35], Generative Pre-trained +Transformer (GPT) [37], PaLM [11], and Bidirectional Encoder Representa- +tions from Transformers (BERT) [14] are pre-trained using large amounts of +text data [24], for instance, BERT has been pre-trained on the BookCorpus +and Wikipedia collections. During the domain-independent pre-training process, +these models encode a variety of latent information, for instance, semantic and +syntactic properties [57], as a result, these models can make reliable predictions +even under a zero-shot setting in different applications [20,41,43]. While the +pre-training process is computationally [51] and financially expensive [47], these +models can be cheaply fine-tuned to reliably handle different downstream tasks +such as document classification [1] and information retrieval [61,50], a process +that is commonly referred to as transfer learning [32]. For instance, BERT has +shown strong performance in natural language understanding [63], text summari- +sation [25], document classification [10] and other Natural Language Processing +(NLP) downstream applications [43]. +Another class of models that continues to dominate the text mining landscape +are probabilistic topic models (PTMs) [8,7]. These models are probabilistic ap- +proaches toward determining dominant topics in a text corpus in a completely +arXiv:2301.04339v1 [cs.CL] 11 Jan 2023 + +2 +Mozhgan Talebpour, Alba Garcia Seco de Herrera, Shoaib Jameel +unsupervised way. A latent topic is described as a probability distribution of +words. Latent Dirichlet Allocation (LDA) [8] is a popular model for discovering +topics. In LDA, the model learns to represent a document as a mixture of latent +topics and each topic is represented by a mixture of words. When LDA is viewed +as a matrix factorisation model, given a term document co-occurrence matrix as +input and the number of topics, the model factorises the matrix into two low- +dimensional matrices that are word topic and document topic representations. +The word topic matrix captures the importance of words in the vocabulary of +each topic whereas the document topic matrix captures the topic distribution in +every document. While LDA has been a popular model that is based on Bayesian +learning, a class of linear algebra-based model called Non-negative Matrix Fac- +torisation (NMF) [56,26] has become equally popular to learn topics [33]. +In [43], the authors dissected BERT to understand the property of every +layer. They find that lower layers, i.e., layer 1 or 2 capture the linear word order, +while the BERT’s middle layers learn the syntactic information reliably and +the higher layers capture the contextualised information. The authors in [49] +and [45] showed that BERT word embedding clustering via simple algorithms +such as k-means results in word clusters as if they are learned by a topic model. +The authors conducted a series of qualitative probe experiments to find out that +most of the word clusters of BERT resemble what is often discovered by the +LDA model. While these studies make relevant observations, what is not well +studied is how the topic information is encoded at the time of pre-training given +that BERT or any other contextual language model is not designed to model +topical word clusters. In this work, by conducting different probe experiments, +we answer how BERT and DistilBERT [44] can capture clusters of words that +resemble what is learnt by topic models. We find that it is the attention [4,9] +mechanism in these language models that plays a key role in modelling what +resembles word topics as discovered by the topic model. +2 +Related work +The main goal of PLMs [31] is to simulate human language understanding by +finding the most probable words sequence and patterns. The traditional language +model used probability distribution to predict the next word, but they were not +very scalable such as those based on unigram, bigram or trigram language mod- +els [36]. The recently developed PLMs are trained using large amounts of text +data where some of them exploit a strategy called masked language modelling +in a self-supervised way. Once these models have been trained, they have been +applied in a wide variety of applications. The key advantage of PLMs is that +they can be applied on different downstream tasks [15] reliably. +BERT has been developed with stacked transformers [52] layers where each +layer captures different properties in text data, e.g., some layers are ideal to +capture semantic information [53,48]. Transformers consist of encoder-decoder +structures. The encoder transforms the sequence of input tokens into a high-level +dimension. Decoder predicts input data from encoder [18]. However, in BERT + +Topics in Contextualised Attention Embeddings +3 +(a) Attention mechanism in BERT via visu- +alisation in Layer 12. We observe that words +that are central to the context are assigned +high attention weights. +(b) Words, ordered by decreasing probabil- +ity, obtained from the LDA model. +only the encoder part of transformers has been used. There is an important +concept in BERT called attention that assigns weights to different input features +given their importance in the underlying task. One example is: given the text +about cats, the model will pay more attention, via attention weights, to words +such as fur, eyes, etc. BERT’s attention has also been studied in [12] where the +authors find that different attention heads focus on different aspects of language, +e.g., they find that heads direct objects of verbs, determiners of nouns, objects of +prepositions, and objects of possessive pronouns with far greater accuracy. While +they have studied the syntactic and semantic information encoded in different +attention heads, they have not separately probed latent topics as learned by the +topic models such as LDA and NMF. In Figure 1a, we depict how attention works +obtained via a popular visualisation tool3. We input two sentences in sequence, +where the first sentence “The player plays football.” is followed by the second +sentence “Football is played in a stadium.”, and both describe the sport football. +The visualisation tool depicts the case when we select the token “football” in +the first sentence and how other semantically related tokens such as “football”, +“stadium”, and “played” are highlighted with high attention weights. +Topic modelling is a machine learning technique that automatically discovers +hidden topics in unlabelled data. A topic is defined as a probability distribution +of words. While these topic models have been inspired by the latent concept- +based models such as Latent Semantic Analysis (LSA) [13] and Probabilistic +Latent Semantic Analysis (pLSA) [21], Latent Dirichlet Allocation (LDA) [8] +has been widely applied to discover latent topics because it addressed some of +the fundamental challenges in LSA and pLSA such as scaling on large datasets +and overfitting. While in [27], the authors demonstrated that static word em- +beddings are related to SVD, which is the core algorithm used in LSA, what +we demonstrate here is that models such as PLMs implicitly learn latent topic +information as encoded by the PTMs. +LDA has been trained considering the exchangeability [17] assumption mean- +ing that word order does not matter in a document. These models describe +3 https://github.com/jessevig/bertviz + +[CLS] +football +the +is +player +played +plays +in +football +a +[SEP] +stadium +[SEP]57 +38 +65 +70 +0 +app +game +time +movie +1 +apps +player +day +film +2 +developer +video game +work +show +3 +application +gaming +hour +story +4 +user +developer +week +episode4 +Mozhgan Talebpour, Alba Garcia Seco de Herrera, Shoaib Jameel +documents as a mixture of words and each document comprises a mixture of +topics defined by the user. Note that BERT does not model document-level in- +formation; there are extensions such as Sentence-BERT (SBERT) [40] to model +documents. +In Figure 1b, we depict a typical output obtained from LDA using a freely +available online topic modelling visualisation tool4. We can observe from this +output that there are five top-ranked probability words in some topics that are +indexed by topic labels as discrete numbers. From topic index 57, we can infer +that the topic describes computer or mobile applications and their development. +Topic number 38 describes video gaming. +BERT has demonstrated state-of-the-art results in many NLP downstream +tasks, such as natural language inference and information retrieval. Some pre- +vious studies have emphasised the importance of contextual information as an +additional feature of topic modelling. In [3], for example, the importance of +sentence contextual representation and neural topic model was investigated. In +SBERT [40], embedding representation was used as the input to the prodLDA [46] +neural topic model. If an input document length exceeded the SBERT prede- +fined length, the rest of the document would be omitted. Despite this limitation, +the model produced a higher coherence score when compared to Bag-of-Words +(BoW) representation embedding. Some other studies have focused on how, and +if, adding topic modelling information to a BERT model can lead to an improve- +ment in its performance. In a study conducted by Peinelt et al., [34], they have +used topic modelling to improve the BERT performance of semantic similarity +domain applications like question answering. They have used BERT-base final +layer’s [CLS] token embedding as the corresponding embedding of an input doc- +ument. Wang et al., [55] have argued that BERT contextual embedding can be +improved by adding topical information to it. In their study, BERT embedding +was derived from topics in the corpus. The findings of this research suggest that +a word vector representation is equal to the weighted average of different topical +vectors. If a topic has high importance in a corpus, words that are related to +that topic gain higher importance. +In another related research conducted by [23], topical text classification was +applied to a scientific domain dataset. The authors compared the findings of +their research with SciBERT [2], which is a pre-trained language model based +on BERT, but on scientific documents. Concatenation of BERT embedding and +document topic vector was used as an input to a two-layer feed-forward neural +network. In a recent study, [49], the role of BERT embedding was examined +from a different perspective. This research argued that clustering token-level +BERT embedding shares many similarities with topic modelling. The authors +used different PLMs such as BERT, GPT-2 [38] and RoBERTa’s [28] last three +layers of embedding. This work found that except RoBERTa, BERT and GPT-2 +word-level clustering resulted in clusters that resemble close to those obtained +using the LDA model. While LDA learns topics as a probability distribution of +words, the word clusters obtained by clustering token-level embeddings in PLM +4 https://pyldavis.readthedocs.io/en/latest/index.html + +Topics in Contextualised Attention Embeddings +5 +cannot be confused with a probability distribution of words. What the authors +showed is that there are some similarities between the word clusters of a PTM +when compared with the clusters obtained from a PLM. +While the works mentioned above demonstrate important relationships be- +tween PTMs and PLMs, what is currently lacking is a further understanding of +how latent topics are encoded in the PLM vectors and what component helps in +encoding this information. There are works mentioned above that have trained +latent topics with pre-trained language models in a unified way. The question +is whether it is needed to learn latent topics with pre-trained language models +again. While these works have shown quantitative improvements, it is unclear +how latent topics are helping them improve upon the results. +3 +Probe Tasks +The problem that we intend to study in this paper is whether latent topic in- +formation is automatically encoded in contextualised word embeddings. While +it is not explicitly evident that latent topic information is encoded, we must de- +sign probe tasks. Our key goal is thus to understand how PLMs such as BERT +and DistilBERT can discover word clusters that are often discovered by PTMs +when they are not specifically designed to model such information. To this end, +we first chose to study in more detail the role that attention heads play in the +PLM model. It is because just as in a topic model, words that are central to +the document’s global context are assigned a high probability and words that +are central to a topic are assigned a high probability. For instance, if the doc- +ument is about “sports”, words such as “football”, “goal”, and “player” will have +a high probability in that document. Similarly, these words will occur with a +high probability in the topic that is about sports. The attention mechanism too +shows similar behaviour in the document where words that are central within the +given contextual window are assigned high attention weights. Attention weight +specifies the importance of a particular word when it is accompanied by other +words [12] in a certain pre-defined contextual window. +We consider BERT-base uncased and DistilBERT-based uncased models as +our PLMs because of their popularity and computational ease. We also know that +the LDA model outputs word and document topic representations [8]. Given the +number of factors or latent dimensions, NMF factorises the co-occurrence ma- +trix into two low-dimensional matrices where one matrix encodes word clusters +and the other matrix encodes document clusters. Since language models capture +word-level patterns, we thus choose word topics in LDA and NMF. Since both +LDA and NMF can explicitly be assigned to soft clusters based on their proba- +bility values, in the case of the attention representations, we must cluster them +using a soft clustering algorithm. This would help us produce word clusters with +cluster assignments. +There are other components that we could also study such as the role played +when different transformers layers when stacked together. However, previous +studies have already found out that the different layers capture different proper- + +6 +Mozhgan Talebpour, Alba Garcia Seco de Herrera, Shoaib Jameel +ties of text data, e.g., in BERT, lower layers capture linear word order, middle +layers capture syntactic information whereas higher layers capture semantic in- +formation. None of these studies has found that word clusters resembling latent +topics are also modelled by one of these layers after thorough experimentation. +As a result, given their findings, we focus on the attention heads in PLMs first. +In BERT-base, there are 12 layers, each layer containing 12 attention heads. +The attention head computes attention weights between all pairs of word combi- +nations in an input sentence. Attention weight can be interpreted as an impor- +tant criterion when considering two words simultaneously. For example (weather, +sunny) pair’s attention weight is higher than the (weather, desk) pair. It is be- +cause when BERT is trained on billions of tokens (weather, sunny) combinations +occurred more frequently than other words such as “desk”. Similarly, in the LDA +model, if words such as “sports” and “football” occur, they will be assigned a high +probability value in the word topic. DistilBERT is also based on the BERT-base +model but is much lighter weight with respect to its parameters. It has been ob- +tained after a process known as knowledge distillation [29,19] where the original +bigger model known as the teacher was used to train the lighter-weight com- +pressed student model to mimic its behaviour. It was found that in the case +of DistilBERT, it retained most of BERT’s advantages with a much-reduced +parameter set. +Using two publicly available benchmark datasets, we conduct two different +probe tasks to demonstrate the generalisability of our findings. In the first probe +task, we conduct word-level clustering on the representations obtained from PTM +and PLM models and compute the coherence measure which has been popularly +used in topic models to evaluate the quality of the topics. In the case of the +language models, we extract attention weights from each layer of the model and +we obtain the word-attention representations for every word in the vocabulary. +We then cluster these attention vectors using a clustering algorithm where the +attention vectors are used as features. Through this attention clustering, we +expect that words that are semantically related are clustered in one cluster. +The motivation is that if the word clusters contain thematically related words, +the clusters will demonstrate a high coherence measure. While there have been +debates around the usefulness of coherence measure [22], in our study, we use +the same measure to compare all models quantitatively. +We intend to probe if there is a comparable coherence performance between +a layer of PLM and the word-topic representations obtained from PTM. By +comparable, we mean whether the coherence results are numerically close to +each other. If the coherence results are comparable, we can expect that in terms +of the thematic modelling of words, the language model and the topic models +are learning semantically related content. While the coherence probe task might +not completely be relied upon, we design an additional probe task to find out the +word overlaps between the word clusters obtained from the PLMs and PTMs. +Our motivation is that if the coherence value between the clusters is high then +there must be a reliable overlap between the words in the clusters. Since the +higher layers, 10, 11 and 12 in the case of the BERT-base model capture semantic + +Topics in Contextualised Attention Embeddings +7 +information more than the lower layers, we expect that the clusters of words in +the high layers of the language model will show higher commonality with those +clusters that are learnt by the PLMs. +3.1 +Experimental Settings +Datasets: We have used 20 NewsGroups (20NG) and IMDB datasets which are +two popular datasets commonly used in the text mining community. The 20NG +dataset contains about 18,000 documents in 20 news categories after removing +duplicate and empty instances. IMDB dataset contains 50,000 movie reviews +that have been labelled as positive or negative. The 20NG dataset contains +several long documents whereas IMDB contains relatively short documents with +relatively more noisy text. +Text preprocessing: In the case of the PTMs, we have followed a common pre- +processing strategy such as the removal of the stop words, the removal of punctu- +ation, and non-ASCII characters. Through our experiments, we have found that +if we do not remove stopwords from text, they tend to dominate most of the +topics including increasing the dimensionality of the semantic space resulting +in high space and time complexities. While some workaround have been pro- +posed to model natural language using PTMs such as using asymmetric priors, +they can be computationally intensive on large datasets [54]. In the case of the +PLMs, we let the default pre-processor handle pre-processing, for instance, the +BERT-base model has the WordPiece tokenizer. Using NLTK [5], we conducted +sentence segmentation. +PLM attention weights: For every word in the vocabulary, we obtain the +word attention weights from the BERT-base uncased and DistilBERT models. As +BERT uses wordPiece tokenisation, if tokenised sentence length is more than 512 +tokens, the input sentence is split which is common in the literature. Attention +weights of all tokens in a sentence would be stored. If a word appears in different +sentences, the average of all words’ attention is used which is also commonly +done including taking their average embedding of their word pieces [59]. We +have obtained attention weights from every layer of BERT. BERT attention +weight has been defined as an average of all attention heads in each layer. +We have obtained attention weights from the vanilla BERT-base model. Be- +sides that, we have also obtained attention weights from the fine-tuned version +of the BERT model to gauge the role fine-tuning might play in the process. +Fine-tuning was done on the text classification task using labels associated with +labelled instances in the 20NG and IMDB datasets. Through cross-validation +in the fine-tuning process, we present the results of the best-performing model +on the test set with the ideal model parameters obtained via a 30% held-out +dataset. We have followed the same configuration with the vanilla DistillBERT- +base model. +Topic modelling: We have used the Latent Dirichlet Allocation (LDA) model +implemented in Gensim [39] to discover latent topics in our datasets. In the +20NG dataset, we have varied the number of topics from 20 to 200. In the +IMDB dataset, we varied the number of topics from 2 to 30 which gave us better + +8 +Mozhgan Talebpour, Alba Garcia Seco de Herrera, Shoaib Jameel +20 Newsgroups +LDA +NMF +# topics c-v +# topics c-v +20 +0.518 20 +0.478 +30 +0.487 30 +0.504 +50 +0.504 50 +0.484 +100 +0.474 100 +0.453 +150 +0.470 150 +0.455 +200 +0.473 200 +0.474 +IMDB +LDA +NMF +# topics c-v +# topics c-v +2 +0.363 2 +0.276 +5 +0.364 5 +0.275 +10 +0.370 10 +0.299 +20 +0.461 20 +0.300 +30 +0.437 30 +0.299 +Table 1: Coherence results for LDA and NMF models. +results. We have used the NMF model implemented in Gensim. According to +[58], larger datasets tend to have more topics than smaller ones. As a result, we +have chosen different topic pools in different datasets. We have not chosen the +number of topics to be equal to the dimensionality of the word vectors obtained +from PTMs because PTMs tend to encode a variety of information in their +vectors, e.g., syntactic and semantic information. Besides that, having many +topics larger than what we have chosen above tends to result in sub-optimal +latent topics leading to the deterioration of performance. +Clustering: We have used the soft Gaussian Mixture Models (GMM) [6] clus- +tering algorithm on the embeddings obtained from PLMs. LDA is already a soft +clustering model where probability values are used to assign soft clusters to in- +stances [60]. In LDA, we can automatically obtain the word-topic assignments +based on the probability values of words in each topic which is also true for clus- +ters obtained via the GMM model. We used GMM because its implementation +is widely and freely available in different software libraries. +Evaluation: In topic modelling, coherence measure has been widely used to +evaluate the quality of the latent topics [30]. Coherence score “c-v” has been used +in our setting which is available in the Gensim library. This measure has been +adapted from the work of Roder et. al. [42]. We use coherence to measure the +semantic relatedness of tokens in the word clusters obtained from both PLM and +PTM models. We also use the number of word overlaps between the top-k words +in clusters obtained from the two models to gauge the word overlaps among +the clusters. We set k = 20 which gives a reliable trade-off between selecting +the most thematically related top-k words and not choosing (general or noisy) +words with low probability estimated in the word clusters. To compute the word +overlap values, for every topic in PTM and every layer’s word cluster in PLMs, +we computed the overlap between the top-k words, followed by computing the +“mode” value. While there are metrics such as entropy and exclusivity [49], we +will use these metrics in the extended version of this paper. +4 +Discussion +We have computed cluster coherence values on two different datasets. Given two +clusters with their respective coherence values. If one cluster’s coherence value +is higher than the other, the one with the higher coherence values is regarded as + +Topics in Contextualised Attention Embeddings +9 +Layer VB30 VB50 VB100 VB150 VB200 FT30 FT50 FT100 FT150 FT200 +1 +0.360 0.502 +0.489 +0.481 +0.343 +0.333 0.477 0.502 +0.466 +0.330 +2 +0.346 0.480 +0.463 +0.464 +0.334 +0.327 0.479 0.480 +0.462 +0.333 +3 +0.329 0.450 +0.453 +0.448 +0.323 +0.315 0.466 0.450 +0.459 +0.324 +4 +0.328 0.466 +0.461 +0.452 +0.332 +0.324 0.466 0.466 +0.461 +0.332 +5 +0.33 +0.460 +0.448 +0.449 +0.324 +0.325 0.458 0.460 +0.453 +0.329 +6 +0.33 +0.459 +0.455 +0.451 +0.318 +0.347 0.466 0.459 +0.460 +0.337 +7 +0.337 0.478 +0.471 +0.454 +0.325 +0.346 0.495 0.478 +0.479 +0.347 +8 +0.347 0.469 +0.468 +0.470 +0.336 +0.353 0.508 0.469 0.496 0.359 +9 +0.346 0.486 +0.474 +0.471 +0.344 0.370 0.508 0.486 +0.494 +0.360 +10 +0.373 0.480 +0.483 +0.476 +0.360 +0.368 0.502 0.480 +0.494 +0.358 +11 +0.369 0.503 0.489 +0.481 +0.360 +0.357 0.483 0.503 0.489 0.361 +12 +0.373 0.502 0.489 0.484 0.363 0.364 0.485 0.502 +0.480 +0.355 +Layer VB2 +VB5 VB10 VB20 VB30 FT2 +FT5 +FT10 FT20 FT30 +1 +0.411 0.390 0.365 0.358 0.355 0.455 0.442 0.372 0.348 0.333 +2 +0.473 0.447 0.374 0.347 0.352 0.469 0.459 0.420 0.391 0.384 +3 +0.480 0.414 0.418 0.385 0.366 0.501 0.452 0.415 0.412 0.404 +4 +0.586 0.478 0.444 0.421 0.404 0.457 0.388 0.386 0.383 0.380 +5 +0.583 0.490 0.439 0.426 0.422 0.410 0.383 0.350 0.359 0.356 +6 +0.563 0.477 0.471 0.429 0.405 0.452 0.438 0.396 0.374 0.357 +7 +0.546 0.485 0.431 0.425 0.416 0.489 0.403 0.399 0.374 0.366 +8 +0.510 0.438 0.428 0.414 0.415 0.514 0.427 0.395 0.397 0.369 +9 +0.452 0.410 0.393 0.383 0.373 0.438 0.425 0.366 0.377 0.374 +10 +0.476 0.430 0.381 0.351 0.349 0.426 0.417 0.369 0.361 0.349 +11 +0.425 0.429 0.400 0.398 0.385 0.430 0.391 0.346 0.354 0.347 +12 +0.523 0.454 0.446 0.439 0.431 0.469 0.433 0.440 0.402 0.385 +Table 2: 20NG GMM (left) and IMDB GMM (right) clustering on BERT-base at- +tention weights on the left and the right. The values depict coherence results. VB +refers to the vanilla BERT-base model and FT refers to the fine-tuned version. +The number followed by VB and FT refers to the number of clusters specified +in the GMM model. +Layer VD30 VD50 VD100 VD150 VD200 FT30 FT50 FT100 FT150 FT200 +1 +0.504 0.497 +0.518 +0.515 +0.521 +0.502 0.508 0.511 +0.517 +0.513 +2 +0.509 0.509 +0.510 +0.514 +0.515 +0.511 0.518 0.510 +0.507 +0.508 +3 +0.514 0.514 +0.508 +0.508 +0.510 +0.507 0.503 0.503 +0.499 +0.507 +4 +0.516 0.509 +0.516 +0.517 +0.513 +0.502 0.502 0.504 +0.503 +0.505 +5 +0.548 0.550 +0.551 +0.544 +0.549 +0.544 0.550 0.546 +0.543 +0.544 +6 +0.593 0.572 0.572 0.573 0.568 0.573 0.576 0.573 0.571 0.571 +Layer VD2 +VD5 VD10 VD20 VD30 FT2 +FT5 +FT10 FT20 FT30 +1 +0.231 0.258 0.249 0.250 0.251 0.219 0.224 0.226 0.248 0.238 +2 +0.166 0.211 0.212 0.224 0.230 0.255 0.225 0.231 0.232 0.238 +3 +0.231 0.244 0.235 0.251 0.244 0.253 0.225 0.230 0.235 0.234 +4 +0.151 0.228 0.204 0.228 0.234 0.170 0.223 0.218 0.219 0.217 +5 +0.317 0.347 0.307 0.270 0.264 0.252 0.268 0.274 0.272 0.261 +6 +0.334 0.327 0.325 0.317 0.312 0.288 0.270 0.267 0.254 0.264 +Table 3: 20NG GMM (left) and IMDB GMM (right) clustering on DistilBERT +attention weights. The values depict coherence results. VD refers to the vanilla +DistilBERT model and FT refers to the fine-tuned version. The number followed +by VD and FT refers to the number of clusters specified to the GMM model. +a coherent cluster, for instance, in the case of text, the tokens in the coherent +clusters tend to be semantically associated with each other. In both LDA and +NMF models, we have varied the number of topics to demonstrate the impact +of topic clusters. In Table 1 we present the topic coherence results in the 20 +Newsgroups and IMDB datasets for the LDA and NMF models. We observe +that in the LDA model when the number of topics is 20, we obtain the best +coherence value of 0.518 in the 20NG dataset. In the case of the NMF model, +the best coherence value is when the number of factors is 30 with 0.504 in the +20NG dataset. In the IMDB dataset, we also obtain the best coherence value +when the number of topics is 20 in the LDA model with a value of 0.461 and the +NMF model gives us the value 0.300 when the number of factors is 20. +PLM & 20NG dataset: In the case of the vanilla BERT-base model in Table 2 +(left), i.e., 20NG dataset, we notice that when the number of soft attention +clusters is 50 there is some comparable performance with the coherence results. +Precisely, we read from the table that for VB50 the coherence value is 0.503 in +layer 11. This coherence value is numerically close to 0.518 when the number +of topics is 20, and in the case of the NMF model, it is approximately equal to +0.504 when the number of factors is 30. This suggests that both LDA and vanilla +BERT-base attention word clusters are semantically coherent when the number +of soft clusters is 50. We also notice that the contextual layers are mainly playing + +10 +Mozhgan Talebpour, Alba Garcia Seco de Herrera, Shoaib Jameel +a key role in modelling such semantically close words, i.e., layer 11. When we +refer to the word overlaps in Table 4, we notice that the top 20 word overlaps +are also consistent with the BERT-base model in layers 7, 8, 9 and 11. It means +that out of 20 words, there are 17 overlapping words. +Upon comparing the results of the fine-tuned version of the BERT-base model +where the fine-tuning was done on the classification task, we notice that soft clus- +ters 50 and 100 in Table 2 lead to comparable coherence performances obtained +by the LDA and NMF models in Table 1. Precisely, we read from the table that +when the number of clusters is 50 and 100, we obtain the coherence value of +0.508 and 0.503, respectively that again are numerically comparable to 0.518 in +the coherence table for LDA and 0.504 for the NMF model, i.e., Table 1. While +it would be ideal to have these coherence results be equal, such results are diffi- +cult to obtain considering noise in the data and the randomness involved when +initiating the training process of these semantic models. What is interesting +in the case of the fine-tuned version of the BERT-base model is that two layers +show comparable coherence performances and both these layers learn contextual +information. +When we look at the topic associated with “computing technology” in the +20NG dataset, we noticed that words such as “organisation”, “com”, and “nntp” +were among the overlapping words which suggest that both BERT and LDA +learn thematically the same words. While it can be argued that even simple +clustering algorithms such as k-means might generate clusters that are coherent +and with high-overlapping words, we have found out that k-means does not lead +to coherent clusters and the word overlap count was also very low, for instance, +in most cases we found the word overlap values to be sometimes 1, and most +often, 0. +In the case of the vanilla DistilBERT model presented in Table 3 (left), +we notice that the higher layers demonstrate the highest soft cluster coherence +results. What we notice is that the contextual layers show a higher degree of +cluster coherence comparable to performance with the LDA model than with +the NMF model in Table 1, for instance, the vanilla DistilBERT version with +200 soft clusters shows a relatively comparable performance when compared +with the LDA model in Table 1. It can be argued that in terms of the absolute +numbers the results in Table 3 are much higher than in Table 1 when we only +look at the highest DistilBERT layers values. One of the reasons is that different +pre-processing strategies have been chosen in both models. However, this was +unavoidable because including stop words in the PTM models would result in +noisy topics. Note that other layers such as Layer 4, soft cluster 30, in the case +of the vanilla DistilBERT model compare well with the LDA coherence results. +Layer 4 in the case of the DistilBERT model compares reliably with the soft +cluster 30 when we consider the NMF model. +PLM & IMDB dataset: In the IMDB dataset, Table 1 presents the ideal +coherence value when the number of topics/factors is 20 for the LDA and the +NMF models. For the LDA model, the coherence value is 0.461 and for the NMF +model, the coherence value is 0.300. Referring to Table 2 (right), we see that the + +Topics in Contextualised Attention Embeddings +11 +comparable LDA value is obtained in layer 6 in the vanilla BERT-base version +when the number of soft clusters is 10. In the fine-tuned version, we see the +comparable value in layer 8 when compared to the LDA model and when the +number of soft clusters is 150. If we consider topic 30 in Table 1, we notice two +comparable values in Table 2 in layer 12 which is a layer that captures contextual +information more than any other layer when the vanilla soft clusters are 20 and +30. +In Table 4, most word overlaps occur in layers 5, 9, 11, and 12 and these +results are consistent with the 20NG results where higher contextual layers have +the maximum word overlap. We also notice that layers 6 and above have the +most ideal coherence values indicating that if the clusters are coherent, they +also have maximum word overlaps. It means that these clusters share common +words. In DistilBERT, in Tables 3 and 4 we see that the NMF model tends to +show comparable coherence values in the higher layers. In Table 4, we observe +that the word overlaps are fairly uniformly distributed across layers. While the +lower layers have shown to have maximum overlaps, we can notice that the +upper layers too have a word similar overlaps. However, their coherence values +are not comparable. It is because IMDB instances are short noisy sentences +where the model seems to be performing not very reliably unlike the 20NG +dataset. What is also noticeable from the results is that the fine-tuned version of +the DistilBERT model does not show comparable coherence performance when +compared with the NMF model. This could suggest that classification fine-tuning +helps DistilBERT lose the latent topic information. +In summary: 1) the attention mechanism is an important component in the +PLMs that help capture some patterns that are also captured by PTMs. 2) +there is correspondence between the coherence results obtained from PLMs and +PTMs because in most cases we obtain comparable coherence performance. 3) +in PLMs, there are high word overlaps in the contextualised layers and clusters +of words obtained from PTMs. 4) in most cases, it is the contextualised layer +that captures the most commonality with PTMs. +One of the limitations of our work is that it does not experiment with other +language models very different from BERT such as XLNet [62] and GPT-3 [16] +to ascertain that similar conclusions could be also derived from them. However, +what is important to note is that our conclusions point toward the importance +of the attention mechanism rather than the way pre-training is done or the +size of the dataset that has been used to pre-train the model, or the model +design. We also have to verify whether the results are generalizable to even larger +models such as BERT-large which requires much more computational resources +to conduct this study. +We show another finding through Figure 2 where we demonstrate the im- +portance of the attention mechanism and how topic weights (probabilities) and +attention weights tend to focus on the same words in a given context. To generate +the figure, we have taken an example from the IMDB dataset. In the BERT-base +model, layer 11 is examined because it is the contextual layer and has the highest +word overlaps in Table 4. In the case of the DistilBERT-base model, we have + +12 +Mozhgan Talebpour, Alba Garcia Seco de Herrera, Shoaib Jameel +Layer 20NG IMDB +1 +16 +14 +2 +16 +13 +3 +16 +12 +4 +16 +14 +5 +16 +17 +6 +16 +14 +7 +17 +12 +8 +17 +12 +9 +17 +17 +10 +16 +11 +11 +17 +17 +12 +16 +17 +Layer 20NG IMDB +1 +12 +10 +2 +12 +10 +3 +9 +10 +4 +12 +10 +5 +12 +10 +6 +12 +9 +Table 4: BERT (left) and DistilBERT (right) attention word overlap with LDA. +Fig. 2: Illustrating attention using a sentence from the IMDB dataset as an +example. We have presented these results from the BERT-base layer 11 and +DistilBERT-based layer 5. The number of topics/factors in the case of PTM is +20. The figure is used to demonstrate that these models tend to focus on relevant +tokens within their context and assign lower weights to general tokens such as +stopwords. +selected layer 5 given that it is one of the contextual layers and has one of the +highest word overlaps in Table 4. We have selected the number of topics as 20 +and the number of NMF factors as 20 which is based on the results obtained in +Table 1. What we observe from the figure all the models tend to focus on the +relevant keywords in the context, for instance, we observe that PLMs focus on +the words such as “good”, “effects”, “terrible”, “movie” that are relevant to the +movie and the PTMs too tend to focus on the same tokens in this context. What +we learn from the figure is that PTMs and PLMs, while they are different, both +tend to focus on the relevant words in a given contextual window. This figure +helps us to draw some relationships between the attention weights and the topic +probabilities in that they focus on the important words only. We also notice that +common words such as stopwords are given less weightage by the models. + +words +BERT-based +DistilBERT-based +LDA +NMF +0 +This +0.000000 +0.000000 +0.000000 +0.000000 +1 +movie +0.071700 +0.091100 +0.041000 +0.000000 +2 +is +0.000000 +0.000000 +0.000000 +0.000000 +3 +terrible +0.111100 +0.086300 +0.002000 +0.001000 +4 +μnq +0.000000 +0.000000 +0.000000 +0.000000 +5 +it +0.000000 +0.000000 +0.000000 +0.000000 +9 +has +0.000000 +0.000000 +0.000000 +0.000000 +7 +some +0.000000 +0.000000 +0.000000 +0.000000 +8 +poob +0.102200 +0.071100 +0.010000 +0.101000 +9 +effects +0.111700 +0.097400 +0.002000 +0.003000Topics in Contextualised Attention Embeddings +13 +While the authors in [49] have found out that the word clusters obtained +from some PLMs tend to cluster the contextualised word vectors that resemble +what is learned by a topic model, our result suggests that it is the attention +mechanism that is playing a key role in obtaining such results which is the key +contribution of our work. It can also be argued that the contextualised token +embeddings obtained from a PLM model can lead to almost similar conclusions, +in this work, we wanted to explicitly study the role of the attention weights. +5 +Conclusions +Topic modelling has remained a dominant modelling paradigm in the last decade +with several topic models developed in the literature [64]. Topic models were not +only modelled using Bayesian statistics but also linear algebra-based such as +the NMF model. While both these models are formulated differently, they both +tend to exhibit similar clustering properties. With the development of PLMs, +these models have now taken over the landscape in text mining and NLP be- +cause they have outperformed existing baselines. Recent research points out that +word-level clustering on BERT embeddings results in word clusters that share +a close relationship with those discovered using topic models. As a result, this +motivated us to study the reason which component in the language model helps +capture such topic information when the model has not been explicitly designed +to model latent word topics. Through probe tasks, we find that it is the atten- +tion mechanism that plays a key role in modelling word patterns that resemble +something that is also discovered using topic models. We strongly believe that +our work helps add further insight into the relationships between topic models +and PLMs including the role that is played by the attention mechanism in the +language model. In the future, we will conduct a thorough theoretical analysis to +find out the key theoretical similarities between a topic model and a PLM. We +will also study how different PLMs other than those that are based on BERT +encode latent topics using attention weights. +Our results are not only applicable to NLP and document modelling fields in +general, but the results are also relevant to information retrieval. For instance, in +an information retrieval setting, we can only use features obtained from PLMs to +retrieve relevant documents without having to worry about latent topics features +that would potentially increase the number of features that might even degrade +the performance of an information retrieval engine. Besides that, we may be +injecting more redundant features into the information retrieval model. Topic +models have been shown to improve information retrieval results and PLMs +have been shown to demonstrate even better results. This could be because +PLMs already have encoded a variety of features in their rich vector space that +includes latent topics. As a result, the improvement that we see also comes from +topics implicitly encoded in the PLM attention vectors. We thus believe that +our paper will have a significant impact in the information retrieval field too. + +14 +Mozhgan Talebpour, Alba Garcia Seco de Herrera, Shoaib Jameel +References +1. Adhikari, A., Ram, A., Tang, R., Lin, J.: Docbert: Bert for document classification. +arXiv preprint arXiv:1904.08398 (2019) +2. Beltagy, I., Lo, K., Cohan, A.: Scibert: A pretrained language model for scientific +text. arXiv (2019) +3. Bianchi, F., Terragni, S., Hovy, D.: Pre-training is a hot topic: Contextualized +document embeddings improve topic coherence. arXiv (2020) +4. Bibal, A., Cardon, R., Alfter, D., Wilkens, R., Wang, X., François, T., Watrin, +P.: Is attention explanation? an introduction to the debate. In: Proceedings of the +60th Annual Meeting of the Association for Computational Linguistics (Volume 1: +Long Papers). pp. 3889–3900. 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Zhao, H., Phung, D., Huynh, V., Jin, Y., Du, L., Buntine, W.: Topic modelling +meets deep neural networks: A survey. arXiv preprint arXiv:2103.00498 (2021) + diff --git a/i9E3T4oBgHgl3EQfJAlP/content/tmp_files/load_file.txt b/i9E3T4oBgHgl3EQfJAlP/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..6da4b33e0f47fcb684a158bf56559a30a73d738a --- /dev/null +++ b/i9E3T4oBgHgl3EQfJAlP/content/tmp_files/load_file.txt @@ -0,0 +1,1218 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf,len=1217 +page_content='Topics in Contextualised Attention Embeddings Mozhgan Talebpour1, Alba Garcia Seco de Herrera1, Shoaib Jameel2 1 Computer Science and Electronic Engineering, University of Essex, United Kingdom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' 2 Electronics and Computer Science, University of Southampton, United Kingdom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' {mozhgan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='talebpour, alba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='garcia}@essex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='uk, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='Jameel@southampton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='uk Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Contextualised word vectors obtained via pre-trained lan- guage models encode a variety of knowledge that has already been ex- ploited in applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Complementary to these language models are probabilistic topic models that learn thematic patterns from the text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Recent work has demonstrated that conducting clustering on the word- level contextual representations from a language model emulates word clusters that are discovered in latent topics of words from Latent Dirichlet Allocation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The important question is how such topical word clusters are automatically formed, through clustering, in the language model when it has not been explicitly designed to model latent topics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' To address this question, we design different probe experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Using BERT and DistilBERT, we find that the attention framework plays a key role in modelling such word topic clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We strongly believe that our work paves way for further research into the relationships between probabilis- tic topic models and pre-trained language models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' 1 Introduction Pre-trained language models (PLMs), e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=', ELMo [35], Generative Pre-trained Transformer (GPT) [37], PaLM [11], and Bidirectional Encoder Representa- tions from Transformers (BERT) [14] are pre-trained using large amounts of text data [24], for instance, BERT has been pre-trained on the BookCorpus and Wikipedia collections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' During the domain-independent pre-training process, these models encode a variety of latent information, for instance, semantic and syntactic properties [57], as a result, these models can make reliable predictions even under a zero-shot setting in different applications [20,41,43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' While the pre-training process is computationally [51] and financially expensive [47], these models can be cheaply fine-tuned to reliably handle different downstream tasks such as document classification [1] and information retrieval [61,50], a process that is commonly referred to as transfer learning [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' For instance, BERT has shown strong performance in natural language understanding [63], text summari- sation [25], document classification [10] and other Natural Language Processing (NLP) downstream applications [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Another class of models that continues to dominate the text mining landscape are probabilistic topic models (PTMs) [8,7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' These models are probabilistic ap- proaches toward determining dominant topics in a text corpus in a completely arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='04339v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='CL] 11 Jan 2023 2 Mozhgan Talebpour, Alba Garcia Seco de Herrera, Shoaib Jameel unsupervised way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' A latent topic is described as a probability distribution of words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Latent Dirichlet Allocation (LDA) [8] is a popular model for discovering topics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In LDA, the model learns to represent a document as a mixture of latent topics and each topic is represented by a mixture of words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' When LDA is viewed as a matrix factorisation model, given a term document co-occurrence matrix as input and the number of topics, the model factorises the matrix into two low- dimensional matrices that are word topic and document topic representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The word topic matrix captures the importance of words in the vocabulary of each topic whereas the document topic matrix captures the topic distribution in every document.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' While LDA has been a popular model that is based on Bayesian learning, a class of linear algebra-based model called Non-negative Matrix Fac- torisation (NMF) [56,26] has become equally popular to learn topics [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In [43], the authors dissected BERT to understand the property of every layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' They find that lower layers, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=', layer 1 or 2 capture the linear word order, while the BERT’s middle layers learn the syntactic information reliably and the higher layers capture the contextualised information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The authors in [49] and [45] showed that BERT word embedding clustering via simple algorithms such as k-means results in word clusters as if they are learned by a topic model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The authors conducted a series of qualitative probe experiments to find out that most of the word clusters of BERT resemble what is often discovered by the LDA model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' While these studies make relevant observations, what is not well studied is how the topic information is encoded at the time of pre-training given that BERT or any other contextual language model is not designed to model topical word clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In this work, by conducting different probe experiments, we answer how BERT and DistilBERT [44] can capture clusters of words that resemble what is learnt by topic models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We find that it is the attention [4,9] mechanism in these language models that plays a key role in modelling what resembles word topics as discovered by the topic model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' 2 Related work The main goal of PLMs [31] is to simulate human language understanding by finding the most probable words sequence and patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The traditional language model used probability distribution to predict the next word, but they were not very scalable such as those based on unigram, bigram or trigram language mod- els [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The recently developed PLMs are trained using large amounts of text data where some of them exploit a strategy called masked language modelling in a self-supervised way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Once these models have been trained, they have been applied in a wide variety of applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The key advantage of PLMs is that they can be applied on different downstream tasks [15] reliably.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' BERT has been developed with stacked transformers [52] layers where each layer captures different properties in text data, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=', some layers are ideal to capture semantic information [53,48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Transformers consist of encoder-decoder structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The encoder transforms the sequence of input tokens into a high-level dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Decoder predicts input data from encoder [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' However, in BERT Topics in Contextualised Attention Embeddings 3 (a) Attention mechanism in BERT via visu- alisation in Layer 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We observe that words that are central to the context are assigned high attention weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' (b) Words, ordered by decreasing probabil- ity, obtained from the LDA model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' only the encoder part of transformers has been used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' There is an important concept in BERT called attention that assigns weights to different input features given their importance in the underlying task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' One example is: given the text about cats, the model will pay more attention, via attention weights, to words such as fur, eyes, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' BERT’s attention has also been studied in [12] where the authors find that different attention heads focus on different aspects of language, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=', they find that heads direct objects of verbs, determiners of nouns, objects of prepositions, and objects of possessive pronouns with far greater accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' While they have studied the syntactic and semantic information encoded in different attention heads, they have not separately probed latent topics as learned by the topic models such as LDA and NMF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In Figure 1a, we depict how attention works obtained via a popular visualisation tool3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We input two sentences in sequence, where the first sentence “The player plays football.” is followed by the second sentence “Football is played in a stadium.”, and both describe the sport football.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The visualisation tool depicts the case when we select the token “football” in the first sentence and how other semantically related tokens such as “football”, “stadium”, and “played” are highlighted with high attention weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Topic modelling is a machine learning technique that automatically discovers hidden topics in unlabelled data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' A topic is defined as a probability distribution of words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' While these topic models have been inspired by the latent concept- based models such as Latent Semantic Analysis (LSA) [13] and Probabilistic Latent Semantic Analysis (pLSA) [21], Latent Dirichlet Allocation (LDA) [8] has been widely applied to discover latent topics because it addressed some of the fundamental challenges in LSA and pLSA such as scaling on large datasets and overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' While in [27], the authors demonstrated that static word em- beddings are related to SVD, which is the core algorithm used in LSA, what we demonstrate here is that models such as PLMs implicitly learn latent topic information as encoded by the PTMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' LDA has been trained considering the exchangeability [17] assumption mean- ing that word order does not matter in a document.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' These models describe 3 https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='com/jessevig/bertviz [CLS] football the is player played plays in football a [SEP] stadium [SEP]57 38 65 70 0 app game time movie 1 apps player day film 2 developer video game work show 3 application gaming hour story 4 user developer week episode4 Mozhgan Talebpour, Alba Garcia Seco de Herrera, Shoaib Jameel documents as a mixture of words and each document comprises a mixture of topics defined by the user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Note that BERT does not model document-level in- formation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' there are extensions such as Sentence-BERT (SBERT) [40] to model documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In Figure 1b, we depict a typical output obtained from LDA using a freely available online topic modelling visualisation tool4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We can observe from this output that there are five top-ranked probability words in some topics that are indexed by topic labels as discrete numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' From topic index 57, we can infer that the topic describes computer or mobile applications and their development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Topic number 38 describes video gaming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' BERT has demonstrated state-of-the-art results in many NLP downstream tasks, such as natural language inference and information retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Some pre- vious studies have emphasised the importance of contextual information as an additional feature of topic modelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In [3], for example, the importance of sentence contextual representation and neural topic model was investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In SBERT [40], embedding representation was used as the input to the prodLDA [46] neural topic model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' If an input document length exceeded the SBERT prede- fined length, the rest of the document would be omitted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Despite this limitation, the model produced a higher coherence score when compared to Bag-of-Words (BoW) representation embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Some other studies have focused on how, and if, adding topic modelling information to a BERT model can lead to an improve- ment in its performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In a study conducted by Peinelt et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=', [34], they have used topic modelling to improve the BERT performance of semantic similarity domain applications like question answering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' They have used BERT-base final layer’s [CLS] token embedding as the corresponding embedding of an input doc- ument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=', [55] have argued that BERT contextual embedding can be improved by adding topical information to it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In their study, BERT embedding was derived from topics in the corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The findings of this research suggest that a word vector representation is equal to the weighted average of different topical vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' If a topic has high importance in a corpus, words that are related to that topic gain higher importance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In another related research conducted by [23], topical text classification was applied to a scientific domain dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The authors compared the findings of their research with SciBERT [2], which is a pre-trained language model based on BERT, but on scientific documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Concatenation of BERT embedding and document topic vector was used as an input to a two-layer feed-forward neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In a recent study, [49], the role of BERT embedding was examined from a different perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' This research argued that clustering token-level BERT embedding shares many similarities with topic modelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The authors used different PLMs such as BERT, GPT-2 [38] and RoBERTa’s [28] last three layers of embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' This work found that except RoBERTa, BERT and GPT-2 word-level clustering resulted in clusters that resemble close to those obtained using the LDA model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' While LDA learns topics as a probability distribution of words, the word clusters obtained by clustering token-level embeddings in PLM 4 https://pyldavis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='readthedocs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='io/en/latest/index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='html Topics in Contextualised Attention Embeddings 5 cannot be confused with a probability distribution of words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' What the authors showed is that there are some similarities between the word clusters of a PTM when compared with the clusters obtained from a PLM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' While the works mentioned above demonstrate important relationships be- tween PTMs and PLMs, what is currently lacking is a further understanding of how latent topics are encoded in the PLM vectors and what component helps in encoding this information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' There are works mentioned above that have trained latent topics with pre-trained language models in a unified way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The question is whether it is needed to learn latent topics with pre-trained language models again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' While these works have shown quantitative improvements, it is unclear how latent topics are helping them improve upon the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' 3 Probe Tasks The problem that we intend to study in this paper is whether latent topic in- formation is automatically encoded in contextualised word embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' While it is not explicitly evident that latent topic information is encoded, we must de- sign probe tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Our key goal is thus to understand how PLMs such as BERT and DistilBERT can discover word clusters that are often discovered by PTMs when they are not specifically designed to model such information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' To this end, we first chose to study in more detail the role that attention heads play in the PLM model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' It is because just as in a topic model, words that are central to the document’s global context are assigned a high probability and words that are central to a topic are assigned a high probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' For instance, if the doc- ument is about “sports”, words such as “football”, “goal”, and “player” will have a high probability in that document.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Similarly, these words will occur with a high probability in the topic that is about sports.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The attention mechanism too shows similar behaviour in the document where words that are central within the given contextual window are assigned high attention weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Attention weight specifies the importance of a particular word when it is accompanied by other words [12] in a certain pre-defined contextual window.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We consider BERT-base uncased and DistilBERT-based uncased models as our PLMs because of their popularity and computational ease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We also know that the LDA model outputs word and document topic representations [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Given the number of factors or latent dimensions, NMF factorises the co-occurrence ma- trix into two low-dimensional matrices where one matrix encodes word clusters and the other matrix encodes document clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Since language models capture word-level patterns, we thus choose word topics in LDA and NMF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Since both LDA and NMF can explicitly be assigned to soft clusters based on their proba- bility values, in the case of the attention representations, we must cluster them using a soft clustering algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' This would help us produce word clusters with cluster assignments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' There are other components that we could also study such as the role played when different transformers layers when stacked together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' However, previous studies have already found out that the different layers capture different proper- 6 Mozhgan Talebpour, Alba Garcia Seco de Herrera, Shoaib Jameel ties of text data, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=', in BERT, lower layers capture linear word order, middle layers capture syntactic information whereas higher layers capture semantic in- formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' None of these studies has found that word clusters resembling latent topics are also modelled by one of these layers after thorough experimentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' As a result, given their findings, we focus on the attention heads in PLMs first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In BERT-base, there are 12 layers, each layer containing 12 attention heads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The attention head computes attention weights between all pairs of word combi- nations in an input sentence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Attention weight can be interpreted as an impor- tant criterion when considering two words simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' For example (weather, sunny) pair’s attention weight is higher than the (weather, desk) pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' It is be- cause when BERT is trained on billions of tokens (weather, sunny) combinations occurred more frequently than other words such as “desk”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Similarly, in the LDA model, if words such as “sports” and “football” occur, they will be assigned a high probability value in the word topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' DistilBERT is also based on the BERT-base model but is much lighter weight with respect to its parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' It has been ob- tained after a process known as knowledge distillation [29,19] where the original bigger model known as the teacher was used to train the lighter-weight com- pressed student model to mimic its behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' It was found that in the case of DistilBERT, it retained most of BERT’s advantages with a much-reduced parameter set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Using two publicly available benchmark datasets, we conduct two different probe tasks to demonstrate the generalisability of our findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In the first probe task, we conduct word-level clustering on the representations obtained from PTM and PLM models and compute the coherence measure which has been popularly used in topic models to evaluate the quality of the topics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In the case of the language models, we extract attention weights from each layer of the model and we obtain the word-attention representations for every word in the vocabulary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We then cluster these attention vectors using a clustering algorithm where the attention vectors are used as features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Through this attention clustering, we expect that words that are semantically related are clustered in one cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The motivation is that if the word clusters contain thematically related words, the clusters will demonstrate a high coherence measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' While there have been debates around the usefulness of coherence measure [22], in our study, we use the same measure to compare all models quantitatively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We intend to probe if there is a comparable coherence performance between a layer of PLM and the word-topic representations obtained from PTM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' By comparable, we mean whether the coherence results are numerically close to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' If the coherence results are comparable, we can expect that in terms of the thematic modelling of words, the language model and the topic models are learning semantically related content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' While the coherence probe task might not completely be relied upon, we design an additional probe task to find out the word overlaps between the word clusters obtained from the PLMs and PTMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Our motivation is that if the coherence value between the clusters is high then there must be a reliable overlap between the words in the clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Since the higher layers, 10, 11 and 12 in the case of the BERT-base model capture semantic Topics in Contextualised Attention Embeddings 7 information more than the lower layers, we expect that the clusters of words in the high layers of the language model will show higher commonality with those clusters that are learnt by the PLMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='1 Experimental Settings Datasets: We have used 20 NewsGroups (20NG) and IMDB datasets which are two popular datasets commonly used in the text mining community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The 20NG dataset contains about 18,000 documents in 20 news categories after removing duplicate and empty instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' IMDB dataset contains 50,000 movie reviews that have been labelled as positive or negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The 20NG dataset contains several long documents whereas IMDB contains relatively short documents with relatively more noisy text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Text preprocessing: In the case of the PTMs, we have followed a common pre- processing strategy such as the removal of the stop words, the removal of punctu- ation, and non-ASCII characters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Through our experiments, we have found that if we do not remove stopwords from text, they tend to dominate most of the topics including increasing the dimensionality of the semantic space resulting in high space and time complexities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' While some workaround have been pro- posed to model natural language using PTMs such as using asymmetric priors, they can be computationally intensive on large datasets [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In the case of the PLMs, we let the default pre-processor handle pre-processing, for instance, the BERT-base model has the WordPiece tokenizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Using NLTK [5], we conducted sentence segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' PLM attention weights: For every word in the vocabulary, we obtain the word attention weights from the BERT-base uncased and DistilBERT models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' As BERT uses wordPiece tokenisation, if tokenised sentence length is more than 512 tokens, the input sentence is split which is common in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Attention weights of all tokens in a sentence would be stored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' If a word appears in different sentences, the average of all words’ attention is used which is also commonly done including taking their average embedding of their word pieces [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We have obtained attention weights from every layer of BERT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' BERT attention weight has been defined as an average of all attention heads in each layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We have obtained attention weights from the vanilla BERT-base model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Be- sides that, we have also obtained attention weights from the fine-tuned version of the BERT model to gauge the role fine-tuning might play in the process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Fine-tuning was done on the text classification task using labels associated with labelled instances in the 20NG and IMDB datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Through cross-validation in the fine-tuning process, we present the results of the best-performing model on the test set with the ideal model parameters obtained via a 30% held-out dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We have followed the same configuration with the vanilla DistillBERT- base model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Topic modelling: We have used the Latent Dirichlet Allocation (LDA) model implemented in Gensim [39] to discover latent topics in our datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In the 20NG dataset, we have varied the number of topics from 20 to 200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In the IMDB dataset, we varied the number of topics from 2 to 30 which gave us better 8 Mozhgan Talebpour, Alba Garcia Seco de Herrera, Shoaib Jameel 20 Newsgroups LDA NMF # topics c-v # topics c-v 20 0.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='453 150 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='470 150 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='455 200 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='473 200 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='474 IMDB LDA NMF # topics c-v # topics c-v 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='363 2 0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='437 30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='299 Table 1: Coherence results for LDA and NMF models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We have used the NMF model implemented in Gensim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' According to [58], larger datasets tend to have more topics than smaller ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' As a result, we have chosen different topic pools in different datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We have not chosen the number of topics to be equal to the dimensionality of the word vectors obtained from PTMs because PTMs tend to encode a variety of information in their vectors, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=', syntactic and semantic information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Besides that, having many topics larger than what we have chosen above tends to result in sub-optimal latent topics leading to the deterioration of performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Clustering: We have used the soft Gaussian Mixture Models (GMM) [6] clus- tering algorithm on the embeddings obtained from PLMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' LDA is already a soft clustering model where probability values are used to assign soft clusters to in- stances [60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In LDA, we can automatically obtain the word-topic assignments based on the probability values of words in each topic which is also true for clus- ters obtained via the GMM model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We used GMM because its implementation is widely and freely available in different software libraries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Evaluation: In topic modelling, coherence measure has been widely used to evaluate the quality of the latent topics [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Coherence score “c-v” has been used in our setting which is available in the Gensim library.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' This measure has been adapted from the work of Roder et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We use coherence to measure the semantic relatedness of tokens in the word clusters obtained from both PLM and PTM models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We also use the number of word overlaps between the top-k words in clusters obtained from the two models to gauge the word overlaps among the clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We set k = 20 which gives a reliable trade-off between selecting the most thematically related top-k words and not choosing (general or noisy) words with low probability estimated in the word clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' To compute the word overlap values, for every topic in PTM and every layer’s word cluster in PLMs, we computed the overlap between the top-k words, followed by computing the “mode” value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' While there are metrics such as entropy and exclusivity [49], we will use these metrics in the extended version of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' 4 Discussion We have computed cluster coherence values on two different datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Given two clusters with their respective coherence values.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='312 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='288 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='270 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='267 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='254 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='264 Table 3: 20NG GMM (left) and IMDB GMM (right) clustering on DistilBERT attention weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The values depict coherence results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' VD refers to the vanilla DistilBERT model and FT refers to the fine-tuned version.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The number followed by VD and FT refers to the number of clusters specified to the GMM model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' a coherent cluster, for instance, in the case of text, the tokens in the coherent clusters tend to be semantically associated with each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In both LDA and NMF models, we have varied the number of topics to demonstrate the impact of topic clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In Table 1 we present the topic coherence results in the 20 Newsgroups and IMDB datasets for the LDA and NMF models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We observe that in the LDA model when the number of topics is 20, we obtain the best coherence value of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='518 in the 20NG dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In the case of the NMF model, the best coherence value is when the number of factors is 30 with 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='504 in the 20NG dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In the IMDB dataset, we also obtain the best coherence value when the number of topics is 20 in the LDA model with a value of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='461 and the NMF model gives us the value 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='300 when the number of factors is 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' PLM & 20NG dataset: In the case of the vanilla BERT-base model in Table 2 (left), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=', 20NG dataset, we notice that when the number of soft attention clusters is 50 there is some comparable performance with the coherence results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Precisely, we read from the table that for VB50 the coherence value is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='503 in layer 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' This coherence value is numerically close to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='518 when the number of topics is 20, and in the case of the NMF model, it is approximately equal to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='504 when the number of factors is 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' This suggests that both LDA and vanilla BERT-base attention word clusters are semantically coherent when the number of soft clusters is 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We also notice that the contextual layers are mainly playing 10 Mozhgan Talebpour, Alba Garcia Seco de Herrera, Shoaib Jameel a key role in modelling such semantically close words, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=', layer 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' When we refer to the word overlaps in Table 4, we notice that the top 20 word overlaps are also consistent with the BERT-base model in layers 7, 8, 9 and 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' It means that out of 20 words, there are 17 overlapping words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Upon comparing the results of the fine-tuned version of the BERT-base model where the fine-tuning was done on the classification task, we notice that soft clus- ters 50 and 100 in Table 2 lead to comparable coherence performances obtained by the LDA and NMF models in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Precisely, we read from the table that when the number of clusters is 50 and 100, we obtain the coherence value of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='508 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='503, respectively that again are numerically comparable to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='518 in the coherence table for LDA and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='504 for the NMF model, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=', Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' While it would be ideal to have these coherence results be equal, such results are diffi- cult to obtain considering noise in the data and the randomness involved when initiating the training process of these semantic models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' What is interesting in the case of the fine-tuned version of the BERT-base model is that two layers show comparable coherence performances and both these layers learn contextual information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' When we look at the topic associated with “computing technology” in the 20NG dataset, we noticed that words such as “organisation”, “com”, and “nntp” were among the overlapping words which suggest that both BERT and LDA learn thematically the same words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' While it can be argued that even simple clustering algorithms such as k-means might generate clusters that are coherent and with high-overlapping words, we have found out that k-means does not lead to coherent clusters and the word overlap count was also very low, for instance, in most cases we found the word overlap values to be sometimes 1, and most often, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In the case of the vanilla DistilBERT model presented in Table 3 (left), we notice that the higher layers demonstrate the highest soft cluster coherence results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' What we notice is that the contextual layers show a higher degree of cluster coherence comparable to performance with the LDA model than with the NMF model in Table 1, for instance, the vanilla DistilBERT version with 200 soft clusters shows a relatively comparable performance when compared with the LDA model in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' It can be argued that in terms of the absolute numbers the results in Table 3 are much higher than in Table 1 when we only look at the highest DistilBERT layers values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' One of the reasons is that different pre-processing strategies have been chosen in both models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' However, this was unavoidable because including stop words in the PTM models would result in noisy topics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Note that other layers such as Layer 4, soft cluster 30, in the case of the vanilla DistilBERT model compare well with the LDA coherence results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Layer 4 in the case of the DistilBERT model compares reliably with the soft cluster 30 when we consider the NMF model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' PLM & IMDB dataset: In the IMDB dataset, Table 1 presents the ideal coherence value when the number of topics/factors is 20 for the LDA and the NMF models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' For the LDA model, the coherence value is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='461 and for the NMF model, the coherence value is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Referring to Table 2 (right), we see that the Topics in Contextualised Attention Embeddings 11 comparable LDA value is obtained in layer 6 in the vanilla BERT-base version when the number of soft clusters is 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In the fine-tuned version, we see the comparable value in layer 8 when compared to the LDA model and when the number of soft clusters is 150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' If we consider topic 30 in Table 1, we notice two comparable values in Table 2 in layer 12 which is a layer that captures contextual information more than any other layer when the vanilla soft clusters are 20 and 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In Table 4, most word overlaps occur in layers 5, 9, 11, and 12 and these results are consistent with the 20NG results where higher contextual layers have the maximum word overlap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We also notice that layers 6 and above have the most ideal coherence values indicating that if the clusters are coherent, they also have maximum word overlaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' It means that these clusters share common words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In DistilBERT, in Tables 3 and 4 we see that the NMF model tends to show comparable coherence values in the higher layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In Table 4, we observe that the word overlaps are fairly uniformly distributed across layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' While the lower layers have shown to have maximum overlaps, we can notice that the upper layers too have a word similar overlaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' However, their coherence values are not comparable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' It is because IMDB instances are short noisy sentences where the model seems to be performing not very reliably unlike the 20NG dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' What is also noticeable from the results is that the fine-tuned version of the DistilBERT model does not show comparable coherence performance when compared with the NMF model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' This could suggest that classification fine-tuning helps DistilBERT lose the latent topic information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In summary: 1) the attention mechanism is an important component in the PLMs that help capture some patterns that are also captured by PTMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' 2) there is correspondence between the coherence results obtained from PLMs and PTMs because in most cases we obtain comparable coherence performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' 3) in PLMs, there are high word overlaps in the contextualised layers and clusters of words obtained from PTMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' 4) in most cases, it is the contextualised layer that captures the most commonality with PTMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' One of the limitations of our work is that it does not experiment with other language models very different from BERT such as XLNet [62] and GPT-3 [16] to ascertain that similar conclusions could be also derived from them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' However, what is important to note is that our conclusions point toward the importance of the attention mechanism rather than the way pre-training is done or the size of the dataset that has been used to pre-train the model, or the model design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We also have to verify whether the results are generalizable to even larger models such as BERT-large which requires much more computational resources to conduct this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We show another finding through Figure 2 where we demonstrate the im- portance of the attention mechanism and how topic weights (probabilities) and attention weights tend to focus on the same words in a given context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' To generate the figure, we have taken an example from the IMDB dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In the BERT-base model, layer 11 is examined because it is the contextual layer and has the highest word overlaps in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In the case of the DistilBERT-base model, we have 12 Mozhgan Talebpour, Alba Garcia Seco de Herrera, Shoaib Jameel Layer 20NG IMDB 1 16 14 2 16 13 3 16 12 4 16 14 5 16 17 6 16 14 7 17 12 8 17 12 9 17 17 10 16 11 11 17 17 12 16 17 Layer 20NG IMDB 1 12 10 2 12 10 3 9 10 4 12 10 5 12 10 6 12 9 Table 4: BERT (left) and DistilBERT (right) attention word overlap with LDA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' 2: Illustrating attention using a sentence from the IMDB dataset as an example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We have presented these results from the BERT-base layer 11 and DistilBERT-based layer 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The number of topics/factors in the case of PTM is 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' The figure is used to demonstrate that these models tend to focus on relevant tokens within their context and assign lower weights to general tokens such as stopwords.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' selected layer 5 given that it is one of the contextual layers and has one of the highest word overlaps in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We have selected the number of topics as 20 and the number of NMF factors as 20 which is based on the results obtained in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' What we observe from the figure all the models tend to focus on the relevant keywords in the context, for instance, we observe that PLMs focus on the words such as “good”, “effects”, “terrible”, “movie” that are relevant to the movie and the PTMs too tend to focus on the same tokens in this context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' What we learn from the figure is that PTMs and PLMs, while they are different, both tend to focus on the relevant words in a given contextual window.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' This figure helps us to draw some relationships between the attention weights and the topic probabilities in that they focus on the important words only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We also notice that common words such as stopwords are given less weightage by the models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' words BERT-based DistilBERT-based LDA NMF 0 This 0.' metadata={'source': 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+page_content='071100 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='010000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='101000 9 effects 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='111700 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='097400 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='002000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content='003000Topics in Contextualised Attention Embeddings 13 While the authors in [49] have found out that the word clusters obtained from some PLMs tend to cluster the contextualised word vectors that resemble what is learned by a topic model, our result suggests that it is the attention mechanism that is playing a key role in obtaining such results which is the key contribution of our work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' It can also be argued that the contextualised token embeddings obtained from a PLM model can lead to almost similar conclusions, in this work, we wanted to explicitly study the role of the attention weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' 5 Conclusions Topic modelling has remained a dominant modelling paradigm in the last decade with several topic models developed in the literature [64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Topic models were not only modelled using Bayesian statistics but also linear algebra-based such as the NMF model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' While both these models are formulated differently, they both tend to exhibit similar clustering properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' With the development of PLMs, these models have now taken over the landscape in text mining and NLP be- cause they have outperformed existing baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Recent research points out that word-level clustering on BERT embeddings results in word clusters that share a close relationship with those discovered using topic models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' As a result, this motivated us to study the reason which component in the language model helps capture such topic information when the model has not been explicitly designed to model latent word topics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Through probe tasks, we find that it is the atten- tion mechanism that plays a key role in modelling word patterns that resemble something that is also discovered using topic models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We strongly believe that our work helps add further insight into the relationships between topic models and PLMs including the role that is played by the attention mechanism in the language model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' In the future, we will conduct a thorough theoretical analysis to find out the key theoretical similarities between a topic model and a PLM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We will also study how different PLMs other than those that are based on BERT encode latent topics using attention weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Our results are not only applicable to NLP and document modelling fields in general, but the results are also relevant to information retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' For instance, in an information retrieval setting, we can only use features obtained from PLMs to retrieve relevant documents without having to worry about latent topics features that would potentially increase the number of features that might even degrade the performance of an information retrieval engine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Besides that, we may be injecting more redundant features into the information retrieval model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Topic models have been shown to improve information retrieval results and PLMs have been shown to demonstrate even better results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' This could be because PLMs already have encoded a variety of features in their rich vector space that includes latent topics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' As a result, the improvement that we see also comes from topics implicitly encoded in the PLM attention vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' We thus believe that our paper will have a significant impact in the information retrieval field too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' 14 Mozhgan Talebpour, Alba Garcia Seco de Herrera, Shoaib Jameel References 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9E3T4oBgHgl3EQfJAlP/content/2301.04339v1.pdf'} +page_content=' Adhikari, A.' metadata={'source': 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/dev/null +++ b/l9E2T4oBgHgl3EQfJAaa/content/tmp_files/2301.03687v1.pdf.txt @@ -0,0 +1,987 @@ +Citation: Tito, E.P.; Goncharov, V.P.; +Pavlov, V.I. Hot Spots in Sgr A* +Accretion Disk: Hydrodynamic +Insights. Universe 2023, 9, 40. +https://doi.org/10.3390/ +universe9010040 +Academic Editor: Lorenzo Iorio +Received: 27 November 2022 +Revised: 2 January 2023 +Accepted: 4 January 2023 +Published: 8 January 2023 +Copyright: +© 2023 by the authors. +Licensee MDPI, Basel, Switzerland. +This article is an open access article +distributed +under +the +terms +and +conditions of the Creative Commons +Attribution (CC BY) license (https:// +creativecommons.org/licenses/by/ +4.0/). +universe +Article +Hot Spots in Sgr A* Accretion Disk: Hydrodynamic Insights +Elizabeth P. Tito 1,* +, Victor P. Goncharov 1,2 +and Vadim I. Pavlov 1,3 +1 +Scientific Advisory Group, Pasadena, CA 91125, USA +2 +A. M. Obukhov Institute of Atmospheric Physics RAS, 109017 Moscow, Russia +3 +Faculté des Sciences et Technologies, Université de Lille, F-59000 Lille, France +* +Correspondence: eptito@gmail.com +Abstract: The recent image of our galaxy’s supermassive black hole Sgr A* derived from the 7 April 2017 +data of the Event Horizon Telescope Collaboration shows multiple hot spots in its accretion disk. Using +the analytical framework, we demonstrate that the observed hot spots may not be disjoint elements but +causally linked components (“petals”) of one rotating quasi-stationary macro-structure formed in the +thermo-vorticial field within the accretion disk. +Keywords: black hole; accretion disk; hydrodynamics; hot spots; methods: analytical +1. Introduction +The image of our galaxy’s central supermassive black hole Sagittarius A* (Sgr A*), derived +recently by the Event Horizon Telescope (EHT) Collaboration (see Figure 1A and Refs. [1–6]) +shows a multi-spot structure of its accretion disk. The disk structure is a product of complex +state-of-the-art data analysis rather than a direct observation. +Figure 1. Left panel (A): Image of Sgr A* from Ref. [1]. Representative EHT image of Sgr A* from +observations on 7 April 2017. This image is an average over different reconstruction methodologies +(CLEAN, RML, and Bayesian) and reconstructed morphologies. Color denotes the specific intensity, +shown in units of brightness temperature. The inset circle shows the restoring beam used for CLEAN +image reconstructions (20 µas FWHM). The bottom panels show average images within subsets with +similar morphologies, with their prevalence indicated by the inset bars. Right panel (B): Normalized +distribution of temperature-excess in an accretion disk for the model of localized vortices (Section 3). +Universe 2023, 9, 40. https://doi.org/10.3390/universe9010040 +https://www.mdpi.com/journal/universe +arXiv:2301.03687v1 [astro-ph.HE] 9 Jan 2023 + +BYSgr A* +April 7, 2017 +50 μas ~ 100 +2 +6 +8 +10 +12 +14 +Brightness Temperature +(109 K)Universe 2023, 9, 40 +2 of 15 +The EHT—a collection of radio-telescopes scattered around the Earth—operates in the +digital interferometer mode: the signal from each antenna is recorded, and then the image of +the object is restored using correlation analysis. Sophisticated data-processing algorithms have +permitted the EHT to achieve angular resolution on the order of 20 microarcseconds. At the +level of sensations, this is equivalent to the ability to read newspaper headlines on the Moon. +However, as Figure 1A indicates, this resolution scale is comparable to the size of Sgr A* itself; +the accretion disk is slightly greater (∼50 µas). Furthermore, the EHT telescopes could only +record data from a small study area for a short period of time (see colored zones in Figure 2). +Many (white) parts have remained unexplored. To restore the full mosaic, the algorithms had +to fill the gaps. +Figure 2. From Ref. [1] (one panel from original Figure 2). EHT baseline coverage, where dimensionless +coordinates u = (u, v) give the projected baseline vector for each antenna pair in units of the observing +wavelength. +The shape of the observed structure (Figure 1A)—even if the structure is short-lived— +appears to indicate that it is likely to be not an artifact of image-reconstruction algorithms, but a +real phenomenon. Using the analytical framework, we demonstrate that the observed hot spots +may be not disjoint but causally linked components (“petals”) of one rotating quasi-stationary +macro-structure formed in the thermo-vorticial field within the accretion disk. +Indeed, when a black hole’s accretion disk—whose rotation axis is perpendicular to the +disk plane—is heated non-homogeneously (so temperatures are higher near the outer edge of +the disk), then, in the field of the centrifugal force, spontaneously self-formed hot “bubbles” +(composed of locally clustered plasma with temperatures in excess of the “average”, hence +with lower densities) should move towards the axis of the disk rotation. However, when the +hot “bubbles” are also vortices, then each such vortex (via the induced velocity field) “forces” +other vortices to rotate around itself, hence diverting their motion “sideways”, curtailing the +movement towards the central axis of accretion-disk rotation. All these vortices are subject to +the influence of the cumulative velocity field induced by all other vortices. Thus, the radial +motion of the vortices towards the axis becomes suppressed. As a result, if stabilized, the +vortices take positions equidistantly from the axis and self-organize into a symmetric thermo- +vorticial macro-structure that rotates as a whole around the mutual center (like in Figure 1B). +The dynamics and longevity of this structure are linked to the thermal and vortical properties +of the system and its elements. Visually, if observed, the petals of this structure look like bright +“hot spots”. +In this paper, we consider the EHT image from the perspective of theoretical hydrody- +namics. In particular, we describe a model of large-scale stationary rotating heated vortices. +However, we consider not the usual hydrodynamic field of vorticity but a complex thermo- +hydrodynamic field system that under certain circumstances may self-organize into regular +structures. The physical and mathematical underpinnings of this analytical approach are +elaborated in the references provided in the relevant places. The explanation of their details +is beyond the scope of this paper. To avoid any confusion, let us also emphasize upfront that + +7.5 +5.0 +2.5 +0.0 +-2.5 +-5.0 +-7.5 +7.5 +5.0 +2.5 +0.0 +2.5 -5.0 -7.5 +(G入) +uUniverse 2023, 9, 40 +3 of 15 +we work with the field, not with individual particles (their trajectories or orbits). Perhaps what +may help the reader grasp this nuance better is the reminder that the velocity of displacement +of electrons in a usual house wire is not the same thing as the speed of propagation of the +electro-magnetic field perturbation along that same wire. As the result of our analysis, we show +that multi-hot-spot thermo-vorticial macro-structures may indeed self-organize in the accretion +disk. The model makes it possible to determine basic characteristics of such structures, for +example, the horizontal space-scale, the period of proper rotation, and the peak temperature +magnitude in the vortex. +The paper is organized as follows: Section 2 presents the model, Section 3 presents the +results, and Section 4 summarizes the conclusions. +2. Model +The model setup is straightforward: a black hole pulls in and crushes the matter from +the surrounding space; the particles are then accelerated to near-light velocities and twisted +around the black hole, forming a flattened accretion plasma disk in the equatorial plane. +We will use the spacetime metric entirely characterized by the black hole mass parameter +and its “spin” (described in our Refs. [7,8]; for more details, see also [9–14], and bibliographies +therein). We will assume that the mass of the accretion disk is negligible compared to the black +hole “mass” M, probably (10−5 ÷ 10−4)M⊙; the radiative cooling does not strongly affect the +dynamics of fluid motion; and the electrons and ions are very weakly coupled by Coulomb +interaction and hence ions and electrons plasmas components have different temperatures, +Te ≫ Ti (see Ref. [15]), and thus it is the electron component that contributes the most to the +equation of state of the accretion disk matter. Due to the large difference in the masses of +electrons and protons, electrons are highly mobile and provide quasi-neutrality of the plasma. +Due to the high conductivity of the plasma, its own magnetic field can be considered as a field +“frozen” into the plasma. +Generally speaking, equations of fluid motion in the vicinity of a black hole must be +written using the concept of relativistic dynamics. The key points are as follows: We suppose +that the space-time near the (non-charged) black hole Sgr A* is described by the Kerr metric—an +exact, singular, stationary, and axially symmetric solution of the Einstein–Hilbert equations of +the gravitational “field” in vacuum. Next, we introduce the Boyer–Lindquist 4-coordinates, +qα = (t, r, θ, φ) (it is well known that besides the Boyer–Lindquist coordinate representation, +other representations of space-time locations exist). In terms of the Boyer–Lindquist coordinates, +the square of interval is written as ds2 = gαβ(r/rg, θ)dqαdqβ with α, β = 0, 1, 2, 3, i.e., the +components of gαβ depend only on the dimensionless combination rg/r and θ. Here, rg = +2GM/c2 is the Schwarzschild radius, c is the speed of light, G is the gravitational constant, and +M is the “mass” of the black hole. The off-diagonal term g03 in the metric tensor is proportional +to the rate of the black hole’s own rotation and to 1/r. For the Minkowski tensor, we use +the metric signature diag(+ − −−) (see, for example, Ref. [8], and Refs. therein). To satisfy +the principle of causality for moving material objects, obviously, ds2 > 0. The four time- +space coordinates qα = (t, r, θ, φ) give the location of a world-event from the viewpoint of a +remote observer. The meaning of space coordinates r, θ, φ is clear once transitioned to the limit +r ≫ rg, r ≫ ωr2 +g/c. When the square of the interval becomes ds2 → c2dt2 − dr2 − r2(dθ2 + +sin2θ dφ2), i.e., at infinity, parameters r, θ, φ may be interpreted as the standard spherical +coordinates in flat space-time. As for the parameter r, strictly speaking, note that it is not the +“distance” in the usual meaning from the center of black hole. This is because, for any material +object, in the space-time defined by equation ds2 = gαβdqαdqβ, no central point r = 0 exists in +the sense of a world-event on a valid world-line. +Next, we consider the motion of the medium far away from the event horizon, i.e., when +parameter r is meaningfully greater than rg. For the flow at r > 3rg, in the expansion of the + +Universe 2023, 9, 40 +4 of 15 +metric tensor, we may neglect the terms of order (rg/r)2 and greater. They contribute less +than (1/3)2 ∼ 10% to the components of the metric tensor. Such omission of smaller terms +makes our approximation Newtonian or post-Newtonian. The non-diagonal metric-tensor +term (describing involvement of the medium in the rotation of space-time in the vicinity of the +black hole) gives rise to the “force” analogous to the traditional Coriolis force in the equations +for medium flow. +Hence, we write the system of equations of relativistic fluid dynamics in the curved +space-time and expand the metric tensor and the fluid energy–momentum tensor into a series +with respect to small parameters rg/r < 1 and ∼ c−1. We keep only the leading terms in the +equations of fluid motion. +Next, the fluid is presumed to be localized near surface θ = π/2 (in a pancake-like +accretion disk)—the flows of the disk medium are considered only near this surface. Then, we +can transition to cylindrical coordinates qi = (r, φ, z) and presume that the gas particles orbit +near the z = 0 plane and the vertical component of their velocity vz ≪ max(vr, vφ). +In this model, when r exceeds the Schwarzschild radius rg (specifically, r > 3rg), then the +vertical component of gravity acceleration gz = − G M z/(r2 + z2)3/2 ≡ −K2z(1 + z2/r2)−3/2 +is balanced by the pressure gradient. Here, G is the gravitational constant, c is the speed of +light, K2 = GM/r3 = c2rg/(2r3), and K ∼ r−3/2 is the radius depending so-called Kepler +parameter: the angular velocity of a test particle in a circular orbit at distance r from a point +mass M in Newtonian approximation of gravity. +Gas pressure along the direction perpendicular to the disk plane (x, y) is determined by +the hydrostatic equilibrium, dP = ρgzdz. Generally speaking, pressure may have important +contributions from electromagnetic radiation and induced magnetic field. The simplest case, +however, is when the pressure is dominated by gas pressure, and the vertical temperature +distribution is isothermal, which is roughly appropriate when the disk is optically thick +and externally heated. The equation of state of gas/plasma is then P = s2ρ, where s is the +“isothermal sound speed” (which is not a function of the transversal coordinate z). +If we further assume that z ≪ r, the equation of hydrostatic equilibrium becomes s2dρ = +−s2h−2ρzdz, the solution of which is ρ(z) = ρ0 exp(−z2/2h2). Here, the transversal space +scale h is introduced, h = s r3/2/(GM)1/2. Parameter ρ0 has the meaning of density at the disk +mid-plane (at z = 0), and parameter h is the characteristic local thickness of the accretion disk. +In order for the accretion disk to be considered thin, it is necessary that h/r ≃ sr1/2/(GM)1/2 ∼ +(s/c)(r/rg)1/2 ≪ 1. On the other hand, for great distances away from the black hole (r > rg), +specific relativistic effects may be neglected or parametrized. Thus, we obtain natural bounds: +rg < r < rg(c/s)2. +Equations of Motion: The equations of motion for an inviscid incompressible fluid express +the laws of conservation for mass, momentum, and energy. The flow of gas may be considered +incompressible (see, for example, [16]) when its velocity v satisfies condition v2 ≪ s2 and the +characteristic time scale of the flow change T ≫ L/s where L is the characteristic spatial scale +where the flow characteristics change substantially. In this case, the mass conservation law is +expressed as div v = 0, i.e., the law is not ρ = Const, but ∂tρ + vj∂jρ = 0. +We assume that the domain of the disk where the vortex structure of interest is formed, is +characterized by an approximately constant angular velocity Ω. In a coordinate system rotating +with the angular velocity Ω = (0, 0, Ω), where x ≡ x1 and y ≡ x2 are the axes in the horizontal +plane and z is vertically upwards, the basic equations of motion become +∂jvj = 0, +(1) +ρ(∂tvi + vj∂jvi + 2ϵijkΩjvk) = −∂iP − ρ∂iΦ, +(2) +∂tθ + vj∂jθ = 0. +(3) + +Universe 2023, 9, 40 +5 of 15 +Here, vi are the components of the velocity field, ρ is density, P is pressure, and θ is temperature. +The potential Φ of the force field is Φ ≃ −K2r2 + (1/2)K2z2 − (1/2)|[Ω, r]|2. Furthermore, +here, [a, b] is the cross product of vectors a and b; and ϵijk is the alternating tensor (ϵ123 = 1, +zero for any two indices being equal, +1 for any even number of permutations from ϵ123, and +−1 for any odd number of permutations). +Due to the assumption of an incompressible medium (implying s−2 → 0), the equation of +state ρ = ρ(θ, P) turns into the density expression, which only depends on the temperature +(and not on the pressure). In fact, ∇ρ = (∂ρ/∂θ)∇θ + (∂ρ/∂P)∇P ≃ −ρβ∇θ. The coefficient +of thermal expansion, β = −ρ−1(∂ρ/∂θ), may be assumed constant and positive. (For gases, +β = 1/θ0.) Thus, we can set ρ = ρ0(1 − β(θ − θ0)), where subscript zero denotes the reference +values. Due to the fact that β(θ − θ0) is generally significantly less then one, one may neglect +the density variations in all principal terms and hence replace ρ with the constant value ρ0, +except in the “buoyancy” term, which is proportional to ∂jΦ (see, for example, [16,17]). +Next, we apply the curl operator ∇× to the linear momentum conservation Equation (2). +This gives +� +∇ − β∇θ, dv +dt + 2 +� +Ω, v +�� += β +� +∇(τs + τ), ∇Φ +� +, +(4) +where brackets symbolize cross-product. Since β|∇θ| ≪ 1, term β[∇θ, A] is small with respect +to [∇, A] at the horizontal scales typical for any hydrodynamical vector A and may be not +taken into account. +Consider now temperature θ as θ = θ0 + τs + τ, where θ0 is the (constant) baseline +temperature of the accretion disk, quantity τs is an axially symmetrical part of the temperature +distribution that is not time-dependent, and τ = τ(t, xj) is the dynamical quantity related to +the vortex structures in the fluid. When r = (x, z), vj = (v, w), then ωi = ϵijk∂jvk + 2Ωi, and +Equation (4) can be rewritten in the tensorial form as +(Dt + w∂3)ωi = ωj∂jvi + βϵijk(∂j(τs + τ))∂kΦ, +(5) +where Dt = ∂t + (v · ∇) is the substantial derivative, v = (v1, v2) is the flow velocity, and +∇ = (∂1, ∂2) is the gradient operator with components ∂i in the (x, y) plane. +In the simplest model—in which the vortex structures are realized in a ”thin” flat sheet of +an incompressible inviscid fluid (i.e., when h ≪ L, V2 ≪ s2 ≪ c2, Re ≫ 1)—the z-component +of velocity, w, vanishes and may be dropped in all formulas (see, for example, [18]). Note also +that ϵ3jk∂jτs∂kΦ ≡ 0 because of an axial symmetry of both τs and Φ. Thus, the set of equations +for the z component of vorticity ω3 and for variation of temperature τ becomes +∂jvj = 0, +(6) +Dtω3 = βϵ3jk∂jτ∂kΦ, +(7) +Dtτ = −vi∂iτs, +(8) +where indices j, k = 1, 2. Equation (6) permits the introduction of the stream function ψ: +vi = ϵ3ij∂jψ ≡ ϵij∂jψ, +(9) +where tensor ϵij is the antisymmetric unit tensor of the second order, ϵ12 = −ϵ21, and diagonal +components are zero. In this case, vorticity ω3 = −∆ψ + 2Ω3 with ∆ = ∂2 +1 + ∂2 +2. +Temperature Stratification: To describe the effect of temperature stratification—i.e., to +show how stationary temperature increases as the distance from the axis of rotation increases— + +Universe 2023, 9, 40 +6 of 15 +we express (using r = |x|, x = (x1, x2) and Taylor series expansion) the background distribution +of the temperature τs in the form +τs = α +2r2 , α > 0 , +(10) +where α is the parameter characterizing the “rapidity” of increase in temperature with distance +from the disk rotation axis. (Generally speaking, the question of what shape the temperature +profile takes within a black hole’s accretion disk is an open one. Experimental measurements +remain challenging, despite significant progress. See, for example, [19,20].) When the leading +contribution to potential Φ comes from the centrifugal effects, we can express Φ = −K2|x|2 − +(1/2)[Ω, x]2 ≃ −(1/2)[Ω, x]2. Thus, when Ω is presumed constant in a band of r where the +vortex hotspots are forming, the set of coupled nonlinear evolution equations becomes +∂t∆ψ + ϵik∂iψ∂k∆ψ = βΩ2ϵikxi∂kτ, +(11) +∂tτ + ϵik∂iψ∂kτ = αϵikxi∂kψ. +(12) +For a general case, ∆ψ should be replaced: ∆ψ → ∆ψ − 2Ω. +Equations (11) and (12) have a transparent physical meaning. Their left sides describe +transport of dynamic quantities: vortex ∆ψ and temperature perturbation τ. Their right sides +describe “sources” that generate the vortices and temperature perturbations. +In other words, the vortices are generated by the source (the right part of Equation (11) +which is effective (non-zero) only when there exists an inhomogeneous gravity-like force field +Φ ∼ Ω2 with which temperature perturbation τ interacts via the equation of state (when +β ̸= 0). The quantity ψ—which characterizes the vortex field in the fluid—is transported by +the self-induced flow (the left part of Equation (11)). On the other hand, in Equation (12), this +temperature perturbation τ is transported by the self-generated flow (ψ ̸= 0); the temperature +perturbation τ(t, x) is generated by the source (the right part of Equation (12)), which is non- +zero only when there exists a spatial and time-independent temperature gradient (i.e., when +τs ̸= 0). The processes are interlinked because the “source” of one dynamic quantity depends +on the complex combination involving another dynamic quantity. The set of Equations (11) and +(12) shows that when temperature stratification is absent (α = 0) and there is no disk rotation +(disk Ω = 0, i.e., centrifugal force is zero), then Equations (11) and (12) degenerate into the +traditional equations for vortex evolution and transport in a two-dimensional ideal fluid. +Linear Approximation: Assuming that an excess of temperature τ above the basic level +of temperature is not too large, in view of the link between fields τ and ψ via Equations (12), +we consider a simple linear dependence between the excess of temperature τ and the vorticity +ψ that generates this excess: +τ = −Cψ . +(13) +Obviously, it follows from Equation (13) and from the meaning of quantities τ and ψ that the +dimension of the coefficient of proportionality is [C] = θL−2T ≡ [temperature] × [lengh]−2 × +[time]. By substituting Equation (13) into Equation (12), we obtain +∂t∆ψ + ϵik∂iψ∂k∆ψ = −CβΩ2ϵikxi∂kψ, +(14) +−C β +α Ω2 × C(∂tψ + ϵik∂iψ∂kψ) = C β +α Ω2 × αϵikxi∂kψ. +(15) + +Universe 2023, 9, 40 +7 of 15 +Hence, we conclude that both the first and second equations in Equations (14) and (15) describe +the evolution of the same physical quantity. The equations will be consistent when the following +condition is imposed on the current function ψ: +(∂t + ϵik∂iψ∂k)(∆ψ − R−2ψ) = 0 . +(16) +Here, parameter R−2 = C2(β/α)Ω2. The dimension of this quantity is (θ1L−2T1)2 × θ−1L2 × +θ−1 × T2 = L−2; i.e., R is a space scale factor. Quantity q = ∆ψ − R−2ψ describes the distri- +bution of generalized vorticity. Its change in time and in space has to satisfy the evolution +equation Equation (16). +The stream function ψ is found via the Green function approach. In the symbolic integral +form, in the boundless space, it is +ψ(x, t) = +� +(∆ − R−2)−1(x, x′) +� +q(x′, t) . +(17) +The subsequent calculation procedure is as follows: (i) The initial vorticity distribution is set; +the stream function ψ is found from Equation (17); together with it, the non-linear evolution +Equation (16) is numerically solved. (ii) The distribution of vorticity is set in the form of a +macrostructure with petals (with constant vorticity inside) whose moving boundaries evolve +according to Equation (16); i.e., we are considering a region bounded by some closed contour +(with possibly a rather complex shape) such that quantity q(x, t) takes a constant value inside +and zero outside. For stationary dynamical regimes, this can be accomplished analytically +(details of the contour dynamics method and of the operator techniques can be found, for +example, in Refs. [21,22]), as well as Refs. [18,23]); (iii) For a strongly localized vortex, quantity +q(x, t) can be parameterized by the function in form F(x − x0(t)), i.e., the one with the center +at coordinate x = x0(t), which satisfies the equation of transport ˙x0i(t) + ϵik∂iψ = 0, i.e., when +the center of vortex moves according to ˙x0(t) − vs.[x0(t)] = 0. (Here, the symbol “dot” signifies +the derivative with respect to time.) +Stationary Vortex Structures: Stationary vortex structures—the ones rotating with con- +stant angular velocity ω—are simpler to consider in a rotating coordinate system where the +structures appear immovable; i.e., when rotation direction is co-aligned with z axis, the deriva- +tive with respect to time becomes ∂t = −ωϵikxi∂k. (The procedure is laid out, for example, in +Ref. [24].) Indeed, when f = f (ρ, φ − ωt), then the calculation relying on the properties of Ja- +cobeans produces ∂t f = −ω∂φ f = −ω∂( f, ρ)/∂(φ, ρ) = −ω(∂( f, ρ)/∂(x1, x2))(∂(x1, x2)/∂(φ, ρ)) = +−ω(ϵikρ−1xi∂k f )(−ρ). Then, Equation (12) may be rewritten as: +ϵik∂i +� +− ω +2 |x|2 + ψ +� +∂k +� +τ + α +2 |x|2 +� += 0 , +(18) +which is satisfied by the ansatz +τ + α +2 |x|2 = F(−ω +2 |x|2 + ψ). +(19) +The explicit expression of function F can be found from the obvious fact that temperature- +driven flow perturbations must vanish when temperature perturbations vanish themselves. +The suitable expressions is function F(u) = −αu/ω. Then, temperature fluctuations are +expressed via the stream function +τ = − α +ω ψ . +(20) + +Universe 2023, 9, 40 +8 of 15 +Combining this with Equation (11) where ∂t = −ωϵikxi∂k is taken into account, we obtain the +second evolution equation: the one that describes rotation of a stationary vortex structure with +angular velocity ω caused by the self-induced field of hydrodynamical velocity: +ϵik(−ωxi + ∂iψ)∂k +� +∆ψ − R−2ψ +� += 0 . +(21) +Once Equation (20) is written out, parameter R2 becomes R2 = (αβ)−1(ω/Ω)2. Here, β is +the coefficient of thermal expansion. For almost all physically realizable situations, β > 0 (the +well-known exception is water in the temperature range between 0 and +4 ◦C). Parameter α +—characterizing the “rapidity” of increase in temperature with distance from the disk rotation +axis—can be either positive or negative. When α > 0, the periphery of the accretion disk is +heated more than the central zone; when α < 0, the central zone of the disk is hotter than +the periphery. Thermal length scale λθ = (|α|β)−1/2 is determined by the background state +of the disk in the framework of the model. Obviously, space scale parameter R characterizes +the “rapidity” of the decrease in temperature (and stream function) with distance from the +disk rotation axis. Below, we write R2 → R2 (Θ(α) − Θ(−α)), where Θ(α) is the Heaviside +step-function (equal to unit for positive argument and zero for negative argument), and, leaving +the old notations, R2 = (|α|β)−1(ω/Ω)2. +3. Results +We use the model described above to gain insights into the three-spot structure in the EHT +image of Sgr A* accretion disk (Figure 1A). The bright spots are the zones with higher (relative +to the base level) temperature τ and (since τ ∼ ψ) with higher vorticity ∆ψ. In this framework, +thermo-hydrodynamical vorticity-field structures may be conceptually analyzed with two limit +approaches: the method of localized vortices and the method of thermo-vorticial spots (blobs). +Localized Vortices: The simplest consideration for a three-spot stationary thermo-vortex +structure (symmetric with respect to the rotation axis of a pancake-like thin accretion disk) is to +analytically treat the hot zones as narrowly localized formations modeled as 2D delta-functions +at the limit case. Doing so would allow us to find the required conditions for the existence +of the observed phenomenon and the resulting relationships between key characteristics of +the structure. (This approach is not limited to only structures with three spots, but can be +generalized to structures with any vortex-number N.) Hence, we write: +∆ψ − R−2(Θ(α) − Θ(−α))ψ = +3 +∑ +j=1 +κR2 δ(2)(x − x(j)), +(22) +where κ characterizes the intensity of one localized vortex, and δ(2)(x − x(j)) ≡ δ(1)(x − x(j)) × +δ(1)(y − y(j)) is the two-dimensional Dirac function in the xy-disk plane. The appearance of the +factor R2 in the right side of Equation (22) is due to the following reasoning: the delta-function +is a dimensional function. Its dimension is [δ(2)] = [length]−2 for 2D space. Obviously, the +argument of the delta-function must be dimensionless. (Indeed, there is no such thing as sin +of “one inch” or tan of “ten gallons”.) Therefore, δ(2) ≡ δ(1)(R−1x − R−1x(j)) × δ(1)(R−1y − +R−1y(j)) = R2 δ(2)(x − x(j)). In view of the meaning of the delta function in the right part of +Equation (22) and of the structure of the left part of Equation (22), the scale-factor R is the same +R that was introduced above—the characteristic size of the vortex kernel. Although alternatives +may exist, following the Occam’s Razor principle—the problem-solving principle of parsimony +that “entities should not be multiplied beyond necessity”—we choose the simplest option. +Indeed, among the options to use R or R multiplied by dimensionless (κ/ω)n, we choose the +simple R. + +Universe 2023, 9, 40 +9 of 15 +We further note that x(j) and y(j) may be expressed as components of the complex quantity +l × exp(i2π(j − 1)/3) in the plane x + iy (where l is the radius of a circumscribed circle). +When a vortex is modeled by a delta-function, a weak (logarithmic) singularity appears +in the distribution of stream function ψ (which is the solution of Equation (22)) when α > 0. +If α < 0, or a smoother distribution is adopted for α > 0, any singularities in ψ function then +disappear. +The solution to Equation (22) for unbounded space is +ψ = −κR2 +2π +3 +∑ +j=1 +Z0(|x − x(j)| +R +) . +(23) +Here, Z0(ξ) = J0(ξ)Θ(−α) + K0(ξ)Θ(α), J0(ξ) is the Bessel function of order n = 0, K0(ξ) is +the modified Bessel (McDonald) function of order n = 0. +Recall that for small values of the argument, function J0(ξ) → 1, function K0(ξ) behaves +logarithmically: K0(ξ) ≃ − log ξ + 0.1156. For large values, function J0(ξ), as known, behaves +as J0(ξ) ≃ +� +2/πξ cos[−ξ + π/4], function K0(ξ) behaves as K0(ξ) ≃ +� +π/(2 ξ) exp (−ξ). +This means that for α > 0 and r ≫ R; i.e., when ξ ∼ r/R ≫ 1, function K0(ξ) exponentially +quickly tends to zero, and therefore, the stream function ψ, and consequently the local vortex +magnitude and temperature excess τ, all will also tend to zero. This is the consequence of the +initial choice to model the vortices via delta-functions. Numerically, for some characteristic +points, K0(1) ≃ 0.421 and K0(0.4569) ≃ 1. The derivative of Z0 with respect to argument is +Z′ +0(ξ) = −Z1(ξ). +By substituting Equation (22) into Equation (21), and then taking into account +Equation (23), and by setting the terms with delta function and their derivatives as equal +to zero, we find the set of conditions for the existence of the modeled vortex structure: +ϵik +3 +∑ +n=1 +� +− ωx(n) +i ++ +3 +∑ +m=1 +′ κR2 +2πR +(x(n) +i +− x(m) +i +) +|z(nm)| +Z1(|z(nm)| +R +� +κR2∂kδ(z(n)) = 0 . +(24) +In this expression, symbol “prime” in the second summation indicates that the effect of vortex +self-action is excluded. When notation z(j) = x − x(j) is used, then z(ij) = x(i) − x(j) and +|z(12)| = |z(23)| = |z(31)| = +√ +3 l (where l is the radius of a circumscribed circle). +To satisfy Equation (24), the coefficients before every singularity must equal zero. Thus, +the following condition for the parameters of the vortex configuration arises: +−ωl2 + 2κR2 +2πR +l2(1 − cos 2π/3) +l +√ +3 +Z1( +√ +3l +R ) = 0 . +(25) +Recall that R = (|α|β)−1/2|ω/Ω)| is a dimensional function of four dimensional parameters. +Equation (25) can be rewritten in a compact dimensionless form, where ξ = +√ +3(l/R): +κ +ω = 2π +3 +ξ +Z1(ξ) +(26) +which says that for any specific ξ, ratio κ/ω is uniquely defined. Figure 3 plots Equation (26). + +Universe 2023, 9, 40 +10 of 15 +Figure 3. Model of Localized Vortices. Left panel (A): Both axes are in linear scale. Right panel (B): +Vertical axis is in log-scale. Both panels (A,B): A structure with three vortices forms only when κ/ω = +(2π/3)(ξ/Z1(ξ)), where ξ = +√ +3(l/R), l is the radius of a circumscribed circle, R = (|α|β)−1/2|ω/Ω)|, +α is the parameter characterizing the “rapidity” of increase in temperature with distance from the disk +rotation axis, β = −ρ−1(∂ρ/∂θ) is the coefficient of thermal expansion, ω is the angular velocity of +rotation of the vortex structure, Ω is the angular velocity of rotation of the accretion disk, and κ is the +characteristic intensity of one localized vortex. The blue curve is for α > 0 (the disk periphery is hotter). +The red curve is for α < 0 (the disk periphery is cooler): intensity κ → ∞ as ξ ≡ +√ +3(l/R) → ξN (red dot) +at which the Bessel function J1(ξN) = 0. (Here ξ1 ≃ 3.8317.) +For the presented model, the temperature excess τ follows from Equation (20) and Equa- +tion (23): +τ = +1 +2πβ( κ +ω )( ω +Ω)2 +3 +∑ +j=1 +Z0(|x − x(j)| +R +). +(27) +The characteristic temperature scale is defined thus as τ0 = (2πβ)−1(κ/ω)(ω/Ω)2. When +α < 0 (disk periphery is cooler), both “anticyclones” (temperatures excesses) and “cyclones” +(temperature depressions) are possible. +Figure 1B (on the front page of the article) illustrates the temperature distribution for a +system with three localized vortices, calculated using Equation (27), for a case when α > 0 (disk +periphery is hotter). In Figure 1B, the unit for the color scale is the characteristic magnitude of +temperature excess τ0 = (2πβ)−1(κ/ω)(ω/Ω)2. For the x and y axes, the unit is R = λθ(ω/Ω); +ω is the angular velocity of rotation of the vortex structure as a whole; Ω is the characteristic +angular velocity of rotation of the accretion disk; and λθ = (αβ)−1/2. In the expression for λθ, +the parameter α (characterizing the “rapidity” of the increase in temperature with distance +from the disk rotation axis) may be estimated as α ∼ (∆θ/R2∗). Here, R∗ is the characteristic +external radius of the active part of the accretion disk (obviously not equal to R) is presumed to +be greater than the size of the macrostructure, and ∆θ may be estimated as the temperature +difference across the disk (from the periphery to the center). In the expression for λθ, the +parameter β = −ρ−1(∂ρ/∂θ) is the coefficient of thermal expansion, which (for the model +whose equation of state is approximated by the equation for an ideal gas) may be written as +β ≃ θ−1, where θ is the averaged temperature of the accretion disk. +Thermo-Vorticial Spots (“Blobs”): Another fruitful approach is to use the concept of +thermo-vortical spots, for which the vorticity is constant inside domains bounded by movable +boundaries (contours) and is zero outside. Then, the problem of vortex evolution becomes +the problem of examination of the movement of the contours and determination of their final +macro-configuration. Examples of such macro-configurations are depicted in Figures 4 and 5 +(discussed below). +Within +this +framework—called +the +contour +dynamics +method +(CDM) +(see +Refs. [18,22–27])—the distribution of vorticity q for a vortex structure may be written as + +w +3 +2 +0 +0.5 +1.0 +1.5 +2.0 +2.5 +3.0 +3.5 +4.0" +-7 +2K +w +100 +50 +0 +2 +6 +8 +10 +50 +100Universe 2023, 9, 40 +11 of 15 +q = q0Θ(x, y). Function Θ(x, y) is a two-dimensional Heaviside step-function equal to one +inside the domain in consideration and zero outside. Parameter q0 describes the vorticity +inside the spot, which is presumed constant. Obviously, the dimension of this parameter is +[q0] = [time]−1. +Using CDM (see the physical foundation and the details on how to perform calculations +using CDM in Ref. [22]), we find the general expression for temperature distribution: +τ(x, y) = −(q0αRL +2πω ) +� +∂D ds +� +K1(|ˆz − z| +µ +) − +µ +|ˆz − z| +� ˆz,s(ˆz − z∗) +|ˆz − z| +. +(28) +Here, the integral is taken along the contour (whose shape is previously found by solving the +problem of the spot configuration); z = (x + iy)/L is the complex variable of the xy-position, +normalized by the characteristic space-scale L = (R/2)(q0/ω)1/3, which is linked to the size of +the macro-configuration; parameter µ = R/L is dimensionless; and domain D in the complex +plane z is a region filled with the vorticity q0. The domain is bounded by a closed contour +∂D; this boundary is expressed in the parametric form z = ˆz(s); parameter s is the contour arc +length beginning from some initial point; and derivative ˆz,s ≡ ∂ˆz/∂s is a unit vector that is +obviously tangential to the contour ∂D. +Based on the contour-integral Equation (28), the temperature distribution τ(x)/τ0 is +solved (and plotted in Figure 4B) for the contour boundary (black line) in Figure 4A. Shaded +gray in Figure 4A is the constant vorticity distribution q(x) = q0. +Figure 4. Illustration of analysis via method of thermo-vorticial spots (“blobs”). Left panel (A): A +three-petal vorticity distribution is specified as q(x) = q0Θ(x, y), where vorticity q0 is constant and +function Θ(x, y) is two-dimensional Heaviside step-function equal to one inside the shaded domain +and zero outside. (Ref. [22] explains in detail the entire theory and methodology. This depicted three- +petal thermo-vorticial structure takes this particular shape when one of the guiding parameters of the +macro-configuration reaches its limit case.) Right Panel (B): For the vorticity distribution specified in +Panel (A), the resulting temperature distribution τ(x) is obtained per Equation (28). The unit along +the vertical axis is the characteristic magnitude of temperature excess τ0 = q0αRL/2πω. (The central +τ peak is a consequence of the vorticity parametrization for the geophysical application in Ref. [22], +which for a black hole accretion disk should be obviously nil.) Both Panels (A,B): For x and y axes, the +unit is R = λθ(ω/Ω); ω is the angular velocity of rotation of the vortex structure as a whole; Ω is the +characteristic angular velocity of rotation of the accretion disk; and λθ = (αβ)−1/2. In the expression +for λθ, the parameter α (characterizing the “rapidity” of increase in temperature with distance from the +disk rotation axis) may be estimated as α = (8/π2)(∆θ/R2∗). Here R∗ is the characteristic radius of the +accretion disk (obviously not equal to R) is presumed to be greater than size of the macro-structure, and +∆θ may be estimated as the temperature difference across the disk (from the periphery to the center). In +the expression for λθ, the parameter β = −ρ−1(∂ρ/∂θ) is the coefficient of thermal expansion, which (for +the model whose equation of state is approximated by the equation for an ideal gas) may be written as +β ≃ θ−1, where θ is the averaged temperature of the accretion disk. + +3 +2 +1 +0 +1 +-2 +3 +-3 +2 +-1 +0 +1 +2Universe 2023, 9, 40 +12 of 15 +The key parameters here are τ0 = q0αRL/2πω, R = λθ(Ω/ω), λθ = (αβ)−1/2, β = +θ−1, (q0/ω) = 8(L/R)3 and α = (8/π2)(∆θ/R2∗), where θ is the averaged temperature of +the accretion disk, R∗(̸= R) is the characteristic radius of the accretion disk, and ∆θ is the +temperature difference across the disk (from the periphery to the center). Thus, the characteristic +level of the temperature excess in this limit case (i.e., in the model of thermo-vorticial spots, not +in the model of localized thermo-vortices) can be estimated by the expression +τ0 = +1 +4πβ(q0 +ω )4/3( ω +Ω)2 . +(29) +The above-mentioned parameters in Equation (29) are the very parameters that must be +measured experimentally to be able to comprehend the phenomena in images such as Figure 1A. +Equation (29) is functionally similar to Equation (27). The difference is in the index of +power dependence of the ratio of the vortex intensity and its angular velocity. This is an +insignificant difference considering the fact that the two models describe radically different +limit cases. +4. Conclusions +Large-scale long-lived vortices are found in many types of hydrodynamic flows. Large +vortices in turbulent flows are called coherent structures. They are observed, for example, in the +planetary atmospheres and in the oceans. The horizontal scales of the vortices are much greater +than the atmospheric or oceanic thicknesses. In the simplest geophysical context, examples of +such structures are the Gulf Stream rings, the vortices shed from coastal currents, the cyclones +and anti-cyclones, the Antarctic Polar Vortex, etc. A very well-known example is Jupiter’s +Great Red Spot: a huge vortex plunged in the equatorial flow, which has persisted for more +than three centuries; the presence of intense small-scale turbulence around it does not destroy +it. This prompts the question: under what conditions do large-scale vortex structures form? +In traditional 3D space, the turbulent motion is usually considered to be homogeneous +and isotropic. Common sense and the laws of thermodynamics show that it is very difficult to +extract energy from a fully chaotic system, and only with some additional specific properties of +such systems is this possible to realize. Homogeneous, isotropic turbulence, which does not +possess any preferred directions or preferred scales, is extremely symmetric, giving birth to +large-scale vortices; self-organization seems to be quasi-improbable in this case. It is evident +that the breaking of some structural symmetry is one of the necessary conditions for the +possibility of self-organization. It becomes clear that turbulent motion of fluid/gas with broken +spherical symmetry can be a candidate for a system where self-organization of 2D turbulence +into large-scale 2D vortex structures can take place. +Notably, quasi-2D flows in “thin” pancake-like accretion disks (see, e.g., [28,29] on the +physics of accretion), where components of hydrodynamical flows that are perpendicular +to the disk plane are strongly suppressed, can be a place where large-scale vortices can be +self-organized. However, another condition is an insignificant influence of a dissipative process +on large-scale motions in the system. As is known, the role of dissipation in a typical hydrody- +namical process is characterized by the so-called number of Reynolds, which is determined as +the ratio of magnitude of the inertial term to the dissipative term in the equation of fluid motion. +For “smooth” flows described by the models of classical hydrodynamics, the introduction of +such a number is not a problem; however, for flows of plasma, the determination of the pre- +dominant mechanism of dissipation is not apparent. However, the three-spot structure in the +EHT image of Sgr A* accretion disk (seen in Figure 1A) is a clear example of self-organization +in plasma. +To examine the observed phenomenon in the Sgr A* disk from the perspective of theoretical +hydrodynamics, we first considered a simplified thermo-hydrodynamic model that permits + +Universe 2023, 9, 40 +13 of 15 +analytical consideration. In the model, the vorticity clusters are approximated via delta- +functions. As the result, we established the condition of existence of a regular thermo-vorticial +structure (Equation (26); see also Figure 2). We also spelled out the relationships that should +take place between, on the one hand, the parameters that determine the vortex-structure +dynamics—each vortex size (l), its period of proper revolution (2πω−1), and temperature +excess τ in the vortex—and, on the other hand, the accretion disk characteristics (α and β, i.e., +λθ) and the angular velocity of the entire accretion disk Ω. +The necessary conditions for the formation of large quasi-stationary symmetric thermo- +vorticial structures in the plasma disk are as follows: (1) the accretion disk has to be pancake-like +thin (i.e., h ≪ R∗, where h is the thickness and R∗ is the characteristic radius) and rotate with +non-zero angular velocity (Ω ̸= 0); and (2) the disk temperature has to decrease towards the +center (i.e., parameter α > 0). A multi-spot thermo-vortex structure forms only when key +system parameters fall within the ranges captured by the dimensionless relationship: for a +three-spot structure, κ/ω = (2π/3)(ξ/K1(ξ)), where ξ = +√ +3(l/λθ)(Ω/ω). The temperature +of the vortices τ (i.e., the excess over the base level) is also linked to another parameter of the +system, vortex intensity κ of the hot spot: τ ∼ κ. Because the bright spots are hot, i.e., τ > 0, +this result also means that the rotation directions of the vortices ω and the entire accretion disk +Ω must co-align. +In the framework of localized vortices, the estimate for temperature excess of the bright +hot spots is given by Equation (27), and in the framework of thermo-vorticial spots (with sharp +contour boundaries), by Equation (29). +Figure 5. The four panels (obtained in Ref. [22] via the method of thermo-vorticial spots) illustrate that +uniformly rotating macro-structures may take various shapes depending on guiding parameters: the +shape may range from a weakly deformed circle to a sharply pronounced three-petal “flower”. Other +guiding parameters define how many petals appear: two, three, etc. The theory and models are explained +in detail in Ref. [22]. The units for axes are the same as in Figure 4. +For quasi-2D flows in thin layers of ideal fluid, another fruitful approach to analysis +also exists (for deeper insight, see, Refs. [18,22–27], and applications and references therein). +This approach is called the contour dynamics method (CDM). The gist of the method is that +the continuous hydrodynamical velocity distribution may be treated as a set of patches with +movable boundaries (contours) and constant vorticity inside. As the underpinnings of the CDM +show, such vortex-patch approximation correctly grasps the general tendency in the dynamics + +2 +2 +0 +0 +-2 +-2 +-2 +0 +2 +-2 +0 +2 +2 +2 +0 +0 +-2 +-2 +-2 +0 +2 +-2 +0 +2Universe 2023, 9, 40 +14 of 15 +and evolution of large-scale flows when the large-scale motions are weakly sensitive to a fine +structure in the hydrodynamical velocity field. The contours of the vortex structures within the +CDM framework are determined by spatially one-dimensional integro-differential nonlinear +equations. Equations of the contour dynamics—which describe the self-induced motion of +the vorticity-discontinuity boundaries, or “contours”, in an inviscid, incompressible, two- +dimensional fluid with piecewise constant vorticity distribution—may be effectively resolved +by either numerical or analytical approaches. Figure 5 illustrates the variability of shapes that a +symmetric stationary macro-structure may take, depending on one of its guiding parameters. +The shape may range from a weakly deformed circle to a sharply pronounced three-petal +“flower”. (Other parameters define how many petals appear: two, three, etc.) +In view of the visual similarity between the hot-spot arrangement in the Sgr A* accretion +disk revealed in Figure 1A and the thermo-vortex-structure plotted in Figure 5, we conclude +that the observed hot spots in the Sgr A* accretion disk are highly likely to be large-scale +quasi-2D quasi-stationary vortices in their nature. +In conclusion, let us emphasize that further improvement in understanding undoubtedly +depends on the progress in numerical simulations, for which solid experimental knowledge +of parameters defining the processes is paramount. Specifically, as discussed above, these +parameters are the background temperature, its contrast, the size of the macro-structure, the +number of petals, the angular velocity of rotation of the structure as a whole, the angular +velocity of rotation of the accretion disk, gradients of velocity of the collective flows of plasma +in the disk, and the characteristic time of existence of this quasi-stationary structure. +Author Contributions: Conceptualization and Writing, E.P.T., V.P.G. and V.I.P. All authors have read and +agreed to the published version of the manuscript. +Funding: This research received no external funding. +Data Availability Statement: Data sharing not applicable. +Conflicts of Interest: The authors declare that there is no conflicts of interests regarding the publication +of this article. +References +1. +Akiyama, K. et al. [Event Horizon Telescope Collaboration]. First Sagittarius A* Event Horizon Telescope Results. I. 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+page_content=' Universe 2023, 9, 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='3390/ universe9010040 Academic Editor: Lorenzo Iorio Received: 27 November 2022 Revised: 2 January 2023 Accepted: 4 January 2023 Published: 8 January 2023 Copyright: © 2023 by the authors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Licensee MDPI, Basel, Switzerland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='org/licenses/by/ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='0/).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' universe Article Hot Spots in Sgr A* Accretion Disk: Hydrodynamic Insights Elizabeth P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Tito 1,* , Victor P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Goncharov 1,2 and Vadim I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Pavlov 1,3 1 Scientific Advisory Group, Pasadena, CA 91125, USA 2 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Obukhov Institute of Atmospheric Physics RAS, 109017 Moscow, Russia 3 Faculté des Sciences et Technologies, Université de Lille, F-59000 Lille, France Correspondence: eptito@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='com Abstract: The recent image of our galaxy’s supermassive black hole Sgr A* derived from the 7 April 2017 data of the Event Horizon Telescope Collaboration shows multiple hot spots in its accretion disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Using the analytical framework, we demonstrate that the observed hot spots may not be disjoint elements but causally linked components (“petals”) of one rotating quasi-stationary macro-structure formed in the thermo-vorticial field within the accretion disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Keywords: black hole;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' accretion disk;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' hydrodynamics;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' hot spots;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' methods: analytical 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Introduction The image of our galaxy’s central supermassive black hole Sagittarius A* (Sgr A*), derived recently by the Event Horizon Telescope (EHT) Collaboration (see Figure 1A and Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' [1–6]) shows a multi-spot structure of its accretion disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The disk structure is a product of complex state-of-the-art data analysis rather than a direct observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Left panel (A): Image of Sgr A* from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Representative EHT image of Sgr A* from observations on 7 April 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' This image is an average over different reconstruction methodologies (CLEAN, RML, and Bayesian) and reconstructed morphologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Color denotes the specific intensity, shown in units of brightness temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The inset circle shows the restoring beam used for CLEAN image reconstructions (20 µas FWHM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The bottom panels show average images within subsets with similar morphologies, with their prevalence indicated by the inset bars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Right panel (B): Normalized distribution of temperature-excess in an accretion disk for the model of localized vortices (Section 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Universe 2023, 9, 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='3390/universe9010040 https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='mdpi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='com/journal/universe arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='03687v1 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='HE] 9 Jan 2023 BYSgr A* April 7, 2017 50 μas ~ 100 2 6 8 10 12 14 Brightness Temperature (109 K)Universe 2023, 9, 40 2 of 15 The EHT—a collection of radio-telescopes scattered around the Earth—operates in the digital interferometer mode: the signal from each antenna is recorded, and then the image of the object is restored using correlation analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Sophisticated data-processing algorithms have permitted the EHT to achieve angular resolution on the order of 20 microarcseconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' At the level of sensations, this is equivalent to the ability to read newspaper headlines on the Moon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' However, as Figure 1A indicates, this resolution scale is comparable to the size of Sgr A* itself;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' the accretion disk is slightly greater (∼50 µas).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Furthermore, the EHT telescopes could only record data from a small study area for a short period of time (see colored zones in Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Many (white) parts have remained unexplored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' To restore the full mosaic, the algorithms had to fill the gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' From Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' [1] (one panel from original Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' EHT baseline coverage, where dimensionless coordinates u = (u, v) give the projected baseline vector for each antenna pair in units of the observing wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The shape of the observed structure (Figure 1A)—even if the structure is short-lived— appears to indicate that it is likely to be not an artifact of image-reconstruction algorithms, but a real phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Using the analytical framework, we demonstrate that the observed hot spots may be not disjoint but causally linked components (“petals”) of one rotating quasi-stationary macro-structure formed in the thermo-vorticial field within the accretion disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Indeed, when a black hole’s accretion disk—whose rotation axis is perpendicular to the disk plane—is heated non-homogeneously (so temperatures are higher near the outer edge of the disk), then, in the field of the centrifugal force, spontaneously self-formed hot “bubbles” (composed of locally clustered plasma with temperatures in excess of the “average”, hence with lower densities) should move towards the axis of the disk rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' However, when the hot “bubbles” are also vortices, then each such vortex (via the induced velocity field) “forces” other vortices to rotate around itself, hence diverting their motion “sideways”, curtailing the movement towards the central axis of accretion-disk rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' All these vortices are subject to the influence of the cumulative velocity field induced by all other vortices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Thus, the radial motion of the vortices towards the axis becomes suppressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' As a result, if stabilized, the vortices take positions equidistantly from the axis and self-organize into a symmetric thermo- vorticial macro-structure that rotates as a whole around the mutual center (like in Figure 1B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The dynamics and longevity of this structure are linked to the thermal and vortical properties of the system and its elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Visually, if observed, the petals of this structure look like bright “hot spots”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In this paper, we consider the EHT image from the perspective of theoretical hydrody- namics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In particular, we describe a model of large-scale stationary rotating heated vortices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' However, we consider not the usual hydrodynamic field of vorticity but a complex thermo- hydrodynamic field system that under certain circumstances may self-organize into regular structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The physical and mathematical underpinnings of this analytical approach are elaborated in the references provided in the relevant places.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The explanation of their details is beyond the scope of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' To avoid any confusion, let us also emphasize upfront that 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='0 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='5 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='5 -5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='0 -7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='5 (G入) uUniverse 2023, 9, 40 3 of 15 we work with the field, not with individual particles (their trajectories or orbits).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Perhaps what may help the reader grasp this nuance better is the reminder that the velocity of displacement of electrons in a usual house wire is not the same thing as the speed of propagation of the electro-magnetic field perturbation along that same wire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' As the result of our analysis, we show that multi-hot-spot thermo-vorticial macro-structures may indeed self-organize in the accretion disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The model makes it possible to determine basic characteristics of such structures, for example, the horizontal space-scale, the period of proper rotation, and the peak temperature magnitude in the vortex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The paper is organized as follows: Section 2 presents the model, Section 3 presents the results, and Section 4 summarizes the conclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Model The model setup is straightforward: a black hole pulls in and crushes the matter from the surrounding space;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' the particles are then accelerated to near-light velocities and twisted around the black hole, forming a flattened accretion plasma disk in the equatorial plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' We will use the spacetime metric entirely characterized by the black hole mass parameter and its “spin” (described in our Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' [7,8];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' for more details, see also [9–14], and bibliographies therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' We will assume that the mass of the accretion disk is negligible compared to the black hole “mass” M, probably (10−5 ÷ 10−4)M⊙;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' the radiative cooling does not strongly affect the dynamics of fluid motion;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' and the electrons and ions are very weakly coupled by Coulomb interaction and hence ions and electrons plasmas components have different temperatures, Te ≫ Ti (see Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' [15]), and thus it is the electron component that contributes the most to the equation of state of the accretion disk matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Due to the large difference in the masses of electrons and protons, electrons are highly mobile and provide quasi-neutrality of the plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Due to the high conductivity of the plasma, its own magnetic field can be considered as a field “frozen” into the plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Generally speaking, equations of fluid motion in the vicinity of a black hole must be written using the concept of relativistic dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The key points are as follows: We suppose that the space-time near the (non-charged) black hole Sgr A* is described by the Kerr metric—an exact, singular, stationary, and axially symmetric solution of the Einstein–Hilbert equations of the gravitational “field” in vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Next, we introduce the Boyer–Lindquist 4-coordinates, qα = (t, r, θ, φ) (it is well known that besides the Boyer–Lindquist coordinate representation, other representations of space-time locations exist).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In terms of the Boyer–Lindquist coordinates, the square of interval is written as ds2 = gαβ(r/rg, θ)dqαdqβ with α, β = 0, 1, 2, 3, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', the components of gαβ depend only on the dimensionless combination rg/r and θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Here, rg = 2GM/c2 is the Schwarzschild radius, c is the speed of light, G is the gravitational constant, and M is the “mass” of the black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The off-diagonal term g03 in the metric tensor is proportional to the rate of the black hole’s own rotation and to 1/r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' For the Minkowski tensor, we use the metric signature diag(+ − −−) (see, for example, Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' [8], and Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' To satisfy the principle of causality for moving material objects, obviously, ds2 > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The four time- space coordinates qα = (t, r, θ, φ) give the location of a world-event from the viewpoint of a remote observer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The meaning of space coordinates r, θ, φ is clear once transitioned to the limit r ≫ rg, r ≫ ωr2 g/c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' When the square of the interval becomes ds2 → c2dt2 − dr2 − r2(dθ2 + sin2θ dφ2), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', at infinity, parameters r, θ, φ may be interpreted as the standard spherical coordinates in flat space-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' As for the parameter r, strictly speaking, note that it is not the “distance” in the usual meaning from the center of black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' This is because, for any material object, in the space-time defined by equation ds2 = gαβdqαdqβ, no central point r = 0 exists in the sense of a world-event on a valid world-line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Next, we consider the motion of the medium far away from the event horizon, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', when parameter r is meaningfully greater than rg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' For the flow at r > 3rg, in the expansion of the Universe 2023, 9, 40 4 of 15 metric tensor, we may neglect the terms of order (rg/r)2 and greater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' They contribute less than (1/3)2 ∼ 10% to the components of the metric tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Such omission of smaller terms makes our approximation Newtonian or post-Newtonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The non-diagonal metric-tensor term (describing involvement of the medium in the rotation of space-time in the vicinity of the black hole) gives rise to the “force” analogous to the traditional Coriolis force in the equations for medium flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Hence, we write the system of equations of relativistic fluid dynamics in the curved space-time and expand the metric tensor and the fluid energy–momentum tensor into a series with respect to small parameters rg/r < 1 and ∼ c−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' We keep only the leading terms in the equations of fluid motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Next, the fluid is presumed to be localized near surface θ = π/2 (in a pancake-like accretion disk)—the flows of the disk medium are considered only near this surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Then, we can transition to cylindrical coordinates qi = (r, φ, z) and presume that the gas particles orbit near the z = 0 plane and the vertical component of their velocity vz ≪ max(vr, vφ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In this model, when r exceeds the Schwarzschild radius rg (specifically, r > 3rg), then the vertical component of gravity acceleration gz = − G M z/(r2 + z2)3/2 ≡ −K2z(1 + z2/r2)−3/2 is balanced by the pressure gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Here, G is the gravitational constant, c is the speed of light, K2 = GM/r3 = c2rg/(2r3), and K ∼ r−3/2 is the radius depending so-called Kepler parameter: the angular velocity of a test particle in a circular orbit at distance r from a point mass M in Newtonian approximation of gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Gas pressure along the direction perpendicular to the disk plane (x, y) is determined by the hydrostatic equilibrium, dP = ρgzdz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Generally speaking, pressure may have important contributions from electromagnetic radiation and induced magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The simplest case, however, is when the pressure is dominated by gas pressure, and the vertical temperature distribution is isothermal, which is roughly appropriate when the disk is optically thick and externally heated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The equation of state of gas/plasma is then P = s2ρ, where s is the “isothermal sound speed” (which is not a function of the transversal coordinate z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' If we further assume that z ≪ r, the equation of hydrostatic equilibrium becomes s2dρ = −s2h−2ρzdz, the solution of which is ρ(z) = ρ0 exp(−z2/2h2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Here, the transversal space scale h is introduced, h = s r3/2/(GM)1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Parameter ρ0 has the meaning of density at the disk mid-plane (at z = 0), and parameter h is the characteristic local thickness of the accretion disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In order for the accretion disk to be considered thin, it is necessary that h/r ≃ sr1/2/(GM)1/2 ∼ (s/c)(r/rg)1/2 ≪ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' On the other hand, for great distances away from the black hole (r > rg), specific relativistic effects may be neglected or parametrized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Thus, we obtain natural bounds: rg < r < rg(c/s)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Equations of Motion: The equations of motion for an inviscid incompressible fluid express the laws of conservation for mass, momentum, and energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The flow of gas may be considered incompressible (see, for example, [16]) when its velocity v satisfies condition v2 ≪ s2 and the characteristic time scale of the flow change T ≫ L/s where L is the characteristic spatial scale where the flow characteristics change substantially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In this case, the mass conservation law is expressed as div v = 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', the law is not ρ = Const, but ∂tρ + vj∂jρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' We assume that the domain of the disk where the vortex structure of interest is formed, is characterized by an approximately constant angular velocity Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In a coordinate system rotating with the angular velocity Ω = (0, 0, Ω), where x ≡ x1 and y ≡ x2 are the axes in the horizontal plane and z is vertically upwards, the basic equations of motion become ∂jvj = 0, (1) ρ(∂tvi + vj∂jvi + 2ϵijkΩjvk) = −∂iP − ρ∂iΦ, (2) ∂tθ + vj∂jθ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (3) Universe 2023, 9, 40 5 of 15 Here, vi are the components of the velocity field, ρ is density, P is pressure, and θ is temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The potential Φ of the force field is Φ ≃ −K2r2 + (1/2)K2z2 − (1/2)|[Ω, r]|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Furthermore, here, [a, b] is the cross product of vectors a and b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' and ϵijk is the alternating tensor (ϵ123 = 1, zero for any two indices being equal, +1 for any even number of permutations from ϵ123, and −1 for any odd number of permutations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Due to the assumption of an incompressible medium (implying s−2 → 0), the equation of state ρ = ρ(θ, P) turns into the density expression, which only depends on the temperature (and not on the pressure).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In fact, ∇ρ = (∂ρ/∂θ)∇θ + (∂ρ/∂P)∇P ≃ −ρβ∇θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The coefficient of thermal expansion, β = −ρ−1(∂ρ/∂θ), may be assumed constant and positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (For gases, β = 1/θ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=') Thus, we can set ρ = ρ0(1 − β(θ − θ0)), where subscript zero denotes the reference values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Due to the fact that β(θ − θ0) is generally significantly less then one, one may neglect the density variations in all principal terms and hence replace ρ with the constant value ρ0, except in the “buoyancy” term, which is proportional to ∂jΦ (see, for example, [16,17]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Next, we apply the curl operator ∇× to the linear momentum conservation Equation (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' This gives � ∇ − β∇θ, dv dt + 2 � Ω, v �� = β � ∇(τs + τ), ∇Φ � , (4) where brackets symbolize cross-product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Since β|∇θ| ≪ 1, term β[∇θ, A] is small with respect to [∇, A] at the horizontal scales typical for any hydrodynamical vector A and may be not taken into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Consider now temperature θ as θ = θ0 + τs + τ, where θ0 is the (constant) baseline temperature of the accretion disk, quantity τs is an axially symmetrical part of the temperature distribution that is not time-dependent, and τ = τ(t, xj) is the dynamical quantity related to the vortex structures in the fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' When r = (x, z), vj = (v, w), then ωi = ϵijk∂jvk + 2Ωi, and Equation (4) can be rewritten in the tensorial form as (Dt + w∂3)ωi = ωj∂jvi + βϵijk(∂j(τs + τ))∂kΦ, (5) where Dt = ∂t + (v · ∇) is the substantial derivative, v = (v1, v2) is the flow velocity, and ∇ = (∂1, ∂2) is the gradient operator with components ∂i in the (x, y) plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In the simplest model—in which the vortex structures are realized in a ”thin” flat sheet of an incompressible inviscid fluid (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', when h ≪ L, V2 ≪ s2 ≪ c2, Re ≫ 1)—the z-component of velocity, w, vanishes and may be dropped in all formulas (see, for example, [18]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Note also that ϵ3jk∂jτs∂kΦ ≡ 0 because of an axial symmetry of both τs and Φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Thus, the set of equations for the z component of vorticity ω3 and for variation of temperature τ becomes ∂jvj = 0, (6) Dtω3 = βϵ3jk∂jτ∂kΦ, (7) Dtτ = −vi∂iτs, (8) where indices j, k = 1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Equation (6) permits the introduction of the stream function ψ: vi = ϵ3ij∂jψ ≡ ϵij∂jψ, (9) where tensor ϵij is the antisymmetric unit tensor of the second order, ϵ12 = −ϵ21, and diagonal components are zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In this case, vorticity ω3 = −∆ψ + 2Ω3 with ∆ = ∂2 1 + ∂2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Temperature Stratification: To describe the effect of temperature stratification—i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', to show how stationary temperature increases as the distance from the axis of rotation increases— Universe 2023, 9, 40 6 of 15 we express (using r = |x|, x = (x1, x2) and Taylor series expansion) the background distribution of the temperature τs in the form τs = α 2r2 , α > 0 , (10) where α is the parameter characterizing the “rapidity” of increase in temperature with distance from the disk rotation axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (Generally speaking, the question of what shape the temperature profile takes within a black hole’s accretion disk is an open one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Experimental measurements remain challenging, despite significant progress.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' See, for example, [19,20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=') When the leading contribution to potential Φ comes from the centrifugal effects, we can express Φ = −K2|x|2 − (1/2)[Ω, x]2 ≃ −(1/2)[Ω, x]2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Thus, when Ω is presumed constant in a band of r where the vortex hotspots are forming, the set of coupled nonlinear evolution equations becomes ∂t∆ψ + ϵik∂iψ∂k∆ψ = βΩ2ϵikxi∂kτ, (11) ∂tτ + ϵik∂iψ∂kτ = αϵikxi∂kψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (12) For a general case, ∆ψ should be replaced: ∆ψ → ∆ψ − 2Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Equations (11) and (12) have a transparent physical meaning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Their left sides describe transport of dynamic quantities: vortex ∆ψ and temperature perturbation τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Their right sides describe “sources” that generate the vortices and temperature perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In other words, the vortices are generated by the source (the right part of Equation (11) which is effective (non-zero) only when there exists an inhomogeneous gravity-like force field Φ ∼ Ω2 with which temperature perturbation τ interacts via the equation of state (when β ̸= 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The quantity ψ—which characterizes the vortex field in the fluid—is transported by the self-induced flow (the left part of Equation (11)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' On the other hand, in Equation (12), this temperature perturbation τ is transported by the self-generated flow (ψ ̸= 0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' the temperature perturbation τ(t, x) is generated by the source (the right part of Equation (12)), which is non- zero only when there exists a spatial and time-independent temperature gradient (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', when τs ̸= 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The processes are interlinked because the “source” of one dynamic quantity depends on the complex combination involving another dynamic quantity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The set of Equations (11) and (12) shows that when temperature stratification is absent (α = 0) and there is no disk rotation (disk Ω = 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', centrifugal force is zero), then Equations (11) and (12) degenerate into the traditional equations for vortex evolution and transport in a two-dimensional ideal fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Linear Approximation: Assuming that an excess of temperature τ above the basic level of temperature is not too large, in view of the link between fields τ and ψ via Equations (12), we consider a simple linear dependence between the excess of temperature τ and the vorticity ψ that generates this excess: τ = −Cψ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (13) Obviously, it follows from Equation (13) and from the meaning of quantities τ and ψ that the dimension of the coefficient of proportionality is [C] = θL−2T ≡ [temperature] × [lengh]−2 × [time].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' By substituting Equation (13) into Equation (12), we obtain ∂t∆ψ + ϵik∂iψ∂k∆ψ = −CβΩ2ϵikxi∂kψ, (14) −C β α Ω2 × C(∂tψ + ϵik∂iψ∂kψ) = C β α Ω2 × αϵikxi∂kψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (15) Universe 2023, 9, 40 7 of 15 Hence, we conclude that both the first and second equations in Equations (14) and (15) describe the evolution of the same physical quantity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The equations will be consistent when the following condition is imposed on the current function ψ: (∂t + ϵik∂iψ∂k)(∆ψ − R−2ψ) = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (16) Here, parameter R−2 = C2(β/α)Ω2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The dimension of this quantity is (θ1L−2T1)2 × θ−1L2 × θ−1 × T2 = L−2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', R is a space scale factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Quantity q = ∆ψ − R−2ψ describes the distri- bution of generalized vorticity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Its change in time and in space has to satisfy the evolution equation Equation (16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The stream function ψ is found via the Green function approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In the symbolic integral form, in the boundless space, it is ψ(x, t) = � (∆ − R−2)−1(x, x′) � q(x′, t) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (17) The subsequent calculation procedure is as follows: (i) The initial vorticity distribution is set;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' the stream function ψ is found from Equation (17);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' together with it, the non-linear evolution Equation (16) is numerically solved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (ii) The distribution of vorticity is set in the form of a macrostructure with petals (with constant vorticity inside) whose moving boundaries evolve according to Equation (16);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', we are considering a region bounded by some closed contour (with possibly a rather complex shape) such that quantity q(x, t) takes a constant value inside and zero outside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' For stationary dynamical regimes, this can be accomplished analytically (details of the contour dynamics method and of the operator techniques can be found, for example, in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' [21,22]), as well as Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' [18,23]);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (iii) For a strongly localized vortex, quantity q(x, t) can be parameterized by the function in form F(x − x0(t)), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', the one with the center at coordinate x = x0(t), which satisfies the equation of transport ˙x0i(t) + ϵik∂iψ = 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', when the center of vortex moves according to ˙x0(t) − vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='[x0(t)] = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (Here, the symbol “dot” signifies the derivative with respect to time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=') Stationary Vortex Structures: Stationary vortex structures—the ones rotating with con- stant angular velocity ω—are simpler to consider in a rotating coordinate system where the structures appear immovable;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', when rotation direction is co-aligned with z axis, the deriva- tive with respect to time becomes ∂t = −ωϵikxi∂k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (The procedure is laid out, for example, in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=') Indeed, when f = f (ρ, φ − ωt), then the calculation relying on the properties of Ja- cobeans produces ∂t f = −ω∂φ f = −ω∂( f, ρ)/∂(φ, ρ) = −ω(∂( f, ρ)/∂(x1, x2))(∂(x1, x2)/∂(φ, ρ)) = −ω(ϵikρ−1xi∂k f )(−ρ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Then, Equation (12) may be rewritten as: ϵik∂i � − ω 2 |x|2 + ψ � ∂k � τ + α 2 |x|2 � = 0 , (18) which is satisfied by the ansatz τ + α 2 |x|2 = F(−ω 2 |x|2 + ψ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (19) The explicit expression of function F can be found from the obvious fact that temperature- driven flow perturbations must vanish when temperature perturbations vanish themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The suitable expressions is function F(u) = −αu/ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Then, temperature fluctuations are expressed via the stream function τ = − α ω ψ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (20) Universe 2023, 9, 40 8 of 15 Combining this with Equation (11) where ∂t = −ωϵikxi∂k is taken into account, we obtain the second evolution equation: the one that describes rotation of a stationary vortex structure with angular velocity ω caused by the self-induced field of hydrodynamical velocity: ϵik(−ωxi + ∂iψ)∂k � ∆ψ − R−2ψ � = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (21) Once Equation (20) is written out, parameter R2 becomes R2 = (αβ)−1(ω/Ω)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Here, β is the coefficient of thermal expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' For almost all physically realizable situations, β > 0 (the well-known exception is water in the temperature range between 0 and +4 ◦C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Parameter α —characterizing the “rapidity” of increase in temperature with distance from the disk rotation axis—can be either positive or negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' When α > 0, the periphery of the accretion disk is heated more than the central zone;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' when α < 0, the central zone of the disk is hotter than the periphery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Thermal length scale λθ = (|α|β)−1/2 is determined by the background state of the disk in the framework of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Obviously, space scale parameter R characterizes the “rapidity” of the decrease in temperature (and stream function) with distance from the disk rotation axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Below, we write R2 → R2 (Θ(α) − Θ(−α)), where Θ(α) is the Heaviside step-function (equal to unit for positive argument and zero for negative argument), and, leaving the old notations, R2 = (|α|β)−1(ω/Ω)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Results We use the model described above to gain insights into the three-spot structure in the EHT image of Sgr A* accretion disk (Figure 1A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The bright spots are the zones with higher (relative to the base level) temperature τ and (since τ ∼ ψ) with higher vorticity ∆ψ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In this framework, thermo-hydrodynamical vorticity-field structures may be conceptually analyzed with two limit approaches: the method of localized vortices and the method of thermo-vorticial spots (blobs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Localized Vortices: The simplest consideration for a three-spot stationary thermo-vortex structure (symmetric with respect to the rotation axis of a pancake-like thin accretion disk) is to analytically treat the hot zones as narrowly localized formations modeled as 2D delta-functions at the limit case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Doing so would allow us to find the required conditions for the existence of the observed phenomenon and the resulting relationships between key characteristics of the structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (This approach is not limited to only structures with three spots, but can be generalized to structures with any vortex-number N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=') Hence, we write: ∆ψ − R−2(Θ(α) − Θ(−α))ψ = 3 ∑ j=1 κR2 δ(2)(x − x(j)), (22) where κ characterizes the intensity of one localized vortex, and δ(2)(x − x(j)) ≡ δ(1)(x − x(j)) × δ(1)(y − y(j)) is the two-dimensional Dirac function in the xy-disk plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The appearance of the factor R2 in the right side of Equation (22) is due to the following reasoning: the delta-function is a dimensional function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Its dimension is [δ(2)] = [length]−2 for 2D space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Obviously, the argument of the delta-function must be dimensionless.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (Indeed, there is no such thing as sin of “one inch” or tan of “ten gallons”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=') Therefore, δ(2) ≡ δ(1)(R−1x − R−1x(j)) × δ(1)(R−1y − R−1y(j)) = R2 δ(2)(x − x(j)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In view of the meaning of the delta function in the right part of Equation (22) and of the structure of the left part of Equation (22), the scale-factor R is the same R that was introduced above—the characteristic size of the vortex kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Although alternatives may exist, following the Occam’s Razor principle—the problem-solving principle of parsimony that “entities should not be multiplied beyond necessity”—we choose the simplest option.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Indeed, among the options to use R or R multiplied by dimensionless (κ/ω)n, we choose the simple R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Universe 2023, 9, 40 9 of 15 We further note that x(j) and y(j) may be expressed as components of the complex quantity l × exp(i2π(j − 1)/3) in the plane x + iy (where l is the radius of a circumscribed circle).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' When a vortex is modeled by a delta-function, a weak (logarithmic) singularity appears in the distribution of stream function ψ (which is the solution of Equation (22)) when α > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' If α < 0, or a smoother distribution is adopted for α > 0, any singularities in ψ function then disappear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The solution to Equation (22) for unbounded space is ψ = −κR2 2π 3 ∑ j=1 Z0(|x − x(j)| R ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (23) Here, Z0(ξ) = J0(ξ)Θ(−α) + K0(ξ)Θ(α), J0(ξ) is the Bessel function of order n = 0, K0(ξ) is the modified Bessel (McDonald) function of order n = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Recall that for small values of the argument, function J0(ξ) → 1, function K0(ξ) behaves logarithmically: K0(ξ) ≃ − log ξ + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='1156.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' For large values, function J0(ξ), as known, behaves as J0(ξ) ≃ � 2/πξ cos[−ξ + π/4], function K0(ξ) behaves as K0(ξ) ≃ � π/(2 ξ) exp (−ξ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' This means that for α > 0 and r ≫ R;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', when ξ ∼ r/R ≫ 1, function K0(ξ) exponentially quickly tends to zero, and therefore, the stream function ψ, and consequently the local vortex magnitude and temperature excess τ, all will also tend to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' This is the consequence of the initial choice to model the vortices via delta-functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Numerically, for some characteristic points, K0(1) ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='421 and K0(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='4569) ≃ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The derivative of Z0 with respect to argument is Z′ 0(ξ) = −Z1(ξ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' By substituting Equation (22) into Equation (21), and then taking into account Equation (23), and by setting the terms with delta function and their derivatives as equal to zero, we find the set of conditions for the existence of the modeled vortex structure: ϵik 3 ∑ n=1 � − ωx(n) i + 3 ∑ m=1 ′ κR2 2πR (x(n) i − x(m) i ) |z(nm)| Z1(|z(nm)| R � κR2∂kδ(z(n)) = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (24) In this expression, symbol “prime” in the second summation indicates that the effect of vortex self-action is excluded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' When notation z(j) = x − x(j) is used, then z(ij) = x(i) − x(j) and |z(12)| = |z(23)| = |z(31)| = √ 3 l (where l is the radius of a circumscribed circle).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' To satisfy Equation (24), the coefficients before every singularity must equal zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Thus, the following condition for the parameters of the vortex configuration arises: −ωl2 + 2κR2 2πR l2(1 − cos 2π/3) l √ 3 Z1( √ 3l R ) = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (25) Recall that R = (|α|β)−1/2|ω/Ω)| is a dimensional function of four dimensional parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Equation (25) can be rewritten in a compact dimensionless form, where ξ = √ 3(l/R): κ ω = 2π 3 ξ Z1(ξ) (26) which says that for any specific ξ, ratio κ/ω is uniquely defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Figure 3 plots Equation (26).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Universe 2023, 9, 40 10 of 15 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Model of Localized Vortices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Left panel (A): Both axes are in linear scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Right panel (B): Vertical axis is in log-scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Both panels (A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='B): A structure with three vortices forms only when κ/ω = (2π/3)(ξ/Z1(ξ)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' where ξ = √ 3(l/R),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' l is the radius of a circumscribed circle,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' R = (|α|β)−1/2|ω/Ω)|,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' α is the parameter characterizing the “rapidity” of increase in temperature with distance from the disk rotation axis,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' β = −ρ−1(∂ρ/∂θ) is the coefficient of thermal expansion,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' ω is the angular velocity of rotation of the vortex structure,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Ω is the angular velocity of rotation of the accretion disk,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' and κ is the characteristic intensity of one localized vortex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The blue curve is for α > 0 (the disk periphery is hotter).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The red curve is for α < 0 (the disk periphery is cooler): intensity κ → ∞ as ξ ≡ √ 3(l/R) → ξN (red dot) at which the Bessel function J1(ξN) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (Here ξ1 ≃ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='8317.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=') For the presented model, the temperature excess τ follows from Equation (20) and Equa- tion (23): τ = 1 2πβ( κ ω )( ω Ω)2 3 ∑ j=1 Z0(|x − x(j)| R ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (27) The characteristic temperature scale is defined thus as τ0 = (2πβ)−1(κ/ω)(ω/Ω)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' When α < 0 (disk periphery is cooler), both “anticyclones” (temperatures excesses) and “cyclones” (temperature depressions) are possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Figure 1B (on the front page of the article) illustrates the temperature distribution for a system with three localized vortices, calculated using Equation (27), for a case when α > 0 (disk periphery is hotter).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In Figure 1B, the unit for the color scale is the characteristic magnitude of temperature excess τ0 = (2πβ)−1(κ/ω)(ω/Ω)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' For the x and y axes, the unit is R = λθ(ω/Ω);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' ω is the angular velocity of rotation of the vortex structure as a whole;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Ω is the characteristic angular velocity of rotation of the accretion disk;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' and λθ = (αβ)−1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In the expression for λθ, the parameter α (characterizing the “rapidity” of the increase in temperature with distance from the disk rotation axis) may be estimated as α ∼ (∆θ/R2∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Here, R∗ is the characteristic external radius of the active part of the accretion disk (obviously not equal to R) is presumed to be greater than the size of the macrostructure, and ∆θ may be estimated as the temperature difference across the disk (from the periphery to the center).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In the expression for λθ, the parameter β = −ρ−1(∂ρ/∂θ) is the coefficient of thermal expansion, which (for the model whose equation of state is approximated by the equation for an ideal gas) may be written as β ≃ θ−1, where θ is the averaged temperature of the accretion disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Thermo-Vorticial Spots (“Blobs”): Another fruitful approach is to use the concept of thermo-vortical spots, for which the vorticity is constant inside domains bounded by movable boundaries (contours) and is zero outside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Then, the problem of vortex evolution becomes the problem of examination of the movement of the contours and determination of their final macro-configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Examples of such macro-configurations are depicted in Figures 4 and 5 (discussed below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Within this framework—called the contour dynamics method (CDM) (see Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' [18,22–27])—the distribution of vorticity q for a vortex structure may be written as w 3 2 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='0" 7 2K w 100 50 0 2 6 8 10 50 100Universe 2023, 9, 40 11 of 15 q = q0Θ(x, y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Function Θ(x, y) is a two-dimensional Heaviside step-function equal to one inside the domain in consideration and zero outside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Parameter q0 describes the vorticity inside the spot, which is presumed constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Obviously, the dimension of this parameter is [q0] = [time]−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Using CDM (see the physical foundation and the details on how to perform calculations using CDM in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' [22]), we find the general expression for temperature distribution: τ(x, y) = −(q0αRL 2πω ) � ∂D ds � K1(|ˆz − z| µ ) − µ |ˆz − z| � ˆz,s(ˆz − z∗) |ˆz − z| .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (28) Here, the integral is taken along the contour (whose shape is previously found by solving the problem of the spot configuration);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' z = (x + iy)/L is the complex variable of the xy-position, normalized by the characteristic space-scale L = (R/2)(q0/ω)1/3, which is linked to the size of the macro-configuration;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' parameter µ = R/L is dimensionless;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' and domain D in the complex plane z is a region filled with the vorticity q0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The domain is bounded by a closed contour ∂D;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' this boundary is expressed in the parametric form z = ˆz(s);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' parameter s is the contour arc length beginning from some initial point;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' and derivative ˆz,s ≡ ∂ˆz/∂s is a unit vector that is obviously tangential to the contour ∂D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Based on the contour-integral Equation (28), the temperature distribution τ(x)/τ0 is solved (and plotted in Figure 4B) for the contour boundary (black line) in Figure 4A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Shaded gray in Figure 4A is the constant vorticity distribution q(x) = q0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Illustration of analysis via method of thermo-vorticial spots (“blobs”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Left panel (A): A three-petal vorticity distribution is specified as q(x) = q0Θ(x, y), where vorticity q0 is constant and function Θ(x, y) is two-dimensional Heaviside step-function equal to one inside the shaded domain and zero outside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' [22] explains in detail the entire theory and methodology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' This depicted three- petal thermo-vorticial structure takes this particular shape when one of the guiding parameters of the macro-configuration reaches its limit case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=') Right Panel (B): For the vorticity distribution specified in Panel (A), the resulting temperature distribution τ(x) is obtained per Equation (28).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The unit along the vertical axis is the characteristic magnitude of temperature excess τ0 = q0αRL/2πω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (The central τ peak is a consequence of the vorticity parametrization for the geophysical application in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' [22], which for a black hole accretion disk should be obviously nil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=') Both Panels (A,B): For x and y axes, the unit is R = λθ(ω/Ω);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' ω is the angular velocity of rotation of the vortex structure as a whole;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Ω is the characteristic angular velocity of rotation of the accretion disk;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' and λθ = (αβ)−1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In the expression for λθ, the parameter α (characterizing the “rapidity” of increase in temperature with distance from the disk rotation axis) may be estimated as α = (8/π2)(∆θ/R2∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Here R∗ is the characteristic radius of the accretion disk (obviously not equal to R) is presumed to be greater than size of the macro-structure, and ∆θ may be estimated as the temperature difference across the disk (from the periphery to the center).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In the expression for λθ, the parameter β = −ρ−1(∂ρ/∂θ) is the coefficient of thermal expansion, which (for the model whose equation of state is approximated by the equation for an ideal gas) may be written as β ≃ θ−1, where θ is the averaged temperature of the accretion disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' 3 2 1 0 1 2 3 3 2 1 0 1 2Universe 2023, 9, 40 12 of 15 The key parameters here are τ0 = q0αRL/2πω, R = λθ(Ω/ω), λθ = (αβ)−1/2, β = θ−1, (q0/ω) = 8(L/R)3 and α = (8/π2)(∆θ/R2∗), where θ is the averaged temperature of the accretion disk, R∗(̸= R) is the characteristic radius of the accretion disk, and ∆θ is the temperature difference across the disk (from the periphery to the center).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Thus, the characteristic level of the temperature excess in this limit case (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', in the model of thermo-vorticial spots, not in the model of localized thermo-vortices) can be estimated by the expression τ0 = 1 4πβ(q0 ω )4/3( ω Ω)2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (29) The above-mentioned parameters in Equation (29) are the very parameters that must be measured experimentally to be able to comprehend the phenomena in images such as Figure 1A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Equation (29) is functionally similar to Equation (27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The difference is in the index of power dependence of the ratio of the vortex intensity and its angular velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' This is an insignificant difference considering the fact that the two models describe radically different limit cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Conclusions Large-scale long-lived vortices are found in many types of hydrodynamic flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Large vortices in turbulent flows are called coherent structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' They are observed, for example, in the planetary atmospheres and in the oceans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The horizontal scales of the vortices are much greater than the atmospheric or oceanic thicknesses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In the simplest geophysical context, examples of such structures are the Gulf Stream rings, the vortices shed from coastal currents, the cyclones and anti-cyclones, the Antarctic Polar Vortex, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' A very well-known example is Jupiter’s Great Red Spot: a huge vortex plunged in the equatorial flow, which has persisted for more than three centuries;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' the presence of intense small-scale turbulence around it does not destroy it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' This prompts the question: under what conditions do large-scale vortex structures form?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In traditional 3D space, the turbulent motion is usually considered to be homogeneous and isotropic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Common sense and the laws of thermodynamics show that it is very difficult to extract energy from a fully chaotic system, and only with some additional specific properties of such systems is this possible to realize.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Homogeneous, isotropic turbulence, which does not possess any preferred directions or preferred scales, is extremely symmetric, giving birth to large-scale vortices;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' self-organization seems to be quasi-improbable in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' It is evident that the breaking of some structural symmetry is one of the necessary conditions for the possibility of self-organization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' It becomes clear that turbulent motion of fluid/gas with broken spherical symmetry can be a candidate for a system where self-organization of 2D turbulence into large-scale 2D vortex structures can take place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Notably, quasi-2D flows in “thin” pancake-like accretion disks (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', [28,29] on the physics of accretion), where components of hydrodynamical flows that are perpendicular to the disk plane are strongly suppressed, can be a place where large-scale vortices can be self-organized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' However, another condition is an insignificant influence of a dissipative process on large-scale motions in the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' As is known, the role of dissipation in a typical hydrody- namical process is characterized by the so-called number of Reynolds, which is determined as the ratio of magnitude of the inertial term to the dissipative term in the equation of fluid motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' For “smooth” flows described by the models of classical hydrodynamics, the introduction of such a number is not a problem;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' however, for flows of plasma, the determination of the pre- dominant mechanism of dissipation is not apparent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' However, the three-spot structure in the EHT image of Sgr A* accretion disk (seen in Figure 1A) is a clear example of self-organization in plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' To examine the observed phenomenon in the Sgr A* disk from the perspective of theoretical hydrodynamics, we first considered a simplified thermo-hydrodynamic model that permits Universe 2023, 9, 40 13 of 15 analytical consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In the model, the vorticity clusters are approximated via delta- functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' As the result, we established the condition of existence of a regular thermo-vorticial structure (Equation (26);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' see also Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' We also spelled out the relationships that should take place between, on the one hand, the parameters that determine the vortex-structure dynamics—each vortex size (l), its period of proper revolution (2πω−1), and temperature excess τ in the vortex—and, on the other hand, the accretion disk characteristics (α and β, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', λθ) and the angular velocity of the entire accretion disk Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The necessary conditions for the formation of large quasi-stationary symmetric thermo- vorticial structures in the plasma disk are as follows: (1) the accretion disk has to be pancake-like thin (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', h ≪ R∗, where h is the thickness and R∗ is the characteristic radius) and rotate with non-zero angular velocity (Ω ̸= 0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' and (2) the disk temperature has to decrease towards the center (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', parameter α > 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' A multi-spot thermo-vortex structure forms only when key system parameters fall within the ranges captured by the dimensionless relationship: for a three-spot structure, κ/ω = (2π/3)(ξ/K1(ξ)), where ξ = √ 3(l/λθ)(Ω/ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The temperature of the vortices τ (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', the excess over the base level) is also linked to another parameter of the system, vortex intensity κ of the hot spot: τ ∼ κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Because the bright spots are hot, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', τ > 0, this result also means that the rotation directions of the vortices ω and the entire accretion disk Ω must co-align.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In the framework of localized vortices, the estimate for temperature excess of the bright hot spots is given by Equation (27), and in the framework of thermo-vorticial spots (with sharp contour boundaries), by Equation (29).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The four panels (obtained in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' [22] via the method of thermo-vorticial spots) illustrate that uniformly rotating macro-structures may take various shapes depending on guiding parameters: the shape may range from a weakly deformed circle to a sharply pronounced three-petal “flower”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Other guiding parameters define how many petals appear: two, three, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The theory and models are explained in detail in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The units for axes are the same as in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' For quasi-2D flows in thin layers of ideal fluid, another fruitful approach to analysis also exists (for deeper insight, see, Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' [18,22–27], and applications and references therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' This approach is called the contour dynamics method (CDM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The gist of the method is that the continuous hydrodynamical velocity distribution may be treated as a set of patches with movable boundaries (contours) and constant vorticity inside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' As the underpinnings of the CDM show, such vortex-patch approximation correctly grasps the general tendency in the dynamics 2 2 0 0 2 2 2 0 2 2 0 2 2 2 0 0 2 2 2 0 2 2 0 2Universe 2023, 9, 40 14 of 15 and evolution of large-scale flows when the large-scale motions are weakly sensitive to a fine structure in the hydrodynamical velocity field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The contours of the vortex structures within the CDM framework are determined by spatially one-dimensional integro-differential nonlinear equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Equations of the contour dynamics—which describe the self-induced motion of the vorticity-discontinuity boundaries, or “contours”, in an inviscid, incompressible, two- dimensional fluid with piecewise constant vorticity distribution—may be effectively resolved by either numerical or analytical approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Figure 5 illustrates the variability of shapes that a symmetric stationary macro-structure may take, depending on one of its guiding parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The shape may range from a weakly deformed circle to a sharply pronounced three-petal “flower”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' (Other parameters define how many petals appear: two, three, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=') In view of the visual similarity between the hot-spot arrangement in the Sgr A* accretion disk revealed in Figure 1A and the thermo-vortex-structure plotted in Figure 5, we conclude that the observed hot spots in the Sgr A* accretion disk are highly likely to be large-scale quasi-2D quasi-stationary vortices in their nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' In conclusion, let us emphasize that further improvement in understanding undoubtedly depends on the progress in numerical simulations, for which solid experimental knowledge of parameters defining the processes is paramount.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Specifically, as discussed above, these parameters are the background temperature, its contrast, the size of the macro-structure, the number of petals, the angular velocity of rotation of the structure as a whole, the angular velocity of rotation of the accretion disk, gradients of velocity of the collective flows of plasma in the disk, and the characteristic time of existence of this quasi-stationary structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Author Contributions: Conceptualization and Writing, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=', V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' All authors have read and agreed to the published version of the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Funding: This research received no external funding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Data Availability Statement: Data sharing not applicable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Conflicts of Interest: The authors declare that there is no conflicts of interests regarding the publication of this article.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' References 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Akiyama, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' [Event Horizon Telescope Collaboration].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' First Sagittarius A* Event Horizon Telescope Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' The Shadow of the Supermassive Black Hole in the Center of the Milky Way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' 2022, 930, L12, https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='3847/2041-8213/ac6674.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Akiyama, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' [Event Horizon Telescope Collaboration].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' First Sagittarius A* Event Horizon Telescope Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' EHT and Multiwavelength Observations, Data Processing, and Calibration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' 2022, 930, L13, https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='3847/2041- 8213/ac6675.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Akiyama, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' [Event Horizon Telescope Collaboration].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' First Sagittarius A* Event Horizon Telescope Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Imaging of the Galactic Center Supermassive Black Hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' 2022, 930, L14, https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='3847/2041-8213/ac6429.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Akiyama, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' [Event Horizon Telescope Collaboration].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' First Sagittarius A* Event Horizon Telescope Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Variability, Morphology, and Black Hole Mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' 2022, 930, L15, https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='3847/2041-8213/ac6736.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Akiyama, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' [Event Horizon Telescope Collaboration].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' First Sagittarius A* Event Horizon Telescope Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Testing Astrophysical Models of the Galactic Center Black Hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' 2022, 930, L16, https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='3847/2041-8213/ac6672.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Akiyama, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Lecture notes on accretion disk physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' arXiv 2022, arXiv:2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content='07262.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} +page_content=' MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/l9E2T4oBgHgl3EQfJAaa/content/2301.03687v1.pdf'} diff --git a/ltE1T4oBgHgl3EQf0wVQ/content/tmp_files/2301.03460v1.pdf.txt b/ltE1T4oBgHgl3EQf0wVQ/content/tmp_files/2301.03460v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..f97c8d6d0a2cf85f800d041970b23424959fb69d --- /dev/null +++ b/ltE1T4oBgHgl3EQf0wVQ/content/tmp_files/2301.03460v1.pdf.txt @@ -0,0 +1,1259 @@ + +High pressure-high temperature bulk synthesis of GaN +and InN by solid state nitridation of binary oxides +Elena Del Canale,1,2* Lorenzo Fornari,1,2 Chiara Coppi,1,2 Giulia Spaggiari,1,3 Francesco +Mezzadri,2,1 Giovanna Trevisi,1 Patrizia Ferro,1 Edmondo Gilioli,1 Massimo Mazzer, 1 Davide +Delmonte.1 +1 CNR – IMEM, 43124, Parma, Italy +2 SCVSA Department, Università degli Studi di Parma,43124, Parma, Italy +3 Department of Mathematical, Physical and Computer Sciences, Università degli Studi di Parma, +43124, Parma, Italy + +*Corresponding Author: elena.delcanale@imem.cnr.it +KEYWORDS gallium nitride, indium nitride, mechanochemistry, high pressure/high temperature +synthesis + +Abstract +We present a new method to synthesize bulk GaN and InN polycrystals by means of a solid-state +chemical reaction in High Pressure/High Temperature conditions. The reaction involves the binary +oxides (Ga2O3 and In2O3) and the highly reactive Li3N as nitrogen source. The formation of the +expected hexagonal phase of GaN and InN, occurring at 900 °C and 350 °C respectively and P ≥ 2.5 + + +GPa, was successfully confirmed by powder X-ray diffraction, with the presence of spurious Li-based +binary and ternary (containing also the III group cation) impurities. A simple washing processes in +aqueous solution followed by centrifugation allowed to obtain pure GaN and InN polycrystalline +powders as precipitates. These results point out a simple, low cost and scalable way to produce +significant quantities of two of the most promising nitrides in the field of electronics and energy +technologies. + +1. Introduction +Gallium and indium nitrides, as well as their solid solutions, are direct band gap III-V semiconductors +widely used in the field of electronics,1,2 high power devices3,4 and LED technologies,5 for their +unique optical absorption properties. From the structural point of view, they crystallize in a wurtzite- +like hexagonal cell (space group P63mc). However, these compounds are characterized by a +significant difference in the lattice parameters: aInN is 12% larger than aGaN and cInN is 10 % larger +than cGaN. This leads to completely different electro-optical behavior. Particularly, GaN is a dull +yellow high band-gap semiconductor (Eg = 3.4 eV)6 with low RT-conductivity, low absorption +coefficient and low thermal conductivity. On the contrary, InN is a black low band-gap semiconductor +(Eg = 0.7 eV)7 with significant RT-conductivity, high absorption coefficient, very high thermal +conductivity and an intrinsic chemical instability related to a very weak In-N covalent bond. This +complementarity can be exploited to reach an outstanding set of different optical, electrical and +thermal properties by finely tuning the ratio between In and Ga in the solid-solid solution of (In,Ga)N +(IGN), opening the route for further possible innovative application in a wide gamma of technologies. +For example, IGN can be exploited in the field of photovoltaics, enabling photoconversion in a wide +range of energy between 0.65 eV (near IR) e 3.4 eV (near UV), covering almost 90% of the solar +spectral irradiance, or rather to select the proper band gap for each specific application. + + +GaN is currently obtained in film form by hetero/homo-epitaxial growth methods (mainly with +CVD,8,9 MOCVD, 10,11,12,13 MBE 14,15,16,17 and MOVPE 18,19,20) and as bulk by various crystal growth +routes, such as sublimation and high pressure/high temperature solution methods, e.g. +ammonothermal method21 or high-pressure nitrogen solution growth process.22 +InN films can be also grown epitaxially, but because of the low InN dissociation temperature (450°C +23) and the high equilibrium N2 vapor pressure over the film24, 25, a very low growth temperature is +required. +The low thermal stability makes the synthesis of bulk crystalline InN much more difficult compared +to GaN. Several combinations of reagents, synthesis techniques and conditions have been attempted, +e.g.: ammonothermal growth from InCl3 and KNH2 in supercritical ammonia at 2.8 kbar,26 +solvothermal reaction of InCl3/InI3 with LiNH2 in benzene,27 microwave plasma sources at sub- +atmospheric pressure by saturating indium with nitrogen,28 low-temperature synthesis via nitridation +of LiInO229or In(OH)330 with NaNH2 flux in autoclave, nitridation of In2O3 and In(OH)3 with NH3 at +600 °C,31 solid-state exchange reaction between Ga/InI3 and Li3N32 or InBr3 and NaN3.33 However, +it should be underlined that most of the current synthesis techniques necessarily imply the exploitation +of harsh conditions, together with the use of toxic, polluting and very hazardous reactants or fluids. +Despite the different methods and conditions, the reactions have a very low yield, producing well +shaped μm-scale crystals, but never a pure bulk product. Therefore, particularly the use of InN is +mainly confined at the lab scale for research purposes due to the complexity of the synthesis +techniques, causing very high production costs and difficult scalability. +Besides, InN and GaN tend not to form a solid solution for the same reasons which guarantees the +described complementary physical behavior: I) the huge difference (larger than the 30%) between the +cations ionic radius and II) the different synthesis thermodynamics required to synthesize bulk + + +quantities of the end members InN and GaN. The few examples of previously obtained IGN phases +are limited to nanostructures (nanodots34, nanorings and nanoarrows35, quantum wells36, quantum +dots37, 38, quantum wires39) and heterostructures.40, 41, 42, 43 +However, some works showed that it is possible to obtain several nitrides also with simpler, cheaper, +and scalable techniques, as in the case of the mechanochemical (MC) reactions exploited for CrN,44 +Si3N4,45 ZrN,46 GaN,47 TiN48 and Fe3N449.Therefore, we investigated the MC of GaN and InN by +applying different ball milling conditions during the treatment. On the basis of this study, the gathered +information have driven us to a completely new and somehow opposite approach for the synthesis of +such nitrides i.e., the use of High Pressure/High Temperature (HP/HT) techniques. To the best of our +knowledge, the only attempts to synthesize GaN and InN in HP/HT conditions (i.e. in the GPa (i.e. +tens of kbar) pressure range, exceeding the kbar regime typical of the solvothermal methods +previously reported), again led to the formation of small crystals, such as µm-sized grains of GaN +grown from metallic gallium and melamine (C3N6H6) at 3.5-5.5 GPa and 900-1200°C,50 and InN +crystals from the direct synthesis of metallic indium ad compressed nitrogen at 2 GPa and 700°C.51 +In this paper we show that a thermodynamic solid-state reaction under HP/HT isotropic conditions +leads to the formation of pure GaN and InN, solely exploiting In or Ga binary oxides and non-toxic +nitrogen-based compounds, without the use any organic solvents during the process. The relatively +mild conditions enable to obtain a significant amount of material, with high yield. Standing these +observations, and due to incompatible activation reaction energies, the IGN solid solution is difficult +to be synthesized in a single stage HP/HT process. + +2. Experimental Methods +The mechano-chemical reactions (MC) were performed using a Pulverisette 7 Classic Line high +energy planetary ball mill (Fristch GmbH), with sealed ZrO2 jars (volume: 45 ml) and spheres + + +(diameter: 10 mm). Ga2O3 (Alfa Aesar, 99.99%), In2O3 (ChemPur, 99.99%) and a super- +stoichiometric content (i.e., +50% of excess) Li3N (Alfa Aesar, 99.4%) were used as precursors and +mixed under inert atmosphere. The reactions were carried out under a controlled inert atmosphere +inserting the ball mill apparatus in a glove box with slight N2 overpressure, varying the combination +of the main MC parameters: rotational speed (RPM), ball-to-powder mass ratio (BPR) and reaction +time (TIME). +High pressure high temperature (HP/HT) syntheses were performed in isotropic conditions through +a multi-anvil 6/8 Walker-type press apparatus (Rockland Inco Corps.). The reaction was carried out +starting from a 600-700 mg homogeneous mixture of powders of Ga2O3 (Alfa Aesar, 99.99%) or +In2O3 (ChemPur, 99.99%) with a super-stoichiometric content (i.e., +50% of excess) of Li3N (Alfa +Aesar, 99.4%) and then placed inside an Au capsule to shield the reaction cell from the outer parts of +the HP/HT assembly. Once the target pressure (in the 2.5 – 6 GPa range) was reached with a ramp +rate of 30 kPa bar/min, the temperature was increased of 50°C/min until the desired value (in the 350 +– 900 °C range). The specific pressures and temperatures of the different syntheses are specified in +the following. After the synthesis, the temperature was quenched down to room temperature and the +pressure slowly released overnight. The products, obtained in form of dense cylinders (about 5*5*5 +mm), are ground in an agate mortar or cut in form of discs to be further characterized. +The phase analysis was performed through Powder X-Ray Diffraction (PXRD), using two different +diffractometers in Bragg-Brentano geometry: (I) for qualitative analysis of the products, A Thermo- +Electron X’Tra diffractometer equipped with a Thermo Electron solid state Si(Li) detector was used. +This instrument utilizes Cu-Kα wavelength (λ=1.5406 Å) and data were collected with 0.05° step and +3s of counting time; (II) For quantitative data collection we exploited a Rigaku Smartlab XE +diffractometer with Cu Kα wavelength. A Ni filter was used to suppress the Kβ contribution. 5.0° +soller slits were located both on the incident and diffracted beam and data were collected using a +HyPix3000 detector operating in 1D mode. + + +The morphology and composition of the samples were investigated with a Zeiss Auriga Compact +Field-Emission Scanning Electron Microscope (SEM) equipped with an Oxford Xplore 30 Energy +Dispersive Spectroscopy (EDS) system. SEM images were acquired by using both 20 kV and 5 kV +acceleration voltages of the primary electron beam. EDS analyses were conducted by exciting the +samples with a 20 kV accelerated electron beam. +Raman measurements were carried out using a micro-Raman spectrometer (Horiba LabRam HR +Evolution Raman) equipped with a confocal Olympus microscope and 10x, 50x, ULWD50x, 100x +objectives (spatial resolutions of approximately 1 µm). The Micro-Raman apparatus is completed by +a He-Ne laser emitting at 632.8 nm, BraggRate Notch Filters, Silicon CCD + InGaAs Diode Array +detectors, gratings 300-600-1800 lines/mm, and density filters. The spectrometer was calibrated using +the standard silicon Raman peak at 520.6 cm-1 before each measurement. The spectra here reported +were recorded using the 100x objective, for 30 s and 4 repetitions. + +3. Results and Discussion +The solid-state chemical reactions are nitridation syntheses of the binary In and Ga oxides by the +use of Li3N (in super-stoichiometric ratio, 50% excess), as reported in equations (1) and (2): +Ga2O3 + 2 Li3N → 2 GaN + 3 Li2O + + + + + + +(1) +In2O3 + 2 Li3N → 2 InN + 3 Li2O + + + + + + +(2) + +3.1. Mechanochemistry +The study of the mechanochemical process, which noteworthy exploits the non-equilibrium +thermodynamics and local temperatures differently from conventional synthesis methods, led to a +better understanding of both the GaN and InN formation process and the energy requirements needed +to initiate and complete the solid state nitridation reactions of equations (1)-(2). + + +In the case of GaN, the activation of the nitridation reaction needs high mechanical energies (RPM +≥ 650, see Figure S1-S2 in the Supporting Information); for lower energies, Ga2O3 crystals are +reduced in size up to quasi-amorphous state, but no reaction occurs. Indeed, proper crystallization of +the phase requires high BPR (>100) and very long milling times (≥40h), as reported in Figure 1. +However, in these conditions hexagonal GaN represents a secondary phase; in fact, the main phase, +observed through “✦” reflections in Figure 1, results to be difficult to be identified in ICCD +databases. It crystallizes in a cubic F-centered cell with a=4.36Å, in line with the symmetry reported +for the cubic structure of GaN.52 It should be noticed that cubic GaN has been observed only as +epitaxial phase; as a consequence, the unambiguous assignment of the present diffraction peaks would +require specific characterizations which go beyond the scope of the present work. Noteworthy, for +intermediate BPR and time, standing the RPM conditions, a very defected GaN product is obtained +together with different Li and Ga based spurious phases, however characterized by the wrong relative +intensities of the PXRD as debated in detail discussing Figure S1-S2 of the Supporting Information. +The overall data suggests that the stabilization of the Ga-N bond is strongly hindered by the high +impact statistics, the high transferred mechanical energy and, also by kinetics. + +Figure 1. PXRD of the MC products obtained for the GaN reaction by using 650RPM, 107 BPR +and 40h of milling time (blue curve). The purple vertical lines represent the calculated pattern of +hexagonal GaN from ICSD using POWD-12++ 239, 282(1997). The blue “❖” symbols represent the + ++ZrO +Experimental +1000 ++Cubicunrecognized +Calculated GaN (hexagonal) +phase +800 +[arb.units] +600 +Intensity +400 +200 +0 +20 +30 +40 +50 +60 +70 +80 +20 +ZrO2 expected reflections calculated from ICSD using POWD-12++ 30, 1621 (1997) and the symbol +“✦” represents a phase with a cubic F-centered cell with a=4.36Å, potentially ascribable to the cubic +polymorph of GaN . + +On the other hand, we failed to synthesize InN via MC. Despite this, we identified different outputs +depending on the applied range of the MC parameters. Particularly, for low MC energies (400 < RPM +≤ 600), independently from the impact statistics and milling time, it is not possible to activate the +nitridation reaction; it just implies a reduction of the mean crystallinity of the In2O3 phase (see Figure +S4 in the Supporting Information). Surprisingly, for high energies (RPM > 600), the lithium ions start +to react with the oxygens of In2O3; however, the local mechanical energies are too high to +metastabilize In-N bonds and consequently an unwanted redox process become favored: specifically, +nitrogen ions oxidize, forming molecular gas by forcing In3+ reduction to metallic indium (Figure 2 +here below and Figure S3 in the Supporting Information). + +Figure 2. PXRD of the MC products obtained for the InN reaction by using 630RPM, 268 BPR +and 40min of milling (yellow curve). The black vertical lines represent the calculated pattern of +metallic In from ICSD using POWD-12++ 539, 3(1997), while the black “*” symbol represents the +calculated In2O3 pattern from ICSD using POWD-12++1928, 1 (1997). + + +*In.O +Metallic In-calculated pattern +1000 +Experimental +800 +[arb.units] +600 +Intensity +400 +200 +0 +20 +25 +30 +35 +40 +45 +50 +55 +60 +65 +20 +To summarize, the energy conditions needed for the formation of both GaN and InN appear to be +quite inaccessible by MC, in contrast to what observed in literature (ref. 47), at least referring to the +process conducted in N2 atmosphere and dry conditions. These results suggest the use of a +complementary approach for the study of these nitridation reactions. Therefore, a novel approach +consisting in the combination of high temperatures and high pressures through equilibrium +thermodynamic solid-state reactions is exploited to metastabilize GaN and InN. + +3.2. HP/HT syntheses +The same solid-state nitridation reactions were consequently performed in the HP/HT regime, +exploring different conditions spanning the thermodynamic range characterized by hydrostatic +pressure between 2.5 to 6 GPa and temperature between 350 to 900°C. +3.2.1 GaN +The results obtained for GaN are resumed in Table 1: it was observed that the GaN hexagonal +phase begins to form at T = 900 °C and P = 2.5 GPa. However, at such pressure and for relatively +short duration (2 h), it is not possible to complete the reaction. In order to obtain the hexagonal GaN +phase, the pressure was increased up to 6 GPa or alternatively the synthesis duration was raised up to +6 h keeping the pressure at 2.5 GPa. PXRD analysis (Figure S5 in the Supplementary Information), +highlights the systematical presence of ternary Li-based compounds, coming from a contamination +of the highly hygroscopic Li3N reactants (Figure S10 in the Supplementary Information). +Table 1. GaN explored HP/HT synthesis conditions. +Sample +Pressure +[GPa] +Temperature +[°C] +Time +[h] +Hexagonal +phase +Spurious +Ga phases +GaN +2.5 +900 +2 +NO +YES +GaN +2.5 +900 +6 +YES +YES +GaN +6 +900 +2 +YES +YES + + +GaN +6 +600 +6 +NO +YES +GaN* +3.5* +900* +3* +YES +NO +*Reaction performed starting with new and pristine Li3N reagents +Accordingly, the contamination is removed when the synthesis is performed using a new and +pristine Li3N bottle. +In Figure 3 (upper panel), we report a synthesis carried out at 3.5 GPa, 900 °C and 3 h. Noteworthy, +besides GaN, only Li2O is present, coherently to what is theoretically expected by the double +exchange reaction expressed in equation (1). +These HP/HT synthesis products can be successfully cleaned with a simple water-based washing- +treatment. The sample powders are poured in acidic water (0.1M HCl) and then centrifuged at 4000 +RPM for 15 min to separate GaN from the other components, which are fully soluble in water. When +Li2O polycrystals are put in water the solution pH rises, due to the formation of LiOH from the +reaction with water. To successfully remove all the amount of Li2O the non-soluble suspension must +be washed, centrifuged, and then separated from the aqueous solution several times, until neutral pH +is reached. The precipitate is finally dried on a heating plate at 130 °C. The PXRD results, reported +in Figure 3 (bottom panel), show the complete removal of the secondary phase, and confirm the +obtainment of a pure GaN polycrystalline powder. + + + + + Figure 3. PXRD pattern collected for GaN after the HP/HT synthesis (upper panel) and after the +subsequent washing treatment (bottom panel), obtained at 3.5 GPa and 900°C. The black lines are the +calculated reflections of the GaN hexagonal phase from ICSD using POWD-12++ 23, 815(1997), +while the orange “*” symbol indicate to the expected reflections of Li2O, calculated from ICSD using +POWD-12++40, 588 (1997). + +Morphological information from SEM images, points out the presence of a unique crystalline phase +with a quite homogeneous distribution of the crystallite size with a mean grain dimension of about 1 +μm. The EDX compositional data indicate a good ratio between gallium and nitrogen close to the +stoichiometric value of 1 (Figure 4), confirming the removal of the Li-based compounds. The C +signal may come from organic contamination of the surfaces, from the SEM environment and, in this +F +i +g +. +6 +: +( +A +) +P +X +R +D +a +n + +Calculated GaN (hex) +1000 +Experimental +800 +Intensity [arb.units] +600 +400 +200 +0 +25 +30 +35 +40 +45 +50 +55 +60 +65 +20 +Calculated GaN (hex) +1000 +Experimental +800 +Intensity [arb.units] +600 +400 +200 +0 +25 +30 +35 +40 +45 +50 +55 +60 +65 +20 +case, also from the carbon tape on which the powders are dispersed to be inserted in the SEM +chamber. + + + +Figure 4. SEM image with 10kX of magnification collected on hexagonal GaN crystallites obtained +at 3.5 GPa, 900°C, 3h and relative atomic composition. + +The same powders were studied with Raman spectroscopy (Figure 5). A clean spectrum was +obtained, showing peaks characteristic only of the hexagonal phase as observed in literature for GaN +polycrystalline powders.53 145 cm-1 E2, 533 cm-1 A1(TO), 560 cm-1 E1 (TO), the high 567 cm-1 E2 and +the 735 cm-1 A1(TO). + + +Atomic % +N +40 +Ga +38 +c +19 +0 +3 + + +Figure 5. Raman spectrum of the HP/HT synthetized GaN after the washing treatment. + +3.2.2 InN +The InN reaction was studied for 2.5 GPa ≤P ≤ 6 GPa and 350 °C ≤ T ≤ 900 °C, for 1 h ≤ time ≤6 +h as summarized in Table 2. Contrarily to GaN, the HP/HT synthesis of InN requires temperatures +well below 750 °C to prevent the formation of metallic In (Figure S7, blue curve in the Supporting +Information) in close analogy to what observed with MC in high RPM regime. The polycrystalline +hexagonal InN was detected to form above around 350 °C (Figure S7, yellow and purple curve in the +Supporting Information). +Table. 2. InN explored HP/HT synthesis conditions. +Sample +Pressure +[GPa] +Temperature +[°C] +Time +[h] +Nitride +presence +Spurious +In phases +InN +6 +900 +2 +NO +YES +InN +3 +750 +2 +NO +YES +InN +6 +390 +6 +YES +YES +InN +3 +350 +6 +YES +YES +InN* +3.5* +350* +6* +YES +NO + +20000 +15000 +lits] +lun +[arb. +10000 - +Intensity +5000 - +200 +400 +600 +800 +Raman Shift [cm-11 +* Reaction performed starting with new and pristine Li3N reagents +As for GaN HP/HT synthesis, spurious Li-based binary and ternary oxides are always present (see +Figure S7 red, yellow and purple reported in the Supporting Information), and a similar washing +treatment was applied to successfully remove the spurious phases (Figure S8 in the Supporting +Information). The complete double exchange reaction (see equation (2)) can be similarly obtained +exploiting pristine Li3N reactants, after a HP/HT synthesis performed at 3.5 GPa, 350 °C and 1 h +(Figure 6, upper panel). The PXRD pattern shows the presence of a pure polycrystalline InN bulk +product (Figure 6, bottom panel). + +Figure 6. PXRD pattern collected for InN after the HP/HT synthesis (upper panel) and after the +subsequent washing treatment (bottom panel), obtained at 3.5 GPa and 350°C. The black lines are the +calculated reflections of the InN hexagonal phase calculated pattern from ICSD using POWD-12++ + +Experimental +1000 +Calculated InN (hex) +Li,O +800 +[arb.units] +600 +Intensity +400 +200 +0 +25 +30 +35 +40 +45 +50 +55 +60 +65 +20 +Calculated InN (hex) +1000 +Experimental +800 +Intensity [arb.units] +600 +400 +200 +0 +25 +30 +35 +40 +45 +50 +55 +60 +65 +20 +46, 10086 (1997), while the orange “*” symbol correspond to the Li2O phase, calculated from ICSD +using POWD-12++40, 588 (1997). + +SEM/EDX measurements (Figure 7) show that InN crystallites are far smaller than GaN’s, with +sub-micrometrical dimensions around 100-200 nm, probably related to the reduced synthesis +temperature, not allowing an effective sintering process. The effectiveness of the washing treatment +in removing Li-based compounds from the HP/HT synthetized InN is again confirmed by the +compositional analysis, which returned In and N in the expected ratio of 1:1 within the instrumental +error and the same main extrinsic contaminations observed for GaN (i.e. C, O) + +Figure 7. SEM image with 50kX magnification collected on hexagonal InN crystallites obtained at +350°C, 3 GPa, 1 h and relative atomic compositions. + +The Raman spectra of InN (Figure 8) presents a noisier signal, ascribable to the inferior +crystallinity with respect to the GaN (Figure 4). However, the main peaks of the hexagonal phase54 +are still identifiable: 480 cm-1 A1 (TO), 476 cm-1 E1 (TO) and 580 cm-1 A1 (LO). + +Atomic % +In +43 +N +43 +c +9 +0 +4 +Other +elements +1 +1000mm + +Figure 8. Raman spectra of InN powders after the washing treatment. + + + +60 +50. +Intensity [arb. units] +40 +30 +20 +10 +.10 +300 +400 +500 +600 +700 +800 +900 +Raman Shift [cm-1 +4. Conclusions +In this work we reported a comprehensive study of the solid state nitridation reaction of GaN and +InN starting from the binary oxides and Li3N as nitrogen source, without the use of any toxic solvents +or gases. Two unconventional synthesis approaches have been carried out: mechanochemistry (MC) +and High Pressure/ High Temperature (HP/HT) synthesis. +MC reaction in non-equilibrium thermodynamic conditions, conducted by high energy planetary +ball milling in dry conditions demonstrated that it possible to obtain GaN through the application of +extreme MC parameters and at least 40h of process but without controlling the phase purity and +reproducibility. On the other hand, InN cannot be obtained by MC route because, at the threshold of +the activation of the Li3N-In2O3 reaction, the In-N bond is not stable, so the synthesis leads to an +unwanted redox process, with the formation of reduced metallic In and N2. This conclusion taught us +about the energy requirements of these nitrides formation and suggested the use of a thermodynamic +approach in which pressure could play the key role to metastabilize and force the formation of the +nitrogen triple bond with the cation. +HP/HT syntheses demonstrated to be a viable method to perform a complete double exchange +nitridation reaction, forming hexagonal GaN and InN polycrystalline powders and Li2O as unique +byproduct. The synthesis succeeded in a wide pressure range (between 2.5 and 6 GPa) and at about +900°C or 350°C respectively for GaN or InN. A simple washing treatment in acidic water allows to +separate as precipitate the nitride from the soluble Li2O, showing a new effective way to produce +significant amount (around 400 mg) of both InN and GaN polycrystalline powders. This could be a +strong starting point for the study of the direct synthesis of their solid solution (In,Ga)N that could +have broad applications in the fields of optoelectronics and third generation photovoltaics. + + + + +5.Acknowledgment +This work has benefited from the equipment and framework of the COMP-HUB Initiative, funded +by the ‘Departments of Excellence’ program of the Italian Ministry for Education, University and +Research (MIUR, 2018-2022) and of the Bio-MoNTANS project, funded by Fondazione Cariparma. + + + + + +References + + +1 Binari, S. C.; Doverspike, K.; Kelner, G.; Dietrich, H. B.; Wickenden, A. E. GaN FETs for +microwave and high-temperature applications. Solid-State Electron. 1997, 41(2), 177-180. DOI: +10.1016/S0038-1101(96)00161-X +2 Ren, R.; Liu, B.; Jones, E. A.; Wang, F. F.; Zhang, Z.; Costinett, D. Capacitor-clamped, three- +level GaN-based DC–DC converter with dual voltage outputs for battery charger applications. IEEE +J. Emerging Sel. Top. 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Lattice dynamics in GaN and AlN probed +with first‐and second‐order Raman spectroscopy. Phys. Status Solidi C 2003, (6), 1710-1731. DOI: +10.1002/pssc.200303130 +54 Inushima, T.; Shiraishi, T.; Davydov, V. Y. Phonon structure of InN grown by atomic layer +epitaxy. Solid State Commun. 1999, 110(9), 491-495. DOI: 10.1016/S0038-1098(99)00108-8 + + + + + + + + + + +For Table of Contents Only + +Ga2O3+2LiN-2GaN+3Li0 +In23+2LigN-→2InN+3Li,0 +@P=3GPa,T=900°℃ +@P=3GPa.T=350°C +SOTROPICHP/HTSYNTHESIS +PUREPOLYCRISTALLINEWURZITEPHASE +1000 +Calculated GaN +1000 +ICalculatedInN +Experimental +-Experimental +800 +800 +n +rb. +600 +600 +400 +200 +200 +Ga/lnN +30 +40 +50 +60 +20 +30 +20 +40, +29 +50 +60Supporting information for + +High pressure-high temperature bulk synthesis of GaN +and InN by solid state nitridation of binary oxides +Elena Del Canale,1,2* Lorenzo Fornari,1,2 Chiara Coppi,1,2 Giulia Spaggiari,1,3 Francesco +Mezzadri,2,1 Giovanna Trevisi,1 Patrizia Ferro,1 Edmondo Gilioli,1 Massimo Mazzer, 1 Davide +Delmonte.1 +1 CNR – IMEM, 43124, Parma, Italy +2 SCVSA Department, Università degli Studi di Parma,43124, Parma, Italy +3 Department of Mathematical, Physical and Computer Sciences, Università degli Studi di Parma, +43124, Parma, Italy +*Corresponding Author: elena.delcanale@imem.cnr.it +S.1 Mechanochemistry of GaN and InN +S.1.1 GaN +The GaN reaction was first performed via dry high energy ball milling process, without the use of +an assisting liquid medium but carrying out the synthesis after saturating the atmosphere with N2 +and closing the jars under a slight overpressure of the inert gas. Two different protocols were used: +(1) an energy-driven protocol, involving high RPM and intermediate BPR, fixed respectively at +750 and 31, studied for different durations of the milling time (1h 30’ to 11h); +(2) a time-driven protocol, involving a long milling time (between 12h 30’ and 40h), studied for +different combinations of lower RPM (400, 600, 650) and higher BPR (31, 54, 107). + +PXRD was used to study the crystal phases obtained, as shown in Figure S1. Protocol (1) pointed +out the time threshold of the activation mechanism: notably, after 1.5h of milling, Ga2O3 started +to dissociate and react, forming a small amount of hexagonal GaN with wurtzite-type crystal +structure (Figure S1, blue line). + +Figure S1. PXRD of the MC products obtained for the GaN reaction within the first protocol, by +using 750RPM, 31 BPR for milling times of 1h 30’ (blue curve), 6h (red curve) and 11h (yellow +curve). The purple vertical lines represent the calculated pattern of GaN from ICSD using POWD- +12++ 23, 815(1997). + +However, the relative low intensity and the width of the GaN diffraction peaks is related to the +low crystallinity of the products. For 6 hours-long MC, no significant improvement of the +diffraction pattern is detected for what concerns the growth of the GaN hexagonal phase; +particularly, the increase of the first peak around 32.4° of hexagonal GaN diffraction triplet is not +followed by a proportional increase of second and third peaks (around 34.6° and 36.9°), (Figure S1, +orange curve vs. purple lines). Noteworthy, the intensity of the (101) reflection (represented by the +most intense theoretical peak of GaN at 36.9°), corresponding to the plane on which the Ga-N bond +lies, is extremely reduced. This suggests that the hexagonal GaN phase which is characterized by +poor crystal quality is probably highly defected both from morphological and compositional point +of view. Tentatively, those deviations from the expected PXRD pattern distribution could have + +750 RPM : 31 BPR +3500 +* Ga.O +× ZrO(mono) + ZrO, (cubic) +2 +GaN (hex) +3000 +ts +2500 +1h30min* +2000 +ntensity +1500 +6h +1000 +11h +500 +0 +20 +30 +40 +50 +60 +20different origins: oxygen substitutions, vacancies at the N site or the presence of extended +dislocations; the growth of highly anisotropic crystals or with high degree of strain. Longer MC +syntheses (11 h) showed no-notable progresses in the product quality, with no increase of the +characteristic peaks of the GaN phase (Figure S1, yellow curve). On the contrary, ZrO2 +contamination is detected, coming from the erosion of the mechanical components, while intense +diffraction peaks are observed at 2θ= 35.87, 41.73, 60.33, 72.4, 76.07° but no database reference +could be retrieved. However, such sequence of intensities can be indexed with a cubic F-centered +cell with a=4.36Å, indicating the presence of a crystal phase with this specific structure, in line with +the theoretical reported cubic structure of GaN. It should be noticed that cubic GaN has been +observed only as epitaxial phase; as a consequence, the unambiguous assignment of the present +diffraction peaks would require specific characterizations which go beyond the scope of the present +work. The influence of time in these processes suggests that kinetics mechanisms are favored and +the energy (i.e., RPM) plays a double role, initially favoring the activation of the reaction and, +secondly, causing a partial deterioration of the products for longer times with the formation of the +Ga binary oxide, which marks a nitrogen loss from the forming Ga-N bond. It should be noticed +that for MC process exceeding the day of duration, the conservation of the N2 internal overpressure +can be compromised, exposing the reaction chamber to oxygen contaminations. + +Figure S2. PXRD of the MC products obtained for the GaN reaction within the second protocol, +by using 650RPM and milling times/BPR of 12h30min/54BPR (blue pattern), 25h/107BPR (red + +650RPM +*Ga.O +GaN(icubic) +3000 +*ZrO +GaN (hex) +hiun +rb. +40h +107BPR +25h +107BPR +1000 +12h30min +54BPR +20 +30 +40 +50 +60 +20pattern), 40h/107BPR (yellow pattern) The purple vertical lines represent the calculated pattern +from ICSD using POWD-12++ 23, 815(1997). + +For this reason, through protocol (2) the influence of lower RPM (i.e., lower exchanged +mechanical energy) and higher BPR (higher impact statistics) was evaluated for longer milling +times (between 12h 30’ and 40h). Even though the beginning of the GaN hexagonal phase +formation (indicated by the calculated reflections reported as purple lines in Figure S2), can be +observed at different conditions, a slight crystalline phase can be obtained only with (650 RPM, 107 +BPR), but this time the peaks’ sequence show the correct relative intensities (see yellow pattern of +Figure S2); however, any control of the phase purity and yield reproducibility was obtained. +Moreover, for such a high impact statistics, energy and long process, the contamination of ZrO2 due +to the jar’s erosion cannot be neglected, ruling out the application of dry MC as a suitable tool for +GaN synthesis. + +S.1.2 InN +The InN MC reaction was studied with a similar approach with respect to GaN applying +processes (1) and (2). +It was observed that, for sufficiently high energies (RPM > 600), In2O3 rapidly reacts with Li3N +forming Li2O; but the local energy exchange is too high and consequently the formation of the weak +In-N bond is unfavored. + + + Figure S3. PXRD of the MC products obtained for the InN reaction with high energy conditions of +700RPM, 300BPR, 4h (blue curve), 630RPM, 300BPR, 2h (red curve), 630RPM, 268BPR, 2h +(yellow curve) and 630RPM, 268BPR, 40min (purple curve). + +Surprisingly, in such conditions, after only 40’ (see Figure S3, purple pattern), In3+ is reduced to +metallic In, and no N-based compounds are detected, suggesting the loss of the element in gas form. +These observations exclude the possibility to induce any further reaction that could lead to InN +phase stabilization. The further increase in TIME (up to 2h) leads to the formation of major +amounts of metallic In and Li-based spurious phases as counterparts (Figure S3, yellow and orange +pattern), while for longer TIME and higher RPM, metallic Indium starts to re-oxidize back to In2O3. +The presence of hydrogen-based spurious phases is due to the high hygroscopic nature of the Li- +reactants, which rapidly react with humidity either if the atmosphere is not perfectly inert or if their +storage is not performed under controlled atmosphere. + + +4000 +*In.O. +o Metallic In +xLi.O +2 +3 +2 +2 +3500 +40min630RPM +3000 +268BPR +its +iun +2500 +arb. +2h630RPM +2000 +268BPR +Intensity +1500 +2h630RPM +1000 +300BPR +500 +4h700RPM +*300BPR +0 +20 +30 +40 +50 +60 +20* In.O. +★ LiOH +V LiOH(H,O) +7Li.O +3000 +? Unidentified secondary phases +2500 +21h30min500RPM +un +200 BPR +2000 +1500 +tensi +18h600RPM +200 BPR +1000 +500 +12h +400RPM +40 BPR +? +20 +25 +30 +35 +40 +45 +50 +55 +20Figure S4. PXRD of the MC products obtained for the InN reaction with a “kinetic” protocol, by +using 400RPM, 40BPR, 12h (blue pattern), 600RPM, 200BPR, 18h (red line), 500RPM, 200BPR, +21h30min (yellow line). + +In the intermediate energy regime, starting from 400 ≤ RPM ≤ 600 and values of BPR ≤ 200, the +MC carried out with longer milling times (12h30min ≤ TIME ≤ 21h30min) within protocol (2) +progressively decomposes and reduces the mean crystallinity of the In2O3 phase together and forms +Li-based oxides spurious phases (Figure S4), without activating any nitridation reaction. + +S.2 HP/HT syntheses +S.2.1 GaN +PXRD data collected for the HP/HT syntheses, displayed in the main text as table 1, are reported +in Figure S5 and show that the products obtained are strongly contaminated with different Li-based +phases like Ga5LiO8, Li5GaO4 and LiOH*(H2O). To investigate the origin of such spurious phases, +a synthesis at 3.5 GPa, 900 °C and 3 h was performed, using a pristine Li3N bottle; the absence of +the mixed ternary oxides (Figure 3, upper panel, in the main text) certified that those ternary oxides +are extrinsic outputs coming from a pre-existing contamination and not reaction intermediates or +degradation products. + + + + + +Figure S5. PXRD analysis of GaN synthesis for some of the conditions reported in Tab. 1: +2.5GPa, 900°C, 2h (blue curve), 2.5GPa, 900°C, 6h (red curve), 6GPa, 900°C, 2h (yellow curve). +The purple vertical lines represent the calculated pattern of hexagonal GaN from ICSD using +POWD-12++ 23, 815(1997). + +These byproducts can be successfully removed with a simple water-based washing-treatment +described in the main text. After this treatment a pure GaN powder is obtained, but with a low yield, +approximately around 15% (Figure S6). + +Figure S6. PXRD of GaN obtained at 6GPa, 900°C and 2h after washing in aqueous solution; the +pattern was calculated from ICSD using POWD-12++ 23, 815(1997). + + +3000 +Ga,Lio +Li,GaO +VLiOH(H.O) +8 +6GPa900°C2h +2500 +2000 +arb. +1500 +2.5GPa 900°C 6h +Intensity +1000 +500 +2.5GPa900°C2h +0 +20 +25 +30 +35 +40 +45 +50 +55 +60 +65 +20100 - +80. +units] +60 +[arb. +Intensity +40 +20 - +0 +20 +30 +40 +50 +60 +70 +20S.2.2 InN +In analogy with the reported study on GaN purity, ternary phases are always present in each +synthesis of Figure S7. The contamination removal was obtained by performing the HP/HT InN +synthesis starting by the same fresh Li3N reagents used for the GaN synthesis reported in Figure 3 +upper panel (main text). Again, the complete double exchange reaction of equation (2) (main text) +is observed after a HP/HT synthesis performed at 3.5 GPa, 350 °C and 1 h (Figure 7, upper panel in +main text). The PXRD pattern shows the presence of a pure polycrystalline InN bulk product +(Figure 7, bottom panel, main text). + + +Figure S7. PXRD analysis of InN synthesis for most significant conditions reported in Tab. +3:6GPa, 900°C, 2h (blue pattern), 6GPa, 390°C, 6h (red pattern), 3GPa, 350°C, 6h (yellow pattern), +3GPa, 350°C, 1h (purple pattern). The green vertical lines represent the InN calculated pattern from +ICSD using POWD-12++ 46, 10086 (1997). + +3000 +oMetallic In +VLi.O +VLilnO +VLi.ino ++Li.InO, +3 +3 +3 +2500 +its +2000 +un +VM +arb. +1500 +Intensity +1000 +500 +0 +20 +25 +30 +35 +40 +45 +50 +55 +60 +20 +Figure S8. PXRD analysis of InN obtained at 350°C and 3 GPa after the washing treatment. The +pattern was calculated from ICSD using POWD-12++ 46, 10086 (1997). + +In the attempt to superimpose the thermodynamic conditions of the GaN and InN synthesis, we +tried to synthetize InN at the same conditions of GaN but the product contained only metallic In and +Li3InO3 (Figure S9). + +Figure S9. PXRD of the HP/HT products obtained for the InN reaction @6GPa, 900°C, 2h (blue +pattern). The black lines represent the calculated pattern of metallic In from ICSD using POWD- +12++ 539, 3(1997). + + +1000 +Experimental +Calculated InN (hex) +800 +units] +600 +[arb. +Intensity +400 +200 +0 +20 +25 +30 +35 +40 +45 +50 +55 +60 +20Experimental +1000 +Metallic In -calculated pattern +kLi.nO +800 +[arb.units] +600 +Intensity +400 +200 +0 +25 +30 +35 +40 +45 +50 +55 +60 +65 +20By investigating the causes of the presence of the spurious phases in the products of the HP/HT +reactions, we hypothesized the presence of massive hydration affecting the nitridation agent, Li3N. +Specifically, as it can be seen in Figure S10, LiOH and Li2O*(H2O) are abundantly present in the +precursor, although the Li3N was kept in a dry environment. + + +Figure S10. PXRD pattern of the contaminated Li3N. + +Li.N +1000 +LiOH + LiOH(H,O) +800 +units +arb. +600 +Intensity +400 +200 +0 +15 +20 +25 +30 +35 +40 +45 +50 +55 +60 +20 \ No newline at end of file diff --git a/ltE1T4oBgHgl3EQf0wVQ/content/tmp_files/load_file.txt b/ltE1T4oBgHgl3EQf0wVQ/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..8eff1e40a990dca30b99ff3f0a8ba490800c6de6 --- /dev/null +++ b/ltE1T4oBgHgl3EQf0wVQ/content/tmp_files/load_file.txt @@ -0,0 +1,1227 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf,len=1226 +page_content='High pressure-high temperature bulk synthesis of GaN and InN by solid state nitridation of binary oxides Elena Del Canale,1,2* Lorenzo Fornari,1,2 Chiara Coppi,1,2 Giulia Spaggiari,1,3 Francesco Mezzadri,2,1 Giovanna Trevisi,1 Patrizia Ferro,1 Edmondo Gilioli,1 Massimo Mazzer, 1 Davide Delmonte.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='1 1 CNR – IMEM, 43124, Parma, Italy 2 SCVSA Department, Università degli Studi di Parma,43124, Parma, Italy 3 Department of Mathematical, Physical and Computer Sciences, Università degli Studi di Parma, 43124, Parma, Italy Corresponding Author: elena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='delcanale@imem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='cnr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='it KEYWORDS gallium nitride, indium nitride, mechanochemistry, high pressure/high temperature synthesis Abstract We present a new method to synthesize bulk GaN and InN polycrystals by means of a solid-state chemical reaction in High Pressure/High Temperature conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The reaction involves the binary oxides (Ga2O3 and In2O3) and the highly reactive Li3N as nitrogen source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The formation of the expected hexagonal phase of GaN and InN, occurring at 900 °C and 350 °C respectively and P ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5 GPa, was successfully confirmed by powder X-ray diffraction, with the presence of spurious Li-based binary and ternary (containing also the III group cation) impurities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' A simple washing processes in aqueous solution followed by centrifugation allowed to obtain pure GaN and InN polycrystalline powders as precipitates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' These results point out a simple, low cost and scalable way to produce significant quantities of two of the most promising nitrides in the field of electronics and energy technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Introduction Gallium and indium nitrides, as well as their solid solutions, are direct band gap III-V semiconductors widely used in the field of electronics,1,2 high power devices3,4 and LED technologies,5 for their unique optical absorption properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' From the structural point of view, they crystallize in a wurtzite- like hexagonal cell (space group P63mc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' However, these compounds are characterized by a significant difference in the lattice parameters: aInN is 12% larger than aGaN and cInN is 10 % larger than cGaN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' This leads to completely different electro-optical behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Particularly, GaN is a dull yellow high band-gap semiconductor (Eg = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='4 eV)6 with low RT-conductivity, low absorption coefficient and low thermal conductivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' On the contrary, InN is a black low band-gap semiconductor (Eg = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='7 eV)7 with significant RT-conductivity, high absorption coefficient, very high thermal conductivity and an intrinsic chemical instability related to a very weak In-N covalent bond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' This complementarity can be exploited to reach an outstanding set of different optical, electrical and thermal properties by finely tuning the ratio between In and Ga in the solid-solid solution of (In,Ga)N (IGN), opening the route for further possible innovative application in a wide gamma of technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' For example, IGN can be exploited in the field of photovoltaics, enabling photoconversion in a wide range of energy between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='65 eV (near IR) e 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='4 eV (near UV), covering almost 90% of the solar spectral irradiance, or rather to select the proper band gap for each specific application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' GaN is currently obtained in film form by hetero/homo-epitaxial growth methods (mainly with CVD,8,9 MOCVD, 10,11,12,13 MBE 14,15,16,17 and MOVPE 18,19,20) and as bulk by various crystal growth routes, such as sublimation and high pressure/high temperature solution methods, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' ammonothermal method21 or high-pressure nitrogen solution growth process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='22 InN films can be also grown epitaxially, but because of the low InN dissociation temperature (450°C 23) and the high equilibrium N2 vapor pressure over the film24, 25, a very low growth temperature is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The low thermal stability makes the synthesis of bulk crystalline InN much more difficult compared to GaN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Several combinations of reagents, synthesis techniques and conditions have been attempted, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' : ammonothermal growth from InCl3 and KNH2 in supercritical ammonia at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='8 kbar,26 solvothermal reaction of InCl3/InI3 with LiNH2 in benzene,27 microwave plasma sources at sub- atmospheric pressure by saturating indium with nitrogen,28 low-temperature synthesis via nitridation of LiInO229or In(OH)330 with NaNH2 flux in autoclave, nitridation of In2O3 and In(OH)3 with NH3 at 600 °C,31 solid-state exchange reaction between Ga/InI3 and Li3N32 or InBr3 and NaN3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='33 However, it should be underlined that most of the current synthesis techniques necessarily imply the exploitation of harsh conditions, together with the use of toxic, polluting and very hazardous reactants or fluids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Despite the different methods and conditions, the reactions have a very low yield, producing well shaped μm-scale crystals, but never a pure bulk product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Therefore, particularly the use of InN is mainly confined at the lab scale for research purposes due to the complexity of the synthesis techniques, causing very high production costs and difficult scalability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Besides, InN and GaN tend not to form a solid solution for the same reasons which guarantees the described complementary physical behavior: I) the huge difference (larger than the 30%) between the cations ionic radius and II) the different synthesis thermodynamics required to synthesize bulk quantities of the end members InN and GaN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The few examples of previously obtained IGN phases are limited to nanostructures (nanodots34, nanorings and nanoarrows35, quantum wells36, quantum dots37, 38, quantum wires39) and heterostructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='40, 41, 42, 43 However, some works showed that it is possible to obtain several nitrides also with simpler, cheaper, and scalable techniques, as in the case of the mechanochemical (MC) reactions exploited for CrN,44 Si3N4,45 ZrN,46 GaN,47 TiN48 and Fe3N449.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='Therefore, we investigated the MC of GaN and InN by applying different ball milling conditions during the treatment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' On the basis of this study, the gathered information have driven us to a completely new and somehow opposite approach for the synthesis of such nitrides i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=', the use of High Pressure/High Temperature (HP/HT) techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' To the best of our knowledge, the only attempts to synthesize GaN and InN in HP/HT conditions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' in the GPa (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' tens of kbar) pressure range, exceeding the kbar regime typical of the solvothermal methods previously reported), again led to the formation of small crystals, such as µm-sized grains of GaN grown from metallic gallium and melamine (C3N6H6) at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5-5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5 GPa and 900-1200°C,50 and InN crystals from the direct synthesis of metallic indium ad compressed nitrogen at 2 GPa and 700°C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='51 In this paper we show that a thermodynamic solid-state reaction under HP/HT isotropic conditions leads to the formation of pure GaN and InN, solely exploiting In or Ga binary oxides and non-toxic nitrogen-based compounds, without the use any organic solvents during the process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The relatively mild conditions enable to obtain a significant amount of material, with high yield.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Standing these observations, and due to incompatible activation reaction energies, the IGN solid solution is difficult to be synthesized in a single stage HP/HT process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Experimental Methods The mechano-chemical reactions (MC) were performed using a Pulverisette 7 Classic Line high energy planetary ball mill (Fristch GmbH), with sealed ZrO2 jars (volume: 45 ml) and spheres (diameter: 10 mm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Ga2O3 (Alfa Aesar, 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='99%), In2O3 (ChemPur, 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='99%) and a super- stoichiometric content (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=', +50% of excess) Li3N (Alfa Aesar, 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='4%) were used as precursors and mixed under inert atmosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The reactions were carried out under a controlled inert atmosphere inserting the ball mill apparatus in a glove box with slight N2 overpressure, varying the combination of the main MC parameters: rotational speed (RPM), ball-to-powder mass ratio (BPR) and reaction time (TIME).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' High pressure high temperature (HP/HT) syntheses were performed in isotropic conditions through a multi-anvil 6/8 Walker-type press apparatus (Rockland Inco Corps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The reaction was carried out starting from a 600-700 mg homogeneous mixture of powders of Ga2O3 (Alfa Aesar, 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='99%) or In2O3 (ChemPur, 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='99%) with a super-stoichiometric content (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=', +50% of excess) of Li3N (Alfa Aesar, 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='4%) and then placed inside an Au capsule to shield the reaction cell from the outer parts of the HP/HT assembly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Once the target pressure (in the 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5 – 6 GPa range) was reached with a ramp rate of 30 kPa bar/min, the temperature was increased of 50°C/min until the desired value (in the 350 – 900 °C range).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The specific pressures and temperatures of the different syntheses are specified in the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' After the synthesis, the temperature was quenched down to room temperature and the pressure slowly released overnight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The products, obtained in form of dense cylinders (about 5*5*5 mm), are ground in an agate mortar or cut in form of discs to be further characterized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The phase analysis was performed through Powder X-Ray Diffraction (PXRD), using two different diffractometers in Bragg-Brentano geometry: (I) for qualitative analysis of the products, A Thermo- Electron X’Tra diffractometer equipped with a Thermo Electron solid state Si(Li) detector was used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' This instrument utilizes Cu-Kα wavelength (λ=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5406 Å) and data were collected with 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='05° step and 3s of counting time;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' (II) For quantitative data collection we exploited a Rigaku Smartlab XE diffractometer with Cu Kα wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' A Ni filter was used to suppress the Kβ contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='0° soller slits were located both on the incident and diffracted beam and data were collected using a HyPix3000 detector operating in 1D mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The morphology and composition of the samples were investigated with a Zeiss Auriga Compact Field-Emission Scanning Electron Microscope (SEM) equipped with an Oxford Xplore 30 Energy Dispersive Spectroscopy (EDS) system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' SEM images were acquired by using both 20 kV and 5 kV acceleration voltages of the primary electron beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' EDS analyses were conducted by exciting the samples with a 20 kV accelerated electron beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Raman measurements were carried out using a micro-Raman spectrometer (Horiba LabRam HR Evolution Raman) equipped with a confocal Olympus microscope and 10x, 50x, ULWD50x, 100x objectives (spatial resolutions of approximately 1 µm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The Micro-Raman apparatus is completed by a He-Ne laser emitting at 632.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='8 nm, BraggRate Notch Filters, Silicon CCD + InGaAs Diode Array detectors, gratings 300-600-1800 lines/mm, and density filters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The spectrometer was calibrated using the standard silicon Raman peak at 520.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='6 cm-1 before each measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The spectra here reported were recorded using the 100x objective, for 30 s and 4 repetitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Results and Discussion The solid-state chemical reactions are nitridation syntheses of the binary In and Ga oxides by the use of Li3N (in super-stoichiometric ratio, 50% excess), as reported in equations (1) and (2): Ga2O3 + 2 Li3N → 2 GaN + 3 Li2O (1) In2O3 + 2 Li3N → 2 InN + 3 Li2O (2) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Mechanochemistry The study of the mechanochemical process, which noteworthy exploits the non-equilibrium thermodynamics and local temperatures differently from conventional synthesis methods, led to a better understanding of both the GaN and InN formation process and the energy requirements needed to initiate and complete the solid state nitridation reactions of equations (1)-(2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' In the case of GaN, the activation of the nitridation reaction needs high mechanical energies (RPM ≥ 650, see Figure S1-S2 in the Supporting Information);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' for lower energies, Ga2O3 crystals are reduced in size up to quasi-amorphous state, but no reaction occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Indeed, proper crystallization of the phase requires high BPR (>100) and very long milling times (≥40h), as reported in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' However, in these conditions hexagonal GaN represents a secondary phase;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' in fact, the main phase, observed through “✦” reflections in Figure 1, results to be difficult to be identified in ICCD databases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' It crystallizes in a cubic F-centered cell with a=4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='36Å, in line with the symmetry reported for the cubic structure of GaN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='52 It should be noticed that cubic GaN has been observed only as epitaxial phase;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' as a consequence, the unambiguous assignment of the present diffraction peaks would require specific characterizations which go beyond the scope of the present work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Noteworthy, for intermediate BPR and time, standing the RPM conditions, a very defected GaN product is obtained together with different Li and Ga based spurious phases, however characterized by the wrong relative intensities of the PXRD as debated in detail discussing Figure S1-S2 of the Supporting Information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The overall data suggests that the stabilization of the Ga-N bond is strongly hindered by the high impact statistics, the high transferred mechanical energy and, also by kinetics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' PXRD of the MC products obtained for the GaN reaction by using 650RPM, 107 BPR and 40h of milling time (blue curve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The purple vertical lines represent the calculated pattern of hexagonal GaN from ICSD using POWD-12++ 239, 282(1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The blue “❖” symbols represent the +ZrO Experimental 1000 +Cubicunrecognized Calculated GaN (hexagonal) phase 800 [arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='units] 600 Intensity 400 200 0 20 30 40 50 60 70 80 20 ZrO2 expected reflections calculated from ICSD using POWD-12++ 30, 1621 (1997) and the symbol “✦” represents a phase with a cubic F-centered cell with a=4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='36Å, potentially ascribable to the cubic polymorph of GaN .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' On the other hand, we failed to synthesize InN via MC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Despite this, we identified different outputs depending on the applied range of the MC parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Particularly, for low MC energies (400 < RPM ≤ 600), independently from the impact statistics and milling time, it is not possible to activate the nitridation reaction;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' it just implies a reduction of the mean crystallinity of the In2O3 phase (see Figure S4 in the Supporting Information).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Surprisingly, for high energies (RPM > 600), the lithium ions start to react with the oxygens of In2O3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' however, the local mechanical energies are too high to metastabilize In-N bonds and consequently an unwanted redox process become favored: specifically, nitrogen ions oxidize, forming molecular gas by forcing In3+ reduction to metallic indium (Figure 2 here below and Figure S3 in the Supporting Information).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' PXRD of the MC products obtained for the InN reaction by using 630RPM, 268 BPR and 40min of milling (yellow curve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The black vertical lines represent the calculated pattern of metallic In from ICSD using POWD-12++ 539, 3(1997), while the black “*” symbol represents the calculated In2O3 pattern from ICSD using POWD-12++1928, 1 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' In.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='O Metallic In calculated pattern 1000 Experimental 800 [arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='units] 600 Intensity 400 200 0 20 25 30 35 40 45 50 55 60 65 20 To summarize, the energy conditions needed for the formation of both GaN and InN appear to be quite inaccessible by MC, in contrast to what observed in literature (ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 47), at least referring to the process conducted in N2 atmosphere and dry conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' These results suggest the use of a complementary approach for the study of these nitridation reactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Therefore, a novel approach consisting in the combination of high temperatures and high pressures through equilibrium thermodynamic solid state reactions is exploited to metastabilize GaN and InN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' HP/HT syntheses The same solid-state nitridation reactions were consequently performed in the HP/HT regime, exploring different conditions spanning the thermodynamic range characterized by hydrostatic pressure between 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5 to 6 GPa and temperature between 350 to 900°C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='1 GaN The results obtained for GaN are resumed in Table 1: it was observed that the GaN hexagonal phase begins to form at T = 900 °C and P = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5 GPa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' However, at such pressure and for relatively short duration (2 h), it is not possible to complete the reaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' In order to obtain the hexagonal GaN phase, the pressure was increased up to 6 GPa or alternatively the synthesis duration was raised up to 6 h keeping the pressure at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5 GPa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' PXRD analysis (Figure S5 in the Supplementary Information), highlights the systematical presence of ternary Li-based compounds, coming from a contamination of the highly hygroscopic Li3N reactants (Figure S10 in the Supplementary Information).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' GaN explored HP/HT synthesis conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Sample Pressure [GPa] Temperature [°C] Time [h] Hexagonal phase Spurious Ga phases GaN 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5 900 2 NO YES GaN 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5 900 6 YES YES GaN 6 900 2 YES YES GaN 6 600 6 NO YES GaN* 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5* 900* 3* YES NO *Reaction performed starting with new and pristine Li3N reagents Accordingly, the contamination is removed when the synthesis is performed using a new and pristine Li3N bottle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' In Figure 3 (upper panel), we report a synthesis carried out at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5 GPa, 900 °C and 3 h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Noteworthy, besides GaN, only Li2O is present, coherently to what is theoretically expected by the double exchange reaction expressed in equation (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' These HP/HT synthesis products can be successfully cleaned with a simple water-based washing- treatment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The sample powders are poured in acidic water (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='1M HCl) and then centrifuged at 4000 RPM for 15 min to separate GaN from the other components, which are fully soluble in water.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' When Li2O polycrystals are put in water the solution pH rises, due to the formation of LiOH from the reaction with water.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' To successfully remove all the amount of Li2O the non-soluble suspension must be washed, centrifuged, and then separated from the aqueous solution several times, until neutral pH is reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The precipitate is finally dried on a heating plate at 130 °C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The PXRD results, reported in Figure 3 (bottom panel), show the complete removal of the secondary phase, and confirm the obtainment of a pure GaN polycrystalline powder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' PXRD pattern collected for GaN after the HP/HT synthesis (upper panel) and after the subsequent washing treatment (bottom panel), obtained at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5 GPa and 900°C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The black lines are the calculated reflections of the GaN hexagonal phase from ICSD using POWD-12++ 23, 815(1997), while the orange “*” symbol indicate to the expected reflections of Li2O, calculated from ICSD using POWD-12++40, 588 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Morphological information from SEM images, points out the presence of a unique crystalline phase with a quite homogeneous distribution of the crystallite size with a mean grain dimension of about 1 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The EDX compositional data indicate a good ratio between gallium and nitrogen close to the stoichiometric value of 1 (Figure 4), confirming the removal of the Li-based compounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The C signal may come from organic contamination of the surfaces, from the SEM environment and, in this F i g .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 6 : ( A ) P X R D a n Calculated GaN (hex) 1000 Experimental 800 Intensity [arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='units] 600 400 200 0 25 30 35 40 45 50 55 60 65 20 Calculated GaN (hex) 1000 Experimental 800 Intensity [arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='units] 600 400 200 0 25 30 35 40 45 50 55 60 65 20 case, also from the carbon tape on which the powders are dispersed to be inserted in the SEM chamber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' SEM image with 10kX of magnification collected on hexagonal GaN crystallites obtained at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5 GPa, 900°C, 3h and relative atomic composition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The same powders were studied with Raman spectroscopy (Figure 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' A clean spectrum was obtained, showing peaks characteristic only of the hexagonal phase as observed in literature for GaN polycrystalline powders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='53 145 cm-1 E2, 533 cm-1 A1(TO), 560 cm-1 E1 (TO), the high 567 cm-1 E2 and the 735 cm-1 A1(TO).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Atomic % N 40 Ga 38 c 19 0 3 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Raman spectrum of the HP/HT synthetized GaN after the washing treatment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='2 InN The InN reaction was studied for 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5 GPa ≤P ≤ 6 GPa and 350 °C ≤ T ≤ 900 °C, for 1 h ≤ time ≤6 h as summarized in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Contrarily to GaN, the HP/HT synthesis of InN requires temperatures well below 750 °C to prevent the formation of metallic In (Figure S7, blue curve in the Supporting Information) in close analogy to what observed with MC in high RPM regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The polycrystalline hexagonal InN was detected to form above around 350 °C (Figure S7, yellow and purple curve in the Supporting Information).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' InN explored HP/HT synthesis conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Sample Pressure [GPa] Temperature [°C] Time [h] Nitride presence Spurious In phases InN 6 900 2 NO YES InN 3 750 2 NO YES InN 6 390 6 YES YES InN 3 350 6 YES YES InN* 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5* 350* 6* YES NO 20000 15000 lits] lun [arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 10000 - Intensity 5000 - 200 400 600 800 Raman Shift [cm-11 * Reaction performed starting with new and pristine Li3N reagents As for GaN HP/HT synthesis, spurious Li-based binary and ternary oxides are always present (see Figure S7 red, yellow and purple reported in the Supporting Information), and a similar washing treatment was applied to successfully remove the spurious phases (Figure S8 in the Supporting Information).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The complete double exchange reaction (see equation (2)) can be similarly obtained exploiting pristine Li3N reactants, after a HP/HT synthesis performed at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5 GPa, 350 °C and 1 h (Figure 6, upper panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The PXRD pattern shows the presence of a pure polycrystalline InN bulk product (Figure 6, bottom panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' PXRD pattern collected for InN after the HP/HT synthesis (upper panel) and after the subsequent washing treatment (bottom panel), obtained at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5 GPa and 350°C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The black lines are the calculated reflections of the InN hexagonal phase calculated pattern from ICSD using POWD-12++ Experimental 1000 Calculated InN (hex) Li,O 800 [arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='units] 600 Intensity 400 200 0 25 30 35 40 45 50 55 60 65 20 Calculated InN (hex) 1000 Experimental 800 Intensity [arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='units] 600 400 200 0 25 30 35 40 45 50 55 60 65 20 46, 10086 (1997), while the orange “*” symbol correspond to the Li2O phase, calculated from ICSD using POWD-12++40, 588 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' SEM/EDX measurements (Figure 7) show that InN crystallites are far smaller than GaN’s, with sub-micrometrical dimensions around 100-200 nm, probably related to the reduced synthesis temperature, not allowing an effective sintering process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The effectiveness of the washing treatment in removing Li-based compounds from the HP/HT synthetized InN is again confirmed by the compositional analysis, which returned In and N in the expected ratio of 1:1 within the instrumental error and the same main extrinsic contaminations observed for GaN (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' C, O) Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' SEM image with 50kX magnification collected on hexagonal InN crystallites obtained at 350°C, 3 GPa, 1 h and relative atomic compositions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The Raman spectra of InN (Figure 8) presents a noisier signal, ascribable to the inferior crystallinity with respect to the GaN (Figure 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' However, the main peaks of the hexagonal phase54 are still identifiable: 480 cm-1 A1 (TO), 476 cm-1 E1 (TO) and 580 cm-1 A1 (LO).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Atomic % In 43 N 43 c 9 0 4 Other elements 1 1000mm Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Raman spectra of InN powders after the washing treatment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 60 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Intensity [arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' units] 40 30 20 10 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='10 300 400 500 600 700 800 900 Raman Shift [cm-1 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Conclusions In this work we reported a comprehensive study of the solid state nitridation reaction of GaN and InN starting from the binary oxides and Li3N as nitrogen source, without the use of any toxic solvents or gases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Two unconventional synthesis approaches have been carried out: mechanochemistry (MC) and High Pressure/ High Temperature (HP/HT) synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' MC reaction in non-equilibrium thermodynamic conditions, conducted by high energy planetary ball milling in dry conditions demonstrated that it possible to obtain GaN through the application of extreme MC parameters and at least 40h of process but without controlling the phase purity and reproducibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' On the other hand, InN cannot be obtained by MC route because, at the threshold of the activation of the Li3N-In2O3 reaction, the In-N bond is not stable, so the synthesis leads to an unwanted redox process, with the formation of reduced metallic In and N2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' This conclusion taught us about the energy requirements of these nitrides formation and suggested the use of a thermodynamic approach in which pressure could play the key role to metastabilize and force the formation of the nitrogen triple bond with the cation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' HP/HT syntheses demonstrated to be a viable method to perform a complete double exchange nitridation reaction, forming hexagonal GaN and InN polycrystalline powders and Li2O as unique byproduct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The synthesis succeeded in a wide pressure range (between 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5 and 6 GPa) and at about 900°C or 350°C respectively for GaN or InN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' A simple washing treatment in acidic water allows to separate as precipitate the nitride from the soluble Li2O, showing a new effective way to produce significant amount (around 400 mg) of both InN and GaN polycrystalline powders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' This could be a strong starting point for the study of the direct synthesis of their solid solution (In,Ga)N that could have broad applications in the fields of optoelectronics and third generation photovoltaics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='Acknowledgment This work has benefited from the equipment and framework of the COMP-HUB Initiative, funded by the ‘Departments of Excellence’ program of the Italian Ministry for Education, University and Research (MIUR, 2018-2022) and of the Bio-MoNTANS project, funded by Fondazione Cariparma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' References 1 Binari, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Doverspike, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=';' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Ohshima, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Fukuda, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Tsuji, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Oshima, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Crystal growth of GaN by ammonothermal method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Cryst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Growth 2004, 260(1-2), 67-72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='jcrysgro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='031 22 Karpiński, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Porowski, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Miotkowska, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' High pressure vapor growth of GaN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Cryst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Growth 1982, 56(1), 77-82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Froyen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Zunger, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Zinc-blende–wurtzite polytypism in semiconductors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' B 1992, 46(16), 10086.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='1103/PhysRevB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='10086 53 Haboeck, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Siegle, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Hoffmann, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Thomsen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Lattice dynamics in GaN and AlN probed with first‐and second‐order Raman spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Status Solidi C 2003, (6), 1710-1731.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='1002/pssc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='200303130 54 Inushima, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Shiraishi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Davydov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Phonon structure of InN grown by atomic layer epitaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Solid State Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 1999, 110(9), 491-495.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='1016/S0038-1098(99)00108-8 For Table of Contents Only Ga2O3+2LiN 2GaN+3Li0 In23+2LigN →2InN+3Li,0 @P=3GPa,T=900°℃ @P=3GPa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='T=350°C SOTROPICHP/HTSYNTHESIS PUREPOLYCRISTALLINEWURZITEPHASE 1000 Calculated GaN 1000 ICalculatedInN Experimental Experimental 800 800 n rb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 600 600 400 200 200 Ga/lnN 30 40 50 60 20 30 20 40, 29 50 60Supporting information for High pressure-high temperature bulk synthesis of GaN and InN by solid state nitridation of binary oxides Elena Del Canale,1,2* Lorenzo Fornari,1,2 Chiara Coppi,1,2 Giulia Spaggiari,1,3 Francesco Mezzadri,2,1 Giovanna Trevisi,1 Patrizia Ferro,1 Edmondo Gilioli,1 Massimo Mazzer, 1 Davide Delmonte.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='1 1 CNR – IMEM, 43124, Parma, Italy 2 SCVSA Department, Università degli Studi di Parma,43124, Parma, Italy 3 Department of Mathematical, Physical and Computer Sciences, Università degli Studi di Parma, 43124, Parma, Italy *Corresponding Author: elena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='delcanale@imem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='cnr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='it S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='1 Mechanochemistry of GaN and InN S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='1 GaN The GaN reaction was first performed via dry high energy ball milling process, without the use of an assisting liquid medium but carrying out the synthesis after saturating the atmosphere with N2 and closing the jars under a slight overpressure of the inert gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Two different protocols were used: (1) an energy-driven protocol, involving high RPM and intermediate BPR, fixed respectively at 750 and 31, studied for different durations of the milling time (1h 30’ to 11h);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' (2) a time-driven protocol, involving a long milling time (between 12h 30’ and 40h), studied for different combinations of lower RPM (400, 600, 650) and higher BPR (31, 54, 107).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' PXRD was used to study the crystal phases obtained, as shown in Figure S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Protocol (1) pointed out the time threshold of the activation mechanism: notably, after 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5h of milling, Ga2O3 started to dissociate and react, forming a small amount of hexagonal GaN with wurtzite-type crystal structure (Figure S1, blue line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Figure S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' PXRD of the MC products obtained for the GaN reaction within the first protocol, by using 750RPM, 31 BPR for milling times of 1h 30’ (blue curve), 6h (red curve) and 11h (yellow curve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The purple vertical lines represent the calculated pattern of GaN from ICSD using POWD- 12++ 23, 815(1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' However, the relative low intensity and the width of the GaN diffraction peaks is related to the low crystallinity of the products.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' For 6 hours-long MC, no significant improvement of the diffraction pattern is detected for what concerns the growth of the GaN hexagonal phase;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' particularly, the increase of the first peak around 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='4° of hexagonal GaN diffraction triplet is not followed by a proportional increase of second and third peaks (around 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='6° and 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='9°), (Figure S1, orange curve vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' purple lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Noteworthy, the intensity of the (101) reflection (represented by the most intense theoretical peak of GaN at 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='9°), corresponding to the plane on which the Ga-N bond lies, is extremely reduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' This suggests that the hexagonal GaN phase which is characterized by poor crystal quality is probably highly defected both from morphological and compositional point of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Tentatively, those deviations from the expected PXRD pattern distribution could have 750 RPM : 31 BPR 3500 * Ga.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='O × ZrO(mono) ZrO, (cubic) 2 GaN (hex) 3000 ts 2500 1h30min* 2000 ntensity 1500 6h 1000 11h 500 0 20 30 40 50 60 20different origins: oxygen substitutions, vacancies at the N site or the presence of extended dislocations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' the growth of highly anisotropic crystals or with high degree of strain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Longer MC syntheses (11 h) showed no-notable progresses in the product quality, with no increase of the characteristic peaks of the GaN phase (Figure S1, yellow curve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' On the contrary, ZrO2 contamination is detected, coming from the erosion of the mechanical components, while intense diffraction peaks are observed at 2θ= 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='87, 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='73, 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='33, 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='4, 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='07° but no database reference could be retrieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' However, such sequence of intensities can be indexed with a cubic F-centered cell with a=4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='36Å, indicating the presence of a crystal phase with this specific structure, in line with the theoretical reported cubic structure of GaN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' It should be noticed that cubic GaN has been observed only as epitaxial phase;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' as a consequence, the unambiguous assignment of the present diffraction peaks would require specific characterizations which go beyond the scope of the present work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The influence of time in these processes suggests that kinetics mechanisms are favored and the energy (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=', RPM) plays a double role, initially favoring the activation of the reaction and, secondly, causing a partial deterioration of the products for longer times with the formation of the Ga binary oxide, which marks a nitrogen loss from the forming Ga-N bond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' It should be noticed that for MC process exceeding the day of duration, the conservation of the N2 internal overpressure can be compromised, exposing the reaction chamber to oxygen contaminations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Figure S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' PXRD of the MC products obtained for the GaN reaction within the second protocol, by using 650RPM and milling times/BPR of 12h30min/54BPR (blue pattern), 25h/107BPR (red 650RPM *Ga.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='O GaN(icubic) 3000 *ZrO GaN (hex) hiun rb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 40h 107BPR 25h 107BPR 1000 12h30min 54BPR 20 30 40 50 60 20pattern), 40h/107BPR (yellow pattern) The purple vertical lines represent the calculated pattern from ICSD using POWD-12++ 23, 815(1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' For this reason, through protocol (2) the influence of lower RPM (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=', lower exchanged mechanical energy) and higher BPR (higher impact statistics) was evaluated for longer milling times (between 12h 30’ and 40h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Even though the beginning of the GaN hexagonal phase formation (indicated by the calculated reflections reported as purple lines in Figure S2), can be observed at different conditions, a slight crystalline phase can be obtained only with (650 RPM, 107 BPR), but this time the peaks’ sequence show the correct relative intensities (see yellow pattern of Figure S2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' however, any control of the phase purity and yield reproducibility was obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Moreover, for such a high impact statistics, energy and long process, the contamination of ZrO2 due to the jar’s erosion cannot be neglected, ruling out the application of dry MC as a suitable tool for GaN synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='2 InN The InN MC reaction was studied with a similar approach with respect to GaN applying processes (1) and (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' It was observed that, for sufficiently high energies (RPM > 600), In2O3 rapidly reacts with Li3N forming Li2O;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' but the local energy exchange is too high and consequently the formation of the weak In-N bond is unfavored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Figure S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' PXRD of the MC products obtained for the InN reaction with high energy conditions of 700RPM, 300BPR, 4h (blue curve), 630RPM, 300BPR, 2h (red curve), 630RPM, 268BPR, 2h (yellow curve) and 630RPM, 268BPR, 40min (purple curve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Surprisingly, in such conditions, after only 40’ (see Figure S3, purple pattern), In3+ is reduced to metallic In, and no N-based compounds are detected, suggesting the loss of the element in gas form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' These observations exclude the possibility to induce any further reaction that could lead to InN phase stabilization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The further increase in TIME (up to 2h) leads to the formation of major amounts of metallic In and Li-based spurious phases as counterparts (Figure S3, yellow and orange pattern), while for longer TIME and higher RPM, metallic Indium starts to re-oxidize back to In2O3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The presence of hydrogen-based spurious phases is due to the high hygroscopic nature of the Li- reactants, which rapidly react with humidity either if the atmosphere is not perfectly inert or if their storage is not performed under controlled atmosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 4000 *In.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' o Metallic In xLi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='O 2 3 2 2 3500 40min630RPM 3000 268BPR its iun 2500 arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 2h630RPM 2000 268BPR Intensity 1500 2h630RPM 1000 300BPR 500 4h700RPM *300BPR 0 20 30 40 50 60 20* In.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' ★ LiOH V LiOH(H,O) 7Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='O 3000 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Unidentified secondary phases 2500 21h30min500RPM un 200 BPR 2000 1500 tensi 18h600RPM 200 BPR 1000 500 12h 400RPM 40 BPR ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 20 25 30 35 40 45 50 55 20Figure S4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' PXRD of the MC products obtained for the InN reaction with a “kinetic” protocol, by using 400RPM, 40BPR, 12h (blue pattern), 600RPM, 200BPR, 18h (red line), 500RPM, 200BPR, 21h30min (yellow line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' In the intermediate energy regime, starting from 400 ≤ RPM ≤ 600 and values of BPR ≤ 200, the MC carried out with longer milling times (12h30min ≤ TIME ≤ 21h30min) within protocol (2) progressively decomposes and reduces the mean crystallinity of the In2O3 phase together and forms Li-based oxides spurious phases (Figure S4), without activating any nitridation reaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='2 HP/HT syntheses S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='1 GaN PXRD data collected for the HP/HT syntheses, displayed in the main text as table 1, are reported in Figure S5 and show that the products obtained are strongly contaminated with different Li-based phases like Ga5LiO8, Li5GaO4 and LiOH*(H2O).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' To investigate the origin of such spurious phases, a synthesis at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5 GPa, 900 °C and 3 h was performed, using a pristine Li3N bottle;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' the absence of the mixed ternary oxides (Figure 3, upper panel, in the main text) certified that those ternary oxides are extrinsic outputs coming from a pre-existing contamination and not reaction intermediates or degradation products.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Figure S5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' PXRD analysis of GaN synthesis for some of the conditions reported in Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 1: 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5GPa, 900°C, 2h (blue curve), 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5GPa, 900°C, 6h (red curve), 6GPa, 900°C, 2h (yellow curve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The purple vertical lines represent the calculated pattern of hexagonal GaN from ICSD using POWD-12++ 23, 815(1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' These byproducts can be successfully removed with a simple water-based washing-treatment described in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' After this treatment a pure GaN powder is obtained, but with a low yield, approximately around 15% (Figure S6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Figure S6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' PXRD of GaN obtained at 6GPa, 900°C and 2h after washing in aqueous solution;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' the pattern was calculated from ICSD using POWD-12++ 23, 815(1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 3000 Ga,Lio Li,GaO VLiOH(H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='O) 8 6GPa900°C2h 2500 2000 arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 1500 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5GPa 900°C 6h Intensity 1000 500 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5GPa900°C2h 0 20 25 30 35 40 45 50 55 60 65 20100 - 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' units] 60 [arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Intensity 40 20 - 0 20 30 40 50 60 70 20S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='2 InN In analogy with the reported study on GaN purity, ternary phases are always present in each synthesis of Figure S7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The contamination removal was obtained by performing the HP/HT InN synthesis starting by the same fresh Li3N reagents used for the GaN synthesis reported in Figure 3 upper panel (main text).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Again, the complete double exchange reaction of equation (2) (main text) is observed after a HP/HT synthesis performed at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='5 GPa, 350 °C and 1 h (Figure 7, upper panel in main text).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The PXRD pattern shows the presence of a pure polycrystalline InN bulk product (Figure 7, bottom panel, main text).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Figure S7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' PXRD analysis of InN synthesis for most significant conditions reported in Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 3:6GPa, 900°C, 2h (blue pattern), 6GPa, 390°C, 6h (red pattern), 3GPa, 350°C, 6h (yellow pattern), 3GPa, 350°C, 1h (purple pattern).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The green vertical lines represent the InN calculated pattern from ICSD using POWD-12++ 46, 10086 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 3000 oMetallic In VLi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='O VLilnO VLi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='ino +Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='InO, 3 3 3 2500 its 2000 un VM arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 1500 Intensity 1000 500 0 20 25 30 35 40 45 50 55 60 20 Figure S8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' PXRD analysis of InN obtained at 350°C and 3 GPa after the washing treatment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The pattern was calculated from ICSD using POWD-12++ 46, 10086 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' In the attempt to superimpose the thermodynamic conditions of the GaN and InN synthesis, we tried to synthetize InN at the same conditions of GaN but the product contained only metallic In and Li3InO3 (Figure S9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Figure S9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' PXRD of the HP/HT products obtained for the InN reaction @6GPa, 900°C, 2h (blue pattern).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' The black lines represent the calculated pattern of metallic In from ICSD using POWD- 12++ 539, 3(1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 1000 Experimental Calculated InN (hex) 800 units] 600 [arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Intensity 400 200 0 20 25 30 35 40 45 50 55 60 20Experimental 1000 Metallic In -calculated pattern kLi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='nO 800 [arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='units] 600 Intensity 400 200 0 25 30 35 40 45 50 55 60 65 20By investigating the causes of the presence of the spurious phases in the products of the HP/HT reactions, we hypothesized the presence of massive hydration affecting the nitridation agent, Li3N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Specifically, as it can be seen in Figure S10, LiOH and Li2O*(H2O) are abundantly present in the precursor, although the Li3N was kept in a dry environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Figure S10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' PXRD pattern of the contaminated Li3N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content='N 1000 LiOH LiOH(H,O) 800 units arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} +page_content=' 600 Intensity 400 200 0 15 20 25 30 35 40 45 50 55 60 20' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ltE1T4oBgHgl3EQf0wVQ/content/2301.03460v1.pdf'} diff --git a/m9FKT4oBgHgl3EQfEy02/content/tmp_files/2301.11717v1.pdf.txt b/m9FKT4oBgHgl3EQfEy02/content/tmp_files/2301.11717v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..e0c1f1e2c2181f58ce1e8348d3c15d42869ec956 --- /dev/null +++ b/m9FKT4oBgHgl3EQfEy02/content/tmp_files/2301.11717v1.pdf.txt @@ -0,0 +1,2693 @@ +θ-diagram technique for N = 1, d = 4 superfields +D. Bason a,b, M. Bill`o c,d +a Universit`a degli Studi di Trieste, Dipertimento di Fisica, +Via Alfonso Valerio, 2, 34127 Trieste, Italy +b I.N.F.N. - sezione di Trieste, +Via Alfonso Valerio, 2, 34127 Trieste, Italy +c Universit`a degli Studi di Torino, Dipartimento di Fisica, +Via P. Giuria 1, I-10125 Torino, Italy +d I.N.F.N. - sezione di Torino, +Via P. Giuria 1, I-10125 Torino, Italy +E-mail: marco.billo@unito.it, davide.bason@phd.units.it +Abstract +We describe a diagrammatic procedure to carry out the Grassmann integration in super- +Feynman diagrams of 4d theories expressed in terms of N = 1 superfields. +This method +is alternative to the well known D-algebra approach. +We develop it in detail for theories +containing vector, chiral and anti-chiral superfields, with the type of interactions which occur in +N = 2 SYM theories with massless matter, but it would be possible to extend it to other cases. +The main advantage is that this method is algorithmic; we implemented it as a Mathematica +program that, given the description of a super Feynman diagram in momentum space, returns +directly the polynomial in the momenta produced by the Grassmann integration. +Keywords: N = 1 susy theories, superdiagrams, Grassmann integration +arXiv:2301.11717v1 [hep-th] 27 Jan 2023 + +Contents +1 +Introduction +1 +2 +N = 1 superdiagrams for N = 2 theories +3 +2.1 +N = 2 SYM theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +3 +2.2 +Factorizing the Grassmann part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +6 +2.3 +External lines in superdiagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +7 +3 +Grassmann integration in superdiagrams +10 +3.1 +A simple example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +10 +3.2 +D-algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +10 +3.3 +Introducing the θ-diagrams +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +11 +3.4 +Diagrams with (anti)chiral superfields +. . . . . . . . . . . . . . . . . . . . . . . . . +13 +3.5 +Diagrams with (internal) vector superfields +. . . . . . . . . . . . . . . . . . . . . . +17 +3.6 +Some θ-diagrammatical properties +. . . . . . . . . . . . . . . . . . . . . . . . . . . +19 +4 +Analyizing an example +22 +4.1 +Ordering issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +26 +5 +Superdiagrams with vector or spinor external states +27 +5.1 +External vectors +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +27 +5.2 +Spinors from (anti-)chiral multiplets as external states . . . . . . . . . . . . . . . . +29 +5.3 +Gauginos as external states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +32 +6 +Use of the Grassmann integration algorithm +34 +A Notations and conventions +41 +A.1 General conventions +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +41 +A.2 Spinorial and grassmannian conventions . . . . . . . . . . . . . . . . . . . . . . . . +42 +1 +Introduction +Supersymmetric field theories have been intensely investigated since their discovery [1–5], for +various important reasons related to their possible phenomenological implications, to their rˆole +as simplified, highly symmetric theoretical scenarios in which to shed light on deep properties +of QFTs and their enticing connections with advanced mathematical structures. In all of these +directions, the fact that supersymmetry simplifies the perturbative expansion exploiting partial +cancellations between bosonic and fermionic loops has always played an important part. +Supersymmetric theories can be described in terms of superfields [6], which collect the bosonic +and fermionic fields that sit in a given representation of the supersymmetry algebra (a multiplet) +within an expansion in terms of Grassmann variables, usually dubbed with the letter θ. The per- +turbative expansion when organized in terms of superfields of the correlation functions is expressed +in terms of super Feynman diagrams. These encompass the contributions of all ordinary Feynman +1 + +diagrams for the component fields of the various multiplets. The evaluation of super Feynman +diagrams requires the integration of their internal vertices over superspace, i.e. over both their +space-time positions and their Grassmann θ coordinates. The Grassmann integration is essentially +an algebraic operation, and poses no conceptual problem. However, from the practical point of +view, it can rapidly become complicated when the order in perturbation theory and/or the number +of external points increases. It is therefore important to develop efficient strategies to tackle it. +Often, the space-time dependence of the diagrams is mapped via Fourier transform to momentum +space. In this setting, the result of the Grassmann integration is a polynomial in the external and +the loop momenta. +In this work we focus on four space-time dimensions. The description of theories with N = 1 +supersymmetry, i.e., with four supercharges, in terms of N = 1 superfields is rather simple. +In fact N = 1 superfields are often used also for theories with higher supersymmetry, such as +N = 2 theories; in this case, a single N = 2 supermultiplet encompasses more than one N = 1 +superfield. +In particular we consider theories that, when decomposed into N = 1 superfields, +contain chiral/anti-chiral and vector superfields. The superpropagators for these superfields and +the vertices for typical interactions are standard, see for instance [7]. +A well-known strategy to carry out Grassmann integrations in superdiagrams of this kind +was proposed long time ago in [8] and it is referred to as “D-algebra approach”. Roughly, one +eliminates all θ integrations but one. The remaining integrand comprises a string of spinorial +covariant derivatives (usually denoted with the symbol D) which have to be simplified using the +algebraic relations satisfied by the latter. +Here we illustrate another strategy in which one remains with multiple Grassmann integrations +of rather simple integrands which can be described in diagrammatical terms and performed using +a few general rules. This θ-diagrammatic procedure is algorithmic and can be implemented in a +computer code. +A partial version of this approach was already proposed in [9] as an instrument to ease the +computation of certain superdiagrams occurring in N = 2 SYM theories with massless matter. +The diagrammatic rules devise in [9], however, did not allow to treat algorithmically diagrams with +self-interaction vertices of the vector superfield. In this work, we generalize the θ-diagrammatic +method so that also applies to such superdiagrams. We also show how to treat diagrams in which +all possible fields, bosonic and fermionic, appear in the external legs. +Our method is quite general. To describe it explicitly, however, we focus on the kind of fields +and interactions which typically occur in the context of N = 2 conformal SYM theories. Thus we +consider massless superfields with the type of interactions that occur in such theories; for instance, +we do not consider vertices with spinorial covariant derivatives acting on the chiral/anti-chiral +superfields. Also, given that in the N = 2 SYM context it is often convenient to study the so +called “difference theory” with respect to N = 4 SYM and in this difference ghost contributions +typically cancel out, we do not consider explicitly diagrams which contain the ghosts. However, +the propagator of the ghost superfield has exactly the same expression as that of chiral superfields, +see for instance [10], and their interaction vertices are of the type that can be described with our +method. They can therefore be included without problems, provided that one takes into account +in the loops their flipped statistics. +Our diagrammatic method is most straightforward if we don’t impose the Wess-Zumino gauge, +at the price of having to include higher and higher interaction vertices when we increase the +2 + +perturbative order. In principle, all such interactions are manageable within our approach. +This paper is organized as follows. Section 2 describes the type of N = 1 superdiagrams we +consider, describing the relevant Feynman rules and in particular their Grassmann content. Section +3 introduces the basics of the θ-diagram approach to the Grassmann integrations in superdiagrams. +In section 4 we analyze in detail an example. Section 5 generalizes the method to all possible +types of fields in the external legs. In section 6 we describe an implementation of our approach in +a Mathematica code, which is provided together with this work. +2 +N = 1 superdiagrams for N = 2 theories +We consider supersymmetric theories in d = 4 whose content can be arranged into chiral (or anti- +chiral) and vector N = 1 superfields. In our conventions, see Appendix A, the expansion of a +chiral superfield has the form +Φ(x, θ, ¯θ) = φ(x) + +√ +2θψ(x) + i(θσµ¯θ)∂µφ(x) − θ2F(x) − +i +√ +2θ2∂µψ(x)σµ¯θ − 1 +4θ2¯θ2□φ(x) , +(2.1) +where φ is a complex scalar, ψ its fermionic partner (a chiral Weyl spinor) and F an auxiliary +field. The antichiral superfield contains ¯φ and the antichiral spinor ¯ψ. For a vector superfield we +have +V (x, θ, ¯θ) = C(x) + iθχ(x) − i¯θ¯χ(x) + (θσµ¯θ)vµ(x) + i +2θ2(M(x) + iN(x)) − i +2θ2(M(x) − iN(x)) ++ iθ2¯θ(¯λ(x) + i +2 ¯σµ∂µχ(x)) − i¯θ2θ(λ(x) + i +2σµ∂µ ¯χ(x)) + 1 +2θ2¯θ2(D(x) − 1 +2□C(x) , (2.2) +where vµ is the connection for a gauge group G, λ and ¯λ are the the (anti)chiral parts of the +gaugino and D a real auxiliary field; they all carry indices in the adjoint of G. The remaining +fields can be fixed exploiting the supersymmetric gauge transformation +V → V + Φgauge + ¯Φgauge , +(2.3) +where the parameter Φgauge is itself a chiral superfield. A typical choice is the Wess-Zumino gauge, +that exploits this invariance to set C, M, N and χ to zero, while retaining the usual gauge freedom +with parameter 2Im φgauge. The Wess-Zumino gauge choice does not commute with supersymmetry +transformations, though, and we will not impose it; thus we retain supersymmetry explicit, at the +price of keeping the full fledged expression (2.2) of the vector superfield and having more terms in +the action. +We consider theories in which the group G is in general non Abelian, and the chiral superfields +are charged, i.e. transform in some representation R – in general reducible – of G. We also include +the possibility of cubic chiral or anti-chiral vertices. For the sake of simplicity, we do not include +other types of interactions among the matter fields, but the method we propose can be generalized +in this sense. +2.1 +N = 2 SYM theories +As we already remarked in the introduction, the initial idea of the method we describe here was +put forward in the context of N = 2 SYM theories with matter [9]. The fields of these theories can +3 + +Figure 1. Superpropagators for the N = 2 gauge action. +be organized, with respect to an N = 1 supersymmetry subalgebra, into vector and (anti)-chiral +superfields with the type of interactions we mentioned above. Indeed the degrees of freedom of the +N = 2 vector multiplet can be encoded in a vector superfield V plus a chiral superfield Φ, both +in the adjoint of the gauge group G. The components of an N = 2 matter hypermultiplet can +instead be arranged in two chiral superfields, Q and ˜Q, transforming in conjugate representations +of G. +The pure gauge action can be written in the N = 1 superspace as follows: +Sgauge = +� +d4x d4θ Tr +� 1 +8g2 +� +WαW αδ2(¯θ) + h.c. +� +− ξ +4D2(V ) ¯D2(V ) +���� +ξ=1 ++ 2e−2gV ¯Φe2gV Φ +� +, (2.4) +where g is the bare gauge coupling and +Wα = −1 +4 +¯D2(e−2gV Dα(e2gV )) , +¯W ˙α = −1 +4D2(e2gV ¯D ˙α(e−2gV )). +(2.5) +This action is given in the Fermi-Feynman gauge (ξ = 1), but we did not write the ghost-antighost +part since it is not needed in order to explain our algorithm1. Expanding up to order g2 and taking +the colour trace we have +Sgauge = +� +d4x d4θ +� +−V a□V a + ¯ΦaΦa + gfabc( i +4( ¯D2(DαV a))V b(DαV c) + 2i¯ΦaV bΦc)+ ++ g2fabefecd(−1 +8V a(DαV b)( ¯D2V c)(DαV d) − 2¯ΦaV bV cΦd) + O(g3) +� +. +(2.6) +From this action one can derive Feynman rules in terms of superpropagators and supervertices. +Note that every vertex carries a superspace integration; one can as usual trade the vertex positions +for the momenta running in the diagram, and remain with a +� +d4θi integral in the i-th vertex. The +Feynman rules in momentum space, understanding these Grassmann integrals at each vertex, are +displayed in figures 1 and 2. +Note that the cubic and quartic vector vertices contain spinorial +derivatives; see Appendix A.2, in particular eq. (A.50), for our conventions and notations. Thus +in figure 2 a covariant derivative placed on one leg in which a momentum p flows out of the vertex +is to be understood as Dα = ∂α − pα ˙α¯θ ˙α. These covariant derivatives are among the chief sources +of algebraic complications in carrying out the Grassmann integrations in the superdiagrams. Our +approach, that will be discussed in section 3.5, associates these covariant derivatives to the vector +1Their propagators can be inserted with the function CP and their vertices with the function GV, as shall be +explained in section 6 +4 + +2 p - 8p: -9, p +i2 bdod ± +J +Sαb +e +α +9 +p? +Sab . 1 S(ar) S(0,) +VV propagator: +d +bFigure 2. Vertex rules for the N = 2 gauge action, up to order g2. +Figure 3. Superpropagators for the N = 2 hypermultiplets. +superpropagators connecting the vertices rather than to the vertices themselves. For this reason, +in the right hand sides of figure 2 we have not written them. +The hypermultiplet part of the action is given by +Shyper = +� +d4x d4θ ¯Qe2gV Q + ˜Qe−2gV ¯˜Q + i +√ +2g ˜QΦQδ2(¯θ) − i +√ +2g ¯Q¯Φ ¯˜Qδ2(θ) . +(2.7) +Expanding up to order g2 and making explicit the colour indices2 we get +Sh = +� +d4xd2θd2¯θ +� +¯QuQu + ˜Qu ¯˜Qu + g +� +2 ¯QuV a(T a +R)v +uQv − 2 ˜QuV a(T a +R)v +u ¯˜Qv ++ i +√ +2 ˜QuΦa(T a +R)v +uQvδ2(¯θ) − i +√ +2 ¯Qu ¯Φa(T a +R)v +u ¯˜Qvδ2(θ) +� ++ g2� +2 ¯QuV aV b(T a +RT b +R)v +uQv + 2 ˜QuV aV b(T a +RT b +R)v +u ¯˜Qv +� ++ O(g3) +� +. +(2.8) +The corresponding superpropagators are displayed in figure 3 and the vertices in figure 4. +2The chiral superfield Q transforms in a representation R whose indices we denote by u, v, . . .; by (T a)u +v we denote +the hermitian generators of the gauge group in this representation. The superfield ˜Q transforms in the conjugate +representation. +5 + +a +labe2 8 P0 - 2 pO: - 0, p3 +0 pvoragatov: +Q +S +p? +2 p. - 9. pO: - 9, PO +@ propagatoz: +p +dnu +Q +从Figure 4. Vertex rules for the N = 2 hypermultiplet action, up to order g2. +2.2 +Factorizing the Grassmann part +We are interested in evaluating superdiagrams, constructed with the Feynman rules described +above, that contributes to a correlator with fixed external states. Such a superdiagram depends +on the set of external momenta, which we label collectively by q, and carries colour structure and +Lorentz indices associated to the external states. We write it in the following form3: +WLorentz +colour (q) = N × Tcolour × +� � +s +ddks +(2π)d δ(d)(cons) ZLorentz(k) +� +s k2s +. +(2.9) +Here N is the product of the symmetry factor of the diagram and all the factors (like the powers +of the coupling constants) appearing in the vertices - except for the color factors which give rise to +the tensor Tcolour. By the index s we enumerate the internal lines of the superdiagram. The scalar +integral over the internal momenta ks is typically performed using dimensional regularization, +setting d = 4 − 2ε. The momenta are subject to the appropriate conservation relations enforced +by the δ-functions δ(d)(cons). Beside the denominator coming from the massless propagators, the +integrand contains also a numerator ZLorentz(k) which is the result of the integration over all the +Grassmann variables of the θ-dependent expressions present in the superdiagram and is the object +of this paper. +Since the difference between the chiral multiplets Φ, Q and ˜Q resides only in their colour +properties and numerical factors in the vertices, which are factored out in the decomposition (2.9), +the Grassmann part of propagators and vertices are the same independently of the specific chiral +multiplets involved. Thus, denoting any chiral field simply by a solid line, and introducing the +symbol θ= such that W θ= Z means “the Grassmann part of W is Z”, we have the following rules. +3In the the N = 2 theory all fields are massless. If we would apply this decomposition in presence of massive +fields, of course we should use massive propagators in the appropriate legs. +6 + +),S(,L) += iq V2 (T*) "S(0) +a +W +d +从For the chiral propagator between two points i and j we have +, +(2.10) +For the chiral and anti-chiral cubic vertices we have +, +(2.11) +where we reinstated the integration over the variables θi and ¯θi pertaining to the vertex which was +understood in figure 4. For the vector propagator we have +(2.12) +and for the vertices involving the vectors +, +(2.13) +where, as discussed above, we do not include in the r.h.s. the spinorial covariant derivatives because +we will associate them with the vector lines connected to the vertices. +2.3 +External lines in superdiagrams +Often we are interested in correlators of specific fields rather than of superfields. In this case, super +Feynman diagrams contain field-superfield propagators in the external lines. Such propagators, +that arise from the Wick contraction of an external field with a superfield appearing in an internal +vertex, are perfectly well defined. For instance, considering a generic chiral superfield and omitting +internal symmetry indexes, we have +⟨φ(x1)¯Φ(x2, θ2, ¯θ2)⟩0 = ⟨φ(x1)(¯φ(x2) + +√ +2¯θ2 ¯ψ(x2) + ...)⟩0 = +(2.14) += ⟨φ(x1)¯φ(x2)⟩0 + +√ +2¯θ2, ˙α ⟨φ(x1) ¯ψ ˙α(x2)⟩0 + ... . +We can also write them in terms of the super-propagators, and this will be useful for us in the +following. Indeed one can see, by eq. (2.1), that for the chiral content we have: +φ(x) = Φ(x, θ, ¯θ) +�� +θ=¯θ=0 , +(2.15) +ψα(x) = +1 +√ +2∂αΦ(x, θ, ¯θ) +���� +θ=¯θ=0 +. +(2.16) +7 + +2po, -3: pg -, po, +P +9 +e +二 +1(9.S(8) +(r9, S(0.)P +9 +S(8.,) +1. +J9 +9 +Q +CThus, considering the above relations for a generic chiral superfield and the similar ones for the +anti-chiral content, we have +⟨φ(xi)¯Φ(xj, θj, ¯θj)⟩0 = ⟨Φ(xi, θi, ¯θi)¯Φ(xj, θj, ¯θj)⟩0 +�� +θi=¯θi=0 , +(2.17) +⟨Φ(xi, θi, ¯θi)¯φ(xj)⟩0 = ⟨Φ(xi, θi, ¯θi)¯Φ(xj, θj, ¯θj)⟩0 +�� +θj=¯θj=0 , +(2.18) +⟨ψα(xi)¯Φ(xj, θj, ¯θj)⟩0 = +1 +√ +2 ∂i,α ⟨Φ(xi, θi, ¯θi)¯Φ(xj, θj, ¯θj)⟩0 +�� +θi=¯θi=0 , +(2.19) +⟨Φ(xi, θi, ¯θi) ¯ψ ˙α(xj)⟩0 = +1 +√ +2 +¯∂ ˙α +j ⟨Φa(xi, θi, ¯θi)¯Φb(xj, θj, ¯θj)⟩0 +��� +θj=¯θj=0 . +(2.20) +Writing the above relations in momenta space we obtain: += 1 +p2 e−θjp¯θj +θ= e−θjp¯θj , +(2.21) += 1 +p2 e−θip¯θi θ= e−θip¯θi , +(2.22) += +√ +2 +p2 pα ˙β ¯θ +˙β +j e−θjp¯θj +θ= pα ˙β ¯θ +˙β +j e−θjp¯θj , +(2.23) += − +√ +2 +p2 ¯p ˙αβθi,βe−θip¯θi θ= ¯p ˙αβθi,βe−θip¯θi . +(2.24) +We can relate the fields in the vector multiplet to the vector superfield in a similar way to what +we did for the chiral supermultiplet, see eq. (2.15), namely using derivatives and the setting some +variables to zero. Indeed one can see, omitting colour indexes, that +vµ(x) = 1 +2 σµ +α ˙β∂α ¯∂ +˙βV (x, θ, ¯θ) +��� +θ=¯θ=0 +(2.25) +from which we can obtain: +⟨vµ(xi)V (xj, θj, ¯θj)⟩0 = 1 +2σµ +α ˙β∂α ¯∂ +˙β ⟨V (xi, θi, ¯θi)V (xj, θj, ¯θj)⟩0 +���� +θi=¯θi=0 +. +(2.26) +Then in momentum space we have: += 1 +p2 (θjp¯θj) θ= 2(θjp¯θj) . +(2.27) +Also these external lines can be treated through the diagrammatical method that we propose in +this paper, but a bit of care is needed. Suppose that the external vector field be connected to a +vector superfield on which a certain expression f(D, ¯D), built of spinorial covariant derivatives, +8 + +14 +1 +: +1 +jP +4P +7 +: +. +1 +J2 +d> +iacts. This happens, for instance, for some of the vector Super Yang-Mills vertices – see fig. 2. +Then the Grassmann part of ⟨v(xi)f(Dj, ¯ +Dj)V (xj, θj, ¯θj)⟩0 would be given by +⟨vµf(Dj, ¯ +Dj)V (θj, ¯θj)⟩0 +θ= σµ +α, ˙β∂α ¯∂ +˙βf(Dj, ¯Dj)δ4(θij) . +(2.28) +Such an expression is not easily handled in our diagrammatical method, but there is a way around. +Instead of expressing vµ in terms of the superfield V by means of Grassmann derivatives, we can +exploit Grassmann integrations and write +vµ(x) = −2 +� +d2θd2¯θ (θσµ¯θ)V (x, θ, ¯θ) , +(2.29) +Then we can also replace eq. (2.28) with +⟨vµ(xi)f(Dj, ¯Dj)V (xj, θj, ¯θj)⟩0 = −2 +� +dθ +i d2¯θi (θiσµ¯θi) ⟨V (xi, θi, ¯θi)f(Dj, ¯Dj)V (xj, θj, ¯θj)⟩0 . +(2.30) +In momentum space this leads to +θ= +� +d2θid2¯θi 2(θiσµ¯θi)f(Dj, ¯Dj) +� +δ4(θij) +� +, +(2.31) +In this way4 we only have to deal with Grassmann integrals and covariant derivatives acting on +δ4(θij), which can be treated within our diagrammatic formalism, as we will discuss in section 3.5. +We can deal similarly with the gaugino, even if the expression is slightly more complicated and +contains two terms5: +⟨λα(xi)V (xj, θj, ¯θj)⟩0 = +� +d4θi +� +−2iθi,α − σµ +α ˙β ¯θβ +i ¯θ2 +i ∂/∂xi,µ +� +⟨V (xi, θi, ¯θi)V (xj, θj, ¯θj)⟩0 , +(2.32) +⟨V (xi, θi, ¯θi)¯λ ˙α(xj)⟩0 = +� +d4θj +� +2i¯θ ˙α +j + ¯σµ, ˙α,βθj,βθ2 +j ∂/∂xj,µ +� +⟨V (xi, θi, ¯θi)V (xj, θj, ¯θj)⟩0 . (2.33) +In momentum space and focusing only on the Grassmann part we obtain: +θ= +� +d2θid2¯θi +� +θi,α + +pα ˙β +2 +¯θ +˙β +i θ2 +i +� +f(Dj, ¯Dj) +� +δ4(θij) +� +, +(2.34) +θ= +� +d2θjd2¯θj +� +¯θ ˙α +j − ¯p ˙αβ +2 θj,β ¯θ2 +j +� +f(Di, ¯Di) +� +δ4(θij) +� +. +(2.35) +In making explicit the spinorial derivatives in the expressions above one has to take into account +that eq. (A.50) is written with the momentum flowing out of the vertex j (so in some of the cases +above it is actually the momentum −p). +4Note that it is also possible to use field to superfield relations based on Grassmann integration, instead of +derivations as in eq. (2.15), also for the fields in the chiral multiplet. Again, this could in principle be useful for +theories containing vertices with covariant spinorial derivatives acting on (anti-)chiral superfields. For theories that +do not contain such vertices, as is the case for instance for the N = 2 SYM theory, this is not needed and it is more +efficient to use the formulas (2.17-2.20) which do not introduce integration of auxiliary variables. +5This is due to the fact that we do not impose the Wess-Zumino gauge and thus we have to disentangle the χ +spinor from the gaugino. +9 + + 4(P; ) +1 +PP13 +Grassmann integration in superdiagrams +As already stated, the focus of this paper is on the Grassmann integration occurring in super- +diagrams, namely on the computation of the quantity ZLorentz defined in eq. (2.9). Of course, +methods to perform such integration are well known, and in particular the so-called D-algebra +approach of [8] is widely used. Here we propose a method that we find efficient and that is very +algorithmic, so that it can be implemented in a symbolic language code. This method is based on +the construction of what we call θ-diagrams. +3.1 +A simple example +To fix the ideas, let us consider a very simple example, the one-loop correction to the propagator +of the scalar in an adjoint chiral multiplet with matter chiral multiplets running in the loop. In +this case the Lorentz structure is trivial, and the colour factor follows easily from the colour part +of the vertices and propagators given in figures 4 and 3, while the normalization factor turns out +to be just 2g2. With respect to eq. (2.9) it is immediate in this example to exploit the momentum +conservation, obtaining += 2g2 × TrR(T bT c) × +� +ddk +(2π)d +1 +(q2)2 +1 +k2(k − q)2 Z(k, q) . (3.1) +The factor Z(k, q) is the result of the integration over the Grassmann variables at each internal +vertex. According to the rules in figures 3 and 4 and eq.s (2.21) and (2.22) it reads +Z(k, q) = +� +d4θ3 d4θ4 (θ3)2(¯θ4)2 e2θ4(k−q)¯θ3−θ4(k−q)¯θ4−θ3(k−q)¯θ3e−2θ4k¯θ3+θ4k¯θ4+θ3k¯θ3 . +(3.2) +This integral is straightforward, as we will describe shortly. +In general, the computation of +ZLorentz(k) through Grassmann integrations remains essentially algebraic and presents in principle +no conceptual difficulty for any superdiagram. Nevertheless, it typically becomes very involved as +the complexity of the superdiagram increases. +3.2 +D-algebra +The key idea of this approach is to make the Grassmann integration local, namely to reduce it to +the integral over a single pair of Grassmann variables. This can be achieved because the Grassmann +variables to be integrated over are associated to the vertices in the superdiagram. The vertices +are connected by superpropagators. The Grassmann part of the vector superpropagator directly +contains δ functions, see eq. (2.12), that identify the θ-variables in the vertices i and j it connects. +Also the Grassmann part of the chiral-antichiral propagator, given in eq. (2.10), can be rewritten +so as to display such δ functions; indeed one can show that +e2θip¯θj−θip¯θi−θjp¯θj = 1 +16 +¯D2 +i,p D2 +i,pδ2(θij)δ2(¯θij) , +(3.3) +10 + +-K +Tb +1 +2 +K-9where we have remarked that the spinorial covariant derivatives contain the momentum p. Exploit- +ing appropriately the δ functions present in the propagators, one can then eliminate the integrals +over all but one of the pair of Grassmann variables. The remaining integrand, however, contains +in general spinor covariant derivatives arising both from the vector vertices, see figure 2, and from +the chiral propagators rewritten using eq. (3.3). This expression needs to be evaluated using the +algebraic properties of the spinorial covariant derivatives D and ¯D, i.e., carrying out the D-algebra. +For the example of eq. (3.2), this procedure amounts to rewrite Z(k, q) as +Z(k, q) = +1 +162 +� +d4¯θ3 d4θ4 θ2 +3 ¯θ2 +4 +� +D2 +4,−k ¯D2 +4,−kδ4(θ34) +� � +D2 +4,k−q ¯D2 +4,k−qδ4(θ34) +� +(3.4) +and integrate it by parts6 to obtain +Z(k, q) = +1 +162 +� +d4¯θ3 d4θ4 +� +D2 +4,q−k ¯D2 +4,q−k +� +θ2 +3 ¯θ2 +4 ¯D2 +4,−k D2 +4,−kδ4(θ34) +�� +δ4(θ34) . +(3.5) +Using the fact that D2 +4 and ¯D2 +4 commute with θ2 +3 and exploiting the δ-function we can write +Z(k, q) = +1 +162 +� +d4¯θ4 θ2 +4 +� +D2 +4,q−k ¯D2 +4,q−k +�¯θ2 +4 ¯D2 +4,−k D2 +4,−kδ4(θ34) +�� +3→4 , +(3.6) +where in the string of covariant derivatives we have to identify the variables in the node 3 with +those in the node 4 after having carried out the derivatives. In this way we have recast Z in term +of a Grassmannian integration at a single node. As argued in [8], this can be done for any loop +within a superdiagram and, iterating the procedure, for any irreducible superdiagram. +The explicit evaluation of Z written in the form (3.6) can be carried out exploiting the algebraic +properties of the covariant derivatives and the final outcome is that +Z(k, q) = −q2 . +(3.7) +3.3 +Introducing the θ-diagrams +In this example, the D-algebra strategy turns out to be rather more involute than carrying out the +integration over the Grassmann variables in both nodes with the propagators in exponential form, +as in eq.s (3.2,3.7). In fact, the latter procedure can be described in a diagrammatic, algorithmic +form which turns out to be generalizable to a large class of superdiagrams and can be implemented +in a computer program. Let us now introduce this strategy starting from the example at hand. +The basic ingredient are the exponentials appearing in the chiral propagators. We introduce +the following diagrammatic notation: +. +(3.8) +Due to the Grassmannian nature of the θ and ¯θ variables, the exponentials are in fact polynomial: +e2(θip¯θj) = 1 + 2(θip¯θj) + 1 +2 × +� +2(θip¯θj) +�2 . +(3.9) +6The rules for Grassmannian integrations by part are collected in Appendix A.2. +11 + +2 (2: p. ) +）In diagrammatic notation, this reads +, +(3.10) +where the momentum and the end-point labels are the same in all lines and are understood. +The superdiagrams contain integrations over Grassmann variables θi and ¯θi at the various sites. +These we represent graphically as black or white dots: +. +(3.11) +The cubic (anti)-chiral super-vertices bring in factors of Grassmannian delta-functions: +θ2 +i = δ2(θi) , +¯θ2 +i = δ2(¯θi) . +(3.12) +Taking into account all this, we can rewrite diagrammatically eq. (3.2) as follows: +Z(k, q) = +. +(3.13) +This expression can be simplified in some obvious ways. The Grassmannian delta-function +δ2(θ3) soaks up the corresponding integration and sets to zero all occurrences of θ3. +On the +diagram, this correspond simply to remove the black dot labeled by 3 and the two solid lines +connecting to it, since the associated exponentials reduce to 1. Similarly, the δ2(θ4) removes the +white dot labeled by 4 and the lines attached to it. We remain thus with +Z(k, q) = +. +(3.14) +Note that the labels 3 and 4 attached to the dots just assign a name to the integration variables, +and they are thus actually redundant. +Moreover, we can take into account the following general property: the product of two solid +lines with the same endpoints gives a single solid line carrying the total momentum, namely +. +(3.15) +12 + +1 + += ++ +220 +"0 +itK- q +3 + ×S(8) S(2) +: +2 +3 +4K- q +3Pa+ P2 +dThis just corresponds to the product rule for the corresponding two exponentials, see eq. (3.8). +Thus we arrive at +Z(k, q) = +. +(3.16) +We can expand the solid θ-lines into dashed lines according to eq. (3.10). Then we have to take +into account the presence of white and black dots, that correspond to Grassmann integrals over +two-component spinors. According to eq. (3.8), each dashed line leaving the vertex i carries one +θi variable, and each dashed line entering the vertex j carries one ¯θj. The Grassmann integrals +� +dθ2 or +� +d¯θ2 vanish unless they act on expression quadratic in θα or ¯θ ˙α. Graphically this means +that a θ-diagram is non-null if and only if exactly two dashed lines are attached to each dot. This +is a very simple but crucial property of the θ-diagrams. In particular, we have +. +(3.17) +Finally, the dashed loop on the r.h.s. above is very easily evaluated. One has += 1 +2 +� +d2θ4 d2¯θ3 2(θ4q¯θ3)2(θ4q¯θ3) = 1 +2 tr(q¯q) = −q2 , +(3.18) +where we made use of a Fierz rearrangement, see eq.s (A.33,A.35), and carried out the integrations +according to the basic rules in eq.s (A.12–A.14). We obtain therefore +Z(k, q) = −q2 , +(3.19) +in agreement with the result of the D-algebra manipulations. +Of course, the Grassmann integrations in this Z(k, q) are very easy. It may seem that our +diagrammatic notation unnecessarily complicates it. However, it readily generalizes and is algo- +rithmic. As a first step, we show how the Grassmann part Z of all superdiagrams involving only +(anti)-chiral superfields can be managed using θ-diagrams. +3.4 +Diagrams with (anti)chiral superfields +This is the simplest case. Let us describe how to manage it. +Deriving the θ-diagram +The Grassmann part of all chiral-superchiral propagators is given by +a momentum dependent exponential of the type considered above, see eq. (2.10), thus we can say +that +. (3.20) +Note that in eq. (3.20) and in the following, the cyan, thick lines that appear on the r.h.s. of the +θ= symbol have a completely different meaning from the black ones on the left: they are the solid +θ-lines defined in eq. (3.8). +13 + +- 9.1 +22P +P +-P/2 +- P/2 +? +1 +1 +) +)For propagators connected to external scalars, given in eq.s (2.21) and (2.22), we have simply +(3.21) +and +(3.22) +Also the contribution of cubic vertices involving chiral superfields to the Grassmann part of +the diagram are very easy to describe: +. +(3.23) +Similarly, for the anti-chiral vertices one has +. +(3.24) +It follows from eq.s (3.21,3.22) that a chiral propagator connecting an external scalar to a +cubic vertex gives a trivial contribution to the θ-diagram. Indeed, suppose for instance that the +propagator (3.21) be attached to a vertex of the type (3.24) in position j; then its θ-line exp(−θjp¯θj) +reduces to 1 since the vertex sets all occurrences of θj to zero. +The properties we have listed are sufficient to determine the θ-diagrammatic form of the Grass- +mann factor Z associated to any superdiagram Wcolour involving only (anti) chiral superfields with +scalar external states; we will consider later the possibility that the external states correspond to +other components of the multiplet. +An example +Let us illustrate this by a specific example, namely +Wab(q) = +. +(3.25) +14 + +6 +: +1 +J += +: +1 +J +~ p/26 +4 +人 +1 += +. +-p/26 +S(0) = +a +二 +t６ +a +二 +25 +53 +q +3 +tb +1 +2 +&This diagram represents a three-loop contribution to the adjoint chiral scalar propagator, and has +been considered for instance in [9]. Using the rules from (3.20) to (3.24) for all the propagators +and vertices and making use of the δ-functions that they contain we obtain +Wab +θ= Z = +. +(3.26) +This is perfectly analogous to the form we obtained in eq. (3.14) for the one-loop example. It +is easy to convince oneself that in fact in all cases involving only chiral/antichiral superfields the +structure of vertices and lines of the θ-diagram mimics the one of the original superdiagram, except +for dropping the external lines attached to scalar components, and associating a white dot to every +chiral cubic vertex and a black dot to every anti-chiral one. +Expanding the θ-diagram +To compute a θ-diagram of the type just described, one can expand +its solid lines according to eq. (3.10). Having done this, we can exploit the crucial observation we +already stated just before eq. (3.17): the only non zero contributions are those in which exactly +two dashed lines enter or leave every dot. As a consequence, such non-zero contributions consist +of products of loops of dashed lines7 going through non-overlapping subsets of dots, leaving no dot +isolated. +Let us illustrate this with another example. Consider a θ-diagram with the following structure: +Z = +. +(3.27) +This can arise, for instance, from a one-loop contribution to a four-point function of chiral/antichiral +scalars. According to the rules just stated, it is given by +Z = +. +(3.28) +The terms in the right hand side represent precisely the possible decompositions of Z into loops +of dashed lines; note that we have drawn the loops involving two dots as single solid lines, see eq. +(3.17). +7Each loop consisting of only two lines, though, comes with a factor 1/2 because it arises from the expansion of +a single solid line as in eq. (3.17). +15 + +PsFigure 5. +An example of the decomposition of a θ-diagram into its non-vanishing contributions. For +simplicity we do not label the vertex and the lines. +Another example of the decomposition of a θ-diagram is given in figure 5. +The decomposition into loops can be realized by means of a path-finding algorithm and im- +plemented in a computer code; this was done in [11]. In the code presented here we follow a +different strategy, based on expanding in turn all lines and taking into account at each steps the +simplifications owing to the rule that selects exactly two dashed lines in each node. This approach +turns out to be computationally more efficient. +Getting the final result +The next ingredient is the following: each loop of dashed lines can +be evaluated explicitly and the result can be given in a general form. Using repeatedly the Fierz +rearrangements in eq.s (A.32–A.35) and the integration rules (A.12,A.13,A.14) one easily shows +that += +� +d2θ1 d2¯θ1 . . . . . . d2θn d2¯θn 2 +� +θ1p1¯θ1 +� +2 +� +θ2k1¯θ1 +� +. . . +× 2 +� +θnpn¯θn +� +2 +� +θ1kn¯θn +� += (−1)n+1 tr +� +p1 ¯k1 . . . pn ¯kn +� +(3.29) +The traces appearing above are of the form +tr(p1¯k1...pn¯kn) = p1,µ1k1,ν1...pn,µnkn,νntr(σµ1¯σν1...σµn¯σνn) +(3.30) +They can be recursively computed using the properties of the matrices σµ and ¯σµ, see Appendix +A.2. +For instance for eq. (3.28) we obtain +Z = p2 +1 p2 +3 − 2(p1 · p2)(p3 · p4) + 2(p1 · p3)(p2 · p4) − 2(p1 · p4)(p2 · p3) + p2 +2 p2 +4 + p1,µp2,νp3,ρp4,σϵµνρσ . +(3.31) +16 + +n +APerspective +Let us summarize. Drawing the θ-diagrams and evaluating them according to the +rules we just described, we can compute explicitly the Grassmannian integrations for all superdia- +grams involving only chiral and antichiral superfields, with scalar external states. All the three +main steps of the procedure, namely writing down the θ-diagram, finding its decomposition into +loops of dashed lines and evaluating the latter, are completely algorithmic and can be implemented +in a computer code. +This procedure was already described in [9], without however detailing the algorithm for de- +termining all non-zero contributions and without providing a computer code. In the present work +we aim at extending this approach to a much larger class of superdiagrams, maintaining its main +advantage, namely that of being algorithmic and readily implemented in a code. The basic idea +is to cast the θ-dependent part of the superdiagram in terms of Grassmannian delta-functions +and exponentials, which we can then evaluate with the θ-diagrammatic method described in the +present section. +3.5 +Diagrams with (internal) vector superfields +The Grassmann part of the propagator of the vector superfields is very simple: +. +(3.32) +As was mentioned in the introduction, we restrict in this paper to theories that can be for- +mulated in terms of N = 1 chiral and vectorial superfields, with interactions that have covariant +derivatives that act only on vectorial superfields. +This class of theories contain in particular +N = 2 SYM theories with matter hypermultiplets. In this case, beside the cubic vertices of the +type considered in eq.s (3.23,3.24), we have other interactions that involve both vectors and chi- +ral superfields. Up to order g2, they are elementary from the point of view of their Grassmann +structure: +. +(3.33) +From the action (2.6) we see that there are also interaction vertices, involving vector superfields +only, which include spinor covariant derivatives. Connecting vertices of this kind to other vertices +by means of the vector superpropagator we effectively obtain expressions in which such covariant +derivatives act on the vector lines. The possible cases, and their Grassmann structure, can be +worked out with a little bit of algebra. For instance, as in eq.(4.4), there might be a case where +we have a single covariant derivative acting on a vector propagator. This implies a contribution +like Di,αδ4(θij). It is straightforward to see that the following two expression coincide: +Di,αδ4(θij) = 2θij,αδ2(¯θij)e +(θipij ¯θi)−(θjpij ¯θi) +2 +. +(3.34) +17 + +('e)s ('r8)s tn'6 +9,3: +>>sSSS +P6 +9 += +1Graphically we have: +. +(3.35) +This can be extended with further derivatives analogously. In two cases we might have two spinor +derivatives: +, +(3.36) +, +(3.37) +(3.38) +In eq. (3.36) we have took into account that a line might have a derivatives coming from both +vertices it attaches to, see figure 7. +We now proceed with the numeration. we have two contributions with three spinor derivatives: +, +(3.39) +, +(3.40) +(3.41) +two with four spinor derivatives: +, +(3.42) +, +(3.43) +(3.44) +18 + +2 2 2ix S(,) Pivs +J +/2J +Pj / 2 +川D: +6 +Psj / 2 +{2 +一2 +D: D +J*J +j / 2Di D' D? +Pj/2 +Pj/2 +0&9 +0 += +P.. +Jone with five spinor derivatives: +(3.45) +and finally a single one with six spinor derivatives: +(3.46) +Once the spinorial covariant derivatives have been assigned to the vector lines, the “bare” gluon +vertices only contain the information about the integration; thus for instance +. +(3.47) +Consider the situation in which the “decorated” vector lines of figure 2 are inserted inside +superdiagrams with scalar external states, which have an overall trivial Lorentz structure. The +various spinor quantities and tensors appearing above, like θα +ij, ϵαβ, and δα +β, must conspire to +produce scalar structure. +Thus they can only give overall numerical factors or Grassmannian +scalar products of the type θij · θkl. Remembering that θij = θi − θj and that δ2(θ) = θ2, one has: +θij · θkl = 1 +2 +� +δ2(θij) + δ2(θkl) − δ2(θi − (θj + θk − θl)) +� +. +(3.48) +Thus, the Grassmann structure of all superdiagrams formed with the elements we considered so +far can be recast as linear combinations of integrals of exponentials and Grassmann δ functions +which we know how to deal with using the θ-diagrammatic technique. +In other theories based on N = 1 superfields, other combinations of spinorial covariant deriva- +tives, beside those appearing in eq.s (3.35-3.46), might appear. They could be treated by applying +the same principle. Furthermore the number of possible different combinations is finite and one +could write down the analogues of the rules in eq.s (3.35-3.46) for all of them. Thus for a generic +theory with chiral/antichiral and vector N = 1 superfields, with spinorial covariant derivatives +appearing on the vectors only, all the Grassmann integrals in any superdiagram can always be +expressed in terms of θ-diagrams. +3.6 +Some θ-diagrammatical properties +Let us pause here to recapitulate some properties of our θ-diagrammatic notation, which have used +somehow implicitly above. +First of all, the order in which white and black dots appear in the graphical representation of +the θ-diagram is not relevant: they represent integrals over certain Grassmann variables, and all +19 + +0 +JD:D: D? De +6 + s() iPi? +2 +2：．/2 +3 2the occurrences of these variables in other elements of the diagram must be integrated over. Thus, +for example, += +� +d2¯θj e2(θip¯θj) , +(3.49) +even if the white dot appears rightmost in the drawing. +Another graphical property that we have been using is the fact that endpoints of solid or dotted +θ lines get attached to dots carrying the same index, remembering that the lines go from a black +to a white dot: thus, for instance, +(3.50) +as well as +. (3.51) +This also works when one end is already attached to a dot, or when a dot has already other lines +attached to it. +In the θ diagram, the lines can be constrained as consequence of the integration of some +Grassmannian delta function. These delta function might set some variable to zero, as in the case +of the δ2(θ) or δ2(¯θ) present in the hyper-multiplet vertices, or identify two different variables, +as in the case of the δ2(θij) = δ2(θi − θj) and the δ2(¯θij) = δ2(¯θi − ¯θj) present in vectorial +superpropagators, see eq. (3.32). +It is easy to see that such constraints amount to the following rules: +(3.52) +and +(3.53) +as well as +(3.54) +20 + +K +tK=1 +6and +. +(3.55) +Another important property is the fact that we can combine the solid lines with the same +endpoints, summing their momenta, as described in eq. (3.15): +. +(3.56) +Finally we would like to point out the fact that solid θ-lines can be stripped off from a θ- +diagram; we will show this through an example. Let’s consider a portion of θ-diagram with the +following form: +(3.57) +and the decomposition of its external line: +. +(3.58) +The only contribution that we can accept is the one where two dashed θ-lines connect to the +external vertex; thus we remain with: +, +(3.59) +where in the last step we took into account that, since two dashed lines are already attached to +the white θ-dot, no further lines can be attached to it. Using eq. (3.17), we can summarize this +property as follows: +. +(3.60) +This property obviously holds independently of the color of the most external θ-dot. +21 + +Pa+ P2 +d21 +1 +2 +24 +Analyizing an example +In this section we illustrate the θ-diagram methodology by means of an example which contains +all the ingredients discussed above. +Let us consider a superdiagram that contributes at the three-loop order to the propagator of +the adjoint scalar in an N = 2 SYM theory with matter, given by +Wab = +. +(4.1) +We have explicitly written here our rather obvious convention for the names of the momenta +running in the various propagators; in the following we will sometimes just assume them. +To the “external” ring of chiral propagators and to all vertices but the central one we can +assign θ-diagrammatic elements according to the rules discussed above, in particular those in eq.s +(3.20,3.23,3.24,3.33). These elements are +. (4.2) +Building up the Feynman diagram, we actually have to take into account six contributions +corresponding to the different ways in which the triple and the single covariant derivative structures +that appear originally in the three-gluon vertex – see figure 2 – can be assigned to the vector +propagators. In other words, the gluon part of this superdiagram is given by +. +(4.3) +We denote by Zijk, with i, j, k in the range 5, 7, 8, the Grassmann part of contribution to the +diagram Wab in which ¯D6Dα +6 acts on the vector propagator from the node 6 to the node i and +22 + +us 3 +5 +1 +2 +43 +8O5 +5 +K53 +Kzs + s3 +K47 + M4? +0 +X45 +5 +3 +5 +5 +4 +2 +2 +4 +5 +3 +t +4 +0 +0 +MA8 +M83 +V4 +&ty +7 +3 +4 +7 +7 +8 +2. +7 +4 +05 +e ber mu fahonsD6,α acts on the propagator from 6 to k. Thus, for instance, +θ= Z875, +(4.4) +where for simplicity we did not write the momenta associated to the various propagators. Alto- +gether we have +Wab +θ= Z875 + Z578 + Z758 + Z857 + Z587 + Z785 . +(4.5) +The term Zijk contains the following ingredients: +(4.6) +which, according to the rules in eq.s (3.47,3.39,3.32) and (3.35), correspond to +. +(4.7) +The contraction θ6i · θ6k appears, for which we can use the property (3.48) obtaining +θ6i · θ6k = 1 +2 +� +−δ2(θki) + δ2(θ6i) + δ2(θ6k) +� +. +(4.8) +Moreover, we can integrate over θ6 and ¯θ6 variables, which appear only inside this portion of the +diagram, using the δ functions δ2(θ6j) and δ2(¯θ6j). We rewrite thus the factors in eq. (4.6) as +. +(4.9) +Here we have used the property (3.15) for the solid lines from j to j; note that these elements were +written in eq. (4.7) as solid lines from 6 to 6, which is the same in presence of δ2(θ6j)δ2(¯θ6j). Eq. +(4.9) contains the sum of three terms, containing different δ functions. Correspondingly, we write +Zijk = 8 +� +A(1) +ijk − A(2) +ijk − A(3) +ijk +� +, +(4.10) +where A(1) +ijk contains δ2(θki), A(2) +ijk contains δ2(θji) and A(3) +ijk contains δ2(θjk). +We will now describe in some detail the evaluation of Z875 and Z578; the other terms can be +treated analogously and we well just quote the result. +23 + +5 +5 +8> +6 +6 +6 +t +K6 +Kci +K6k /2 +9 +9 +S(8;) S(00) - 2 0k× S(0. +K6/2 +k +G +K6i/2KG /2 +K6i. +8 [S(0a-S(g,)-S(8m]S(0u) +(MGn- KG=)/2 +Kg< /2 +以Evaluation of Z875 +We start from A(1) +875. We put together the contributions in eq. (4.2) with +the first addend in (4.9) with i, j, k = 8, 7, 5, we take into account the factor of δ2(θ58)δ2(¯θ75) and +we collect the lines between the same nodes according to the property (3.15). Finally, we exploit +momentum conservation at each node of the diagram, see eq. (4.1). In this way we obtain a +θ-diagram that we can easily evaluate using the rules discussed in sections 3.3 and 3.4: +A(1) +875 = +(4.11) +In the second step we simply stripped off the external lines, according to the procedure discussed +around eq. (3.60). This simplification is implemented in the code that we will discuss in section +6. Now we can apply to the r.h.s. the results (3.17,3.18) obtaining +A(1) +875 = −k2 +83 (q2)2 . +(4.12) +Let us now consider A(2) +875. We combine the contributions in eq. (4.2) with the second addend +in (4.9) with i, j, k = 8, 7, 5. We have now a factor of δ2(θ78)δ2(¯θ75); collecting the lines and using +momentum conservation we arrive at the following θ-diagram: +A(2) +875 = +. +(4.13) +In the second step we have stripped off the line ⟨47⟩. The resulting expression can be evaluated +using the results for a single line and the one for a four-nodes loop. The second one was given in +eq. (3.31), in which we now have to set p1 = k53, p2 = −p3 = p4 = k83: taking into account the +momentum conservation relation k53 + k83 = −q, the result is simply q2 k2 +83. Altogether we get +thus +A(2) +875 = −k2 +83(q2)2 . +(4.14) +For what concerns A(3) +875, the terms in eq. (4.2) have to be combined with the third addend in +(4.9) with i, j, k = 8, 7, 5, which contains a factor of δ2(θ75)δ2(¯θ75). Collecting the lines and using +momentum conservation, we get this time +A(3) +875 = +. +(4.15) +24 + +以33 +7 +O +~ K33 +8 +α +70 +XKs3 +了 +Ws3 +4 +7 +q +4 +-以g3 +8 +8 +870 +W53 +7 +0 +5 +7This diagram is obviously vanishing because the integration over the Grassmann variables of the +isolated white dot cannot be saturated by any line. Thus +A(3) +875 = 0 . +(4.16) +Inserting the results (4.12,4.14,4.16) into eq. (4.10) we get +Z875 = 8 +� +A(1) +875 − A(2) +875 − A(3) +875 +� += 0 . +(4.17) +Evaluation of Z578 +This contribution is obtained by combining the elements in eq. (4.2) with +those in eq. (4.9) with i, j, k = 5, 7, 8. We split it into the three terms A(a) +578, with a = 1, 2, 3, +according to eq. (4.10). Thus A(1) +578 corresponds to the first addend in (4.9), and contains the +factor δ2(θ85)δ2(¯θ78). Collecting the lines and using momentum conservation we obtain +A(1) +578 = += +, +(4.18) +where in the second step we have simplified the θ-diagram by stripping off the line ⟨35⟩. We can +now evaluate the single line and the four-nodes loop using eq.s (3.17,3.18) and (3.31). We obtain +in the end +A(1) +578 = −(q2)2(k45 − k53)2 . +(4.19) +The term A(2) +578 corresponds to the second addend in eq. (4.9), and contains the factor δ2(θ75)δ2(¯θ78). +Proceeding in the by now usual way we arrive at the following θ-diagram: +A(2) +578 = +. +(4.20) +The decomposition of such a double-box diagram was exhibited in figure 5. Each of the terms in +the decomposition is either a single line or a dashed loop whose value is obtained from eq.s (3.29) +and (A.39-A.43). After a bit of algebra, the final outcome is +A(2) +578 = −(q + k45)2 k2 +53 (q + k53)2 . +(4.21) +25 + +3 +-9 +5 +WS +5 +145 +45以45-N53 +7 +30 +5 +45 +4 +3 +7Figure 6. An example of diagram in which ordering issues must be taken into account when applying the +θ-diagrammatic rules. +The term A(3) +578 comes from the third addend in (4.9). It is proportional to δ2(θ78)δ2(¯θ78) and +the associated θ-diagram is found to be the following: +A(3) +578 = +. +(4.22) +This double box diagram can be evaluated analogously to the one of eq. (4.20) and the result is +A(3) +578 = −q2 k2 +45(q + k53)2 . +(4.23) +It is now straightforward to obtain +Z578 = 8 +� +A(1) +578 − A(2) +578 − A(3) +578 +� += 16q2 (k2 +45 k2 +53 + q2 k45 · k53 + k2 +45 q · k53 + k2 +53 q · k45) . +(4.24) +Similarly one can compute all the terms Zijk in the Grassmann part of the diagram Wab. +The total result agrees with [9], where the computation was performed only partly by means of +θ-diagrammatic techniques as the covariant spinorial derivatives were treated by brute force. +4.1 +Ordering issues +The techniques introduced here allow to compute the Grassmann part of more complicated dia- +grams that would really be hard to deal with other methods. For diagrams which contain more +than one vertex with spinor covariant derivatives, one has to pay attention to ordering issues which +are relevant for determining the overall sign of each contribution. +Suppose for instance having to compute the diagram in figure 6. Using the condensed notation +Vi = V (xi, θi, ¯θi), the contractions that lead to the term singled out in the right hand side of figure +6 are the following: +...V7...V8...( ¯D5)2[Dα +5 [V5]]V5D5,α[V5]( ¯D6)2[Dα +6 [V6]]V6D6,α[V6]...V9...V10... +(4.25) +Our approach is to separate this superdiagram in its elementary constituents, to which we assign +their θ-diagrammatical counterparts. In doing this we have to take into account that, while the +26 + +以43 +5 +K +33/ +$+y- b- +4 +8YFigure 7. An example of a decomposition where the overall sign is non trivial. +vectorial superfield is a commuting object, each covariant spinor derivative flips its statistics. We +must thus pay attention to the signs that arise if some exchanges of such elements in the Wick +contractions. These signs are accounted for in the code that accompanies this paper. In the case +at hand, the decomposition of the particular contribution we are considering is given in figure 7 +and includes a global (−1) factor. +5 +Superdiagrams with vector or spinor external states +We will now discuss how to handle the Grassmann integrations in n-point functions whose ex- +ternal states are spinorial or vectorial. To extend the θ-diagrammatic method to these cases it +suffices to understand what Grassmannian factors the non-scalar external lines introduce. The +necessary ingredients have already been written down in section 2.3; here we will recast them in a +θ-diagrammatic form. +We shall begin with vector external states, which are quite easy to handle. +5.1 +External vectors +The Grassmann part of a vector line attached on one end to an external vector state vµ has been +given in eq. (2.31). We can introduce a θ-diagrammatical notation for it as follows: +, +(5.1) +where the element +. +(5.2) +is nothing else that the dashed line introduced in eq. (3.8) with the momentum p replaced by the +versor ˆeµ in the direction µ. This versor has components ˆeµ +ν = δµ +ν , so that its scalar product with +any vector a yields +ˆeµ · a = aµ . +(5.3) +Thus in particular ˆeµ · σ = σµ and ˆeµ · ¯σ = ¯σµ. +27 + +2 +(-1) +? +?>S +?S +5 +5 +10 +G +5 +8 +6 +5 +2 +3) +6 +0. +1 +e +0 +1 +一JLet us note that, in the case in which the external vector line carries no spinorial covariant +derivatives, its expression simplifies into +(5.4) +since the supervector propagator is given by δ2(θij)δ2(¯θij) and can be used to integrate the θi and +¯θi variables, which only occur in this part of the diagram, according to (2.31). +Consider a very simple example, akin to the case with scalar external states considered in +section 3.1, namely the one-loop superdiagram +Wµν +ab = +. +(5.5) +Its Grassmann part Zµν +θ= Wµν +ab is given, according to the rule just introduced and to eq.s +(3.20,3.33), by +Zµν = +. +(5.6) +This θ-diagram can be expanded as usual into cycles of dotted lines, but such cycles are bound to +contain the two ˆeµ and ˆeν dotted lines. Therefore one gets +Zµν = +. +(5.7) +Both terms can now be computed using the trace rule of eq. (3.29) and the formulæ in Appendix +A.2, treating the versors ˆeµ and ˆeν as any other quadri-momentum and then taking into account +eq. (5.3). +As another example, let us consider the following superdiagram, corresponding to a one loop +cubic vertex correction: +Wµ +abc = +. +(5.8) +28 + +6 +二 +. +1 +J-K +V +α 1 +9-KK_ g-b6 +P +c +a +4 +-e +b+d +5 +2Its Grassmann part Zµ θ= Wµ +abc is given, using the rules introduced above, by +Zµ = +. +(5.9) +Expanding this θ-diagram into cycles of dotted lines, bound to contain the ˆeµ dotted line, we get +Zµ = +. +(5.10) +Again, both terms can be computed using eq. (3.29) and Appendix A.2. +5.2 +Spinors from (anti-)chiral multiplets as external states +Let us now consider superdiagrams whose external states are spinors sitting in N = 1 chiral or +anti-chiral multiplets8. +The Grassmann part of a chiral line attached at one end to a chiralino or to an anti-chiralino +has been given in eq.s (2.23,2.24). In a (partially) θ-diagrammatic notation it can be expressed as +follows: +(5.11) +and +. +(5.12) +The novelty is the presence of “bare” θ-variables whose spinorial indices are not contracted +with the spinor indices carried by other θ variables. This leads, when these external lines are +combined with the inner vertices, to the appearance of new θ-diagrammatic elements. Indeed, +consider for instance an external line of the type (5.11) attached to a chiral cubic vertex, whose +8Note that, from the N = 2 point of view, if the N = 1 chiral or antichiral multiplet is the adjoint one which, +together with the N = 1 vector multiplet, makes up the N = 2 gauge multiplet, then these spinors are among the +gauginos of the theory. +29 + +-l +G + l-(p+9) +5q-t +q-t +G +4 +G + l-(p+9 +0 +? +-l +5 +5P +6 +d +Tx +二 +7 +αid +P +二 +taGrassmann part was given in eq. (3.24). We have +(5.13) +and similarly +, +(5.14) +where we introduced the notation +. +(5.15) +Consider for instance the following simple one-loop example: +W ˙α +ab,α = +. +(5.16) +Using the rules just stated, its Grassmann part Z ˙α +α +θ= W ˙α +ab,α is given by +Z ˙α +α = +. +(5.17) +Let us note that the external spinors appear in a specific order, dictated by the Wick contrac- +tions that originate the diagram one is considering, which implies a specific ordering of the “bare” +θ-variables in the θ-diagram that carry the spinor indices of the external spinors. If this order is +altered, we have to keep track of the ensuing overall sign - again, this is automatic in the code. +The crucial property of these triangular symbols is that, in the expansion of a θ-diagram, only +the terms where precisely one dotted line is attached to each triangular vertex survive since these +represent an integration already containing a fermionic coordinate. This is analogous to the fact +that exactly two dotted lines must be attached to each black or white dot, as stated after eq. +30 + +0. +9.二 +R +10:~K +4 +α,1 +1 +K-qb-n(3.16). Thus the possible decompositions of the θ-diagram must contain open trajectories – which +cannot intersect or overlap – starting on a triangle end ending on another one. In the case of eq. +(5.17) there is just one possibility: +Z ˙α +α = +. +(5.18) +Let us consider a more elaborate example, namely the following two-loop quartic diagram, which +we indicate only schematically, without labeling the momenta and the nodes: +. +(5.19) +In this case there are many more possibilities to draw the open lines and the decomposition of the +θ-diagram contains the following structures (we omit writing the factors of the external momenta +attached to the triangles): +. +(5.20) +The open paths connecting the triangles represent Grassmannian integrations; for instance += +� +dΘ θ1,α2(θ1p1¯θ1) . . . 2(θnpn¯θn)¯θ +˙β +n , +(5.21) +where by dΘ we indicate the integration over all the involved Grassmann variables. These expres- +sions can be evaluated by the same Fierz techniques utilized in eq. (3.29) for the closed paths. +The result is += (−1)n+1 +2 +(p1¯q1 . . . ¯qn−1pn) ˙γ +α . +(5.22) +Similarly, one has += (−1)n +2 +(p1¯q1 . . . pn−1¯qn−1)αβ +(5.23) +and += (−1)n +2 +(¯q1p1 . . . ¯qn−1pn−1) ˙α ˙β +(5.24) +All of these products of σµ-matrices can be treated algorithmically as described in Appendix (A.2). +31 + +dA +AJ +n4 +n-1 +n +n~1J +n~1 +n +Pn-1 +14For instance, in the first two cases we have += 1 +2(p1) +˙β +α = 1 +2(p1)µ (σµ) +˙β +α +(5.25) +and += 1 +2(p1)µ (q1)ν (σµ¯σν)αβ = −1 +2p1 · q1 ϵαβ + 1 +2(p1)µ (q1)ν (σµν)αβ . +(5.26) +Note that the open chains with two black triangles, i.e. with two external chiral spinor indices, +transform in the (2, 1)⊗(2, 1) representation of the spin group, which is reducible into (1, 1)⊕(3, 1), +i.e., into an antisymmetric and a symmetric part in these spinor indices. +Coming back to the simple case of eq. (5.18), the final result is +Z ˙α +α = (−1)¯q ˙αβ × (−1) +2 +(−q)β ˙γϵ ˙γ ˙βqα ˙β = −1 +2(¯qq¯q) ˙α +α = q2 +2 (¯q) ˙α +α = q2 +2 qµ(σµ) ˙α +α . +(5.27) +The first (−1) factor comes from exchanging the theta-variables of the triangular θ-vertices in +eq. (5.18) to match the one in the formula (5.21). +5.3 +Gauginos as external states +Let us consider now the case in which we have a spinor from the N = 1 vector multiplet in an +external state. The Grassmann parts of a vector line attached at one end to an external gaugino +or anti-gaugino were given in eq.s (2.34) and (2.35). We can describe them in θ-diagrammatic +notation as follows: +(5.28) +and +. +(5.29) +Thus each gaugino external line leads to the sum of two diagrammatic elements; this is a con- +sequence of the fact that we chose not to impose the Wess-Zumino gauge. The θ-diagrams with +gauginos as external states will therefore comprise multiple terms already before effecting their +decomposition. +Let us note that if the external gaugino line carries no spinorial derivatives its contributions +simplify because they involve the vector line with no spinor derivatives, which is just δ2(θij)δ2(¯θij). +32 + +MD:... +9 +D... +二 +& +>>>>S +→ +2D.... +）J +2 +JThis allows to integrate out the θ variables in the external node. Thus, for instance, if the external +gaugino is attached to a cubic adjoint vertex, see figure 2, we have +(5.30) +and +. +(5.31) +Let us consider, for instance, the following one-loop superdiagram: +W ˙α +ab,α = +. +(5.32) +According to the rules we just described, its Grassmann part Z ˙α +α +θ= W ˙α +ab,α is given in θ-diagrammatical +terms by +Z ˙α +α = +. +(5.33) +It comprises therefore four θ-diagrams: we write Z ˙α +α = Z ˙α +(1)α + Z ˙α +(2)α + Z ˙α +(3)α + Z ˙α +(4)α and we have +Z ˙α +(1)α = +. +(5.34) +In the first step we kept the labels on the nodes to facilitate the comparison with eq. (5.33); in +the second step we omitted such labels and we joined the lines between the same nodes. In the +following terms we will write directly the analogue of this second expression, namely +Z ˙α +(2)α = +, +Z ˙α +(3)α = +(5.35) +33 + +9 +J +2K +q +5 2 +9+Vx-b +(u-q) /2 + iacts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' This happens, for instance, for some of the vector Super Yang-Mills vertices – see fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Then the Grassmann part of ⟨v(xi)f(Dj, ¯ Dj)V (xj, θj, ¯θj)⟩0 would be given by ⟨vµf(Dj, ¯ Dj)V (θj, ¯θj)⟩0 θ= σµ α, ˙β∂α ¯∂ ˙βf(Dj, ¯Dj)δ4(θij) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='28) Such an expression is not easily handled in our diagrammatical method, but there is a way around.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Instead of expressing vµ in terms of the superfield V by means of Grassmann derivatives, we can exploit Grassmann integrations and write vµ(x) = −2 � d2θd2¯θ (θσµ¯θ)V (x, θ, ¯θ) , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='29) Then we can also replace eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='28) with ⟨vµ(xi)f(Dj, ¯Dj)V (xj, θj, ¯θj)⟩0 = −2 � dθ i d2¯θi (θiσµ¯θi) ⟨V (xi, θi, ¯θi)f(Dj, ¯Dj)V (xj, θj, ¯θj)⟩0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='30) In momentum space this leads to θ= � d2θid2¯θi 2(θiσµ¯θi)f(Dj, ¯Dj) � δ4(θij) � , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='31) In this way4 we only have to deal with Grassmann integrals and covariant derivatives acting on δ4(θij), which can be treated within our diagrammatic formalism, as we will discuss in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' We can deal similarly with the gaugino, even if the expression is slightly more complicated and contains two terms5: ⟨λα(xi)V (xj, θj, ¯θj)⟩0 = � d4θi � −2iθi,α − σµ α ˙β ¯θβ i ¯θ2 i ∂/∂xi,µ � ⟨V (xi, θi, ¯θi)V (xj, θj, ¯θj)⟩0 , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='32) ⟨V (xi, θi, ¯θi)¯λ ˙α(xj)⟩0 = � d4θj � 2i¯θ ˙α j + ¯σµ, ˙α,βθj,βθ2 j ∂/∂xj,µ � ⟨V (xi, θi, ¯θi)V (xj, θj, ¯θj)⟩0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='33) In momentum space and focusing only on the Grassmann part we obtain: θ= � d2θid2¯θi � θi,α + pα ˙β 2 ¯θ ˙β i θ2 i � f(Dj, ¯Dj) � δ4(θij) � , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='34) θ= � d2θjd2¯θj � ¯θ ˙α j − ¯p ˙αβ 2 θj,β ¯θ2 j � f(Di, ¯Di) � δ4(θij) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='35) In making explicit the spinorial derivatives in the expressions above one has to take into account that eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='50) is written with the momentum flowing out of the vertex j (so in some of the cases above it is actually the momentum −p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 4Note that it is also possible to use field to superfield relations based on Grassmann integration, instead of derivations as in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='15), also for the fields in the chiral multiplet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Again, this could in principle be useful for theories containing vertices with covariant spinorial derivatives acting on (anti-)chiral superfields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' For theories that do not contain such vertices, as is the case for instance for the N = 2 SYM theory, this is not needed and it is more efficient to use the formulas (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='17-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='20) which do not introduce integration of auxiliary variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 5This is due to the fact that we do not impose the Wess-Zumino gauge and thus we have to disentangle the χ spinor from the gaugino.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 9 4(P;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' ) 1 PP13 Grassmann integration in superdiagrams As already stated, the focus of this paper is on the Grassmann integration occurring in super- diagrams, namely on the computation of the quantity ZLorentz defined in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Of course, methods to perform such integration are well known, and in particular the so-called D-algebra approach of [8] is widely used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Here we propose a method that we find efficient and that is very algorithmic, so that it can be implemented in a symbolic language code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' This method is based on the construction of what we call θ-diagrams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='1 A simple example To fix the ideas, let us consider a very simple example, the one-loop correction to the propagator of the scalar in an adjoint chiral multiplet with matter chiral multiplets running in the loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' In this case the Lorentz structure is trivial, and the colour factor follows easily from the colour part of the vertices and propagators given in figures 4 and 3, while the normalization factor turns out to be just 2g2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' With respect to eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='9) it is immediate in this example to exploit the momentum conservation, obtaining = 2g2 × TrR(T bT c) × � ddk (2π)d 1 (q2)2 1 k2(k − q)2 Z(k, q) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='1) The factor Z(k, q) is the result of the integration over the Grassmann variables at each internal vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' According to the rules in figures 3 and 4 and eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='s (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='21) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='22) it reads Z(k, q) = � d4θ3 d4θ4 (θ3)2(¯θ4)2 e2θ4(k−q)¯θ3−θ4(k−q)¯θ4−θ3(k−q)¯θ3e−2θ4k¯θ3+θ4k¯θ4+θ3k¯θ3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='2) This integral is straightforward, as we will describe shortly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' In general, the computation of ZLorentz(k) through Grassmann integrations remains essentially algebraic and presents in principle no conceptual difficulty for any superdiagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Nevertheless, it typically becomes very involved as the complexity of the superdiagram increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='2 D-algebra The key idea of this approach is to make the Grassmann integration local, namely to reduce it to the integral over a single pair of Grassmann variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' This can be achieved because the Grassmann variables to be integrated over are associated to the vertices in the superdiagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The vertices are connected by superpropagators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The Grassmann part of the vector superpropagator directly contains δ functions, see eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='12), that identify the θ-variables in the vertices i and j it connects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Also the Grassmann part of the chiral-antichiral propagator, given in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='10), can be rewritten so as to display such δ functions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' indeed one can show that e2θip¯θj−θip¯θi−θjp¯θj = 1 16 ¯D2 i,p D2 i,pδ2(θij)δ2(¯θij) , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='3) 10 K Tb 1 2 K-9where we have remarked that the spinorial covariant derivatives contain the momentum p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Exploit- ing appropriately the δ functions present in the propagators, one can then eliminate the integrals over all but one of the pair of Grassmann variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The remaining integrand, however, contains in general spinor covariant derivatives arising both from the vector vertices, see figure 2, and from the chiral propagators rewritten using eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' This expression needs to be evaluated using the algebraic properties of the spinorial covariant derivatives D and ¯D, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=', carrying out the D-algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' For the example of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='2), this procedure amounts to rewrite Z(k, q) as Z(k, q) = 1 162 � d4¯θ3 d4θ4 θ2 3 ¯θ2 4 � D2 4,−k ¯D2 4,−kδ4(θ34) � � D2 4,k−q ¯D2 4,k−qδ4(θ34) � (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='4) and integrate it by parts6 to obtain Z(k, q) = 1 162 � d4¯θ3 d4θ4 � D2 4,q−k ¯D2 4,q−k � θ2 3 ¯θ2 4 ¯D2 4,−k D2 4,−kδ4(θ34) �� δ4(θ34) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='5) Using the fact that D2 4 and ¯D2 4 commute with θ2 3 and exploiting the δ-function we can write Z(k, q) = 1 162 � d4¯θ4 θ2 4 � D2 4,q−k ¯D2 4,q−k �¯θ2 4 ¯D2 4,−k D2 4,−kδ4(θ34) �� 3→4 , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='6) where in the string of covariant derivatives we have to identify the variables in the node 3 with those in the node 4 after having carried out the derivatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' In this way we have recast Z in term of a Grassmannian integration at a single node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' As argued in [8], this can be done for any loop within a superdiagram and, iterating the procedure, for any irreducible superdiagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The explicit evaluation of Z written in the form (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='6) can be carried out exploiting the algebraic properties of the covariant derivatives and the final outcome is that Z(k, q) = −q2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='7) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='3 Introducing the θ-diagrams In this example, the D-algebra strategy turns out to be rather more involute than carrying out the integration over the Grassmann variables in both nodes with the propagators in exponential form, as in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='s (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='2,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' In fact, the latter procedure can be described in a diagrammatic, algorithmic form which turns out to be generalizable to a large class of superdiagrams and can be implemented in a computer program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Let us now introduce this strategy starting from the example at hand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The basic ingredient are the exponentials appearing in the chiral propagators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' We introduce the following diagrammatic notation: .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='8) Due to the Grassmannian nature of the θ and ¯θ variables, the exponentials are in fact polynomial: e2(θip¯θj) = 1 + 2(θip¯θj) + 1 2 × � 2(θip¯θj) �2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='9) 6The rules for Grassmannian integrations by part are collected in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 11 2 (2: p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' ) ）In diagrammatic notation, this reads , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='10) where the momentum and the end-point labels are the same in all lines and are understood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The superdiagrams contain integrations over Grassmann variables θi and ¯θi at the various sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' These we represent graphically as black or white dots: .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='11) The cubic (anti)-chiral super-vertices bring in factors of Grassmannian delta-functions: θ2 i = δ2(θi) , ¯θ2 i = δ2(¯θi) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='12) Taking into account all this, we can rewrite diagrammatically eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='2) as follows: Z(k, q) = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='13) This expression can be simplified in some obvious ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The Grassmannian delta-function δ2(θ3) soaks up the corresponding integration and sets to zero all occurrences of θ3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' On the diagram, this correspond simply to remove the black dot labeled by 3 and the two solid lines connecting to it, since the associated exponentials reduce to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Similarly, the δ2(θ4) removes the white dot labeled by 4 and the lines attached to it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' We remain thus with Z(k, q) = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='14) Note that the labels 3 and 4 attached to the dots just assign a name to the integration variables, and they are thus actually redundant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Moreover, we can take into account the following general property: the product of two solid lines with the same endpoints gives a single solid line carrying the total momentum, namely .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='15) 12 1 + = + 220 "0 itK- q 3 ×S(8) S(2) : 2 3 4K- q 3Pa+ P2 dThis just corresponds to the product rule for the corresponding two exponentials, see eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Thus we arrive at Z(k, q) = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='16) We can expand the solid θ-lines into dashed lines according to eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Then we have to take into account the presence of white and black dots, that correspond to Grassmann integrals over two-component spinors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' According to eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='8), each dashed line leaving the vertex i carries one θi variable, and each dashed line entering the vertex j carries one ¯θj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The Grassmann integrals � dθ2 or � d¯θ2 vanish unless they act on expression quadratic in θα or ¯θ ˙α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Graphically this means that a θ-diagram is non-null if and only if exactly two dashed lines are attached to each dot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' This is a very simple but crucial property of the θ-diagrams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' In particular, we have .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='17) Finally, the dashed loop on the r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' above is very easily evaluated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' One has = 1 2 � d2θ4 d2¯θ3 2(θ4q¯θ3)2(θ4q¯θ3) = 1 2 tr(q¯q) = −q2 , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='18) where we made use of a Fierz rearrangement, see eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='s (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='33,A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='35), and carried out the integrations according to the basic rules in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='s (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='12–A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' We obtain therefore Z(k, q) = −q2 , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='19) in agreement with the result of the D-algebra manipulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Of course, the Grassmann integrations in this Z(k, q) are very easy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' It may seem that our diagrammatic notation unnecessarily complicates it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' However, it readily generalizes and is algo- rithmic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' As a first step, we show how the Grassmann part Z of all superdiagrams involving only (anti)-chiral superfields can be managed using θ-diagrams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='4 Diagrams with (anti)chiral superfields This is the simplest case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Let us describe how to manage it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Deriving the θ-diagram The Grassmann part of all chiral-superchiral propagators is given by a momentum dependent exponential of the type considered above, see eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='10), thus we can say that .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='20) Note that in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='20) and in the following, the cyan, thick lines that appear on the r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' of the θ= symbol have a completely different meaning from the black ones on the left: they are the solid θ-lines defined in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 13 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='1 22P P P/2 P/2 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 1 1 ) )For propagators connected to external scalars, given in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='s (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='21) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='22), we have simply (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='21) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='22) Also the contribution of cubic vertices involving chiral superfields to the Grassmann part of the diagram are very easy to describe: .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='23) Similarly, for the anti-chiral vertices one has .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='24) It follows from eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='s (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='21,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='22) that a chiral propagator connecting an external scalar to a cubic vertex gives a trivial contribution to the θ-diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Indeed, suppose for instance that the propagator (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='21) be attached to a vertex of the type (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='24) in position j;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' then its θ-line exp(−θjp¯θj) reduces to 1 since the vertex sets all occurrences of θj to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The properties we have listed are sufficient to determine the θ-diagrammatic form of the Grass- mann factor Z associated to any superdiagram Wcolour involving only (anti) chiral superfields with scalar external states;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' we will consider later the possibility that the external states correspond to other components of the multiplet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' An example Let us illustrate this by a specific example, namely Wab(q) = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='25) 14 6 : 1 J = : 1 J ~ p/26 4 人 1 = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' p/26 S(0) = a 二 t６ a 二 25 53 q 3 tb 1 2 &This diagram represents a three-loop contribution to the adjoint chiral scalar propagator, and has been considered for instance in [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Using the rules from (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='20) to (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='24) for all the propagators and vertices and making use of the δ-functions that they contain we obtain Wab θ= Z = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='26) This is perfectly analogous to the form we obtained in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='14) for the one-loop example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' It is easy to convince oneself that in fact in all cases involving only chiral/antichiral superfields the structure of vertices and lines of the θ-diagram mimics the one of the original superdiagram, except for dropping the external lines attached to scalar components, and associating a white dot to every chiral cubic vertex and a black dot to every anti-chiral one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Expanding the θ-diagram To compute a θ-diagram of the type just described, one can expand its solid lines according to eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Having done this, we can exploit the crucial observation we already stated just before eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='17): the only non zero contributions are those in which exactly two dashed lines enter or leave every dot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' As a consequence, such non-zero contributions consist of products of loops of dashed lines7 going through non-overlapping subsets of dots, leaving no dot isolated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Let us illustrate this with another example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Consider a θ-diagram with the following structure: Z = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='27) This can arise, for instance, from a one-loop contribution to a four-point function of chiral/antichiral scalars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' According to the rules just stated, it is given by Z = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='28) The terms in the right hand side represent precisely the possible decompositions of Z into loops of dashed lines;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' note that we have drawn the loops involving two dots as single solid lines, see eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 7Each loop consisting of only two lines, though, comes with a factor 1/2 because it arises from the expansion of a single solid line as in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 15 PsFigure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' An example of the decomposition of a θ-diagram into its non-vanishing contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' For simplicity we do not label the vertex and the lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Another example of the decomposition of a θ-diagram is given in figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The decomposition into loops can be realized by means of a path-finding algorithm and im- plemented in a computer code;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' this was done in [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' In the code presented here we follow a different strategy, based on expanding in turn all lines and taking into account at each steps the simplifications owing to the rule that selects exactly two dashed lines in each node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' This approach turns out to be computationally more efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Getting the final result The next ingredient is the following: each loop of dashed lines can be evaluated explicitly and the result can be given in a general form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Using repeatedly the Fierz rearrangements in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='s (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='32–A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='35) and the integration rules (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='12,A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='13,A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='14) one easily shows that = � d2θ1 d2¯θ1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' d2θn d2¯θn 2 � θ1p1¯θ1 � 2 � θ2k1¯θ1 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' × 2 � θnpn¯θn � 2 � θ1kn¯θn � = (−1)n+1 tr � p1 ¯k1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' pn ¯kn � (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='29) The traces appearing above are of the form tr(p1¯k1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='pn¯kn) = p1,µ1k1,ν1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='pn,µnkn,νntr(σµ1¯σν1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='σµn¯σνn) (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='30) They can be recursively computed using the properties of the matrices σµ and ¯σµ, see Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' For instance for eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='28) we obtain Z = p2 1 p2 3 − 2(p1 · p2)(p3 · p4) + 2(p1 · p3)(p2 · p4) − 2(p1 · p4)(p2 · p3) + p2 2 p2 4 + p1,µp2,νp3,ρp4,σϵµνρσ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='31) 16 n APerspective Let us summarize.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Drawing the θ-diagrams and evaluating them according to the rules we just described, we can compute explicitly the Grassmannian integrations for all superdia- grams involving only chiral and antichiral superfields, with scalar external states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' All the three main steps of the procedure, namely writing down the θ-diagram, finding its decomposition into loops of dashed lines and evaluating the latter, are completely algorithmic and can be implemented in a computer code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' This procedure was already described in [9], without however detailing the algorithm for de- termining all non-zero contributions and without providing a computer code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' In the present work we aim at extending this approach to a much larger class of superdiagrams, maintaining its main advantage, namely that of being algorithmic and readily implemented in a code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The basic idea is to cast the θ-dependent part of the superdiagram in terms of Grassmannian delta-functions and exponentials, which we can then evaluate with the θ-diagrammatic method described in the present section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='5 Diagrams with (internal) vector superfields The Grassmann part of the propagator of the vector superfields is very simple: .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='32) As was mentioned in the introduction, we restrict in this paper to theories that can be for- mulated in terms of N = 1 chiral and vectorial superfields, with interactions that have covariant derivatives that act only on vectorial superfields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' This class of theories contain in particular N = 2 SYM theories with matter hypermultiplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' In this case, beside the cubic vertices of the type considered in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='s (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='23,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='24), we have other interactions that involve both vectors and chi- ral superfields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Up to order g2, they are elementary from the point of view of their Grassmann structure: .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='33) From the action (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='6) we see that there are also interaction vertices, involving vector superfields only, which include spinor covariant derivatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Connecting vertices of this kind to other vertices by means of the vector superpropagator we effectively obtain expressions in which such covariant derivatives act on the vector lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The possible cases, and their Grassmann structure, can be worked out with a little bit of algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' For instance, as in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='4), there might be a case where we have a single covariant derivative acting on a vector propagator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' This implies a contribution like Di,αδ4(θij).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' It is straightforward to see that the following two expression coincide: Di,αδ4(θij) = 2θij,αδ2(¯θij)e (θipij ¯θi)−(θjpij ¯θi) 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content="34) 17 ('e)s ('r8)s tn'6 9,3: >>sSSS P6 9 = 1Graphically we have: ." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='35) This can be extended with further derivatives analogously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' In two cases we might have two spinor derivatives: , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='36) , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='37) (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='38) In eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='36) we have took into account that a line might have a derivatives coming from both vertices it attaches to, see figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' We now proceed with the numeration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' we have two contributions with three spinor derivatives: , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='39) , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='40) (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='41) two with four spinor derivatives: , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='42) , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='43) (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content="44) 18 2 2 2ix S(,) Pivs J /2J Pj / 2 川D: 6 Psj / 2 {2 一2 D: D J*J j / 2Di D' D?" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Pj/2 Pj/2 0&9 0 = P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='. Jone with five spinor derivatives: (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='45) and finally a single one with six spinor derivatives: (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='46) Once the spinorial covariant derivatives have been assigned to the vector lines, the “bare” gluon vertices only contain the information about the integration;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' thus for instance .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='47) Consider the situation in which the “decorated” vector lines of figure 2 are inserted inside superdiagrams with scalar external states, which have an overall trivial Lorentz structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The various spinor quantities and tensors appearing above, like θα ij, ϵαβ, and δα β, must conspire to produce scalar structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Thus they can only give overall numerical factors or Grassmannian scalar products of the type θij · θkl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Remembering that θij = θi − θj and that δ2(θ) = θ2, one has: θij · θkl = 1 2 � δ2(θij) + δ2(θkl) − δ2(θi − (θj + θk − θl)) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='48) Thus, the Grassmann structure of all superdiagrams formed with the elements we considered so far can be recast as linear combinations of integrals of exponentials and Grassmann δ functions which we know how to deal with using the θ-diagrammatic technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' In other theories based on N = 1 superfields, other combinations of spinorial covariant deriva- tives, beside those appearing in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='s (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='35-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='46), might appear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' They could be treated by applying the same principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Furthermore the number of possible different combinations is finite and one could write down the analogues of the rules in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='s (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='35-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='46) for all of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Thus for a generic theory with chiral/antichiral and vector N = 1 superfields, with spinorial covariant derivatives appearing on the vectors only, all the Grassmann integrals in any superdiagram can always be expressed in terms of θ-diagrams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='6 Some θ-diagrammatical properties Let us pause here to recapitulate some properties of our θ-diagrammatic notation, which have used somehow implicitly above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' First of all, the order in which white and black dots appear in the graphical representation of the θ-diagram is not relevant: they represent integrals over certain Grassmann variables, and all 19 0 JD:D: D?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' De 6 s() iPi?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 2 2：．/2 3 2the occurrences of these variables in other elements of the diagram must be integrated over.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Thus, for example, = � d2¯θj e2(θip¯θj) , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='49) even if the white dot appears rightmost in the drawing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Another graphical property that we have been using is the fact that endpoints of solid or dotted θ lines get attached to dots carrying the same index, remembering that the lines go from a black to a white dot: thus, for instance, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='50) as well as .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='51) This also works when one end is already attached to a dot, or when a dot has already other lines attached to it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' In the θ diagram, the lines can be constrained as consequence of the integration of some Grassmannian delta function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' These delta function might set some variable to zero, as in the case of the δ2(θ) or δ2(¯θ) present in the hyper-multiplet vertices, or identify two different variables, as in the case of the δ2(θij) = δ2(θi − θj) and the δ2(¯θij) = δ2(¯θi − ¯θj) present in vectorial superpropagators, see eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='32).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' It is easy to see that such constraints amount to the following rules: (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='52) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='53) as well as (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='54) 20 K tK=1 6and .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='55) Another important property is the fact that we can combine the solid lines with the same endpoints, summing their momenta, as described in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='15): .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='56) Finally we would like to point out the fact that solid θ-lines can be stripped off from a θ- diagram;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' we will show this through an example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Let’s consider a portion of θ-diagram with the following form: (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='57) and the decomposition of its external line: .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='58) The only contribution that we can accept is the one where two dashed θ-lines connect to the external vertex;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' thus we remain with: , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='59) where in the last step we took into account that, since two dashed lines are already attached to the white θ-dot, no further lines can be attached to it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Using eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='17), we can summarize this property as follows: .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='60) This property obviously holds independently of the color of the most external θ-dot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 21 Pa+ P2 d21 1 2 24 Analyizing an example In this section we illustrate the θ-diagram methodology by means of an example which contains all the ingredients discussed above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Let us consider a superdiagram that contributes at the three-loop order to the propagator of the adjoint scalar in an N = 2 SYM theory with matter, given by Wab = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='1) We have explicitly written here our rather obvious convention for the names of the momenta running in the various propagators;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' in the following we will sometimes just assume them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' To the “external” ring of chiral propagators and to all vertices but the central one we can assign θ-diagrammatic elements according to the rules discussed above, in particular those in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='s (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='20,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='23,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='24,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='33).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' These elements are .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='2) Building up the Feynman diagram, we actually have to take into account six contributions corresponding to the different ways in which the triple and the single covariant derivative structures that appear originally in the three-gluon vertex – see figure 2 – can be assigned to the vector propagators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' In other words, the gluon part of this superdiagram is given by .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='3) We denote by Zijk, with i, j, k in the range 5, 7, 8, the Grassmann part of contribution to the diagram Wab in which ¯D6Dα 6 acts on the vector propagator from the node 6 to the node i and 22 us 3 5 1 2 43 8O5 5 K53 Kzs + s3 K47 + M4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 0 X45 5 3 5 5 4 2 2 4 5 3 t 4 0 0 MA8 +M83 V4 &ty 7 3 4 7 7 8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 7 4 05 e ber mu fahonsD6,α acts on the propagator from 6 to k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Thus, for instance, θ= Z875, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='4) where for simplicity we did not write the momenta associated to the various propagators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Alto- gether we have Wab θ= Z875 + Z578 + Z758 + Z857 + Z587 + Z785 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='5) The term Zijk contains the following ingredients: (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='6) which, according to the rules in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='s (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='47,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='39,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='32) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='35), correspond to .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='7) The contraction θ6i · θ6k appears, for which we can use the property (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='48) obtaining θ6i · θ6k = 1 2 � −δ2(θki) + δ2(θ6i) + δ2(θ6k) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='8) Moreover, we can integrate over θ6 and ¯θ6 variables, which appear only inside this portion of the diagram, using the δ functions δ2(θ6j) and δ2(¯θ6j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' We rewrite thus the factors in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='6) as .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='9) Here we have used the property (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='15) for the solid lines from j to j;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' note that these elements were written in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='7) as solid lines from 6 to 6, which is the same in presence of δ2(θ6j)δ2(¯θ6j).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='9) contains the sum of three terms, containing different δ functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Correspondingly, we write Zijk = 8 � A(1) ijk − A(2) ijk − A(3) ijk � , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='10) where A(1) ijk contains δ2(θki), A(2) ijk contains δ2(θji) and A(3) ijk contains δ2(θjk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' We will now describe in some detail the evaluation of Z875 and Z578;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' the other terms can be treated analogously and we well just quote the result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 23 5 5 8> 6 6 6 t K6 Kci K6k /2 9 9 S(8;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=') S(00) - 2 0k× S(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' K6/2 k G K6i/2KG /2 K6i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 8 [S(0a-S(g,)-S(8m]S(0u) (MGn- KG=)/2 Kg< /2 以Evaluation of Z875 We start from A(1) 875.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' We put together the contributions in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='2) with the first addend in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='9) with i, j, k = 8, 7, 5, we take into account the factor of δ2(θ58)δ2(¯θ75) and we collect the lines between the same nodes according to the property (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Finally, we exploit momentum conservation at each node of the diagram, see eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' In this way we obtain a θ-diagram that we can easily evaluate using the rules discussed in sections 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='3 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='4: A(1) 875 = (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='11) In the second step we simply stripped off the external lines, according to the procedure discussed around eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='60).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' This simplification is implemented in the code that we will discuss in section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Now we can apply to the r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' the results (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='17,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='18) obtaining A(1) 875 = −k2 83 (q2)2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='12) Let us now consider A(2) 875.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' We combine the contributions in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='2) with the second addend in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='9) with i, j, k = 8, 7, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' We have now a factor of δ2(θ78)δ2(¯θ75);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' collecting the lines and using momentum conservation we arrive at the following θ-diagram: A(2) 875 = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='13) In the second step we have stripped off the line ⟨47⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The resulting expression can be evaluated using the results for a single line and the one for a four-nodes loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The second one was given in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='31), in which we now have to set p1 = k53, p2 = −p3 = p4 = k83: taking into account the momentum conservation relation k53 + k83 = −q, the result is simply q2 k2 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Altogether we get thus A(2) 875 = −k2 83(q2)2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='14) For what concerns A(3) 875, the terms in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='2) have to be combined with the third addend in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='9) with i, j, k = 8, 7, 5, which contains a factor of δ2(θ75)δ2(¯θ75).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Collecting the lines and using momentum conservation, we get this time A(3) 875 = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='15) 24 以33 7 O ~ K33 8 α 70 XKs3 了 Ws3 4 7 q 4 以g3 8 8 870 W53 7 0 5 7This diagram is obviously vanishing because the integration over the Grassmann variables of the isolated white dot cannot be saturated by any line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Thus A(3) 875 = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='16) Inserting the results (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='12,4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='14,4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='16) into eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='10) we get Z875 = 8 � A(1) 875 − A(2) 875 − A(3) 875 � = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='17) Evaluation of Z578 This contribution is obtained by combining the elements in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='2) with those in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='9) with i, j, k = 5, 7, 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' We split it into the three terms A(a) 578, with a = 1, 2, 3, according to eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Thus A(1) 578 corresponds to the first addend in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='9), and contains the factor δ2(θ85)δ2(¯θ78).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Collecting the lines and using momentum conservation we obtain A(1) 578 = = , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='18) where in the second step we have simplified the θ-diagram by stripping off the line ⟨35⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' We can now evaluate the single line and the four-nodes loop using eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='s (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='17,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='18) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='31).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' We obtain in the end A(1) 578 = −(q2)2(k45 − k53)2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='19) The term A(2) 578 corresponds to the second addend in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='9), and contains the factor δ2(θ75)δ2(¯θ78).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Proceeding in the by now usual way we arrive at the following θ-diagram: A(2) 578 = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='20) The decomposition of such a double-box diagram was exhibited in figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Each of the terms in the decomposition is either a single line or a dashed loop whose value is obtained from eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='s (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='29) and (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='39-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='43).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' After a bit of algebra, the final outcome is A(2) 578 = −(q + k45)2 k2 53 (q + k53)2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='21) 25 3 9 5 WS 5 145 45以45-N53 7 30 5 45 4 3 7Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' An example of diagram in which ordering issues must be taken into account when applying the θ-diagrammatic rules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The term A(3) 578 comes from the third addend in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' It is proportional to δ2(θ78)δ2(¯θ78) and the associated θ-diagram is found to be the following: A(3) 578 = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='22) This double box diagram can be evaluated analogously to the one of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='20) and the result is A(3) 578 = −q2 k2 45(q + k53)2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='23) It is now straightforward to obtain Z578 = 8 � A(1) 578 − A(2) 578 − A(3) 578 � = 16q2 (k2 45 k2 53 + q2 k45 · k53 + k2 45 q · k53 + k2 53 q · k45) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='24) Similarly one can compute all the terms Zijk in the Grassmann part of the diagram Wab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The total result agrees with [9], where the computation was performed only partly by means of θ-diagrammatic techniques as the covariant spinorial derivatives were treated by brute force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='1 Ordering issues The techniques introduced here allow to compute the Grassmann part of more complicated dia- grams that would really be hard to deal with other methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' For diagrams which contain more than one vertex with spinor covariant derivatives, one has to pay attention to ordering issues which are relevant for determining the overall sign of each contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Suppose for instance having to compute the diagram in figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Using the condensed notation Vi = V (xi, θi, ¯θi), the contractions that lead to the term singled out in the right hand side of figure 6 are the following: .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='V7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='V8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='( ¯D5)2[Dα 5 [V5]]V5D5,α[V5]( ¯D6)2[Dα 6 [V6]]V6D6,α[V6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='V9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='V10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='25) Our approach is to separate this superdiagram in its elementary constituents, to which we assign their θ-diagrammatical counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' In doing this we have to take into account that, while the 26 以43 5 K 33/ $+y- b- 4 8YFigure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' An example of a decomposition where the overall sign is non trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' vectorial superfield is a commuting object, each covariant spinor derivative flips its statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' We must thus pay attention to the signs that arise if some exchanges of such elements in the Wick contractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' These signs are accounted for in the code that accompanies this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' In the case at hand, the decomposition of the particular contribution we are considering is given in figure 7 and includes a global (−1) factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 5 Superdiagrams with vector or spinor external states We will now discuss how to handle the Grassmann integrations in n-point functions whose ex- ternal states are spinorial or vectorial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' To extend the θ-diagrammatic method to these cases it suffices to understand what Grassmannian factors the non-scalar external lines introduce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The necessary ingredients have already been written down in section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' here we will recast them in a θ-diagrammatic form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' We shall begin with vector external states, which are quite easy to handle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='1 External vectors The Grassmann part of a vector line attached on one end to an external vector state vµ has been given in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='31).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' We can introduce a θ-diagrammatical notation for it as follows: , (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='1) where the element .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='2) is nothing else that the dashed line introduced in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='8) with the momentum p replaced by the versor ˆeµ in the direction µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' This versor has components ˆeµ ν = δµ ν , so that its scalar product with any vector a yields ˆeµ · a = aµ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='3) Thus in particular ˆeµ · σ = σµ and ˆeµ · ¯σ = ¯σµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 27 2 (-1) ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='>S ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='S 5 5 10 G 5 8 6 5 2 3) 6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 1 e 0 1 一JLet us note that, in the case in which the external vector line carries no spinorial covariant derivatives, its expression simplifies into (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='4) since the supervector propagator is given by δ2(θij)δ2(¯θij) and can be used to integrate the θi and ¯θi variables, which only occur in this part of the diagram, according to (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='31).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Consider a very simple example, akin to the case with scalar external states considered in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='1, namely the one-loop superdiagram Wµν ab = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='5) Its Grassmann part Zµν θ= Wµν ab is given, according to the rule just introduced and to eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='s (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='20,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='33), by Zµν = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='6) This θ-diagram can be expanded as usual into cycles of dotted lines, but such cycles are bound to contain the two ˆeµ and ˆeν dotted lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Therefore one gets Zµν = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='7) Both terms can now be computed using the trace rule of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='29) and the formulæ in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='2, treating the versors ˆeµ and ˆeν as any other quadri-momentum and then taking into account eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' As another example, let us consider the following superdiagram, corresponding to a one loop cubic vertex correction: Wµ abc = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='8) 28 6 二 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 1 J-K V α 1 9-KK_ g-b6 P c a 4 e b+d 5 2Its Grassmann part Zµ θ= Wµ abc is given, using the rules introduced above, by Zµ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='9) Expanding this θ-diagram into cycles of dotted lines, bound to contain the ˆeµ dotted line, we get Zµ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='10) Again, both terms can be computed using eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='29) and Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='2 Spinors from (anti-)chiral multiplets as external states Let us now consider superdiagrams whose external states are spinors sitting in N = 1 chiral or anti-chiral multiplets8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The Grassmann part of a chiral line attached at one end to a chiralino or to an anti-chiralino has been given in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='s (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='23,2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='24).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' In a (partially) θ-diagrammatic notation it can be expressed as follows: (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='11) and .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='12) The novelty is the presence of “bare” θ-variables whose spinorial indices are not contracted with the spinor indices carried by other θ variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' This leads, when these external lines are combined with the inner vertices, to the appearance of new θ-diagrammatic elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Indeed, consider for instance an external line of the type (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='11) attached to a chiral cubic vertex, whose 8Note that, from the N = 2 point of view, if the N = 1 chiral or antichiral multiplet is the adjoint one which, together with the N = 1 vector multiplet, makes up the N = 2 gauge multiplet, then these spinors are among the gauginos of the theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 29 l G l-(p+9) 5q-t q-t G 4 G l-(p+9 0 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' l 5 5P 6 d Tx 二 7 αid P 二 taGrassmann part was given in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='24).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' We have (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='13) and similarly , (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='14) where we introduced the notation .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='15) Consider for instance the following simple one-loop example: W ˙α ab,α = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='16) Using the rules just stated, its Grassmann part Z ˙α α θ= W ˙α ab,α is given by Z ˙α α = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='17) Let us note that the external spinors appear in a specific order, dictated by the Wick contrac- tions that originate the diagram one is considering, which implies a specific ordering of the “bare” θ-variables in the θ-diagram that carry the spinor indices of the external spinors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' If this order is altered, we have to keep track of the ensuing overall sign - again, this is automatic in the code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The crucial property of these triangular symbols is that, in the expansion of a θ-diagram, only the terms where precisely one dotted line is attached to each triangular vertex survive since these represent an integration already containing a fermionic coordinate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' This is analogous to the fact that exactly two dotted lines must be attached to each black or white dot, as stated after eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='二 R 10:~K 4 α,1 1 K-qb-n(3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Thus the possible decompositions of the θ-diagram must contain open trajectories – which cannot intersect or overlap – starting on a triangle end ending on another one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' In the case of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='17) there is just one possibility: Z ˙α α = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='18) Let us consider a more elaborate example, namely the following two-loop quartic diagram, which we indicate only schematically, without labeling the momenta and the nodes: .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='19) In this case there are many more possibilities to draw the open lines and the decomposition of the θ-diagram contains the following structures (we omit writing the factors of the external momenta attached to the triangles): .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='20) The open paths connecting the triangles represent Grassmannian integrations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' for instance = � dΘ θ1,α2(θ1p1¯θ1) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 2(θnpn¯θn)¯θ ˙β n , (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='21) where by dΘ we indicate the integration over all the involved Grassmann variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' These expres- sions can be evaluated by the same Fierz techniques utilized in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='29) for the closed paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The result is = (−1)n+1 2 (p1¯q1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' ¯qn−1pn) ˙γ α .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='22) Similarly, one has = (−1)n 2 (p1¯q1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' pn−1¯qn−1)αβ (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='23) and = (−1)n 2 (¯q1p1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' ¯qn−1pn−1) ˙α ˙β (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='24) All of these products of σµ-matrices can be treated algorithmically as described in Appendix (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 31 dA AJ n4 n-1 n n~1J n~1 n Pn-1 14For instance, in the first two cases we have = 1 2(p1) ˙β α = 1 2(p1)µ (σµ) ˙β α (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='25) and = 1 2(p1)µ (q1)ν (σµ¯σν)αβ = −1 2p1 · q1 ϵαβ + 1 2(p1)µ (q1)ν (σµν)αβ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='26) Note that the open chains with two black triangles, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' with two external chiral spinor indices, transform in the (2, 1)⊗(2, 1) representation of the spin group, which is reducible into (1, 1)⊕(3, 1), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=', into an antisymmetric and a symmetric part in these spinor indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Coming back to the simple case of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='18), the final result is Z ˙α α = (−1)¯q ˙αβ × (−1) 2 (−q)β ˙γϵ ˙γ ˙βqα ˙β = −1 2(¯qq¯q) ˙α α = q2 2 (¯q) ˙α α = q2 2 qµ(σµ) ˙α α .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='27) The first (−1) factor comes from exchanging the theta-variables of the triangular θ-vertices in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='18) to match the one in the formula (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='3 Gauginos as external states Let us consider now the case in which we have a spinor from the N = 1 vector multiplet in an external state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The Grassmann parts of a vector line attached at one end to an external gaugino or anti-gaugino were given in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='s (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='34) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='35).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' We can describe them in θ-diagrammatic notation as follows: (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='28) and .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='29) Thus each gaugino external line leads to the sum of two diagrammatic elements;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' this is a con- sequence of the fact that we chose not to impose the Wess-Zumino gauge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' The θ-diagrams with gauginos as external states will therefore comprise multiple terms already before effecting their decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Let us note that if the external gaugino line carries no spinorial derivatives its contributions simplify because they involve the vector line with no spinor derivatives, which is just δ2(θij)δ2(¯θij).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 32 MD:.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 9 D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' 二 & >>>>S → 2D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='. ）J 2 JThis allows to integrate out the θ variables in the external node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' Thus, for instance, if the external gaugino is attached to a cubic adjoint vertex, see figure 2, we have (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='30) and .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='31) Let us consider, for instance, the following one-loop superdiagram: W ˙α ab,α = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='32) According to the rules we just described, its Grassmann part Z ˙α α θ= W ˙α ab,α is given in θ-diagrammatical terms by Z ˙α α = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='33) It comprises therefore four θ-diagrams: we write Z ˙α α = Z ˙α (1)α + Z ˙α (2)α + Z ˙α (3)α + Z ˙α (4)α and we have Z ˙α (1)α = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='34) In the first step we kept the labels on the nodes to facilitate the comparison with eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='33);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' in the second step we omitted such labels and we joined the lines between the same nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content=' In the following terms we will write directly the analogue of this second expression, namely Z ˙α (2)α = , Z ˙α (3)α = (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/m9FKT4oBgHgl3EQfEy02/content/2301.11717v1.pdf'} +page_content='35) 33 9 J 2K q 5 2 9+Vx-b (u-q) /2 Q is satisfied, whereas for M < Q the horizon no longer exists. To reach the latter the radially falling +charged particle should carry mass m and charge q to the Reissner-Nordstr¨om black hole. Here, it is worth noting +that we suppose δE ≪ M and q ≪ Q for test particle approximation to hold good so that the radially falling charged +particle transfers the mass and charge to black hole’s mass and charge, respectively. +With the mass and charge +absorbed, the final state of the black hole parameters is given by M + δE and Q + q, respectively. +Thereafter, the black hole can be overcharged when the condition below is satisfied only: +( ¯ +M + δE)2 < ( ¯Q + q)2 , +(16) +for the lower and an upper bounds on the energy of the charged particle +qQ +r2 ++ += δEmin < δE , +(17) +δE < δEmax = ¯Q + q − ¯ +M . +(18) +Note that the black hole starts out very close to extremal one. It is certain that the above Eqs. (17) and (18) cannot +be satisfied simultaneously for the extremal case, Q = M = r+. +The effective potential for radial motion of the radially falling charged particle can be given in terms of the energy, +charge and mass of the charged particle, as given by Eq. (15). This effective potential has turning points at which +Veff(r) = 0. However, it also has maximum at +rmax = +� +Q +� q2 +m2 − 1 +� �δEq +m2 − M +Q +�−1�1/2 +. +(19) +For this maximum one must choose reasonable parameters of charged test particle so that Veff(r) < 0, thus allowing +the particle to cross through the horizon swimmingly. For this purpose we select the appropriate parameters of the +charged particle to satisfy the condition (see Eq. (16)) and explore Veff(r) numerically [10] +Q = 1 − 2ϵ2 +q = α′ϵ with α′ > 1 +δE = α′ϵ − 2β′ϵ2 with +1 < β′ < α′ +m = γ′ϵ with +γ′ < +� +α′2 − β′2 . +(20) +with suitable choice of parameters α′, β′, and γ′. In the above equation, ϵ is regarded as a small parameter, so +that it represents a near-extremality. We note that parameters α′, β′, and γ′ have no particular meanings, but are +used to satisfy the above-mentioned condition; i.e. ( ¯ +M + δE)2 < ( ¯Q + q)2. To ensure this we explore it numerically. +For this thought experiment, we can choose Q = 0.99999 for the given value ϵ = 0.0022 by setting M = 1. One +can however choose even smaller values of ϵ. So for the given background spacetime with parameters M = 1 and +Q = 0.99999 as stated in [10], we can then select the appropriate parameters of the charged particle by setting +α′ = 1.33902, β′ = 1.0301, and γ′ = 0.80505. In doing so, we suppose that the particle of mass m = 1.8 × 10−3 +has charge q = 3 × 10−3, and falls past the horizon with energy δE = 2.9897 × 10−3, thus satisfying the condition +( ¯ +M + δE) − ( ¯Q + q) < 0. +Let us then consider the charged particle thrown inward the black hole radially with δJ = 0. For charged particles +to enter the black hole without any restriction Veff(r) must be negative or ˙r2 must be positive everywhere outside the + +5 +1.00266 +1.00268 +1.00270 +1.00272 +1.00274 +1.475 � 10�6 +1.48 � 10�6 +1.485 � 10�6 +1.49 � 10�6 +r +r� 2 +FIG. 1: +Radial dependence of the motion of charged particle falling into the near-extremal Reissner-Nordstr¨om black hole +for given values of charge q = 3 × 10−3, energy δE = 2.9897 × 10−3, and mass m = 1.8 × 10−3 that satisfy the test particle +approximation. +horizon, thereby converting a near extremality to over extremality. For this, we analyse the radial motion of charged +test particle in terms of the effective potential, ˙r2 = −2Veff(r). In Fig. 1, we show the radial motion of charged +test particle. As seen in Fig. 1, the charged particle with appropriate parameters could fall across the horizon, thus +violating the WCCC – so-called ”over extremality” can be reached. +TABLE I: The values of rmax outside the horizon and effective potential are tabulated for different values of energy and mass +of test particles. The charge parameter is considered here as q = 3 × 10−3. +m +δE +rmax +Veff +0.9 × 10−3 +2.9874 × 10−3 +1.00231 +−5.23 × 10−7 +1.4 × 10−3 +2.9884 × 10−3 +1.00248 +−7.87 × 10−7 +1.8 × 10−3 +2.9897 × 10−3 +1.00269 +−1.47 × 10−6 +1.85 × 10−3 +2.9899 × 10−3 +1.00273 +−1.60 × 10−6 +In Table I we show the maximum values of the effective potential in a variety of test particle parameters. For +these parameters, we explore the effective potential numerically. As can be seen from Table I, Veff < 0 is always +satisfied for chosen values, thus allowing test particle to fall across the horizon and violating the WCCC. This result +also reflects the behavior of Fig. 1 for a particular case. +B. +Effect of external magnetic field on dynamics of overcharging of Reissner-Nordstr¨om black hole +Now we consider the Reissner-Nordstr¨om black hole immersed in an external magnetic field to understand more +deeply the impact of the external magnetic field on the dynamics of overcharging process. The magnetic field can +alter the geodesics of charged particles, and it can also influence the process of overcharging of the black hole. +Following to Wald [8] one can study the magnetic field in vicinity of the black hole and assume that the magnetic +field is asymptotically uniform with strength B at infinity. The non-vanishing components of potential Aα of the +electromagnetic field around the Reissner-Nordstr¨om black hole in the presence of external magnetic field reads as +At = −Q +r , +Ar = Aθ = 0, +Aϕ = B +2 r2 sin2 θ . +(21) +We further analyze effective potential for the radial motion. Using Eqs. (11) and (12) and setting θ = π/2 the +effective potential describing the radial motion for the charged particle around the Reissner-Nordstr¨om black hole + +6 +Β = 0 +Β = 0.5 +Β = 0.7198 +Β = 0.9 +1.002 +1.003 +1.004 +1.005 +1.006 +1.007 +1.008 +1.009 +�0.000025 +�0.00002 +�0.000015 +�0.00001 +�5. �10�6 +0 +5. �10�6 +r +Veff +FIG. 2: +Radial profile of the effective potential for the radial motion of the charged particles around the Reissner-Nordstr¨om +black hole immersed in an external uniform magnetic field for different values of magnetic parameter β. Note that we select +q = 3 × 10−3 and m = 1.8 × 10−3 for test particle’s charge and mass, respectively. +immersed in an external magnetic field can be written in the following form +Veff(r) = M +r +� Q +M +δEq +m2 − 1 +� +− 1 +2 +�δE2 +m2 − 1 +� +− +Q2 +2r2 +� q2 +m2 − 1 +� ++ +� +1 − 2M +r ++ Q2 +r2 +� β2r2 +8M 2 , +(22) +with the magnetic parameter β = qBM/m. In the limit when β → 0, one can easily recover Eq. (15), i.e. the result +presented in Ref. 15. We now analyze the impact of the external magnetic field on the radial profile of the effective +potential. +By imposing the following conditions +∂Veff(r) +∂r += 0 and +Veff(rmax) = 0 , +(23) +one can easily find the critical value for the magnetic field at which it prevents the charged particles from falling into +the black hole. Taking this in consideration, with the values chosen for the charged test particle, q = 3 × 10−3 and +m = 1.8 × 10−3, one can get the critical value for the magnetic parameter β given by +βcr ∼ 0.7198 . +(24) +To analyze the impact of the magnetic parameter β on the dynamics of overcharging of the black hole we present +the radial profile of the the effective potential in Fig. 2. +From Fig. 2, in the limit β → 0 we have the effective +potential that is always negative for the charged particle with appropriate parameters, as presented in Table I and +Fig. 1. However, the shape of the effective potential moves upward as a consequence of the increase in the value of +the magnetic parameter β. As seen in Fig. 2, the height of maximum of the effective potential tends to zero when +the magnetic parameter approaches its critical value βcr. Then the maximum value of the effective potential crosses +zero and becomes positive, thereby preventing particles from entering the black hole. It turns out that the external +magnetic field would act as a cosmic censorship beyond its threshold value; see Fig. 2. Table II also reflects the +behavior of the obtained results in detail. +From the above analysis it turns out that the Reissner-Nordstr¨om black hole could be overcharged. This result +is however overturned when the external magnetic field around the black hole is taken into account. That is, the +magnetic field can restore the WCCC beyond when it reaches its critical value (for example, see also, [14]). However, +we have yet to reach the definite conclusion whether the magnetic field still act as a cosmic censor or not. Thus, we +need to consider the magnetized black hole solution that includes the magnetic field in the background spacetime [48] +as our main purpose is to study the backreaction effect of the magnetic field on the validity of the WCCC. This is +what we plan to address in the next. + +7 +B = 0.0 +1.002 +1.003 +1.004 +1.005 +1.006 +1.007 +1.008 +1.009 +-0.000025 +-0.000020 +-0.000015 +-0.000010 +-5. × 10-6 +0.000000 +r +Veff +B = 0.020262 +B = 0.020264 +1.00553 +1.00554 +1.00555 +1.00556 +1.00557 +1.00558 +-6. × 10-10 +-4. × 10-10 +-2. × 10-10 +0 +2. × 10-10 +4. × 10-10 +r +Veff +FIG. 3: +Radial profile of the effective potential for the charged particle around the magnetized Reissner-Nordstr¨om black hole +in the case of fixed parameters δE = 2.9897 × 10−3, q = 3 × 10−3 and m = 1.8 × 10−3. Left panel: Veff is plotted in the case +of vanishing magnetic field, i.e. B = 0. Right panel: Veff is plotted for different values of magnetic field B, red line shows the +case when B = Bcr. Note that in the case of B > Bcr the magnetic field can restore the WCCC as the maximum height of +Veff crosses horizontal zero line. +TABLE II: +The values of rmax outside the horizon and effective potential Veff(rmax) for different values of the magnetic +parameter β for the fixed q = 3 × 10−3 and m = 1.8 × 10−3. +δE = 2.9897 × 10−3 +β +rmax +Veff +0 +1.005389149 +−1.18000 × 10−6 +0.01 +1.005389226 +−1.17937 × 10−6 +0.05 +1.005391085 +−1.17503 × 10−6 +0.1 +1.005396903 +−1.16139 × 10−6 +0.2 +1.005420304 +−1.10587 × 10−6 +0.3 +1.005459767 +−1.00993 × 10−6 +0.4 +1.005516007 +−0.86830 × 10−6 +0.5 +1.005590070 +−6.73278 × 10−7 +0.6 +1.005683387 +−4.14325 × 10−7 +0.7 +1.005797845 +−7.78888 × 10−8 +0.7198 +1.005823285 +0.00000 +0.8 +1.005935891 +3.54872 × 10−7 +0.9 +1.006100678 +0.90611 × 10−6 +1.0 +1.006296273 +1.60574 × 10−6 +C. +The effect of magnetic field on dynamics of overcharging of magnetized Reissner-Nordstr¨om black hole +We have shown that the external magnetic field can potentially serve as the cosmic censor beyond its critical value, +preventing particle from entering the Reissner-Nordstr¨om black hole. Here, we analyze the impact of the magnetic +field backreaction in the process of overcharging of a magnetized Reissner-Nordstr¨om black hole, as described by the +metric Eq.1. We further consider a radially falling charged particle, δJ = 0, that can violate the WCCC in the +absence of magnetic field in the environment of the black hole [10]. In doing so, we try to understand whether the +backreaction effect of the magnetic field can still serve as the cosmic censor, thus stopping particles with appropriate +parameters from entering the black hole. +As was mentioned above we assume that a charged particle that has energy δE ≪ M and charge q ≪ Q remains +valid for the test particle approximation. Then, it adds extra mass and charge to black hole’s mass and charge, +respectively, when it gets absorbed by the black hole. A so-called ”Overcharged” can be realized if and only if the +conditions given by Eqs. (16-18) are hold. We then analyze the effective potential so as to understand more deeply +the effect of the magnetic field backreaction on the process of overcharging of a black hole. To ensure that the particle +enters the black hole without encountering any turning point the effective potential (14) has to be always negative +everywhere outside the horizon, i.e. Veff < 0. For that we assume M = 1 and Q = 0.99999 as stated previously and +focus on the charged particle that has q = 3 × 10−3. Using suitable choice of parameters α′, β′, and γ′ given by + +8 +TABLE III: The values of rmax outside the horizon and effective potential are tabulated in the case of different values of δE, +m and B. Note that the charge of test particle is taken to be q = 3 × 10−3. +δE = 2.9874 × 10−3 +m = 0.9 × 10−3 +δE = 2.9884 × 10−3 +m = 1.4 × 10−3 +B +rmax +Veff +B +rmax +Veff +0 +1.004630 +−4.2 × 10−6 +0 +1.004960 +−2.17 × 10−6 +0.013841 +1.004681 +0 +0.016084 +1.005045 +0 +0.013843 +1.004685 +4.2 × 10−10 +0.016085 +1.005050 +1.2 × 10−10 +δE = 2.9897 × 10−3 +m = 1.8 × 10−3 +δE = 2.9899 × 10−3 +m = 1.85 × 10−3 +B +rmax +Veff +B +rmax +Veff +0 +1.005390 +−1.18 × 10−6 +0 +1.005460 +−1.07 × 10−6 +0.020262 +1.005555 +0 +0.020861 +1.005640 +0 +0.020263 +1.005556 +2.0 × 10−10 +0.020862 +1.005640 +0.87 × 10−10 +Eqs. (20) we find the the appropriate range of energy as +2.9866135 × 10−3 = δEmin < δE < δEmax = 2.99 × 10−3 . +(25) +The particle mass for that can have m ≲ 1.96 × 10−3 for given value of charge q. +In Fig. 3 we show the impact of the magnetic field backraction on the radial profile of the effective potential. From +the Fig. 3, if the magnetic field is absence there exists parameter space available for test particle that could reach the +horizon and lead to overcharging of black hole, i.e. it could violate the WCCC (see, left panel). From the right panel +of Fig. 3, Veff tends upward as a consequence of the increase in the value of the magnetic field B. The charged particle +then cannot reach the horizon when Veff reaches the zero at which B = Bcr. This happens because the parameter +space required for overcharging turns out to be closed for particle to reach the horizon. Thus there is no parameter +space available for charged test particles for violating the WCCC. This is exactly what happens for the magnetized +black hole, the threshold value of the magnetic field could lead to restoring the WCCC. In Table III we show the +numerical values of the effective potential for charged test particle in a variety of possible cases. Note that the result +shown in Fig. 3 refers to a particular case of results presented in Table I. As shown in Fig. 3 one can easily notice +that Bcr corresponds to Veff = 0 and increases as one increases appropriate parameters of charged test particle; see +Table III. From the above analysis, overcharging test particle would not be able to approach horizon to enter the +black hole when the magnetic field reaches its minimum threshold value. Thus, the magnetic field can serve as the +cosmic censor, resulting in restoring the CCC in the weak form. +IV. +CONCLUSION +In this paper, we have studied the dynamics of overcharging the magnetized Reissner-Nordstr¨om black hole via +the charged test particle with appropriate geodesic parameters. It is possible to allow a transition to occur from a +Reissner-Nordstr¨om black hole to Reissner-Nordstr¨om naked singularity. In the astrophysical scenario, it is believed +that black holes are surrounded with an external magnetic field that can affect drastically on the charged particle +motion due to dominating Lorentz force. Thus, we have investigated the effect of the test magnetic field on the +dynamics of overcharging a black hole. +Interestingly we show that it is not possible for a charged particle with +the appropriate parameters to violate the WCCC in the case of sufficiently large values of the magnetic field. To +understand the effect of magnetic field in detail, we used the solution depicting the magnetized Reissner– Nordstr¨om +black hole that involves the effect of the magnetic field on the background geometry. We show that the magnetic field +restores the WCCC when it reaches its threshold value. +The main conclusions of investigation performed are summarized as follows: +• It is well known that test magnetic field surrounding black hole could give a dominating effect to the motion of +charged test particles due to the Lorentz force. It turns out that a test magnetic field would serve as a cosmic +censor, thus being impossible for particles to enter the black hole [14]. However, the situation is radically different +for a black hole immersed in an external test magnetic field in contrast to the exact solution representing the +magnetized black hole containing the backreaction of the magnetic field on the background geometry. Thus, the + +9 +magnetized black hole solution [48] allows to consider the backreaction of the magnetic field both on background +geometry and the charged particle motion as well. In order to understand the behavior of the magnetic field, the +process of overcharging a near extremal magnetized Reissner-Nordstr¨om black hole [48] with a charged particle +is studied. +• We have found that it is also possible for a charged particle to overcharge the magnetized black hole for sufficiently +small values (in contrast to its critical value) of the magnetic field. However, it is intriguing that overcharging +is controlled by the magnetic field. The magnetic field would therefore restore the cosmic censorship conjecture. +This happens because magnetic field would not allow charged particle to reach the black hole horizon. With +this we have shown that the same is true for backreaction of the magnetic field – it would act as cosmic censor. +Acknowledgments +S.S. and B.A. wish to acknowledge the support from Research Grant No. F-FA-2021-432 of the Uzbekistan Ministry +for Innovative Development and from the Abdus Salam International Centre for Theoretical Physics under the Grant +No. OEA-NT-01. +Data Availability Statement +This manuscript has no associated data. +[1] R. Penrose, Phys. Rev. Lett. 14, 57 (1965). +[2] S. W. Hawking and R. Penrose, Proc R. Soc. Lond. A 314, 529 (1970). +[3] R. Penrose, Riv. Nuovo Cimento 1, 252 (1969). +[4] B. P. Abbott and et al. (Virgo and LIGO Scientific Collaborations), Phys. Rev. Lett. 116, 061102 (2016), arXiv:1602.03837 +[gr-qc] . +[5] B. P. Abbott and et al. (Virgo and LIGO Scientific Collaborations), Phys. Rev. Lett. 116, 241102 (2016), arXiv:1602.03840 +[gr-qc] . +[6] K. Akiyama and et al. (Event Horizon Telescope Collaboration), Astrophys. 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Freeman, San Francisco, 1973). + diff --git a/n9FAT4oBgHgl3EQfdR2i/content/tmp_files/load_file.txt b/n9FAT4oBgHgl3EQfdR2i/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..c781852a263f52a86a6b098b5fb5148f6e88e524 --- /dev/null +++ b/n9FAT4oBgHgl3EQfdR2i/content/tmp_files/load_file.txt @@ -0,0 +1,973 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf,len=972 +page_content='Overcharging process around a magnetized black hole: Can the backreaction effect of magnetic field restore cosmic censorship conjecture?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Sanjar Shaymatov1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' ∗ and Bobomurat Ahmedov6,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' † 1Institute of Fundamental and Applied Research,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' National Research University TIIAME,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Kori Niyoziy 39,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Tashkent 100000,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Uzbekistan 2Akfa University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Milliy Bog Street 264,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Tashkent 111221,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Uzbekistan 3National University of Uzbekistan,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Tashkent 100174,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Uzbekistan 4Tashkent State Technical University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Tashkent 100095,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Uzbekistan 5Samarkand State University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' University Avenue 15,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Samarkand 140104,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Uzbekistan 6Ulugh Beg Astronomical Institute,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Astronomicheskaya 33,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Tashkent 100052,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Uzbekistan It is well known that the electrically charged Reissner-Nordstr¨om black hole could be overcharged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Here, we investigate the process of overcharging of a magnetized Reissner-Nordstr¨om black hole that includes effect of the magnetic field generated by own magnetic charge of source on the background geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' It is found that magnetic field prevents a transition to occur from black hole to naked singularity, thus overcharging cannot be attained which happens due to the fact that the magnetic field reaches its threshold value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' It turns out that beyond threshold value the magnetic field can exert large Lorentz force on particles and dominate over the gravitational force, allowing charged particles not to fall into the black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' One may conclude, there occurs no evidence for violation of cosmic censorship conjecture for a magnetized Reissner-Nordstr¨om black hole beyond threshold value of the magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' PACS numbers: I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' INTRODUCTION In general relativity (GR) the singularity theorems was first proposed by Penrose in 1965 in pioneering paper [1], implying that the singularities likely occur in case matter obeys certain energy conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Later, this theorem was extended to investigate the conditions as to the emergence of singularities in GR, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' called Penrose-Hawking theo- rem [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' The occurrence of singularities is a breakdown of Einstein’s theory because of their geodesic incompleteness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Irrespective of the fact that the Penrose-Hawking theorem has given the evidence in favour of the existence of singu- larities in GR, it did not shed light on the properties of the singularities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Thus, the cosmic censorship hypothesis in the weak form was proposed by Penrose [3] in 1969 in order for the Einstein gravity to keep valid, thus hiding the singularity from being seen for outside observers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' The validity of the weak cosmic censorship conjecture (WCCC) would not make the singularities possible to observe the final state of a sufficiently compact massive object as a result of gravitational collapse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Consequently, black holes are very intriguing objects as a generic solution of the field equations of GR as well as with their remarkable geometric nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' It is worth noting here that recent observational studies of gravitational wave astronomy [4, 5] and supermassive black hole that exists at the center of the elliptical galaxy Messier 87 (M87) through imaging by the Event Horizon Telescope (EHT) and BlackHoleCam [6, 7] have provided solid and trustful information in strong gravity regime that verifies the existence of black holes in nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' These gravitational wave and sub-millimeter radiowave observations (together with infrared one around Sgr A* at the center of our galaxy) provide strong and very potent tests to understand deeply the unknown aspects of black holes, yet there still exist open questions associated with the occurrence of physical singularity which marks the limit of classical Einstein’s theory applicability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' In this regard, WCCC can be considered as the main tool in testing GR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Wald first proposed the formulation of the validity of the WCCC to destroy the black hole horizon by test particles [8] and it was shown that the WCCC can not be violated for extremal black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Later, such a process was extended by somewhat different prospective, according to which it is not possible for test particle with appropriate parameters to reach the black hole horizon as there is no parameter space [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' However, Hubeny addressed this issue somewhat differently [10], accordingly showing the possibility of turning a nearly extremal black hole into a naked singularity via charged test particles with appropriate parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' The above process was extended to the rotating black holes, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' it was shown that Kerr/Kerr-Newman black hole could be overspun/overcharged in case when a falling in particle ∗Electronic address: sanjar@astrin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='uz †Electronic address: ahmedov@astrin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='uz arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='08569v1 [gr-qc] 20 Jan 2023 2 adds enough angular momentum/charge to the black hole’s angular momentum/charge [11, 12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Numerous papers have since been devoted to the study of testing the WCCC in this context in various gravity models [see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 13–24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Later on, it was shown that the WCCC could be held if and only if self-force effects are included [25–31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' The above analysis was also extended to the variety of situations, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' for BTZ black holes [32], black hole with charged scalar field [33], black hole dynamics [34] and higher dimensions [35, 36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Recently, the above thought experiment has been developed by Sorce and Wald [37, 38], thus referring to the new gedanken experiment including the nonlinear particle accretion process always favoring the validity of the WCCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Following Sorce and Wald there has been a extensive body of research work [39–47] addressing the question of overcharging/spinning of black hole under the nonlinear order perturbations for D ≥ 4 dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' From astrophysical point of view, it is believed that a test magnetic field may exist in the environment surrounding the black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' With this in view, the magnetic field could play a decisive role in altering the geodesics of charged test particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' There was investigation that explores the effect of the external magnetic field on the particle geodesics to test whether it could violate the WCCC [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' It was shown that the magnetic field can serve as a cosmic censorship conjecture beyond its certain critical value, thus affecting on the particle geodesics drastically and preventing particles from reaching the black hole horizon as that of large Lorentz force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' It happens because the magnetic field backreaction on the background geometry must be slightly stronger as compared to the small backreaction induced by the test particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' This was true for the external magnetic field, however, what happens provided that the charged black hole is magnetized one, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' does it still act as a cosmic censorship conjecture?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' To settle this question we use the magnetized black hole solution that includes the magnetic field in the background spacetime [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Note that the inclusion of the magnetic field backreaction on the background spacetime is impossible due to the fact that there is no exact solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' However, the solution describing the magnetized Reissner-Nordstr¨om solution has recently been derived in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' In this paper, following [48] we investigate the magnetized black hole to understand more deeply the backreaction effect of the magnetic field on the validity of the WCCC, thus leading to reach the definite conclusion for the magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Interestingly we show that the magnetic field could still serve as a cosmic censor, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' the black hole can never be overcharged beyond the critical value of the magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' In realistic astrophysical scenario, it is particularly important to understand completely the impact of the existing fields on the particle geodesics in the environment surrounding the black holes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Of them the magnetic field is increasingly important to explain rich astrophysical phenomena around black holes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' For example, the magnetic field can influence the motion of charged particles drastically and can alter the particle geodesics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' There have been numerous works [49–65] addressing the impact of the magnetic field on the particle motion in a variety of situations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' The magnitude of the magnetic field B is gauged to be of order ≈ 108 G for stellar mass black holes and ≈ 104 G for supermassive black holes, respectively (see for example [66]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Also there is another way that can be considered to estimate its magnitude at the black hole horizon radius [67, 68], and it was later shown that the magnetic field is estimated to be between 200 G and 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='3 × 104 G at 1 Schwarzschild radius [69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Recent advances in infrared, optical, x-ray, and radio observational studies of binary black holes system V404 Cygni has provided that the magnitude of the magnetic field would be of 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='1 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='9G (see for example [70]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' II, we describe briefly the magnetized Reissner-Nordstr¨om black hole and charged particle motion which is followed by the main study of dynamics of overcharging of the magnetized Reissner-Nordstr¨om black hole in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' We end up with a conclusion in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Throughout the manuscript we use a geometric system of units in which G = c = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' MAGNETIZED REISSNER-NORDSTR¨OM BLACK HOLE AND PARTICLE MOTION The spacetime metric describing a magnetized charged Reissner- Nordstr¨om black hole in Schwarzschild coordinates (t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' θ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' φ) is given by [48] ds2 = H [−fdt2 + f −1 dr2 + r2dθ2] + H−1 r2 sin2 θ (dφ − ωdt)2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (1) where f = 1 − 2M r + Q2 r2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (2) ω = −2QB r + 1 2QB3 r(1 + f cos2 θ) ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (3) H = 1 + 1 2B2(r2 sin2 θ + 3Q2 cos2 θ) + 1 16B4(r2 sin2 θ + Q2 cos2 θ)2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (4) with M and Q which,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' respectively,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' refer to the black hole’s total mass and charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Note that the parameter B is related to the magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' With Q and B given for the magnetized charged black hole vector potential for the 3 electromagnetic field is written as follows A = Atdt + Aφ(dφ − ωdt) , (5) with the following electromagnetic vector potential components At = −Q r + 3 4QB2r (1 + f cos2 θ) , Aφ = 2 B − H−1� 2 B + 1 2B(r2 sin2 θ + 3Q2 cos2 θ) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (6) Further we focus on a charged particle’s motion around magnetized Reissner-Nordstr¨om black hole, for which the Hamiltonian of the system is defined by [71] H = 1 2gµν (πµ − qAµ) (πν − qAν) , (7) with πµ and Aµ referred to as a charged particle’s canonical momentum and the four-vector potential of the electro- magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' In the Hamiltonian, the charged particle’s four-momentum is given as pµ = gµν (πν − qAν) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (8) Hence, one can then write the equations of motion for the charged particle as dxα dλ = ∂H ∂πα , (9) dπα dλ = − ∂H ∂xα , (10) with λ = τ/m being the affine parameter associated with the proper time τ for timelike geodesics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' From Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (9) and (10) it is then straightforward to obtain the equations of motion for the charged particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' According to the symmetry property of the magnetized black hole spacetime admitting two Killing vectors, ξα (t) = (∂/∂t)α and ξα (φ) = (∂/∂φ)α being responsible for stationarity and axisymmetry, the energy and angular momentum of the charged particle are determined by −δE = −gµν(ξt)µπν = gttπt + gtφπφ + qAt, (11) δJ = −gµν(ξφ)µπν = gφtπt + gφφπφ + qAφ, (12) where πν is the four velocity defined by πν = dxν dτ with the proper time τ for timelike geodesics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Here we note that the system represents four independent constants of motion of which we have specified three, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=', δE, δJ and m2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' The other constant is related to the latitudinal particle motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' However, in the following, we will restrict ourselves to the equatorial motion, setting θ = π/2 and therefore ignoring the fourth constant of motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Taking into account Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (9-12) with the normalization condition gµνpµpν = −m2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' we write the radial part of the equation of motion for massive particles in the following form 1 2 ˙r2 + Veff (r) = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (13) where the effective potential for radial motion of charged particle,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Veff (r),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' is given by [56] Veff (r) = � fH−1 − Hf −1 m2r2 (ω2r2 − fH2) � q2 �ω2r2 H − fH � � 2 B − H−1 � 2 B + 1 2Br2 ��2 + 2 qωr2 H � 2 B − H−1 � 2 B + 1 2Br2 �� � δE − qQ r + 3 4qQB2r � + r2 H � δE − qQ r + 3 4qQB2r �2�� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (14) In the limiting case when magnetic field vanishes B → 0 one can recover Hubeny’s result for effective potential [10] Veff(r) = M r � Q M δEq m2 − 1 � − 1 2 �δE2 m2 − 1 � − Q2 2r2 � q2 m2 − 1 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (15) 4 III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' DYNAMICS OF OVERCHARGING OF THE MAGNETIZED REISSNER-NORDSTR¨OM BLACK HOLE Here, we test the validity of the WCCC in the case of charged particles interacting with the magnetized Reissner- Nordstr¨om black hole by applying the gedanken experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' This is what we wish to address in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Overcharging of Reissner-Nordstr¨om black hole Now we first consider the Reissner-Nordstr¨om black hole immersed in the external magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Here the main purpose is to ensure that whether the charged particle with appropriate parameters can reach the black hole horizon in the presence of external magnetic field, thereby violating the WCCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Note that the horizon radius for Reissner- Nordstr¨om black hole is given by r± = M + � M 2 − Q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' In this regard, the horizon stability must be hold provided that M > Q is satisfied, whereas for M < Q the horizon no longer exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' To reach the latter the radially falling charged particle should carry mass m and charge q to the Reissner-Nordstr¨om black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Here, it is worth noting that we suppose δE ≪ M and q ≪ Q for test particle approximation to hold good so that the radially falling charged particle transfers the mass and charge to black hole’s mass and charge, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' With the mass and charge absorbed, the final state of the black hole parameters is given by M + δE and Q + q, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Thereafter, the black hole can be overcharged when the condition below is satisfied only: ( ¯ M + δE)2 < ( ¯Q + q)2 , (16) for the lower and an upper bounds on the energy of the charged particle qQ r2 + = δEmin < δE , (17) δE < δEmax = ¯Q + q − ¯ M .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (18) Note that the black hole starts out very close to extremal one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' It is certain that the above Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (17) and (18) cannot be satisfied simultaneously for the extremal case, Q = M = r+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' The effective potential for radial motion of the radially falling charged particle can be given in terms of the energy, charge and mass of the charged particle, as given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' This effective potential has turning points at which Veff(r) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' However, it also has maximum at rmax = � Q � q2 m2 − 1 � �δEq m2 − M Q �−1�1/2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (19) For this maximum one must choose reasonable parameters of charged test particle so that Veff(r) < 0, thus allowing the particle to cross through the horizon swimmingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' For this purpose we select the appropriate parameters of the charged particle to satisfy the condition (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (16)) and explore Veff(r) numerically [10] Q = 1 − 2ϵ2 q = α′ϵ with α′ > 1 δE = α′ϵ − 2β′ϵ2 with 1 < β′ < α′ m = γ′ϵ with γ′ < � α′2 − β′2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (20) with suitable choice of parameters α′, β′, and γ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' In the above equation, ϵ is regarded as a small parameter, so that it represents a near-extremality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' We note that parameters α′, β′, and γ′ have no particular meanings, but are used to satisfy the above-mentioned condition;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' ( ¯ M + δE)2 < ( ¯Q + q)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' To ensure this we explore it numerically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' For this thought experiment, we can choose Q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='99999 for the given value ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='0022 by setting M = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' One can however choose even smaller values of ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' So for the given background spacetime with parameters M = 1 and Q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='99999 as stated in [10], we can then select the appropriate parameters of the charged particle by setting α′ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='33902, β′ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='0301, and γ′ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='80505.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' In doing so, we suppose that the particle of mass m = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='8 × 10−3 has charge q = 3 × 10−3, and falls past the horizon with energy δE = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='9897 × 10−3, thus satisfying the condition ( ¯ M + δE) − ( ¯Q + q) < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Let us then consider the charged particle thrown inward the black hole radially with δJ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' For charged particles to enter the black hole without any restriction Veff(r) must be negative or ˙r2 must be positive everywhere outside the 5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='00266 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='00268 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='00270 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='00272 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='00274 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='475 � 10�6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='48 � 10�6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='485 � 10�6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='49 � 10�6 r r� 2 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 1: Radial dependence of the motion of charged particle falling into the near-extremal Reissner-Nordstr¨om black hole for given values of charge q = 3 × 10−3, energy δE = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='9897 × 10−3, and mass m = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='8 × 10−3 that satisfy the test particle approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' horizon, thereby converting a near extremality to over extremality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' For this, we analyse the radial motion of charged test particle in terms of the effective potential, ˙r2 = −2Veff(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 1, we show the radial motion of charged test particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' As seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 1, the charged particle with appropriate parameters could fall across the horizon, thus violating the WCCC – so-called ”over extremality” can be reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' TABLE I: The values of rmax outside the horizon and effective potential are tabulated for different values of energy and mass of test particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' The charge parameter is considered here as q = 3 × 10−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' m δE rmax Veff 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='9 × 10−3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='9874 × 10−3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='00231 −5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='23 × 10−7 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='4 × 10−3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='9884 × 10−3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='00248 −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='87 × 10−7 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='8 × 10−3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='9897 × 10−3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='00269 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='47 × 10−6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='85 × 10−3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='9899 × 10−3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='00273 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='60 × 10−6 In Table I we show the maximum values of the effective potential in a variety of test particle parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' For these parameters, we explore the effective potential numerically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' As can be seen from Table I, Veff < 0 is always satisfied for chosen values, thus allowing test particle to fall across the horizon and violating the WCCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' This result also reflects the behavior of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 1 for a particular case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Effect of external magnetic field on dynamics of overcharging of Reissner-Nordstr¨om black hole Now we consider the Reissner-Nordstr¨om black hole immersed in an external magnetic field to understand more deeply the impact of the external magnetic field on the dynamics of overcharging process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' The magnetic field can alter the geodesics of charged particles, and it can also influence the process of overcharging of the black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Following to Wald [8] one can study the magnetic field in vicinity of the black hole and assume that the magnetic field is asymptotically uniform with strength B at infinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' The non-vanishing components of potential Aα of the electromagnetic field around the Reissner-Nordstr¨om black hole in the presence of external magnetic field reads as At = −Q r , Ar = Aθ = 0, Aϕ = B 2 r2 sin2 θ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (21) We further analyze effective potential for the radial motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (11) and (12) and setting θ = π/2 the effective potential describing the radial motion for the charged particle around the Reissner-Nordstr¨om black hole 6 Β = 0 Β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='5 Β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='7198 Β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='002 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='003 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='004 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='006 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='007 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='008 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='009 �0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='000025 �0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='00002 �0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='000015 �0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='00001 �5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' �10�6 0 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' �10�6 r Veff FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 2: Radial profile of the effective potential for the radial motion of the charged particles around the Reissner-Nordstr¨om black hole immersed in an external uniform magnetic field for different values of magnetic parameter β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Note that we select q = 3 × 10−3 and m = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='8 × 10−3 for test particle’s charge and mass, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' immersed in an external magnetic field can be written in the following form Veff(r) = M r � Q M δEq m2 − 1 � − 1 2 �δE2 m2 − 1 � − Q2 2r2 � q2 m2 − 1 � + � 1 − 2M r + Q2 r2 � β2r2 8M 2 , (22) with the magnetic parameter β = qBM/m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' In the limit when β → 0, one can easily recover Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (15), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' the result presented in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' We now analyze the impact of the external magnetic field on the radial profile of the effective potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' By imposing the following conditions ∂Veff(r) ∂r = 0 and Veff(rmax) = 0 , (23) one can easily find the critical value for the magnetic field at which it prevents the charged particles from falling into the black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Taking this in consideration, with the values chosen for the charged test particle, q = 3 × 10−3 and m = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='8 × 10−3, one can get the critical value for the magnetic parameter β given by βcr ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='7198 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (24) To analyze the impact of the magnetic parameter β on the dynamics of overcharging of the black hole we present the radial profile of the the effective potential in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 2, in the limit β → 0 we have the effective potential that is always negative for the charged particle with appropriate parameters, as presented in Table I and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' However, the shape of the effective potential moves upward as a consequence of the increase in the value of the magnetic parameter β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' As seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 2, the height of maximum of the effective potential tends to zero when the magnetic parameter approaches its critical value βcr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Then the maximum value of the effective potential crosses zero and becomes positive, thereby preventing particles from entering the black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' It turns out that the external magnetic field would act as a cosmic censorship beyond its threshold value;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Table II also reflects the behavior of the obtained results in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' From the above analysis it turns out that the Reissner-Nordstr¨om black hole could be overcharged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' This result is however overturned when the external magnetic field around the black hole is taken into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' That is, the magnetic field can restore the WCCC beyond when it reaches its critical value (for example, see also, [14]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' However, we have yet to reach the definite conclusion whether the magnetic field still act as a cosmic censor or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Thus, we need to consider the magnetized black hole solution that includes the magnetic field in the background spacetime [48] as our main purpose is to study the backreaction effect of the magnetic field on the validity of the WCCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' This is what we plan to address in the next.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 7 B = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='002 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='003 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='004 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='006 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='007 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='008 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='009 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='000025 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='000020 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='000015 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='000010 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' × 10-6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='000000 r Veff B = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='020262 B = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='020264 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='00553 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='00554 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='00555 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='00556 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='00557 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='00558 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' × 10-10 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' × 10-10 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' × 10-10 0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' × 10-10 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' × 10-10 r Veff FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 3: Radial profile of the effective potential for the charged particle around the magnetized Reissner-Nordstr¨om black hole in the case of fixed parameters δE = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='9897 × 10−3, q = 3 × 10−3 and m = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='8 × 10−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Left panel: Veff is plotted in the case of vanishing magnetic field, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' B = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Right panel: Veff is plotted for different values of magnetic field B, red line shows the case when B = Bcr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Note that in the case of B > Bcr the magnetic field can restore the WCCC as the maximum height of Veff crosses horizontal zero line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' TABLE II: The values of rmax outside the horizon and effective potential Veff(rmax) for different values of the magnetic parameter β for the fixed q = 3 × 10−3 and m = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='8 × 10−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' δE = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='9897 × 10−3 β rmax Veff 0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005389149 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='18000 × 10−6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='01 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005389226 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='17937 × 10−6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='05 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005391085 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='17503 × 10−6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005396903 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='16139 × 10−6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005420304 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='10587 × 10−6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005459767 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='00993 × 10−6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005516007 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='86830 × 10−6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005590070 −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='73278 × 10−7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005683387 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='14325 × 10−7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='7 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005797845 −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='78888 × 10−8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='7198 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005823285 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='00000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005935891 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='54872 × 10−7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='006100678 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='90611 × 10−6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='006296273 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='60574 × 10−6 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' The effect of magnetic field on dynamics of overcharging of magnetized Reissner-Nordstr¨om black hole We have shown that the external magnetic field can potentially serve as the cosmic censor beyond its critical value, preventing particle from entering the Reissner-Nordstr¨om black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Here, we analyze the impact of the magnetic field backreaction in the process of overcharging of a magnetized Reissner-Nordstr¨om black hole, as described by the metric Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' We further consider a radially falling charged particle, δJ = 0, that can violate the WCCC in the absence of magnetic field in the environment of the black hole [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' In doing so, we try to understand whether the backreaction effect of the magnetic field can still serve as the cosmic censor, thus stopping particles with appropriate parameters from entering the black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' As was mentioned above we assume that a charged particle that has energy δE ≪ M and charge q ≪ Q remains valid for the test particle approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Then, it adds extra mass and charge to black hole’s mass and charge, respectively, when it gets absorbed by the black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' A so-called ”Overcharged” can be realized if and only if the conditions given by Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (16-18) are hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' We then analyze the effective potential so as to understand more deeply the effect of the magnetic field backreaction on the process of overcharging of a black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' To ensure that the particle enters the black hole without encountering any turning point the effective potential (14) has to be always negative everywhere outside the horizon, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Veff < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' For that we assume M = 1 and Q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='99999 as stated previously and focus on the charged particle that has q = 3 × 10−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Using suitable choice of parameters α′, β′, and γ′ given by 8 TABLE III: The values of rmax outside the horizon and effective potential are tabulated in the case of different values of δE, m and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Note that the charge of test particle is taken to be q = 3 × 10−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' δE = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='9874 × 10−3 m = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='9 × 10−3 δE = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='9884 × 10−3 m = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='4 × 10−3 B rmax Veff B rmax Veff 0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='004630 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='2 × 10−6 0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='004960 −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='17 × 10−6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='013841 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='004681 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='016084 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005045 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='013843 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='004685 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='2 × 10−10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='016085 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005050 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='2 × 10−10 δE = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='9897 × 10−3 m = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='8 × 10−3 δE = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='9899 × 10−3 m = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='85 × 10−3 B rmax Veff B rmax Veff 0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005390 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='18 × 10−6 0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005460 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='07 × 10−6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='020262 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005555 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='020861 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005640 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='020263 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005556 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='0 × 10−10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='020862 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='005640 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='87 × 10−10 Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (20) we find the the appropriate range of energy as 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='9866135 × 10−3 = δEmin < δE < δEmax = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='99 × 10−3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' (25) The particle mass for that can have m ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='96 × 10−3 for given value of charge q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 3 we show the impact of the magnetic field backraction on the radial profile of the effective potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' From the Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 3, if the magnetic field is absence there exists parameter space available for test particle that could reach the horizon and lead to overcharging of black hole, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' it could violate the WCCC (see, left panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' From the right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 3, Veff tends upward as a consequence of the increase in the value of the magnetic field B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' The charged particle then cannot reach the horizon when Veff reaches the zero at which B = Bcr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' This happens because the parameter space required for overcharging turns out to be closed for particle to reach the horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Thus there is no parameter space available for charged test particles for violating the WCCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' This is exactly what happens for the magnetized black hole, the threshold value of the magnetic field could lead to restoring the WCCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' In Table III we show the numerical values of the effective potential for charged test particle in a variety of possible cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Note that the result shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 3 refers to a particular case of results presented in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 3 one can easily notice that Bcr corresponds to Veff = 0 and increases as one increases appropriate parameters of charged test particle;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' see Table III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' From the above analysis, overcharging test particle would not be able to approach horizon to enter the black hole when the magnetic field reaches its minimum threshold value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Thus, the magnetic field can serve as the cosmic censor, resulting in restoring the CCC in the weak form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' CONCLUSION In this paper, we have studied the dynamics of overcharging the magnetized Reissner-Nordstr¨om black hole via the charged test particle with appropriate geodesic parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' It is possible to allow a transition to occur from a Reissner-Nordstr¨om black hole to Reissner-Nordstr¨om naked singularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' In the astrophysical scenario, it is believed that black holes are surrounded with an external magnetic field that can affect drastically on the charged particle motion due to dominating Lorentz force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Thus, we have investigated the effect of the test magnetic field on the dynamics of overcharging a black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Interestingly we show that it is not possible for a charged particle with the appropriate parameters to violate the WCCC in the case of sufficiently large values of the magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' To understand the effect of magnetic field in detail, we used the solution depicting the magnetized Reissner– Nordstr¨om black hole that involves the effect of the magnetic field on the background geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' We show that the magnetic field restores the WCCC when it reaches its threshold value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' The main conclusions of investigation performed are summarized as follows: It is well known that test magnetic field surrounding black hole could give a dominating effect to the motion of charged test particles due to the Lorentz force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' It turns out that a test magnetic field would serve as a cosmic censor, thus being impossible for particles to enter the black hole [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' However, the situation is radically different for a black hole immersed in an external test magnetic field in contrast to the exact solution representing the magnetized black hole containing the backreaction of the magnetic field on the background geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Thus, the 9 magnetized black hole solution [48] allows to consider the backreaction of the magnetic field both on background geometry and the charged particle motion as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' In order to understand the behavior of the magnetic field, the process of overcharging a near extremal magnetized Reissner-Nordstr¨om black hole [48] with a charged particle is studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' We have found that it is also possible for a charged particle to overcharge the magnetized black hole for sufficiently small values (in contrast to its critical value) of the magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' However, it is intriguing that overcharging is controlled by the magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' The magnetic field would therefore restore the cosmic censorship conjecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' This happens because magnetic field would not allow charged particle to reach the black hole horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' With this we have shown that the same is true for backreaction of the magnetic field – it would act as cosmic censor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Acknowledgments S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' wish to acknowledge the support from Research Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' F-FA-2021-432 of the Uzbekistan Ministry for Innovative Development and from the Abdus Salam International Centre for Theoretical Physics under the Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' OEA-NT-01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Data Availability Statement This manuscript has no associated data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' [1] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Penrose, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' 14, 57 (1965).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' [2] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Hawking and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Penrose, Proc R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Soc.' 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and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Ahmedov, Astrophys Space Sci 350, 413 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' [52] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Shaymatov, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Ahmedov, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Stuchl´ık, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Abdujabbarov, International Journal of Modern Physics D 27, 1850088 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' [53] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Dadhich, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Tursunov, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Ahmedov, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Stuchl´ık, Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} 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Jusufi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Lin, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Mann, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' D 99, 044015 (2019), arXiv:1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='04103 [gr-qc] .' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' C 80, 296 (2020), arXiv:2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content='01591 [gr-qc] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' [60] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Jusufi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Jamil, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/n9FAT4oBgHgl3EQfdR2i/content/2301.08569v1.pdf'} +page_content=' Salucci, T.' metadata={'source': 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sha256:7f47f01dc842957cacac3a30249e2a0c39b8268d2a0deb0eb3cac25d5bd16158 +size 3211309 diff --git a/q9AzT4oBgHgl3EQfcPzN/vector_store/index.pkl b/q9AzT4oBgHgl3EQfcPzN/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..776576b1e7c3971e1c91780da68c23ced4d3385c --- /dev/null +++ b/q9AzT4oBgHgl3EQfcPzN/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:cb09579ce7261d0b1dff98683544871a6ab8bc143d5f9d2b982c81bd5894e399 +size 114046 diff --git a/q9E1T4oBgHgl3EQf2wUi/content/tmp_files/2301.03481v1.pdf.txt b/q9E1T4oBgHgl3EQf2wUi/content/tmp_files/2301.03481v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..d9f152b8cb6f6bff9d7b4ce7a272722e3c98ef62 --- /dev/null +++ b/q9E1T4oBgHgl3EQf2wUi/content/tmp_files/2301.03481v1.pdf.txt @@ -0,0 +1,1895 @@ +arXiv:2301.03481v1 [math.PR] 9 Jan 2023 +On the KPZ scaling and the KPZ fixed point for TASEP +Yuta Arai ∗ +Abstract +We consider all totally asymmetric simple exclusion processes (TASEPs) whose transition +probabilities are given in the Sch¨utz-type formulas and which jump with homogeneous rates. We +show that the multi-point distribution of particle positions and the coefficient of KPZ scaling +are described using the probability generating function of the distribution followed when the +rightmost particle jumps. +For all TASEPs satisfying certain assumptions, We also prove the +pointwise convergence of the kernels appearing in the joint distribution of particle positions to +those appearing in the KPZ fixed point formula. Our result generalizes the result of Matetski, +Quastel, and Remenik [16]. +1 +Introduction +The KPZ universal class was introduced in [15] to describe the universality of the growth model of +an interface. The totally asymmetric simple exclusion process (TASEP) is one of the most typical +interacting stochastic particle systems. It can be interpreted as a stochastic interface growth model +belonging to the KPZ universal class. Furthermore, the TASEP is known as an important model for +studying the KPZ universality because its distribution function can be calculated for some quantities. +Research on the KPZ universality of TASEP has been actively conducted since around 2000. First, +in the case of the step initial condition, by considering the relationship stochastically growing Young +diagram and TASEP, Johansson [13] has derived the one-point limit distribution of the particle current +by using the RSK correspondence. In this case, the limiting distribution turned out to be the GUE +Tracy-Widom distribution from random matrix theory [28]. As a related work, in the case of the flat +polynuclear growth (PNG) model, the one-point limit distribution of the height distribution has been +obtained in [19]. In addition, for the last passage percolation, similar results have been derived in +[2, 3]. The results of [2, 3, 19] include the result of the one-point limit distribution of particle current +for the periodic initial condition in the language of TASEP. It turned out that the limiting distribution +is the GOE Tracy-Widom distribution from random matrix theory [29]. +The above are the results for one-point fluctuations, but many results for multi-point fluctuations +have also been given. For the case corresponding to the step initial condition, the Fredholm deter- +minant formula for the limiting multi-point distribution has been obtained in the PNG model with +different settings [14, 20]. +In this case, the limiting process characterized by the multi-point dis- +tribution is the Airy2 process. On the other hand, for the periodic initial condition, the Fredholm +determinant formula for the limiting multi-point distribution has been derived in the continuous time +TASEP [9, 25] by using the result of the transition probability in TASEP [26]. In this case, the lim- +iting process characterized by the multi-point distribution is called the Airy1 process. The technique +in [9, 25] has been applied to various models. Therefore, the limit distribution of the multi-point +distribution has been obtained for the TASEP and PNG models with different settings [6, 8, 10]. +The case of generalized initial conditions for particle positions has also been studied. Matetski, +Quastel, and Remenik [16] first extended the method of [9, 25] to get the limit distribution of multi- +point distribution in the continuous time TASEP for arbitrary initial conditions: In [9, 25], the +∗Platform for Arts and Science, Chiba University of Commerce, Ichikawa-shi 263-8522, Japan. +Email: +yu- +taarai@cuc.ac.jp +1 + +correlation kernel for the Fredholm determinant was expressed in terms of the biorthogonal functions +Ψn +k(x) and Φn +k(x). However, there was the problem that Φn +k(x) does not have an explicit representation +while Ψn +k(x) does. +Therefore, it was not clear how to take the KPZ scaling limit of this kernel. +Matetski, Quastel, and Remenik [16] solved this problem. They represent the function Φn +k(x) by the +hitting probability of the geometric random walk. From Donsker’s invariance principle, the hitting +time of the geometric random walk converges to the hitting time of the Brownian motion when the +time-space limit is taken, so this representation of Φn +k(x) allows us to take the KPZ scaling limit. Based +on this method, they have derived the limit distribution of multi-point distribution in the continuous +time TASEP for arbitrary initial conditions. +The limiting process with this limit distribution of +the multi-point distribution is known as the KPZ fixed point. The KPZ fixed point has also been +obtained in the one-sided reflected Brownian motion [18] and two variations of discrete time TASEP +with geometric and Bernoulli jumps [1] by using the method of [16]. There have also been various +other interesting progresses on the KPZ fixed point for example in [11, 22, 24]. +There have been studies to get the distribution of particle positions in the discrete time TASEP +using the result of [12]: Dieker and Warren [12] have derived the transitive kernels of the four processes +that correspond to the four variants of the discrete time TASEP by using the RSK correspondence. +Matetski and Remenik [17] have given the distribution of particle positions in the four variants of the +discrete time TASEP from the above result and the method of [16]. They have also obtained a formula +for the distribution of particle positions that can be applied for example to continuous time TASEP +and discrete time TASEP with sequential update. In [5], they have generalized the method of [12] so +that it can be applied to the discrete time Bernoulli TASEP with particle- and time-inhomogeneous +rates. Combining the above method with the method of [16], they gave the distribution of particle +positions in the discrete time Bernoulli TASEP with particle- and time-inhomogeneous rates. However, +in [5, 17], the formula for obtaining the KPZ fixed point that can be uniformly applied to TASEP +with different settings was not derived. +In this paper, we consider all TASEPs whose transition probabilities are given in the Sch¨utz-type +formulas and which jump with homogeneous rates. Then we show that the distribution of particle +positions can be described by using the probability generating function of the distribution followed +when the rightmost particle jumps. We remark that this method using the probability generating +function is quite different from the method of [5, 17]. +We also state that the coefficient of KPZ +scaling used to get the KPZ fixed point can be expressed by the probability generating function of +the distribution followed when the rightmost particle jumps. Furthermore, we show the property of +the coefficient of KPZ scaling. Finally, by generalizing the method of [16], we prove the pointwise +convergence of the kernels appearing in the joint distribution of particle positions to those appearing +in the KPZ fixed point formula for all TASEPs that satisfy certain assumptions, for example, the +continuous time TASEP, the discrete time Bernoulli TASEP with sequential update, and the discrete +time geometric TASEP with parallel update. It implies that our method can adapt to multiple models, +not to only one model. Note that our method derives the KPZ fixed point even in the case of the +continuous time TASEP with jump rate β ∈ (0, ∞) where the KPZ fixed point has not been given +(see Example 2.2 and Appendix A). +The paper is organized as follows: In Section 2, we state the TASEPs whose transition probabilities +are given in the Sch¨utz-type formulas (see Assumption 2.1). +We also give our main result: the +Fredholm determinant formula for the TASEPs satisfying Assumption 2.1 (Theorem 2.8), the property +of the coefficient of KPZ scaling (Theorem 2.15), and the KPZ scaling limit in the TASEPs satisfying +Assumption 2.1 when Assumption 2.11, and Assumption 2.16 hold (Theorem 2.21). In Section 3, for +the TASEPs which satisfy Assumption 2.1, we show Theorem 2.8 after the transition probabilities +are represented by the probability generating function of the distribution followed when the rightmost +particle jumps. In Section 4, we prove Theorem 2.15. In Section 5, we give proofs of Theorem 2.21 and +Proposition 2.24. In Appendix A, we use our method to show that the KPZ fixed point is obtained +in the continuous time TASEP with jump rate β ∈ (0, ∞). The key to our proofs is the saddle point +analysis for the kernels by using the probability generating function of the distribution followed when +the rightmost particle jumps. +2 + +2 +Models and results +2.1 +Models +We consider the TASEPs on Z. Each particle independently and stochastically jumps to the right +only if the target site is empty and cannot move if the target site is occupied by other particles. The +above represents the exclusion rule. +We mainly focus on the position of each particle. We put t ∈ Z or t ∈ R according to the version. +Then we define Xt(i) ∈ Z as a position of the ith particle at time t. The dynamics of the TASEPs +preserve the order of the particles, that is, +· · · < Xt(i + 2) < Xt(i + 1) < Xt(i) < Xt(i − 1) < Xt(i − 2) < · · · +where the particles at ±∞ are playing no role in the dynamics when adding ±∞ into the state space. +Now we set +ΩN = {⃗x = (xN, xN−1, · · · , x1) ∈ ZN : xN < · · · < x2 < x1} +as the Weyl chamber, whose elements express the particle positions of the TASEPs. Also, we put +Fn(x, t) = (−1)n +2πi +� +Γ0,1 +dw(1 − w)−n +wx−n+1 M(t, w) +(2.1) +where Γ0,1 is any simple loop oriented anticlockwise which includes w = 0 and w = 1, and M(t, w) is +analytic on {w ∈ C : |w| < R} with the radius R ≥ 1. +In this paper, we deal with the TASEP which satisfies the following assumption, where we do not +consider the TASEP whose jump rate or jump probability changes depending on time. +Assumption 2.1. The transition probability from ⃗y ∈ ΩN to ⃗x ∈ ΩN is given by +P(Xt = ⃗x|X0 = ⃗y) = det[Fi−j(xN+1−i − yN+1−j, t)]1≤i,j≤N, +(2.2) +where Xt = (Xt(1), Xt(2), . . . , Xt(N)) are the locations of a system of particles. +Assumption 2.1 is fulfilled in many TASEPs illustrated in the following example. +Example 2.2. Here we introduce three typical examples. +• The continuous time TASEP with jump rate β +The continuous time TASEP was introduced in [27] as a mathematical model. The process Xt, +t ∈ R≥0 evolves as follows: each particle independently attempts to jump to the right neighboring +site at rate β ∈ (0, ∞) provided this site is empty. The continuous time TASEP is a Markov +process with the generator L defined as follows: We put η = {η(x) : x ∈ Z} ∈ {0, 1}Z as a particle +configuration where η(x) = 1 means the site x is occupied by a particle while η(x) = 0 means it +is empty. Then the generator L acting on cylinder functions f : {0, 1}Z → R is introduced by +(Lf)(η) = β +� +x∈Z +η(x)(1 − η(x + 1))(f(ηx,x+1) − f(η)) +where +η(x) = +� +1, +if the site is occupied by a particle, +0, +if the site x is empty, +and ηx,x+1 is the configuration η with the occupations at site x and x+1 have been interchanged, +that is, +ηx,x+1(y) = + + + + + +η(x + 1) +for y = x, +η(x) +for y = x + 1, +η(y) +otherwise. +3 + +The transition probability of Xt is given by [26] using Bethe ansatz: +P(Xt = ⃗x|X0 = ⃗y) = det[Fi−j(xN+1−i − yN+1−j, t)]1≤i,j≤N, +with +Fn(x, t) = (−1)n +2πi +� +Γ0,1 +dw(1 − w)−n +wx−n+1 eβt(w−1) +where Γ0,1 is any simple loop oriented anticlockwise which includes w = 0 and w = 1. It is clear +that this model satisfies Assumption 2.1 with the function +M(t, w) = eβt(w−1). +(2.3) +Note that when β ∈ (0, 1), this model can be interpreted as the continuous time version of the +discrete time Bernoulli TASEP introduced next. The KPZ fixed point has been derived in [16] +when β = 1, but our results show that the KPZ fixed point can also be obtained when β ∈ (0, ∞) +(see Appendix A). +• The discrete time Bernoulli TASEP with sequential update +The discrete time Bernoulli TASEP with sequential update on Z was studied previously in [7] as +a marginal of dynamics on Gelfand-Tsetlin patterns which preserve the class of Schur processes. +The evolution of the process Xt, t ∈ Z≥0 is given by the recursion relation +Xt+1(1) = Xt(1) + wt+1,1 +and +Xt+1(i) = min {Xt(i) + wt+1,i, Xt+1(i − 1) − 1} , +i = 2, 3, . . . , N +where wt,i are independent random variables following the Bernoulli distribution with parameter +p ∈ (0, 1). The transition probability of this model is given by [23]: +P(Xt = ⃗x|X0 = ⃗y) = det[Fi−j(xN+1−i − yN+1−j, t)]1≤i,j≤N, +with +Fn(x, t) = (−1)n +2πi +� +Γ0,1 +dw(1 − w)−n +wx−n+1 (1 + p(w − 1))t +where Γ0,1 is any simple loop oriented anticlockwise which includes w = 0 and w = 1. One can +readily see that this model satisfies Assumption 2.1 with the function +M(t, w) = (1 + p(w − 1))t. +• The discrete time geometric TASEP with parallel update +The discrete time geometric TASEP with parallel update on Z was studied previously in [30] as +a marginal of dynamics on Gelfand-Tsetlin patterns which preserve the class of Schur processes. +The evolution of the process Xt, t ∈ Z≥0 is given by the recursion relation +Xt+1(1) = Xt(1) + �wt+1,1 +and +Xt+1(i) = min {Xt(i) + �wt+1,i, Xt+1(i − 1) − 1} , +i = 2, 3, . . . , N +where �wt,i are independent random variables following the Geometric distribution with parameter +α ∈ (0, 1). The transition probability of this process is given by [1, 12, 17]: +P(Xt = ⃗x|X0 = ⃗y) = det[Fi−j(xN+1−i − yN+1−j, t)]1≤i,j≤N, +(2.4) +4 + +with +Fn(x, t) = (−1)n +2πi +� +Γ0,1 +dw(1 − w)−n +wx−n+1 +� 1 − α +1 − αw +�t +(2.5) +where Γ0,1 is any simple loop oriented anticlockwise which includes w = 0 and w = 1. Note +that it was first shown in [12] that the transition probabilities are given by determinants: Dieker +and Warren [12] have represented the transition probabilities by using certain sums involving +symmetric polynomials. On the other hand, the expression of the transition probability by contour +integral formulas like (2.5) has first been given in [1]. Besides, it was shown in [17] that the +expression of transition probability in [1] and the expression of transition probability in [12] are +equivalent. It is easy to see that this model satisfies Assumption 2.1 with the function +M(t, w) = +� 1 − α +1 − αw +�t +. +2.2 +Results +In this subsection, we state our main results. +2.2.1 +The representation of the distribution of the particle positions +Now we give a single Fredholm determinant formula for the joint distribution of the particle position +in TASEP satisfies Assumption 2.1. For describing our results, we state some definitions. +Definition 2.3 (epigraph and hypograph). For a real single-valued function �f : A → (−∞, ∞] with +(in general an uncountable) domain A, we set +epi( �f) = {(x, y) : y ≥ �f(x)}, hypo( �f) = {(x, y) : y ≤ �f(x)}. +Definition 2.4. We put RW m, m = 0, 1, 2 . . . as the position of a random walker with Geom[ 1 +2] +jumps strictly to the left starting at some fixed site c, that is to say, +RW m = c − χ1 − χ2 − · · · − χm, +where χi, i = 1, 2, . . . are the i.i.d. random variable with P(χi = k) = 1/2k+1, k = 0, 1, 2, . . .. +We also set the stopping time +τ = min{m ≥ 0 : RWm > X0(m + 1)} +(2.6) +where τ is the hitting time of the strict epigraph of the curve (X0(k +1))k=0,...,n−1 by the random walk +RWk, X0(m) is constant and defined only m ≤ N when the number of particles is N. +At last we set the multiplication operators. +Definition 2.5. For a fixed vector a ∈ Rm and indices n1 < · · · < nm, we define +χa(nj, x) = 1x>aj, +¯χa(nj, x) = 1x≤aj. +as the multiplication operators acting on the space ℓ2({n1, . . . , nm}×Z)(or acting on the space L2({x1, . . . , xm}× +R)). +When considering the distribution of particle positions, we assume that the rightmost particle exists +and is labeled 1. Now we remark that the following: The rightmost particle of TASEP Xt(1) is a +(right) one-sided jump random walk or a compound Poisson process because the exclusion rule does +not work. Therefore +5 + +• If t ∈ Z≥0, then +Xt(1) := Y1 + Y2 + · · · + Yt +(2.7) +where Y1, Y2, . . . , Yt are independent and identically distributed non-negative integer-valued ran- +dom variables. +• If t ∈ R≥0, then +Xt(1) = SNt := Z1 + Z2 + · · · + ZNt +(2.8) +where Z1, Z2, . . . are independent and identically distributed non-negative integer-valued ran- +dom variables, Nt is Poisson process with parameter λ ∈ (0, ∞), independent of the process Sn, +n ∈ Z≥0. +Noting that (2.7) and (2.8), we have the following result. +Proposition 2.6. We consider the TASEP that satisfies Assumption 2.1. Then +M(t, w) = M(w)t +(2.9) +where +M(w) = +� +GY1(w) +if t ∈ Z≥0, +GX(GZ1(w)) +if t ∈ R≥0, +(2.10) +GZ(w) is a probability generating function of the non-negative integer-valued random variable Z, that +is, +GZ(w) = +∞ +� +k=0 +wkP(Z = k), +(2.11) +Y1 is defined in (2.7), Z1 is defined in (2.8) and X is Poisson random variable with parameter λ ∈ +(0, ∞). +This proof is given in Section 3.1. +Furthermore, we get the following by using Proposition 2.6. +Theorem 2.7. We consider the TASEP that satisfies Assumption 2.1. Then the transition probability +of TASEP is given as the following: +P(Xt = ⃗x|X0 = ⃗y) = det[F i−j(xN+1−i − yN+1−j, t)]1≤i,j≤N +where ⃗x, ⃗y ∈ ΩN, +F n(x, t) = (−1)n +2πi +� +Γ0,1 +dw(1 − w)−n +wx−n+1 M(w)t, +(2.12) +where Γ0,1 is any simple loop oriented anticlockwise which includes w = 0 and w = 1 and M(w) is +defined in (2.10). +Proof is given in Section 3.1. +From Theorem 2.7 and Theorem 1.2 of [17], we obtain the following results. The following results +represent that the distribution of particle positions can be expressed by the probability generating +function of the distribution followed when the rightmost particle jumps. +Theorem 2.8. We consider the TASEP which satisfies Assumption 2.1. Let t ∈ Z or t ∈ R. Also, +we put Xt(j), j ∈ Z as a position of the jth particle at time t. Assume that the initial positions +X0(j) ∈ Z for j = 1, 2, . . . are arbitrary constants satisfying X0(1) > X0(2) > · · · while X0(j) = ∞ +for j ≤ 0. +For nj ∈ Z≥1 j = 1, 2, . . . , M with 1 ≤ n1 < n2 < · · · < nM, and a = (a1, a2, . . . , aM) ∈ ZM, we get +P(Xt(nj) > aj, j = 1, . . . , M) = det(I − ¯χaKt ¯χa)ℓ2({n1,...,nM}×Z). +(2.13) +6 + +Here ¯χa(nj, x) is introduced in Definition 2.5 and +Kt(ni, x; nj, y) = −Qnj−ni(x, y)1ni 0 +(2.24) +where γ(n)(w) is the n-th derivative of γ(w). +Remark 2.12. Several well-known TASEP models meet the above assumption. For example, it is easy +to see that the continuous time TASEP, the discrete time Bernoulli TASEP with sequential update, +and the discrete time geometric TASEP with parallel update satisfy Assumption 2.11. However, we +can give the probability generating function M(w) (2.10) that does not satisfy Assumption 2.11. For +example, we consider the case where the update rule is given as follows: +P(Xt+1(1) = a1 + b|Xt(1) = a1) = + + + + + +p +for b = 4, +1 − p +for b = 0, +0 +otherwise, +where a1 ∈ Z and 0 < p < 1. Then +M(w) = 1 − p + pw4 +and +γ(3)(0) − 3γ(2)(0)γ +′(0) + 2{γ +′(0)}3 − 2γ +′(0) = p(1 − p)(23p − 16) +16 +� +M( 1 +2) +�3 +. +Therefore, when 0 < p < 16 +23, +γ(3)(0) − 3γ(2)(0)γ +′(0) + 2{γ +′(0)}3 − 2γ +′(0) < 0. +From the above, we see that Assumption 2.11 is necessary. +Supposing that Assumption 2.11, the constants A, B, and C are given as follows: +A = +2{γ +′(0) + {γ +′(0)}2 − γ(2)(0)} +γ(3)(0) − 3γ(2)(0)γ +′(0) + 2{γ +′(0)}3 − 2γ +′(0), B = 2, C = 1. +(2.25) +By the property of the height function, we put the scaled height, which is equivalent to (2.25). This +is known as ‘‘1:2:3 scaling” which is defined in [16]. +Definition 2.13. For t ∈ R≥0 and x ∈ R, we set the scaling height function +�hε(t, x) = ε +1 +2 +� +ht(x) + +2{γ(2)(0) − {γ +′(0)}2 − γ +′(0)} +γ(3)(0) − 3γ(2)(0)γ +′(0) + 2{γ +′(0)}3 − 2γ +′(0)ε− 3 +2 t +� +, +(2.26) +where t and x are scaled as +t = +2 +γ(3)(0) − 3γ(2)(0)γ +′(0) + 2{γ +′(0)}3 − 2γ +′(0)ε− 3 +2 t, x = 2ε−1x. +(2.27) +8 + +Remark 2.14. (2.26) and (2.27) show that the coefficient of ε− 3 +2 t can be expressed by the probability +generating function of the distribution followed when the rightmost particle jumps. This implies that +the coefficient of ε− 3 +2 t is described by the probability generating functions of the particles unaffected +by the exclusion rule. +In (2.26) and (2.27), we focus on the denominator and numerator of the coefficient of ε− 3 +2 t. Then +we can give the properties needed to obtain the scaling limit of distribution of height function. +Theorem 2.15. We have +0 ≤ γ(2)(0) − {γ +′(0)}2 − γ +′(0) < ∞, +(2.28) +|γ(3)(0) − 3γ(2)(0)γ +′(0) + 2{γ +′(0)}3 − 2γ +′(0)| < ∞ +(2.29) +where γ(w) is introduced in (2.23). +This proof is given in Section 4. +Our goal is to compute the ε → 0 limit of the joint distribution function +lim +ε−→0 P�hε +0(�hε(t, x1) ≤ a1, . . . ,�hε(t, xm) ≤ am) +(2.30) +for x1 < x2 < · · · < xm ∈ R and a1, . . . , am ∈ R where P�hε +0(·) is the probability measure and �hε(0, x) +is the initial height profile. Here we introduce the assumption necessary to calculate (2.30). +Assumption 2.16. For θ ∈ [−π, − π +3 ) ∪ ( π +3 , π], +E log |2 − eiθ| + D log |γ(1 − eiθ)| < 0 +(2.31) +and +F log |2 − eiθ| − D log |γ(eiθ − 1)| < 0 +(2.32) +where +D = +2 +γ(3)(0) − 3γ(2)(0)γ +′(0) + 2{γ +′(0)}3 − 2γ +′(0), +(2.33) +E = +γ(2)(0) − {γ +′(0)}2 − γ +′(0) +γ(3)(0) − 3γ(2)(0)γ +′(0) + 2{γ +′(0)}3 − 2γ +′(0), +(2.34) +F = +{γ +′(0)}2 − γ(2)(0) − γ +′(0) +γ(3)(0) − 3γ(2)(0)γ +′(0) + 2{γ +′(0)}3 − 2γ +′(0) +(2.35) +and γ(w) is introduced in (2.23). +Note that considering the well-known TASEP, Assumption 2.16 holds similarly to Assumption 2.11. +We will prove that the limit (2.30) converges to the joint distribution function characterizing the +KPZ fixed point defined in [16]. Now we introduce the KPZ fixed point. First we define UC and LC. +Definition 2.17. (UC and LC [16]). +We set UC as the space of upper semicontinuous functions �h : R → [−∞, ∞) with �h(x) ≤ C1 + C2|x| +for some C1, C2 < ∞ and �h(x) > −∞ for some x and LC as LC = {�g : −�g ∈ UC}. +Next we put the integral representation for the Airy function. +Definition 2.18. the integral representation for the Airy function is given by +Ai(z) = +1 +2πi +� +⟨ +dw e +1 +3 w3−zw, +where ⟨ is the positively oriented contour going the straight lines from e− iπ +3 ∞ to e +iπ +3 ∞ through 0. +9 + +Now we are ready to state the KPZ fixed point (for more detail, see [16]). +Definition 2.19 (The KPZ fixed point [16]). The KPZ fixed point is the unique Markov process on +UC, (�h(t, ·))t>0 with transition probabilities +P�h0(�h(t, x1) ≤ a1, . . . ,�h(t, xm) ≤ am) = det +� +I − χaKhypo(�h0) +t,ext +χa +� +L2({x1,...,xm}×R) +(2.36) +where in LHS, x1 < x2 < · · · < xm ∈ R and a1, . . . , am ∈ R, �h0 ∈ UC and P�h0 means the measure on +the process with initial data �h0. In RHS, we give the kernel by +Khypo(�h0) +t,ext +(xi, v; xj, u) += − +1 +� +4π(xj − xi) +exp +� +− (u − v)2 +4(xj − xi) +� +1xi 0. +Then, for x1 < x2 < · · · < xm ∈ R and a1, . . . , am ∈ R, we obtain +lim +ε−→0 P�hε +0(�hε(t, x1) ≤ a1, . . . ,�hε(t, xm) ≤ am) = det +� +I − χaKhypo(�h0) +t,ext +χa +� +L2({x1,...,xm}×R) , +(2.44) +where RHS is equivalent to (2.36). +This proof is given in Section 5. +10 + +Remark 2.22. In previous studies, the one-sided fixed point formula was obtained only for each +model. However, the above results show that the one-sided fixed point formula was obtained for all +TASEPs that satisfy Assumption 2.1, 2.11, 2.16. +Remark 2.23. By using the similar argument in Theorem 3.8. in [16], we can remove the assumption +�h0(x) = −∞ for x > 0 in Theorem 2.21 (See subsection 3.4 of [16] for more details.). +To prove Theorem 2.21, we use the following relationship between the particle positions Xt(j) and +the height function ht(z) (2.19). We put s1, . . . , sk, m1, . . . , mk ∈ R and z1, . . . , zk, n1, . . . , nk ∈ Z. +Then, by Definition 2.10, we get +P(ht(z1) ≤ s1, . . . , ht(zk) ≤ sk) = P(Xt(n1) ≥ m1, . . . , Xt(nk) ≥ mk). +(2.45) +By the above relation, we see +lim +ε−→0 P�hε +0(�hε(t, x1) ≤ a1, . . . ,�hε(t, xm) ≤ am) = lim +ε→0 PXε +0 (Xε +t (n1) > a1, . . . , Xε +t (nm) > am) , +(2.46) +where a1, . . . , am ∈ R and t, ni, ai are scaled as +t = Dε− 3 +2 t, ni = Eε− 3 +2 t − ε−1xi − 1 +2ε− 1 +2 ai + 1, ai = 2ε−1xi − 2, +(2.47) +where D and E are introduced in (2.33) and (2.34), respectively. +Therefore our goal (2.46) can be gotten by taking the ε → 0 limit of the expression (2.13) in +Theorem 2.8 under the scaling (2.47). The major important step of this problem is the following +proposition about pointwise convergence. +Proposition 2.24. (Pointwise convergence). +We consider the TASEP that satisfies Assumption +2.1. Suppose that Assumption 2.11, 2.16 and (2.42) hold. Under the scaling (2.47),(dropping the i +subscripts), if we set z = Gε− 3 +2 t + 2ε−1x + ε− 1 +2 (u + a) − 2 and y′ = ε− 1 +2 v, then we have for t > 0 as +ε −→ 0, +Sε +−t,x(v, u) := ε− 1 +2 S−t,−n(y′, z) −→ S−t,x(v, u) +(2.48) +¯Sε +−t,−x(v, u) := ε− 1 +2 ¯S−t,n(y′, z) −→ S−t,−x(v, u) +(2.49) +¯Sε,epi(−hε,− +0 +) +−t,−x +(v, u) := ε− 1 +2 ¯Sepi(X0) +−t,n +(y′, z) −→ Sepi(−�h− +0 ) +−t,−x +(v, u) +(2.50) +pointwise, where +G = +2[{γ +′(0)}2 − γ(2)(0)] +γ(3)(0) − 3γ(2)(0)γ +′(0) + 2{γ +′(0)}3 − 2γ +′(0), +�h− +0 (x) = �h0(−x) for x ≥ 0, St,x(v, u) is given by (2.38) and for �g ∈ LC, +Sepi(�g) +t,x +(v, u) = EB(0)=v[St,x−τ ′(B(τ ′), u)1τ ′ <∞] +and S−t,−n(z1, z2), ¯S−t,n(z1, z2) and ¯Sepi(X0) +−t,n +(z1, z2) are defined in (2.16), (2.17) and (2.18), respec- +tively. +Proof is given in Section 5. +3 +Distribution representation for the TASEP +3.1 +The representation of the transition probability for TASEP: Proof of +Proposition 2.6 and Theorem 2.7 +In this subsection, we show that the transition probability can be expressed by a probability generating +function of the distribution followed when the rightmost particle jumps. First, we see that the property +of the transition probability when the number of particles is one. +11 + +Lemma 3.1. Suppose that Assumption 2.1 holds. When N = 1, for x, y ∈ Z such that x ≥ y, +P(Xt(1) = x|X0(1) = y) = F0(x − y, t) +(3.1) +Proof. It is easy to see that (3.1) holds if N = 1, x1 = x and y1 = y are substituted in (2.2). +Next, we prove the space-homogeneity when N = 1. +Lemma 3.2 (space-homogeneity). Assume that Assumption 2.1 holds. When N = 1, for x, y ∈ Z +such that x ≥ y, +P(Xt(1) = x|X0(1) = y) = P(Xt(1) = x − y|X0(1) = 0). +Proof. By Lemma 3.1, we get +P(Xt(1) = x|X0(1) = y) = F0(x − y, t) += P(Xt(1) = x − y|X0(1) = 0). +Note that when N = 1, the exclusion rule doesn’t work, so the TASEP is just a one-sided jump +random walk or a compound Poisson process. For convenience, we set the following: +P(Xt(1) = x) := P(Xt(1) = x|X0(1) = 0). +(3.2) +Now, we show that the following holds. +Lemma 3.3. We consider the TASEP that satisfies Assumption 2.1. Then the following two are +equivalent: +(i) M(t, w) = +∞ +� +x=0 +wxP(Xt(1) = x) where radius of convergence is R ≥ 1. +(ii) F0(x, t) = P(Xt(1) = x). +Proof. First we prove (i) ⇒ (ii). By (2.1), +F0(x, t) = +1 +2πi +� +Γ0 +dw +1 +wx+1 M(t, w) +(3.3) +where Γ0 is any simple loop oriented anticlockwise and includes w = 0. By changing variables as +w = reiv when we define r ∈ R such that 0 < r < R, +(3.3) = +1 +2πi +� 2π +0 +dv +1 +(reiv)x+1 ireivM(t, reiv) += 1 +2π +� 2π +0 +dvr−xe−ixvM(t, reiv). +(3.4) +Since +M(t, reiv) = +∞ +� +k=0 +rkeikvP(Xt(1) = k) +is absolutely convergent, +(3.4) = 1 +2π +� 2π +0 +dvr−xe−ixv +∞ +� +k=0 +rkeikvP(Xt(1) = k) += 1 +2π +∞ +� +k=0 +rk−xP(Xt(1) = k) +� 2π +0 +ei(k−x)vdv += 1 +2π +∞ +� +k=0 +rk−xP(Xt(1) = k)2πδk,x += P(Xt(1) = x) +(3.5) +12 + +where δk,x is the Kronecker delta, that is, +δk,x := +� +1 +for k = x, +0 +otherwise. +(3.6) +Next we show (ii) ⇒ (i). For s ∈ C, we put +φ(s) = +∞ +� +x=0 +sxP(Xt(1) = x) +where radius of convergence is R ≥ 1. From the condition (ii), +φ(s) = +∞ +� +x=0 +F0(x, t)sx +(3.7) +holds. By substituting (3.3) for (3.7), we obtain +φ(s) = +∞ +� +x=0 +� 1 +2πi +� +Γ0 +dw +1 +wx+1 M(t, w) +� +sx += +1 +2πi +� +Γ0 +dwM(t, w) +w +∞ +� +x=0 +� s +w +�x += +1 +2πi +� +Γ0 +dwM(t, w) +w +1 +1 − s +w += +1 +2πi +� +Γ0 +dwM(t, w) +w − s += M(t, s) +(3.8) +provided that the integration domain satisfy |s| < |w|. Therefore, we get +M(t, w) = +∞ +� +x=0 +wxP(Xt(1) = x) +where radius of convergence is R ≥ 1. +Remark 3.4. By (2.2), Lemma 3.1 and Lemma 3.2, it can be seen that (ii) F0(x, t) = P(Xt(1) = x) +holds. Thus, Lemma 3.3 implies that the function M(t, w) which constitutes the transition probability +of TASEP is given as the probability generating function. +Now, we prove Proposition 2.6. +Proof of Proposition 2.6. By Lemma 3.1, Lemma 3.2 and Lemma 3.3, +M(t, w) = +∞ +� +x=0 +wxP(Xt(1) = x). +Now, we first show the case of t ∈ Z≥0. By (2.7), +M(t, w) = E +� +wXt(1)� += E +� +wY1+Y2+···+Yt� += +� +E +� +wY1��t += M(w)t. +(3.9) +13 + +Next, we prove the case of t ∈ R≥0. By (2.8) and (2.11), +M(t, w) = E[wSNt ] += +∞ +� +n=0 +E[wSNt |Nt = n]P(Nt = n) += +∞ +� +n=0 +E[wSn]P(Nt = n) += +∞ +� +n=0 +E[wZ1+Z2+···+Zn]P(Nt = n) += +∞ +� +n=0 +(E[wZ1])nP(Nt = n) += +∞ +� +n=0 +{GZ1(w)}ne−λt (λt)n +n! += eλt{GZ1 (w)−1}. +On the other hand, by (2.10), +M(w) = GX(GZ1(w)) += +∞ +� +n=0 +{GZ1(w)}ne−λ λn +n! += eλ{GZ1 (w)−1}. +(3.10) +Therefore we get +M(t, w) = M(w)t. +Next, we show Theorem 2.7. +Proof of Theorem 2.7. By (2.1) and Proposition 2.6, +Fn(x, t) = (−1)n +2πi +� +Γ0,1 +dw(1 − w)−n +wx−n+1 M(t, w) += (−1)n +2πi +� +Γ0,1 +dw(1 − w)−n +wx−n+1 M(w)t += F n(x, t). +From the above, the transition probability of TASEP is given by +P(Xt = ⃗x|X0 = ⃗y) = det[F i−j(xN+1−i − yN+1−j, t)]1≤i,j≤N. +3.2 +Proof of Theorem 2.8 +In this subsection, we prove Theorem 2.8. +It is easy to check that M(w) satisfies Assumption 1.1 in [16]. Therefore, by Theorem 1.2 in [16] +and Theorem 2.7, we have the distribution of particle positions: +P(Xt(nj) > aj, j = 1, . . . , M) = det(I − ¯χaKt ¯χa)ℓ2({n1,...,nM}×Z) +14 + +where +Kt(ni, x; nj, y) = −Qnj−ni(x, y)1ni 0. Hence the part +C +π +3 +ǫ of the integral vanishes and this completes the proof of (2.48). +Next, we prove (2.49). By changing variables w = 1 +2(1 − ε +1 +2 y), +¯Sε +−t,−x(v, u) = +1 +2πi +� +Cε +dy { 1 +2(1 + ε +1 +2 y)}z−y′+n−1 +2y′−z+1{ 1 +2(1 − ε +1 +2 y)}n +� +M( 1 +2(1 + ε +1 +2 y)) +M +� 1 +2 +� +�−t += +1 +2πi +� +Cε +dy (1 + ε +1 +2 y)z−y′+n−1 +(1 − ε +1 +2 y)n +γ +� +ε +1 +2 y +�−t +where Cε is a circle of radius ε− 1 +2 centred at ε− 1 +2 and +γ(w) = M( 1 +2(1 + w)) +M +� 1 +2 +� +. +We remark that +γ(0) = γ(0), γ +′(0) = −γ +′(0), γ(2)(0) = γ(2)(0), γ(3)(0) = −γ(3)(0). +Using the saddle point method and (2.32) of Assumption 2.16, we can also show (2.49) in the similar +way to (2.48). +For (2.50), we can prove it similarly to (3.17) of Lemma 3.5 in [16]. Therefore, only a sketch of the +proof is given here. We set the scaled walk Bε(x) = ε +1 +2 (RWε−1x+2ε−1x−1) for x ∈ εZ≥0, interpolated +linearly in between, and put τ ε as the hitting time by Bε of epi(−�hε(0, ·)−) where �hε(t, x) is introduced +by (2.26) and �hε(t, x)− = �hε(t, −x). By Donsker’s invariance principle [4], Bε(x) converges locally +uniformly in distribution to a Brownian motion B(x) with diffusion coefficient 2. Also, combining this +with (2.42) and Proposition 3.2 in [16], we see that the hitting time τ ε converges to τ. (For more +detail, see Lemma 3.5 in [16]).) This leads to (2.50). +18 + +5.2 +Proof of Theorem 2.21 +In this subsection, we show Theorem 2.21 by using Propositions 2.24. This proof is almost the same +as Proposition 3.6 in [16]. First, we change variables in the kernel as in Proposition 2.24. Then, for +zi = Gε− 3 +2 t + 2ε−1xi + ε− 1 +2 (ui + ai) − 2, we compute the limiting kernel +Klim(xi, ui; xj, uj) := lim +ε−→0 ε− 1 +2 (¯χ2ε−1x−2Kt ¯χ2ε−1x−2)(zi, zj) +where +G = +2[{γ +′(0)}2 − γ(2)(0)] +γ(3)(0) − 3γ(2)(0)γ +′(0) + 2{γ +′(0)}3 − 2γ +′(0) +and γ(w) is defined in (2.23). We remark that the change of variables turns ¯χ2ε−1x−2(z) into ¯χ−a(u). +We obtain ni < nj for small ε if and only if xj < xi and in this case we get +lim +ε−→0 ε− 1 +2 Qnj−ni(zi, zj) = e(xi−xj)∂2(ui, uj). +(5.7) +For the second term in (2.14), we have +ε− 1 +2 (S−t,−ni)∗ ¯Sepi(X0) +−t,nj (zi, zj) = ε− 1 +2 +� ∞ +−∞ +dν(S−t,−ni)∗(zi, ν) ¯Sepi(X0) +−t,nj (ν, zj) += ε−1 +� ∞ +−∞ +dν(S−t,−ni)∗(zi, ε− 1 +2 ν) ¯Sepi(X0) +−t,nj (ε− 1 +2 ν, zj) += +� ∞ +−∞ +dν(Sε +−t,xi)∗(ui, ν)¯S +ε,epi(−hε,− +0 +) +−t,−xj +(ν, uj) += (Sε +−t,xi)∗¯S +ε,epi(−hε,− +0 +) +−t,−xj +(ui, uj). +By Proposition 2.24, we obtain +lim +ε−→0 ε− 1 +2 (S−t,−ni)∗ ¯Sepi(X0) +−t,nj (zi, zj) = (S−t,xi)∗S +epi(−�h− +0 ) +−t,−xj (ui, uj). +(5.8) +By (5.7) and (5.8), we get +Klim(xi, ui; xj, uj) = −e(xi−xj)∂2(ui, uj)1xi>xj + (S−t,xi)∗S +epi(−�h− +0 ) +−t,−xj (ui, uj) +surrounded by projection ¯χ−a. It is nicer to have projection χa, so we change variables ui �→ −ui and +replace the Fredholm determinant of the kernel by that of its adjoint to get det +� +I − χaKhypo(�h0) +t,ext +χa +� +with Khypo(�h0) +t,ext +(ui, uj) = Klim(xj, −uj; xi, −ui). +By using (St,x)∗St,−x = I and Sepi(�h) +−t,x (v, u) = Shypo(−�h) +t,x +(−v, −u) (see [16] for more information on +these equations), we have +Khypo(�h0) +t,ext +(xi, ·; xj, ·) = −e(xj−xi)∂21xi 0. +Next we prove that γ(w) satisfies Assumption 2.16. By (2.33), (2.34), (2.35), and (A.2), we have +D = 2 +β , E = 1 +2, F = 1 +2. +(A.3) +Note that log(1 + x) < x for x ∈ (−1, ∞) \ {0}. For θ ∈ [−π, − π +3 ) ∪ ( π +3 , π], by (A.3), we obtain +E log |2 − eiθ| + D log |γ(1 − eiθ)| < 1 +4(4 − 4 cosθ) + cos θ − 1 = 0 +and +F log |2 − eiθ| − D log |γ(eiθ − 1)| < 1 +4(4 − 4 cosθ) + cos θ − 1 = 0. +This completes the proof. +References +[1] Y. Arai, The KPZ fixed point for discrete time TASEPs, J. Phys. A, 53, 415202, (2020). +[2] J. Baik, E. M. 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Windridge, Some Examples of Dynamics for Gelfand-Tsetlin Patterns, Electron. J. +Probab.,14, 1745-1769, (2009). +22 + diff --git a/q9E1T4oBgHgl3EQf2wUi/content/tmp_files/load_file.txt b/q9E1T4oBgHgl3EQf2wUi/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..c0b05a282dd64e4a70ee2bb44ce594d3eed70035 --- /dev/null +++ b/q9E1T4oBgHgl3EQf2wUi/content/tmp_files/load_file.txt @@ -0,0 +1,965 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf,len=964 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='03481v1 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='PR] 9 Jan 2023 On the KPZ scaling and the KPZ fixed point for TASEP Yuta Arai ∗ Abstract We consider all totally asymmetric simple exclusion processes (TASEPs) whose transition probabilities are given in the Sch¨utz-type formulas and which jump with homogeneous rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' We show that the multi-point distribution of particle positions and the coefficient of KPZ scaling are described using the probability generating function of the distribution followed when the rightmost particle jumps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' For all TASEPs satisfying certain assumptions, We also prove the pointwise convergence of the kernels appearing in the joint distribution of particle positions to those appearing in the KPZ fixed point formula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Our result generalizes the result of Matetski, Quastel, and Remenik [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' 1 Introduction The KPZ universal class was introduced in [15] to describe the universality of the growth model of an interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The totally asymmetric simple exclusion process (TASEP) is one of the most typical interacting stochastic particle systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' It can be interpreted as a stochastic interface growth model belonging to the KPZ universal class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Furthermore, the TASEP is known as an important model for studying the KPZ universality because its distribution function can be calculated for some quantities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Research on the KPZ universality of TASEP has been actively conducted since around 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' First, in the case of the step initial condition, by considering the relationship stochastically growing Young diagram and TASEP, Johansson [13] has derived the one-point limit distribution of the particle current by using the RSK correspondence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' In this case, the limiting distribution turned out to be the GUE Tracy-Widom distribution from random matrix theory [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' As a related work, in the case of the flat polynuclear growth (PNG) model, the one-point limit distribution of the height distribution has been obtained in [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' In addition, for the last passage percolation, similar results have been derived in [2, 3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The results of [2, 3, 19] include the result of the one-point limit distribution of particle current for the periodic initial condition in the language of TASEP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' It turned out that the limiting distribution is the GOE Tracy-Widom distribution from random matrix theory [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The above are the results for one-point fluctuations, but many results for multi-point fluctuations have also been given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' For the case corresponding to the step initial condition, the Fredholm deter- minant formula for the limiting multi-point distribution has been obtained in the PNG model with different settings [14, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' In this case, the limiting process characterized by the multi-point dis- tribution is the Airy2 process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' On the other hand, for the periodic initial condition, the Fredholm determinant formula for the limiting multi-point distribution has been derived in the continuous time TASEP [9, 25] by using the result of the transition probability in TASEP [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' In this case, the lim- iting process characterized by the multi-point distribution is called the Airy1 process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The technique in [9, 25] has been applied to various models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Therefore, the limit distribution of the multi-point distribution has been obtained for the TASEP and PNG models with different settings [6, 8, 10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The case of generalized initial conditions for particle positions has also been studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Matetski, Quastel, and Remenik [16] first extended the method of [9, 25] to get the limit distribution of multi- point distribution in the continuous time TASEP for arbitrary initial conditions: In [9, 25], the ∗Platform for Arts and Science, Chiba University of Commerce, Ichikawa-shi 263-8522, Japan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Email: yu- taarai@cuc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='jp 1 correlation kernel for the Fredholm determinant was expressed in terms of the biorthogonal functions Ψn k(x) and Φn k(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' However, there was the problem that Φn k(x) does not have an explicit representation while Ψn k(x) does.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Therefore, it was not clear how to take the KPZ scaling limit of this kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Matetski, Quastel, and Remenik [16] solved this problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' They represent the function Φn k(x) by the hitting probability of the geometric random walk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' From Donsker’s invariance principle, the hitting time of the geometric random walk converges to the hitting time of the Brownian motion when the time-space limit is taken, so this representation of Φn k(x) allows us to take the KPZ scaling limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Based on this method, they have derived the limit distribution of multi-point distribution in the continuous time TASEP for arbitrary initial conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The limiting process with this limit distribution of the multi-point distribution is known as the KPZ fixed point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The KPZ fixed point has also been obtained in the one-sided reflected Brownian motion [18] and two variations of discrete time TASEP with geometric and Bernoulli jumps [1] by using the method of [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' There have also been various other interesting progresses on the KPZ fixed point for example in [11, 22, 24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' There have been studies to get the distribution of particle positions in the discrete time TASEP using the result of [12]: Dieker and Warren [12] have derived the transitive kernels of the four processes that correspond to the four variants of the discrete time TASEP by using the RSK correspondence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Matetski and Remenik [17] have given the distribution of particle positions in the four variants of the discrete time TASEP from the above result and the method of [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' They have also obtained a formula for the distribution of particle positions that can be applied for example to continuous time TASEP and discrete time TASEP with sequential update.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' In [5], they have generalized the method of [12] so that it can be applied to the discrete time Bernoulli TASEP with particle- and time-inhomogeneous rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Combining the above method with the method of [16], they gave the distribution of particle positions in the discrete time Bernoulli TASEP with particle- and time-inhomogeneous rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' However, in [5, 17], the formula for obtaining the KPZ fixed point that can be uniformly applied to TASEP with different settings was not derived.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' In this paper, we consider all TASEPs whose transition probabilities are given in the Sch¨utz-type formulas and which jump with homogeneous rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Then we show that the distribution of particle positions can be described by using the probability generating function of the distribution followed when the rightmost particle jumps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' We remark that this method using the probability generating function is quite different from the method of [5, 17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' We also state that the coefficient of KPZ scaling used to get the KPZ fixed point can be expressed by the probability generating function of the distribution followed when the rightmost particle jumps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Furthermore, we show the property of the coefficient of KPZ scaling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Finally, by generalizing the method of [16], we prove the pointwise convergence of the kernels appearing in the joint distribution of particle positions to those appearing in the KPZ fixed point formula for all TASEPs that satisfy certain assumptions, for example, the continuous time TASEP, the discrete time Bernoulli TASEP with sequential update, and the discrete time geometric TASEP with parallel update.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' It implies that our method can adapt to multiple models, not to only one model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Note that our method derives the KPZ fixed point even in the case of the continuous time TASEP with jump rate β ∈ (0, ∞) where the KPZ fixed point has not been given (see Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='2 and Appendix A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The paper is organized as follows: In Section 2, we state the TASEPs whose transition probabilities are given in the Sch¨utz-type formulas (see Assumption 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' We also give our main result: the Fredholm determinant formula for the TASEPs satisfying Assumption 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='1 (Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='8), the property of the coefficient of KPZ scaling (Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='15), and the KPZ scaling limit in the TASEPs satisfying Assumption 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='1 when Assumption 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='11, and Assumption 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='16 hold (Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' In Section 3, for the TASEPs which satisfy Assumption 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='1, we show Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='8 after the transition probabilities are represented by the probability generating function of the distribution followed when the rightmost particle jumps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' In Section 4, we prove Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' In Section 5, we give proofs of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='21 and Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' In Appendix A, we use our method to show that the KPZ fixed point is obtained in the continuous time TASEP with jump rate β ∈ (0, ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The key to our proofs is the saddle point analysis for the kernels by using the probability generating function of the distribution followed when the rightmost particle jumps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' 2 2 Models and results 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='1 Models We consider the TASEPs on Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Each particle independently and stochastically jumps to the right only if the target site is empty and cannot move if the target site is occupied by other particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The above represents the exclusion rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' We mainly focus on the position of each particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' We put t ∈ Z or t ∈ R according to the version.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Then we define Xt(i) ∈ Z as a position of the ith particle at time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The dynamics of the TASEPs preserve the order of the particles, that is, · · < Xt(i + 2) < Xt(i + 1) < Xt(i) < Xt(i − 1) < Xt(i − 2) < · · · where the particles at ±∞ are playing no role in the dynamics when adding ±∞ into the state space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Now we set ΩN = {⃗x = (xN, xN−1, · · · , x1) ∈ ZN : xN < · · · < x2 < x1} as the Weyl chamber, whose elements express the particle positions of the TASEPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Also, we put Fn(x, t) = (−1)n 2πi � Γ0,1 dw(1 − w)−n wx−n+1 M(t, w) (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='1) where Γ0,1 is any simple loop oriented anticlockwise which includes w = 0 and w = 1, and M(t, w) is analytic on {w ∈ C : |w| < R} with the radius R ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' In this paper, we deal with the TASEP which satisfies the following assumption, where we do not consider the TASEP whose jump rate or jump probability changes depending on time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Assumption 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The transition probability from ⃗y ∈ ΩN to ⃗x ∈ ΩN is given by P(Xt = ⃗x|X0 = ⃗y) = det[Fi−j(xN+1−i − yN+1−j, t)]1≤i,j≤N, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='2) where Xt = (Xt(1), Xt(2), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' , Xt(N)) are the locations of a system of particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Assumption 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='1 is fulfilled in many TASEPs illustrated in the following example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Here we introduce three typical examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The continuous time TASEP with jump rate β The continuous time TASEP was introduced in [27] as a mathematical model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The process Xt, t ∈ R≥0 evolves as follows: each particle independently attempts to jump to the right neighboring site at rate β ∈ (0, ∞) provided this site is empty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The continuous time TASEP is a Markov process with the generator L defined as follows: We put η = {η(x) : x ∈ Z} ∈ {0, 1}Z as a particle configuration where η(x) = 1 means the site x is occupied by a particle while η(x) = 0 means it is empty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Then the generator L acting on cylinder functions f : {0, 1}Z → R is introduced by (Lf)(η) = β � x∈Z η(x)(1 − η(x + 1))(f(ηx,x+1) − f(η)) where η(x) = � 1, if the site is occupied by a particle, 0, if the site x is empty, and ηx,x+1 is the configuration η with the occupations at site x and x+1 have been interchanged, that is, ηx,x+1(y) = \uf8f1 \uf8f4 \uf8f2 \uf8f4 \uf8f3 η(x + 1) for y = x, η(x) for y = x + 1, η(y) otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' 3 The transition probability of Xt is given by [26] using Bethe ansatz: P(Xt = ⃗x|X0 = ⃗y) = det[Fi−j(xN+1−i − yN+1−j, t)]1≤i,j≤N, with Fn(x, t) = (−1)n 2πi � Γ0,1 dw(1 − w)−n wx−n+1 eβt(w−1) where Γ0,1 is any simple loop oriented anticlockwise which includes w = 0 and w = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' It is clear that this model satisfies Assumption 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='1 with the function M(t, w) = eβt(w−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='3) Note that when β ∈ (0, 1), this model can be interpreted as the continuous time version of the discrete time Bernoulli TASEP introduced next.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The KPZ fixed point has been derived in [16] when β = 1, but our results show that the KPZ fixed point can also be obtained when β ∈ (0, ∞) (see Appendix A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The discrete time Bernoulli TASEP with sequential update The discrete time Bernoulli TASEP with sequential update on Z was studied previously in [7] as a marginal of dynamics on Gelfand-Tsetlin patterns which preserve the class of Schur processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The evolution of the process Xt, t ∈ Z≥0 is given by the recursion relation Xt+1(1) = Xt(1) + wt+1,1 and Xt+1(i) = min {Xt(i) + wt+1,i, Xt+1(i − 1) − 1} , i = 2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' , N where wt,i are independent random variables following the Bernoulli distribution with parameter p ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The transition probability of this model is given by [23]: P(Xt = ⃗x|X0 = ⃗y) = det[Fi−j(xN+1−i − yN+1−j, t)]1≤i,j≤N, with Fn(x, t) = (−1)n 2πi � Γ0,1 dw(1 − w)−n wx−n+1 (1 + p(w − 1))t where Γ0,1 is any simple loop oriented anticlockwise which includes w = 0 and w = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' One can readily see that this model satisfies Assumption 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='1 with the function M(t, w) = (1 + p(w − 1))t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The discrete time geometric TASEP with parallel update The discrete time geometric TASEP with parallel update on Z was studied previously in [30] as a marginal of dynamics on Gelfand-Tsetlin patterns which preserve the class of Schur processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The evolution of the process Xt, t ∈ Z≥0 is given by the recursion relation Xt+1(1) = Xt(1) + �wt+1,1 and Xt+1(i) = min {Xt(i) + �wt+1,i, Xt+1(i − 1) − 1} , i = 2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' , N where �wt,i are independent random variables following the Geometric distribution with parameter α ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The transition probability of this process is given by [1, 12, 17]: P(Xt = ⃗x|X0 = ⃗y) = det[Fi−j(xN+1−i − yN+1−j, t)]1≤i,j≤N, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='4) 4 with Fn(x, t) = (−1)n 2πi � Γ0,1 dw(1 − w)−n wx−n+1 � 1 − α 1 − αw �t (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='5) where Γ0,1 is any simple loop oriented anticlockwise which includes w = 0 and w = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Note that it was first shown in [12] that the transition probabilities are given by determinants: Dieker and Warren [12] have represented the transition probabilities by using certain sums involving symmetric polynomials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' On the other hand, the expression of the transition probability by contour integral formulas like (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='5) has first been given in [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Besides, it was shown in [17] that the expression of transition probability in [1] and the expression of transition probability in [12] are equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' It is easy to see that this model satisfies Assumption 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='1 with the function M(t, w) = � 1 − α 1 − αw �t .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='2 Results In this subsection, we state our main results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='1 The representation of the distribution of the particle positions Now we give a single Fredholm determinant formula for the joint distribution of the particle position in TASEP satisfies Assumption 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' For describing our results, we state some definitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='3 (epigraph and hypograph).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' For a real single-valued function �f : A → (−∞, ∞] with (in general an uncountable) domain A, we set epi( �f) = {(x, y) : y ≥ �f(x)}, hypo( �f) = {(x, y) : y ≤ �f(x)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' We put RW m, m = 0, 1, 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' as the position of a random walker with Geom[ 1 2] jumps strictly to the left starting at some fixed site c, that is to say, RW m = c − χ1 − χ2 − · · · − χm, where χi, i = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' are the i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' random variable with P(χi = k) = 1/2k+1, k = 0, 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='. We also set the stopping time τ = min{m ≥ 0 : RWm > X0(m + 1)} (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='6) where τ is the hitting time of the strict epigraph of the curve (X0(k +1))k=0,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=',n−1 by the random walk RWk, X0(m) is constant and defined only m ≤ N when the number of particles is N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' At last we set the multiplication operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' For a fixed vector a ∈ Rm and indices n1 < · · · < nm, we define χa(nj, x) = 1x>aj, ¯χa(nj, x) = 1x≤aj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' as the multiplication operators acting on the space ℓ2({n1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' , nm}×Z)(or acting on the space L2({x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' , xm}× R)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' When considering the distribution of particle positions, we assume that the rightmost particle exists and is labeled 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Now we remark that the following: The rightmost particle of TASEP Xt(1) is a (right) one-sided jump random walk or a compound Poisson process because the exclusion rule does not work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Therefore 5 If t ∈ Z≥0, then Xt(1) := Y1 + Y2 + · · · + Yt (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='7) where Y1, Y2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' , Yt are independent and identically distributed non-negative integer-valued ran- dom variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' If t ∈ R≥0, then Xt(1) = SNt := Z1 + Z2 + · · · + ZNt (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='8) where Z1, Z2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' are independent and identically distributed non-negative integer-valued ran- dom variables, Nt is Poisson process with parameter λ ∈ (0, ∞), independent of the process Sn, n ∈ Z≥0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Noting that (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='7) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='8), we have the following result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' We consider the TASEP that satisfies Assumption 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Then M(t, w) = M(w)t (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='9) where M(w) = � GY1(w) if t ∈ Z≥0, GX(GZ1(w)) if t ∈ R≥0, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='10) GZ(w) is a probability generating function of the non-negative integer-valued random variable Z, that is, GZ(w) = ∞ � k=0 wkP(Z = k), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='11) Y1 is defined in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='7), Z1 is defined in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='8) and X is Poisson random variable with parameter λ ∈ (0, ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' This proof is given in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Furthermore, we get the following by using Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' We consider the TASEP that satisfies Assumption 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Then the transition probability of TASEP is given as the following: P(Xt = ⃗x|X0 = ⃗y) = det[F i−j(xN+1−i − yN+1−j, t)]1≤i,j≤N where ⃗x, ⃗y ∈ ΩN, F n(x, t) = (−1)n 2πi � Γ0,1 dw(1 − w)−n wx−n+1 M(w)t, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='12) where Γ0,1 is any simple loop oriented anticlockwise which includes w = 0 and w = 1 and M(w) is defined in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Proof is given in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' From Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='7 and Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='2 of [17], we obtain the following results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' The following results represent that the distribution of particle positions can be expressed by the probability generating function of the distribution followed when the rightmost particle jumps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' We consider the TASEP which satisfies Assumption 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Let t ∈ Z or t ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Also, we put Xt(j), j ∈ Z as a position of the jth particle at time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' Assume that the initial positions X0(j) ∈ Z for j = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' are arbitrary constants satisfying X0(1) > X0(2) > · · · while X0(j) = ∞ for j ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' For nj ∈ Z≥1 j = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' , M with 1 ≤ n1 < n2 < · · · < nM, and a = (a1, a2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' , aM) ∈ ZM, we get P(Xt(nj) > aj, j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' , M) = det(I − ¯χaKt ¯χa)ℓ2({n1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=',nM}×Z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='13) 6 Here ¯χa(nj, x) is introduced in Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content='5 and Kt(ni, x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/q9E1T4oBgHgl3EQf2wUi/content/2301.03481v1.pdf'} +page_content=' nj, y) = −Qnj−ni(x, y)1ni 0, where pi = ∂p(x) +∂xi , qi = ∂q(x) +∂xi , i = +1, 2. +For K-quasiconformal mappings, the apriori interior H¨older estimate is well known +(Cf. [10, Lemma 2] and [4, Theorem 1]). +For exterior K-quasiconformal mappings, we have the following H¨older estimate +over exterior domain and the asymptotic behavior at infinity. +Theorem 2.2. Let w = (p, q) be exterior K-quasiconformal in R2 \ ¯Ω (Ω ⊂ R2 +is bounded ) with K ≥ 1, and suppose |w| ≤ M. Then, for any Ω′ ⊃⊃ Ω with +d = dist(Ω, ∂Ω′), +|w(x) − w(y)| ≤ C |x − y|α , x, y ∈ R2 \ Ω′. +and w(x) tends to a limit w(∞) at infinity such that +|w(x) − w(∞)| ≤ C|x|−α for any x ∈ R2 \ Ω′, +(2.2) +where α = K − (K2 − 1) +1 +2, C depends only on K, d and M. + +4 +DONGSHENG LI AND RULIN LIU +Remark 2.3. The results in Theorem 2.2 are also valid for p, q ∈ W 1,2 +loc (R2 \ ¯Ω) ∩ +L∞(R2 \ ¯Ω). +To prove Theorem 2.2, we first state the following H¨older continuity of K-quasiconformal +mappings with singularities. +Lemma 2.4 ( [4, Theorem 3]). Let w = (p, q) be K-quasiconformal in a domain Ω +of x = (x1, x2) plane, except at a set T of isolated points in Ω. Assume |w| ≤ M. +Then w can be defined, or redefined, at the points of T so that the resulting function +is continuous in Ω, and in any compact subregion Ω′ of Ω with d = dist(Ω′, ∂Ω), +w(x) satisfies a uniform H¨older inequality +|w(x) − w(y)| ≤ C|x − y|α, x, y ∈ Ω′, +(2.3) +where α = K − (K2 − 1) +1 +2, C depends only on K, d and M. +We prove Theorem 2.2 by making use of the Kelvin transform. For this purpose, +we establish the following lemma, which states that the Kelvin transform of an ex- +terior K-quasiconformal mapping is K-quasiconformal with an isolated singularity. +Lemma 2.5. Let w = (p, q) be exterior K-quasiconformal in R2 \ ¯B1(0). Let ˜p and +˜q be the Kelvin transform of p and q respectively, namely +˜p(x) = p +� x +|x|2 +� +, ˜q(x) = q +� x +|x|2 +� +, x ∈ B1(0) \ {0}. +Then, ˜w = (˜q, ˜p) is K-quasiconformal in B1(0) \ {0}. +Proof. Calculating directly, we have +˜p1 = +� +|x|−2 − 2x2 +1|x|−4� +p1 + +� +−2x1x2|x|−4� +p2, +˜p2 = +� +−2x1x2|x|−4� +p1 + +� +|x|−2 − 2x2 +2|x|−4� +p2, +˜q1 = +� +|x|−2 − 2x2 +1|x|−4� +q1 + +� +−2x1x2|x|−4� +q2, +and +˜q2 = +� +−2x1x2|x|−4� +q1 + +� +|x|−2 − 2x2 +2|x|−4� +q2. +It’s easy to see that +˜p2 +1 + ˜p2 +2 + ˜q2 +1 + ˜q2 +2 = |x|−4 � +p2 +1 + p2 +2 + q2 +1 + q2 +2 +� +, +and +˜p1˜q2 − ˜p2˜q1 = −|x|−4 (p1q2 − p2q1) . +Since w = (p, q) is exterior K-quasiconformal over R2 \ ¯B1(0), we deduce by Defini- +tion 2.1 that p and q satisfy (2.1) in R2 \ ¯B1(0) for some K ≥ 1. So, we obtain that +in B1(0) \ {0}, +˜p2 +1 + ˜p2 +2 + ˜q2 +1 + ˜q2 +2 ≤ 2K (˜p2˜q1 − ˜p1˜q2) , +which implies ˜w = (˜q, ˜p) is K-quasiconformal in B1(0) \ {0}. +□ +Proof of Theorem 2.2. Assume without loss of generality that B1(0) ⊂ Ω. Let ˜p +and ˜q be the Kelvin transform of p and q respectively given by Lemma 2.5. Let + +QUASICONFORMAL MAPPINGS AND A BERNSTEIN TYPE THEOREM +5 +ˆΩ = +� +x +|x|2 +���x ∈ R2 \ ¯Ω +� +and for any Ω′ ⊃⊃ Ω, ˜Ω = +� +x +|x|2 +���x ∈ R2 \ Ω′ +� +. Then by +Lemma 2.5, ˜w = (˜q, ˜p) is K-quasiconformal in ˆΩ \ {0} with K ≥ 1. Since |w| ≤ M +implies | ˜w| ≤ M, applying Lemma 2.4 to ˜w with T = {0}, we know that +| ˜w(x) − ˜w(y)| ≤ C|x − y|α, x, y ∈ ˜Ω, +which implies that ˜w(x) has a limit ˜w(0) at 0 and for all x ∈ ˜Ω, +| ˜w(x) − ˜w(0)| ≤ C|x|α, α = K − +� +K2 − 1 +� 1 +2 . +Transforming back to exterior domain, we have that +|w(x) − w(y)| ≤ C|x − y|α, x, y ∈ R2 \ Ω′ +and w(x) has a limit w(∞) = ˜w(0) at infinity with +|w(x) − w(∞)| ≤ C|x|−α, x ∈ R2 \ Ω′, +where α = K − (K2 − 1) +1 +2, C depends only on K, d and M. +The theorem is therefore proved. +□ +Next we consider linear elliptic equation +L(u) = a11(x)u11(x) + 2a12(x)u12(x) + a22(x)u22(x) = 0, +(2.4) +where L is uniformly elliptic, that is, there exist 0 < λ ≤ Λ such that +λ(ξ2 +1 + ξ2 +2) ≤ a11ξ2 +1 + 2a12ξ1ξ2 + a22ξ2 +2 ≤ Λ(ξ2 +1 + ξ2 +2), ∀ξ = (ξ1, ξ2) ∈ R2 +(2.5) +and +Λ +λ ≤ γ +(2.6) +for some constant γ ≥ 1. +For uniformly elliptic equation (2.4) in a domain Ω of R2, it follows from the +interior H¨older estimate of K-quasiconformal mappings that its bounded solutions +have interior C1,α estimate [5, Theorem 12.4]. +For uniformly elliptic equation (2.4) over exterior domain in R2, we can establish +the gradient H¨older estimate and the gradient asymptotic behavior of solutions at +infinity by the virtue of Theorem 2.2. +Theorem 2.6. Let Ω be a bounded domain of R2 and u ∈ C2(R2 \ ¯Ω) be a solution +of equation (2.4) in R2 \ ¯Ω. Suppose |Du(x)| ≤ M. Then for any Ω′ ⊃⊃ Ω with +d = dist(Ω, ∂Ω′), +|Du(x) − Du(y)| ≤ C |x − y|α , x, y ∈ R2 \ Ω′ +and Du(x) has a limit Du(∞) at infinity with +|Du(x) − Du(∞)| ≤ C|x|−α, x ∈ R2 \ Ω′, +(2.7) +where α depends only on γ, C depends only on γ, d and M. +Remark 2.7. The results in Theorem 2.6 are also valid for u ∈ W 2,2(R2 \ ¯Ω). + +6 +DONGSHENG LI AND RULIN LIU +Proof of Theorem 2.6. Assume without loss of generality that λ = 1. Let p = u1, q = +u2. By equation (2.4), (2.5) and (2.6), we have (see details in [5]) +p2 +1 + p2 +2 ≤ a11p2 +1 + 2a12p1p2 + a22p2 +2 = a22J, J = p2q1 − p1q2, x ∈ R2 \ ¯Ω +and +q2 +1 + q2 +2 ≤ a11J, x ∈ R2 \ ¯Ω. +Noticing that 2 ≤ a11 + a22 = 1 + Λ ≤ 1 + γ, we arrive at +p2 +1 + p2 +2 + q2 +1 + q2 +2 ≤ (a11 + a22) J ≤ (1 + γ) J, x ∈ R2 \ ¯Ω, +which implies that w = (q, p) is exterior K-quasiconformal over R2\ ¯Ω with K = 1+γ +2 . +Since |Du| ≤ M in R2 \ ¯Ω, Theorem 2.2 therefore asserts that for any Ω′ ⊃⊃ Ω, +|Du(x) − Du(y)| ≤ C|x|−α, x, y ∈ R2 \ Ω′ +and Du(x) tends to a limit Du(∞) = (p(∞), q(∞)) at infinity with +|Du(x) − Du(∞)| ≤ C|x|−α, x ∈ R2 \ Ω′, +where α depends only on γ, C depends only on γ, d and M. +□ +3. Exterior Bernstein type theorem +In this section, we give the proof of the exterior Bernstein type theorem, i.e., +Theorem 1.1. As we remarked before, we don’t need the concavity or convexity of +F. +We find the limit A of the Hessian D2u at infinity and estimate the decay rate of +|D2u − A| first. +Theorem 3.1. Let u be as in Theorem 1.1. Then there exists a symmetric matrix +A ∈ R2×2 such that +D2u(x) → A as |x| → ∞ +and +|D2u(x) − A| ≤ C|x|−α as |x| → ∞, +which implies +����u(x) − 1 +2xTAx +���� ≤ C|x|2−α as |x| → ∞, +(3.1) +where α ∈ (0, 1) is a constant depending only on λ and Λ, C is a positive constant +depending only on λ, Λ, and M. +Remark 3.2. If u ∈ C2, then we don’t need F ∈ C1,1 in Theorem 3.1. +Proof of Theorem 3.1. By the virtue of the Nirenberg estimate, we can see that +viscosity solutions to the equation (1.2) in R2 are always C2,α for some α ∈ (0, 1) +depending only on the ellipticity constants of F. It follows from F ∈ C1,1 and the +Schauder estimate that u ∈ C3,γ(R2 \ ¯Ω) for any γ ∈ (0, 1). Then we take derivative + +QUASICONFORMAL MAPPINGS AND A BERNSTEIN TYPE THEOREM +7 +with respect to xk (k = 1, 2) on both sides of equation (1.2) to obtain +aij(x)vij(x) = 0, x ∈ R2 \ ¯Ω, +(3.2) +where aij(x) = FMij (D2u(x)) and v(x) = uk(x). +Since ∥D2u∥L∞(R2\¯Ω) ≤ M, we know |Dv(x)| ≤ M. Applying Theorem 2.6 to +equation (3.2) in R2 \ ¯Ω, we have that Dv(x) tends to a limit Dv(∞) at infinity and +for any Ω′ ⊃⊃ Ω, +|Dv(x) − Dv(∞)| ≤ C|x|−α, x ∈ R2 \ Ω′. +Then by the arbitrarity of k, we conclude that there exists a symmetric matrix +A ∈ R2×2 such that D2u(x) → A as |x| → ∞ and +��D2u(x) − A +�� ≤ C|x|−α as |x| → ∞. +It follows that +����u(x) − 1 +2xTAx +���� ≤ C|x|2−α as |x| → ∞, +where α ∈ (0, 1) depends only on λ and Λ, C > 0 depends only on λ, Λ and M. +□ +Based on Theorem 3.1, we will find the finer asymptotic behavior of u by standard +arguments. To do this, we need the following three lemmas which are well known. +For readers’ convenience, we show the proofs of them. Lemma 3.3 gives the higher +order estimates. Lemma 3.4 and Lemma 3.5 are used to determine the linear term, +logarithm term and constant term of the asymptotics of u. +Lemma 3.3. Let φ be a viscosity solution of the equation +F +� +D2φ(x) + A +� += 0, x ∈ R2 \ ¯B1(0), +where F ∈ C1,1 is a fully nonlinear uniformly elliptic operator with ellipticity con- +stants λ and Λ, and A ∈ R2×2 is symmetric matrix, satisfying F(A) = 0. Suppose +that for some constants β > 0 and ρ < 2, +|φ(x)| ≤ β|x|ρ, x ∈ R2 \ ¯B1(0). +Then there exists some constant r = r(β, ρ) ≥ 1 such that for k = 0, 1, 2, 3, +��Dkφ(x) +�� ≤ C|x|ρ−k, x ∈ R2 \ ¯Br(0), +where C depends only on λ, Λ, β and ρ. +Proof. By F ∈ C1,1, the Nirenberg estimate and the Schauder estimate, φ(x) ∈ C3,γ +for any γ ∈ (0, 1). +Fix x ∈ R2 \ ¯B1(0) with |x| > 6 and let +¯φ(y) = +� 2 +|x| +�2 +φ +� +x + |x| +2 y +� +, y ∈ B1(0). +Since +F(A) = 0 + +8 +DONGSHENG LI AND RULIN LIU +and +F(D2 ¯φ(y) + A) = 0, y ∈ B1(0), +we see that +¯aij(y)¯φij(y) = 0, y ∈ B1(0), +where ¯aij(y) = +� 1 +0 FMij +� +tD2 ¯φ(y) + A +� +dt. By the Schauder estimate, we have that +for k = 0, 1, 2, 3, +��Dk ¯φ(0) +�� ≤ ∥¯φ∥L∞( ¯B1(0)) ≤ C|x|ρ−2, +which implies +��Dkφ(x) +�� ≤ C|x|ρ−k, +where C depends only on λ, Λ, β and ρ. +□ +Lemma 3.4. Suppose f(x) = O(|x|−β) as |x| → ∞ with β > 1. Then for any ε > 0, +the equation +∆u(x) = f(x) in R2 \ ¯B1(0) +has a solution u(x) = O(|x|2−β+ε) as |x| → ∞. +Proof. Let +u(x) = − 1 +2π +� +R2\ ¯B1(0) +(log |x − y| − log |y|)f(y)dy. +Then +∆u(x) = f(x), x ∈ R2 \ ¯B1(0) +and for any ε > 0, +|u(x)| ≤ C(ε)|x|2−β+ε, x ∈ R2 \ ¯B1(0). +□ +Lemma 3.5. Let u(x) = O(|x|β) be a smooth solution of +∆u(x) = 0, x ∈ R2 \ ¯B1(0) +for some 0 < β < 2. Then +u = b · x + d log |x| + c + O +� +|x|−1� +as |x| → ∞, +(3.3) +where b ∈ R2, c, d ∈ R. Particularly, for 0 < β < 1, (3.3) holds with b = 0. +Proof. Let ξ(z) = u1(x) − iu2(x), z = x1 + ix2. Then ξ(z) is an analytic function in +R2 \ ¯B1(0) and the growth of ξ(z) is at most of order |z|β−1. Since 0 < β < 2, the +Laurent expansion of ξ(z) has the form +ξ(z) = a0 + a−1z−1 + a−2z−2 + · · · , z ∈ R2 \ ¯B1(0), +(3.4) +where a0, a−1, a−2, · · · are all complex numbers. Thus we have +Du(x) = D(b · x + c1) + D(a−1 log |x| + c2) + O(|x|−2) as |x| → ∞, +where b = (Re a0, −Im a0)T, c1, c2 ∈ R. Since Re +� +a−1z−1 = Re(a−1 log z) as a part +of expansion of a real function u, a−1 must be a real number. Integrating the above, + +QUASICONFORMAL MAPPINGS AND A BERNSTEIN TYPE THEOREM +9 +we see that +u = b · x + d log |x| + c + O(|x|−1) as |x| → ∞, +where c ∈ R, d = a−1 ∈ R. +Particularly, for 0 < β < 1, (3.4) holds with a0 = 0. Therefore, the above equality +also holds with b = 0. +□ +Proof of Theorem 1.1. We divide the proof into six steps. +Step 1. Improving estimate (3.1). +Let +ϕ(x) = u(x) − 1 +2xTAx. +Then by Theorem 3.1, +ϕ(x) = O(|x|2−α) +and ϕ(x) satisfies +F(D2ϕ(x) + A) = 0, x ∈ R2 \ ¯Ω. +(3.5) +Suppose R0 ≥ 1 such that Ω ⊂ BR0(0). It follows from Lemma 3.3 that for all +x ∈ R2 \ ¯BR0(0), +|Dϕ(x)| ≤ C|x|1−α, +��D2ϕ(x) +�� ≤ C|x|−α, +��D3ϕ(x) +�� ≤ C|x|−1−α. +(3.6) +Taking derivative to both sides of equation (3.5) with respect to xk (k = 1, 2), we +know that ϕk satisfies equation +aij(x) (ϕk(x))ij = 0, x ∈ R2 \ ¯BR0(0), +(3.7) +where aij(x) = FMij (D2ϕ(x) + A). Since it follows from Theorem 3.1 that D2ϕ(x) → +0 as |x| → ∞, we know +aij(x) → FMij(A) as |x| → ∞. +(3.8) +Assuming without loss of generality that FMij(A) = δij, then by F ∈ C1,1, +|δij − aij| ≤ C|x|−α +(3.9) +for some C > 0. We obtain that for all x ∈ R2 \ ¯BR0(0), +ϕk(x) = O(|x|1−α) +and +∆(ϕk)(x) = (δij − aij(x)) (ϕk)ij(x) = O( +��x|−α|x|−1−α� += O +� +|x|−1−2α� +. +(3.10) +By Lemma 3.4, for any 0 < ε < α, there exists +v(x) = O(|x|1−2α+ε) +satisfying the equation (3.10). Then +∆(ϕk − v)(x) = 0, x ∈ R2 \ ¯BR0(0) +(3.11) +and +ϕk(x) − v(x) = O(|x|1−α). + +10 +DONGSHENG LI AND RULIN LIU +Therefore Lemma 3.5 states +ϕk(x) − v(x) = d log |x| + c + O +� +|x|−1� +as |x| → ∞ +for some b ∈ R2, c ∈ R. Hence, for k = 1, 2, +ϕk(x) = O(|x|1−2α+ε). +By the arbitrarity of k, we see +ϕ(x) = O(|x|2−2α+ε). +Since 0 < ε < α, we have improved the estimate (3.1) a little. +We repeat the arguments above n times, where n is determined by the following +way. Fix 0 < ε < α and let n be an integer such that 0 < 1 − 2nα + (2n − 1)ε < 1 +8, +i.e. n = +� +log2 +7 +8 −ε +α−ε +� ++ 1. Then we get an appropriate improved estimate +ϕ(x) = O(|x|2−2nα+(2n−1)ε) = O(|x|1+δ), x ∈ R2 \ ¯BR0(0) +with δ = 1 − 2nα + (2n − 1)ε < 1 +8. +Step 2. Determining the linear term. +We obtain by Lemma 3.3 that for δ ∈ (0, 1 +8) and all x ∈ R2 \ ¯BR0(0), +|Dϕ(x)| ≤ C|x|δ, |D2ϕ(x)| ≤ C|x|−1+δ. +Since ϕ(x) satisfies equation +¯aij(x)ϕij(x) = 0, x ∈ R2 \ ¯BR0(0), +(3.12) +where ¯aij(x) = +� 1 +0 FMij (tD2ϕ(x) + A) dt, it follows from F ∈ C1,1 that for some +C > 0, +|¯aij(x) − δij| ≤ C|x|−1+δ. +Thus +∆ϕ(x) = (δij − ¯aij(x)) ϕij(x) = O +� +|x|−2+2δ� +, x ∈ R2 \ ¯BR0(0). +Then Lemma 3.4 implies that for any ε ∈ (0, 1 +8), there exists +v(x) = O(|x|2δ+ε), +satisfying +∆(ϕ − v)(x) = 0, x ∈ R2 \ ¯BR0(0). +Since +ϕ(x) − v(x) = O(|x|1+δ), +it follows from Lemma 3.5 that there exists b ∈ R2 such that +ϕ(x) − v(x) = b · x + O(log |x|). +Hence +ϕ(x) = b · x + O(|x|2δ+ε). + +QUASICONFORMAL MAPPINGS AND A BERNSTEIN TYPE THEOREM +11 +Step 3. Determining the logarithm term and constant term. +Let +¯ϕ(x) = u − +�1 +2xTAx + b · x +� +. +Then +¯ϕ(x) = O(|x|2δ+ε) +and ¯ϕ(x) satisfies equation (3.12). +By Lemma 3.3, we see that for all x ∈ R2 \ ¯BR0(0), +|D ¯ϕ(x)| ≤ C|x|−1+2δ+ε, |D2 ¯ϕ(x)| ≤ C|x|−2+2δ+ε. +Consequently, for some C > 0, +|¯aij − δij| ≤ C|x|−2+2δ+ε +and +∆ ¯ϕ(x) = (δij − ¯aij) ¯ϕij = O(|x|−4+4δ+2ε). +Since δ, ε ∈ (0, 1 +8), then by Lemma 3.4, there exists +v(x) = O(|x|−2+ε′) +with ε′ ∈ (0, 1), satisfying +∆( ¯ϕ − v)(x) = 0 +and +¯ϕ(x) − v(x) = O(|x|2δ+ε). +Thus, Lemma 3.5 leads to +¯ϕ(x) = d log |x| + c + O +� +|x|−1� +as |x| → ∞ +for some c, d ∈ R, namely, +u(x) = 1 +2xTAx + b · x + d log |x| + c + O(|x|−1). +(3.13) +Step 4. Determining the +x +|x|2 term. +Let +ˆϕ(x) = u(x) − +�1 +2xTAx + b · x + d log |x| + c +� +. +Then +D2 ˆϕ = D2u − A + O(|x|−2). +By (3.13), D2u = A + O(|x|−2), which implies +��D2 ˆϕ +�� = O(|x|−2). +Since ˆϕ(x) satisfies equation (3.12) with ¯aij(x) = +� 1 +0 FMij (t (D2 ˆϕ(x) + D2(d log |x|)) + A) dt, +we have that for some R0 ≥ 1 such that Ω ⊂ BR0(0), +∆ ˆϕ(x) = (¯aij(x) − δij) ˆϕij(x) =: f(x) = O(|x|−2|x|−2) = O(|x|−4), x ∈ R2 \ ¯BR0(0). + +12 +DONGSHENG LI AND RULIN LIU +Let ψ(x) = ˆϕ( x +|x|2) and ˜f(x) = f( x +|x|2) be the Kelvin transform of ˆϕ(x) and f(x) +respectively. Then we see +ψ(x) = O(|x|) +and +∆ψ(x) = |x|−4 ˜f(x) =: g(x) = O(1), x ∈ B 1 +R0 (0). +From g ∈ Lp(B1/R0(0)) for any p > 2, it follows that ψ(x) ∈ W 2,p(B1/R0(0)) and +hence ψ(x) ∈ C1,α(B1/R0(0)) for α = 1 − 2 +p ∈ (0, 1). Then there exists e ∈ R2 and +˜c ∈ R such that for some C > 0, +|ψ(x) − (e · x + ˜c)| ≤ C|x|1+α, x ∈ B 1 +R0 (0). +Since ψ(0) = 0 implies ˜c = 0, we go back to exterior domain to get +���� ˆϕ(x) − e · x +|x|2 +���� ≤ C|x|−1−α, x ∈ R2 \ ¯BR0(0), +which leads to +u = 1 +2xTAx + b · x + d log |x| + c + e x +|x|2 + O(|x|−1−α). +Step 5. Calculating the value of d. +Let Q(x) = 1 +2xTAx + b · x + c. Then +u(x) = Q(x) + d log |x| + O(|x|−1) +and +∆(u − Q)(x) = O(|x|−3) +is integrable. Let ν be the unit outward normal of boundaries ∂Ω and CR = ∂BR(0). +Then by the divergence theorem, we have that for some R > 0 large enough, +�� +BR(0)\¯Ω +∆(u − Q)(x)dx1dx2 = +� +∂(BR(0)\¯Ω) +(u − Q)νds += +� +CR +(d log |x| + O(|x|−1))ν(x)ds − +� +∂Ω +(u − Q)νds += d +� +CR +x +|x|2 · νds + O +� 1 +R +� +− +� +∂Ω +uνds + +� +∂Ω +Qνds += 2πd + O +� 1 +R +� +− +� +∂Ω +uνds + +� +Ω +∆Qdx += 2πd + O +� 1 +R +� +− +� +∂Ω +uνds + trA|Ω|. +Letting R → ∞, we get (1.3). +Step 6. Improving smoothness of the error. + +QUASICONFORMAL MAPPINGS AND A BERNSTEIN TYPE THEOREM +13 +Furthermore, suppose F is smooth. Let +˜ϕ(x) = u − +�1 +2xTAx + b · x + d log |x| + c + e x +|x|2 +� +. +Then, the Schauder estimate asserts that for all k ∈ N, +��Dk ˜ϕ(x) +�� ≤ C(k)|x|−1−α−k. +We complete the proof of Theorem 1.1. +□ +Remark 3.6. (i). If the equation has some divergence structure, then we can obtain +another representation for the constant d, for example, the Monge-Amp`ere equations, +the special Lagrangian equations and the inverse harmonic Hessian equations. We +refer to [1] and [8] to see details. +(ii). By the virtue of Theorem 1.1, we have expansion for the solutions to the +Monge-Amp`ere equations, the special Lagrangian equations and the inverse harmonic +Hessian equations at infinity in R2 \ ¯Ω, namely, any solution tends to a quadratic +polynomial plus a logarithm term and e x +|x|2 with the error at least |x|−1−α, which is +finer than the results in [1] and [8]. +References +[1] Caffarelli, L.; Li, Yanyan. An extension to a theorem of J¨orgens, Calabi, and Pogorelov. Comm. +Pure Appl. Math. 56 (2003), no. 5, 549-583. +[2] Calabi, Eugenio. Improper affine hyperspheres of convex type and a generalization of a theorem +by K. J¨orgens. Michigan Math. J. 5 (1958), 105-126. +[3] Ferrer, L.; Mart´ınez, A.; Mil´an, F. An extension of a theorem by K. J¨orgens and a maximum +principle at infinity for parabolic affine spheres. Math. Z. 230 (1999), no. 3, 471-486. +[4] Finn, Robert; Serrin, James. On the H¨older continuity of quasi-conformal and elliptic map- +pings. Trans. Amer. Math. Soc. 89 (1958), 1-15. +[5] Gilbarg, David; Trudinger, Neil S. Elliptic partial differential equations of second order. +Reprint of the 1998 edition. Classics in Mathematics. Springer-Verlag, Berlin, 2001. +[6] Jia, Xiaobiao; Li, Dongsheng; Li, Zhisu. Asymptotic behavior at infinity of solutions of Monge- +Amp`ere equations in half spaces. J. Differential Equations. 269 (2020), no. 1, 326-348. +[7] J¨orgens, Konrad. ¨Uber die L¨osungen der Differentialgleichung rt − s2 = 1. Math. Ann. 127 +(1954), 130-134. +[8] Li, Dongsheng; Li, Zhisu; Yuan, Yu. A Bernstein problem for special Lagrangian equations in +exterior domains. Adv. Math. 361 (2020), 106927, 29pp. +[9] Morrey, Charles B., Jr. On the solutions of quasi-linear elliptic partial differential equations. +Trans. Amer. Math. Soc. 43 (1938), no. 1, 126-166. +[10] Nirenberg, Louis. On nonlinear elliptic partial differential equations and H¨older continuity. +Comm. Pure Appl. Math. 6 (1953), 103-156; addendum, 395. +[11] Pogorelov, A. V. On the improper convex affine hyperspheres. Geometriae Dedicata 1 (1972), +no. 1, 33-46. +[12] Savin, Ovidiu. A localization theorem and boundary regularity for a class of degenerate Monge- +Amp`ere equations. J. Differential Equations 256 (2014), no. 2, 327-388. + diff --git a/t9E3T4oBgHgl3EQfNgks/content/tmp_files/load_file.txt b/t9E3T4oBgHgl3EQfNgks/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..79e3bb8b2b02e3f6e33218e0e409f471db99eade --- /dev/null +++ b/t9E3T4oBgHgl3EQfNgks/content/tmp_files/load_file.txt @@ -0,0 +1,421 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf,len=420 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='04383v1 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='AP] 11 Jan 2023 QUASICONFORMAL MAPPINGS AND A BERNSTEIN TYPE THEOREM OVER EXTERIOR DOMAINS IN R2 DONGSHENG LI AND RULIN LIU Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' We establish the H¨older estimate and the asymptotic behavior at infinity for K-quasiconformal mappings over exterior domains in R2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' As a conse- quence, we prove an exterior Bernstein type theorem for fully nonlinear uniformly elliptic equations of second order in R2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Introduction For Bernstein type theorems for fully nonlinear elliptic equations, a famous the- orem of J¨orgens [7] asserts that any solution of the Monge-Amp`ere equation detD2u = 1 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1) in R2 is a quadratic polynomial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' This result was proved to be valid in higher di- mensions by Calabi (n ≤ 5 [2]) and Pogolove (n ≥ 2 [11]) for convex u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' The extension to the classical theorem of J¨orgens, Calabi and Pogorelov above follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' In 2003, Caffarelli and Li [1] proved that for n ≥ 3, any convex viscosity solution of the Monge-Amp`ere equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1) outside a bounded open subset of Rn approaches a quadratic polynomial near infinity and for n = 2, any viscosity solution tends to a quadratic polynomial plus a logarithm term, where for the later case, Ferrer, Mart´ınez and Mil´an [3] obtained the same result in 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' For the case of half space Rn +, Savin [12] established the Bernstein type theorem for equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1) in 2014, and later, in 2020, Jia, Li and Li [6] extended this theorem to exterior domains in half space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' By the virtue of the Evans-Krylov estimate, we can see that for n ≥ 3, any smooth entire solution of the general fully nonlinear elliptic equation F � D2u(x) � = 0 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2) Key words and phrases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Quasiconformal Mappings, Exterior Bernstein Type Theorem, Fully Non- linear Elliptic Equations, Asymptotic Behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' This research is supported by NSFC 12071365.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Dongsheng Li lidsh@mail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='xjtu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='cn School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='China 710049.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Rulin Liu lrl001@stu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='xjtu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='cn School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='China 710049.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' 1 2 DONGSHENG LI AND RULIN LIU in Rn is a quadratic polynomial if we assume the concavity of F and the bounded- ness of the Hessian D2u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' For n = 2, the same conclusion follows from the Nirenberg estimate [10] and the boundedness of D2u without the concavity of F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' In 2020, Li, Li and Yuan [8] established a higher dimensional exterior Bernstein type theorem for the fully nonlinear elliptic equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2), namely, for n ≥ 3, the solution of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2) in Rn \\ ¯B1(0) tends to a quadratic polynomial as |x| → ∞ if F is convex (or concave or the level set of F is convex) and D2u is bounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' As applications of this theorem, the authors obtained the exterior Bernstein type theo- rems of Monge-Amp`ere equations, special Lagrangian equations, quadratic Hessian equations and inverse harmonic Hessian equations for n ≥ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' As for n = 2, the au- thors studied these three specific equations one by one to obtain the corresponding exterior Bernstein type theorem instead of establishing the general theorem to equa- tion (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Indeed, the method in [8] does not work for two dimensional problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Roughly speaking, there are two steps in [8] to establish the exterior Bernstein type theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' First, by the concavity of F and the boundedness of D2u, the authors made use of the Evans-Krylov estimate and the weak Harnack inequality to show the existence of the limit A of D2u at infinity, which actually holds for all n ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Second, it is crucial to get the decay rate of |D2u − A| as |x| → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' This can be done by using barrier functions as n ≥ 3 while unfortunately, such barrier does not exist as n = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' In this paper, we establish the exterior Bernstein type theorem for fully nonlinear elliptic equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2) in R2 by using K-quasiconformal mappings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' The main result goes as the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Let u be a viscosity solution of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2) in the exterior domain R2 \\ ¯Ω, where F ∈ C1,1 is a fully nonlinear uniformly elliptic operator with ellipticity constants λ and Λ, and Ω is a bounded domain of R2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' If ∥D2u∥L∞(R2\\¯Ω) ≤ M < +∞, then there exists a unique symmetric matrix A ∈ R2×2, b, e ∈ R2, c, d ∈ R such that for any 0 < α < 1, u(x) = 1 2xTAx + b · x + d log |x| + c + e x |x|2 + O � |x|−1−α� as |x| → ∞, where d = 1 2π \uf8eb \uf8ec \uf8ed � ∂Ω uνds + �� R2\\¯Ω (∆u(x) − trA)dx1dx2 − trA|Ω| \uf8f6 \uf8f7 \uf8f8 , (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='3) ν is the unit outward normal of the boundary ∂Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Furthermore, if F is smooth, then we have ����Dk � u(x) − 1 2xTAx − b · x − d log |x| − c − e x |x|2 ����� = O � |x|−1−α−k� as |x| → ∞ for all k ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' QUASICONFORMAL MAPPINGS AND A BERNSTEIN TYPE THEOREM 3 Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' In Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1, the concavity (or convexity or convexity of the level set {N|F(N) = 0}) of F is not needed that is however an essential assumption in [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' As aforementioned, we will use K-quasiconformal mappings to study equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2) over exterior domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' K-quasiconformal mappings play a special role in studying the H¨older continuity of solutions of two dimensional second order par- tial differential equations, which was developed by Morrey [9], Nirenberg [10] and Finn and Serrin [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' In this paper, we will demonstrate the asymptotic behavior of K-quasiconformal mappings at infinity over exterior domains (Cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2 in Section 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' By using this result to (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2) over exterior domains, we shall not only show D2u has a limit A at infinity, but get the decay rate of |D2u − A| as |x| → ∞ as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' After this, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1 will be proved by standard arguments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' The organization of this paper goes as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' In section 2, we study the H¨older continuity and asymptotic behavior at infinity of K-quasiconformal mappings over exterior domains, which implies the gradient H¨older estimate and the gradient as- ymptotic behavior at infinity of solutions of linear elliptic equations over exterior domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' In section 3, we give the proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Exterior K-quasiconformal mappings Let’s begin with the definition of exterior K-quasiconformal mappings in R2 \\ ¯Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' We refer to [5] for the original definition of K-quasiconformal mappings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Defnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' A mapping w(x) = (p(x), q(x)) from R2 \\ ¯Ω (Ω ⊂ R2 is bounded ) in x = (x1, x2) plane to w = (p, q) plane is exterior K-quasiconformal in R2 \\ ¯Ω if p, q ∈ C1 � R2 \\ ¯Ω � and p2 1 + p2 2 + q2 1 + q2 2 ≤ 2K (p1q2 − p2q1) (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1) holds for all x ∈ R2 \\ ¯Ω with some constant K > 0, where pi = ∂p(x) ∂xi , qi = ∂q(x) ∂xi , i = 1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' For K-quasiconformal mappings, the apriori interior H¨older estimate is well known (Cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' [10, Lemma 2] and [4, Theorem 1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' For exterior K-quasiconformal mappings, we have the following H¨older estimate over exterior domain and the asymptotic behavior at infinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Let w = (p, q) be exterior K-quasiconformal in R2 \\ ¯Ω (Ω ⊂ R2 is bounded ) with K ≥ 1, and suppose |w| ≤ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then, for any Ω′ ⊃⊃ Ω with d = dist(Ω, ∂Ω′), |w(x) − w(y)| ≤ C |x − y|α , x, y ∈ R2 \\ Ω′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' and w(x) tends to a limit w(∞) at infinity such that |w(x) − w(∞)| ≤ C|x|−α for any x ∈ R2 \\ Ω′, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2) where α = K − (K2 − 1) 1 2, C depends only on K, d and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' 4 DONGSHENG LI AND RULIN LIU Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' The results in Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2 are also valid for p, q ∈ W 1,2 loc (R2 \\ ¯Ω) ∩ L∞(R2 \\ ¯Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' To prove Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2, we first state the following H¨older continuity of K-quasiconformal mappings with singularities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='4 ( [4, Theorem 3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Let w = (p, q) be K-quasiconformal in a domain Ω of x = (x1, x2) plane, except at a set T of isolated points in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Assume |w| ≤ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then w can be defined, or redefined, at the points of T so that the resulting function is continuous in Ω, and in any compact subregion Ω′ of Ω with d = dist(Ω′, ∂Ω), w(x) satisfies a uniform H¨older inequality |w(x) − w(y)| ≤ C|x − y|α, x, y ∈ Ω′, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='3) where α = K − (K2 − 1) 1 2, C depends only on K, d and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' We prove Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2 by making use of the Kelvin transform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' For this purpose, we establish the following lemma, which states that the Kelvin transform of an ex- terior K-quasiconformal mapping is K-quasiconformal with an isolated singularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Let w = (p, q) be exterior K-quasiconformal in R2 \\ ¯B1(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Let ˜p and ˜q be the Kelvin transform of p and q respectively, namely ˜p(x) = p � x |x|2 � , ˜q(x) = q � x |x|2 � , x ∈ B1(0) \\ {0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then, ˜w = (˜q, ˜p) is K-quasiconformal in B1(0) \\ {0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Calculating directly, we have ˜p1 = � |x|−2 − 2x2 1|x|−4� p1 + � −2x1x2|x|−4� p2, ˜p2 = � −2x1x2|x|−4� p1 + � |x|−2 − 2x2 2|x|−4� p2, ˜q1 = � |x|−2 − 2x2 1|x|−4� q1 + � −2x1x2|x|−4� q2, and ˜q2 = � −2x1x2|x|−4� q1 + � |x|−2 − 2x2 2|x|−4� q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' It’s easy to see that ˜p2 1 + ˜p2 2 + ˜q2 1 + ˜q2 2 = |x|−4 � p2 1 + p2 2 + q2 1 + q2 2 � , and ˜p1˜q2 − ˜p2˜q1 = −|x|−4 (p1q2 − p2q1) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Since w = (p, q) is exterior K-quasiconformal over R2 \\ ¯B1(0), we deduce by Defini- tion 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1 that p and q satisfy (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1) in R2 \\ ¯B1(0) for some K ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' So, we obtain that in B1(0) \\ {0}, ˜p2 1 + ˜p2 2 + ˜q2 1 + ˜q2 2 ≤ 2K (˜p2˜q1 − ˜p1˜q2) , which implies ˜w = (˜q, ˜p) is K-quasiconformal in B1(0) \\ {0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' □ Proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Assume without loss of generality that B1(0) ⊂ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Let ˜p and ˜q be the Kelvin transform of p and q respectively given by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Let QUASICONFORMAL MAPPINGS AND A BERNSTEIN TYPE THEOREM 5 ˆΩ = � x |x|2 ���x ∈ R2 \\ ¯Ω � and for any Ω′ ⊃⊃ Ω, ˜Ω = � x |x|2 ���x ∈ R2 \\ Ω′ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='5, ˜w = (˜q, ˜p) is K-quasiconformal in ˆΩ \\ {0} with K ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Since |w| ≤ M implies | ˜w| ≤ M, applying Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='4 to ˜w with T = {0}, we know that | ˜w(x) − ˜w(y)| ≤ C|x − y|α, x, y ∈ ˜Ω, which implies that ˜w(x) has a limit ˜w(0) at 0 and for all x ∈ ˜Ω, | ˜w(x) − ˜w(0)| ≤ C|x|α, α = K − � K2 − 1 � 1 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Transforming back to exterior domain, we have that |w(x) − w(y)| ≤ C|x − y|α, x, y ∈ R2 \\ Ω′ and w(x) has a limit w(∞) = ˜w(0) at infinity with |w(x) − w(∞)| ≤ C|x|−α, x ∈ R2 \\ Ω′, where α = K − (K2 − 1) 1 2, C depends only on K, d and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' The theorem is therefore proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' □ Next we consider linear elliptic equation L(u) = a11(x)u11(x) + 2a12(x)u12(x) + a22(x)u22(x) = 0, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='4) where L is uniformly elliptic, that is, there exist 0 < λ ≤ Λ such that λ(ξ2 1 + ξ2 2) ≤ a11ξ2 1 + 2a12ξ1ξ2 + a22ξ2 2 ≤ Λ(ξ2 1 + ξ2 2), ∀ξ = (ξ1, ξ2) ∈ R2 (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='5) and Λ λ ≤ γ (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='6) for some constant γ ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' For uniformly elliptic equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='4) in a domain Ω of R2, it follows from the interior H¨older estimate of K-quasiconformal mappings that its bounded solutions have interior C1,α estimate [5, Theorem 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' For uniformly elliptic equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='4) over exterior domain in R2, we can establish the gradient H¨older estimate and the gradient asymptotic behavior of solutions at infinity by the virtue of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Let Ω be a bounded domain of R2 and u ∈ C2(R2 \\ ¯Ω) be a solution of equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='4) in R2 \\ ¯Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Suppose |Du(x)| ≤ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then for any Ω′ ⊃⊃ Ω with d = dist(Ω, ∂Ω′), |Du(x) − Du(y)| ≤ C |x − y|α , x, y ∈ R2 \\ Ω′ and Du(x) has a limit Du(∞) at infinity with |Du(x) − Du(∞)| ≤ C|x|−α, x ∈ R2 \\ Ω′, (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='7) where α depends only on γ, C depends only on γ, d and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' The results in Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='6 are also valid for u ∈ W 2,2(R2 \\ ¯Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' 6 DONGSHENG LI AND RULIN LIU Proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Assume without loss of generality that λ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Let p = u1, q = u2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' By equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='4), (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='5) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='6), we have (see details in [5]) p2 1 + p2 2 ≤ a11p2 1 + 2a12p1p2 + a22p2 2 = a22J, J = p2q1 − p1q2, x ∈ R2 \\ ¯Ω and q2 1 + q2 2 ≤ a11J, x ∈ R2 \\ ¯Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Noticing that 2 ≤ a11 + a22 = 1 + Λ ≤ 1 + γ, we arrive at p2 1 + p2 2 + q2 1 + q2 2 ≤ (a11 + a22) J ≤ (1 + γ) J, x ∈ R2 \\ ¯Ω, which implies that w = (q, p) is exterior K-quasiconformal over R2\\ ¯Ω with K = 1+γ 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Since |Du| ≤ M in R2 \\ ¯Ω, Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2 therefore asserts that for any Ω′ ⊃⊃ Ω, |Du(x) − Du(y)| ≤ C|x|−α, x, y ∈ R2 \\ Ω′ and Du(x) tends to a limit Du(∞) = (p(∞), q(∞)) at infinity with |Du(x) − Du(∞)| ≤ C|x|−α, x ∈ R2 \\ Ω′, where α depends only on γ, C depends only on γ, d and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' □ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Exterior Bernstein type theorem In this section, we give the proof of the exterior Bernstein type theorem, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=', Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' As we remarked before, we don’t need the concavity or convexity of F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' We find the limit A of the Hessian D2u at infinity and estimate the decay rate of |D2u − A| first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Let u be as in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then there exists a symmetric matrix A ∈ R2×2 such that D2u(x) → A as |x| → ∞ and |D2u(x) − A| ≤ C|x|−α as |x| → ∞, which implies ����u(x) − 1 2xTAx ���� ≤ C|x|2−α as |x| → ∞, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1) where α ∈ (0, 1) is a constant depending only on λ and Λ, C is a positive constant depending only on λ, Λ, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' If u ∈ C2, then we don’t need F ∈ C1,1 in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' By the virtue of the Nirenberg estimate, we can see that viscosity solutions to the equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2) in R2 are always C2,α for some α ∈ (0, 1) depending only on the ellipticity constants of F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' It follows from F ∈ C1,1 and the Schauder estimate that u ∈ C3,γ(R2 \\ ¯Ω) for any γ ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then we take derivative QUASICONFORMAL MAPPINGS AND A BERNSTEIN TYPE THEOREM 7 with respect to xk (k = 1, 2) on both sides of equation (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2) to obtain aij(x)vij(x) = 0, x ∈ R2 \\ ¯Ω, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2) where aij(x) = FMij (D2u(x)) and v(x) = uk(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Since ∥D2u∥L∞(R2\\¯Ω) ≤ M, we know |Dv(x)| ≤ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Applying Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='6 to equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='2) in R2 \\ ¯Ω, we have that Dv(x) tends to a limit Dv(∞) at infinity and for any Ω′ ⊃⊃ Ω, |Dv(x) − Dv(∞)| ≤ C|x|−α, x ∈ R2 \\ Ω′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then by the arbitrarity of k, we conclude that there exists a symmetric matrix A ∈ R2×2 such that D2u(x) → A as |x| → ∞ and ��D2u(x) − A �� ≤ C|x|−α as |x| → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' It follows that ����u(x) − 1 2xTAx ���� ≤ C|x|2−α as |x| → ∞, where α ∈ (0, 1) depends only on λ and Λ, C > 0 depends only on λ, Λ and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' □ Based on Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1, we will find the finer asymptotic behavior of u by standard arguments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' To do this, we need the following three lemmas which are well known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' For readers’ convenience, we show the proofs of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='3 gives the higher order estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='4 and Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='5 are used to determine the linear term, logarithm term and constant term of the asymptotics of u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Let φ be a viscosity solution of the equation F � D2φ(x) + A � = 0, x ∈ R2 \\ ¯B1(0), where F ∈ C1,1 is a fully nonlinear uniformly elliptic operator with ellipticity con- stants λ and Λ, and A ∈ R2×2 is symmetric matrix, satisfying F(A) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Suppose that for some constants β > 0 and ρ < 2, |φ(x)| ≤ β|x|ρ, x ∈ R2 \\ ¯B1(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then there exists some constant r = r(β, ρ) ≥ 1 such that for k = 0, 1, 2, 3, ��Dkφ(x) �� ≤ C|x|ρ−k, x ∈ R2 \\ ¯Br(0), where C depends only on λ, Λ, β and ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' By F ∈ C1,1, the Nirenberg estimate and the Schauder estimate, φ(x) ∈ C3,γ for any γ ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Fix x ∈ R2 \\ ¯B1(0) with |x| > 6 and let ¯φ(y) = � 2 |x| �2 φ � x + |x| 2 y � , y ∈ B1(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Since F(A) = 0 8 DONGSHENG LI AND RULIN LIU and F(D2 ¯φ(y) + A) = 0, y ∈ B1(0), we see that ¯aij(y)¯φij(y) = 0, y ∈ B1(0), where ¯aij(y) = � 1 0 FMij � tD2 ¯φ(y) + A � dt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' By the Schauder estimate, we have that for k = 0, 1, 2, 3, ��Dk ¯φ(0) �� ≤ ∥¯φ∥L∞( ¯B1(0)) ≤ C|x|ρ−2, which implies ��Dkφ(x) �� ≤ C|x|ρ−k, where C depends only on λ, Λ, β and ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' □ Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Suppose f(x) = O(|x|−β) as |x| → ∞ with β > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then for any ε > 0, the equation ∆u(x) = f(x) in R2 \\ ¯B1(0) has a solution u(x) = O(|x|2−β+ε) as |x| → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Let u(x) = − 1 2π � R2\\ ¯B1(0) (log |x − y| − log |y|)f(y)dy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then ∆u(x) = f(x), x ∈ R2 \\ ¯B1(0) and for any ε > 0, |u(x)| ≤ C(ε)|x|2−β+ε, x ∈ R2 \\ ¯B1(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' □ Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Let u(x) = O(|x|β) be a smooth solution of ∆u(x) = 0, x ∈ R2 \\ ¯B1(0) for some 0 < β < 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then u = b · x + d log |x| + c + O � |x|−1� as |x| → ∞, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='3) where b ∈ R2, c, d ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Particularly, for 0 < β < 1, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='3) holds with b = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Let ξ(z) = u1(x) − iu2(x), z = x1 + ix2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then ξ(z) is an analytic function in R2 \\ ¯B1(0) and the growth of ξ(z) is at most of order |z|β−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Since 0 < β < 2, the Laurent expansion of ξ(z) has the form ξ(z) = a0 + a−1z−1 + a−2z−2 + · · · , z ∈ R2 \\ ¯B1(0), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='4) where a0, a−1, a−2, · · · are all complex numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Thus we have Du(x) = D(b · x + c1) + D(a−1 log |x| + c2) + O(|x|−2) as |x| → ∞, where b = (Re a0, −Im a0)T, c1, c2 ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Since Re � a−1z−1 = Re(a−1 log z) as a part of expansion of a real function u, a−1 must be a real number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Integrating the above, QUASICONFORMAL MAPPINGS AND A BERNSTEIN TYPE THEOREM 9 we see that u = b · x + d log |x| + c + O(|x|−1) as |x| → ∞, where c ∈ R, d = a−1 ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Particularly, for 0 < β < 1, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='4) holds with a0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Therefore, the above equality also holds with b = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' □ Proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' We divide the proof into six steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Step 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Improving estimate (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Let ϕ(x) = u(x) − 1 2xTAx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then by Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1, ϕ(x) = O(|x|2−α) and ϕ(x) satisfies F(D2ϕ(x) + A) = 0, x ∈ R2 \\ ¯Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='5) Suppose R0 ≥ 1 such that Ω ⊂ BR0(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' It follows from Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='3 that for all x ∈ R2 \\ ¯BR0(0), |Dϕ(x)| ≤ C|x|1−α, ��D2ϕ(x) �� ≤ C|x|−α, ��D3ϕ(x) �� ≤ C|x|−1−α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='6) Taking derivative to both sides of equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='5) with respect to xk (k = 1, 2), we know that ϕk satisfies equation aij(x) (ϕk(x))ij = 0, x ∈ R2 \\ ¯BR0(0), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='7) where aij(x) = FMij (D2ϕ(x) + A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Since it follows from Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1 that D2ϕ(x) → 0 as |x| → ∞, we know aij(x) → FMij(A) as |x| → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='8) Assuming without loss of generality that FMij(A) = δij, then by F ∈ C1,1, |δij − aij| ≤ C|x|−α (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='9) for some C > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' We obtain that for all x ∈ R2 \\ ¯BR0(0), ϕk(x) = O(|x|1−α) and ∆(ϕk)(x) = (δij − aij(x)) (ϕk)ij(x) = O( ��x|−α|x|−1−α� = O � |x|−1−2α� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='10) By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='4, for any 0 < ε < α, there exists v(x) = O(|x|1−2α+ε) satisfying the equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then ∆(ϕk − v)(x) = 0, x ∈ R2 \\ ¯BR0(0) (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='11) and ϕk(x) − v(x) = O(|x|1−α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' 10 DONGSHENG LI AND RULIN LIU Therefore Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='5 states ϕk(x) − v(x) = d log |x| + c + O � |x|−1� as |x| → ∞ for some b ∈ R2, c ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Hence, for k = 1, 2, ϕk(x) = O(|x|1−2α+ε).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' By the arbitrarity of k, we see ϕ(x) = O(|x|2−2α+ε).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Since 0 < ε < α, we have improved the estimate (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1) a little.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' We repeat the arguments above n times, where n is determined by the following way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Fix 0 < ε < α and let n be an integer such that 0 < 1 − 2nα + (2n − 1)ε < 1 8, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' n = � log2 7 8 −ε α−ε � + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then we get an appropriate improved estimate ϕ(x) = O(|x|2−2nα+(2n−1)ε) = O(|x|1+δ), x ∈ R2 \\ ¯BR0(0) with δ = 1 − 2nα + (2n − 1)ε < 1 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Step 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Determining the linear term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' We obtain by Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='3 that for δ ∈ (0, 1 8) and all x ∈ R2 \\ ¯BR0(0), |Dϕ(x)| ≤ C|x|δ, |D2ϕ(x)| ≤ C|x|−1+δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Since ϕ(x) satisfies equation ¯aij(x)ϕij(x) = 0, x ∈ R2 \\ ¯BR0(0), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='12) where ¯aij(x) = � 1 0 FMij (tD2ϕ(x) + A) dt, it follows from F ∈ C1,1 that for some C > 0, |¯aij(x) − δij| ≤ C|x|−1+δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Thus ∆ϕ(x) = (δij − ¯aij(x)) ϕij(x) = O � |x|−2+2δ� , x ∈ R2 \\ ¯BR0(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='4 implies that for any ε ∈ (0, 1 8), there exists v(x) = O(|x|2δ+ε), satisfying ∆(ϕ − v)(x) = 0, x ∈ R2 \\ ¯BR0(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Since ϕ(x) − v(x) = O(|x|1+δ), it follows from Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='5 that there exists b ∈ R2 such that ϕ(x) − v(x) = b · x + O(log |x|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Hence ϕ(x) = b · x + O(|x|2δ+ε).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' QUASICONFORMAL MAPPINGS AND A BERNSTEIN TYPE THEOREM 11 Step 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Determining the logarithm term and constant term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Let ¯ϕ(x) = u − �1 2xTAx + b · x � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then ¯ϕ(x) = O(|x|2δ+ε) and ¯ϕ(x) satisfies equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='3, we see that for all x ∈ R2 \\ ¯BR0(0), |D ¯ϕ(x)| ≤ C|x|−1+2δ+ε, |D2 ¯ϕ(x)| ≤ C|x|−2+2δ+ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Consequently, for some C > 0, |¯aij − δij| ≤ C|x|−2+2δ+ε and ∆ ¯ϕ(x) = (δij − ¯aij) ¯ϕij = O(|x|−4+4δ+2ε).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Since δ, ε ∈ (0, 1 8), then by Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='4, there exists v(x) = O(|x|−2+ε′) with ε′ ∈ (0, 1), satisfying ∆( ¯ϕ − v)(x) = 0 and ¯ϕ(x) − v(x) = O(|x|2δ+ε).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Thus, Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='5 leads to ¯ϕ(x) = d log |x| + c + O � |x|−1� as |x| → ∞ for some c, d ∈ R, namely, u(x) = 1 2xTAx + b · x + d log |x| + c + O(|x|−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='13) Step 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Determining the x |x|2 term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Let ˆϕ(x) = u(x) − �1 2xTAx + b · x + d log |x| + c � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then D2 ˆϕ = D2u − A + O(|x|−2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' By (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='13), D2u = A + O(|x|−2), which implies ��D2 ˆϕ �� = O(|x|−2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Since ˆϕ(x) satisfies equation (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='12) with ¯aij(x) = � 1 0 FMij (t (D2 ˆϕ(x) + D2(d log |x|)) + A) dt, we have that for some R0 ≥ 1 such that Ω ⊂ BR0(0), ∆ ˆϕ(x) = (¯aij(x) − δij) ˆϕij(x) =: f(x) = O(|x|−2|x|−2) = O(|x|−4), x ∈ R2 \\ ¯BR0(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' 12 DONGSHENG LI AND RULIN LIU Let ψ(x) = ˆϕ( x |x|2) and ˜f(x) = f( x |x|2) be the Kelvin transform of ˆϕ(x) and f(x) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then we see ψ(x) = O(|x|) and ∆ψ(x) = |x|−4 ˜f(x) =: g(x) = O(1), x ∈ B 1 R0 (0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' From g ∈ Lp(B1/R0(0)) for any p > 2, it follows that ψ(x) ∈ W 2,p(B1/R0(0)) and hence ψ(x) ∈ C1,α(B1/R0(0)) for α = 1 − 2 p ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then there exists e ∈ R2 and ˜c ∈ R such that for some C > 0, |ψ(x) − (e · x + ˜c)| ≤ C|x|1+α, x ∈ B 1 R0 (0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Since ψ(0) = 0 implies ˜c = 0, we go back to exterior domain to get ���� ˆϕ(x) − e · x |x|2 ���� ≤ C|x|−1−α, x ∈ R2 \\ ¯BR0(0), which leads to u = 1 2xTAx + b · x + d log |x| + c + e x |x|2 + O(|x|−1−α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Step 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Calculating the value of d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Let Q(x) = 1 2xTAx + b · x + c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then u(x) = Q(x) + d log |x| + O(|x|−1) and ∆(u − Q)(x) = O(|x|−3) is integrable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Let ν be the unit outward normal of boundaries ∂Ω and CR = ∂BR(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then by the divergence theorem, we have that for some R > 0 large enough, �� BR(0)\\¯Ω ∆(u − Q)(x)dx1dx2 = � ∂(BR(0)\\¯Ω) (u − Q)νds = � CR (d log |x| + O(|x|−1))ν(x)ds − � ∂Ω (u − Q)νds = d � CR x |x|2 · νds + O � 1 R � − � ∂Ω uνds + � ∂Ω Qνds = 2πd + O � 1 R � − � ∂Ω uνds + � Ω ∆Qdx = 2πd + O � 1 R � − � ∂Ω uνds + trA|Ω|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Letting R → ∞, we get (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Step 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Improving smoothness of the error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' QUASICONFORMAL MAPPINGS AND A BERNSTEIN TYPE THEOREM 13 Furthermore, suppose F is smooth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Let ˜ϕ(x) = u − �1 2xTAx + b · x + d log |x| + c + e x |x|2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Then, the Schauder estimate asserts that for all k ∈ N, ��Dk ˜ϕ(x) �� ≤ C(k)|x|−1−α−k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' We complete the proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' □ Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' (i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' If the equation has some divergence structure, then we can obtain another representation for the constant d, for example, the Monge-Amp`ere equations, the special Lagrangian equations and the inverse harmonic Hessian equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' We refer to [1] and [8] to see details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' By the virtue of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content='1, we have expansion for the solutions to the Monge-Amp`ere equations, the special Lagrangian equations and the inverse harmonic Hessian equations at infinity in R2 \\ ¯Ω, namely, any solution tends to a quadratic polynomial plus a logarithm term and e x |x|2 with the error at least |x|−1−α, which is finer than the results in [1] and [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' References [1] Caffarelli, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Li, Yanyan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' An extension to a theorem of J¨orgens, Calabi, and Pogorelov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Pure Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' 56 (2003), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' 5, 549-583.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' [2] Calabi, Eugenio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Improper affine hyperspheres of convex type and a generalization of a theorem by K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' J¨orgens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Michigan Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' 5 (1958), 105-126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' [3] Ferrer, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Mart´ınez, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Mil´an, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' An extension of a theorem by K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' J¨orgens and a maximum principle at infinity for parabolic affine spheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' 230 (1999), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' 3, 471-486.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' [4] Finn, Robert;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Serrin, James.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' On the H¨older continuity of quasi-conformal and elliptic map- pings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' 89 (1958), 1-15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' [5] Gilbarg, David;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Trudinger, Neil S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Elliptic partial differential equations of second order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Reprint of the 1998 edition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Classics in Mathematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Springer-Verlag, Berlin, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' [6] Jia, Xiaobiao;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Li, Dongsheng;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Li, Zhisu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Asymptotic behavior at infinity of solutions of Monge- Amp`ere equations in half spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Differential Equations.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' 127 (1954), 130-134.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' [8] Li, Dongsheng;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Li, Zhisu;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Yuan, Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' A Bernstein problem for special Lagrangian equations in exterior domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' 361 (2020), 106927, 29pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' [9] Morrey, Charles B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=', Jr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' On the solutions of quasi-linear elliptic partial differential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' 43 (1938), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' 1, 126-166.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' [10] Nirenberg, Louis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' On nonlinear elliptic partial differential equations and H¨older continuity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Pure Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' 6 (1953), 103-156;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' addendum, 395.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' [11] Pogorelov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' On the improper convex affine hyperspheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Geometriae Dedicata 1 (1972), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' 1, 33-46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' [12] Savin, Ovidiu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' A localization theorem and boundary regularity for a class of degenerate Monge- Amp`ere equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' Differential Equations 256 (2014), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} +page_content=' 2, 327-388.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/t9E3T4oBgHgl3EQfNgks/content/2301.04383v1.pdf'} diff --git a/t9FJT4oBgHgl3EQfdywM/content/2301.11549v1.pdf b/t9FJT4oBgHgl3EQfdywM/content/2301.11549v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2560d166024191dce6b05b893a254737a25113c7 --- /dev/null +++ b/t9FJT4oBgHgl3EQfdywM/content/2301.11549v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c833665cbc917846d572934d996f8d5fb278f27afe73e9922e32c00f321e1a97 +size 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b/udE0T4oBgHgl3EQfsQEM/content/tmp_files/2301.02575v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..d64c0aa8600621d709bfe151a35861607a9299f2 --- /dev/null +++ b/udE0T4oBgHgl3EQfsQEM/content/tmp_files/2301.02575v1.pdf.txt @@ -0,0 +1,7152 @@ +Cognitive Endurance, Talent Selection, and the Labor +Market Returns to Human Capital +Germán Reyes∗ +January 2023 +Abstract +Cognitive endurance—the ability to sustain performance on a cognitively-demanding +task over time—is thought to be a crucial productivity determinant. However, a lack +of data on this variable has limited researchers’ ability to understand its role for suc- +cess in college and the labor market. This paper uses college-admission-exam records +from 15 million Brazilian high school students to measure cognitive endurance based +on changes in performance throughout the exam. By exploiting exogenous variation +in the order of exam questions, I show that students are 7.1 percentage points more +likely to correctly answer a given question when it appears at the beginning of the +day versus the end (relative to a sample mean of 34.3%). I develop a method to +decompose test scores into fatigue-adjusted ability and cognitive endurance. I then +merge these measures into a higher-education census and the earnings records of the +universe of Brazilian formal-sector workers to quantify the association between en- +durance and long-run outcomes. I find that cognitive endurance has a statistically +and economically significant wage return. Controlling for fatigue-adjusted ability and +other student characteristics, a one-standard-deviation higher endurance predicts a +5.4% wage increase. This wage return to endurance is sizable, equivalent to a third of +the wage return to ability. I also document positive associations between endurance +and college attendance, college quality, college graduation, firm quality, and other +outcomes. Finally, I show how systematic differences in endurance across students +interact with the exam design to determine the sorting of students to colleges. I dis- +cuss the implications of these findings for the use of cognitive assessments for talent +selection and investments in interventions that build cognitive endurance. +∗Department of Economics, Cornell University, 457 Uris Hall, Ithaca, NY 14853, United States (e- +mail: gjr66@cornell.edu). I thank especially my advisor Ted O’Donoghue for invaluable guidance. For +helpful discussions and comments, I thank Ned Augenblick, Michèle Belot, Nicolas Bottan, Emily Breza, +Aviv Caspi, Zoë Cullen, Neel Datta, Stefano DellaVigna, Josh Dean, Christa Deneault, Rebecca Dera- +nian, Gary Fields, Thomas Graeber, Ori Heffetz, Alex Imas, Guy Ishai, Judd Kessler, Yizhou (Kyle) +Kuang, Shengwu Li, Yucheng Liang, George Loewenstein, Michael Lovenheim, Suraj Malladi, Alejan- +dro Martínez-Marquina, Francesca Molinari, Kevin Ng, Muriel Niederle, Ricardo Perez-Truglia, Grace +Phillips, Alex Rees-Jones, Evan Riehl, Seth Sanders, Paola Sapienza, Frank Schilbach, Heather Schofield, +Peter Schwardmann, Dmitry Taubinsky, participants in the Cornell behavioral economics group, partic- +ipants in the UC Berkeley psychology and economics group, and numerous seminar participants. I also +thank Marco Pereira and other members of SEDAP for invaluable help using the secured data room. +Financial support from the National Science Foundation is gratefully acknowledged. +1 +arXiv:2301.02575v1 [econ.GN] 6 Jan 2023 + +1 +Introduction +The human capital framework posits that individuals’ skills and knowledge act as a form of +capital that improves productivity and, thus, labor earnings (Becker, 1962). The positive +relationship between human capital and earnings is one of the most robust findings in the +social sciences (Deming, 2022), and is supported by a large body of work (e.g., Mincer, +1958; Griliches, 1977; Card, 1999, 2001). While early studies focused on aggregate measures +of human capital—like years of schooling—more recent work has focused on estimating the +economic returns to specific skills, such as social skills (Deming, 2017) or cognitive skills +(Hermo et al., 2022). Identifying skills that foster productivity is essential for the design +of effective education and labor-market policies (Almlund et al., 2011; Kautz et al., 2014). +In this paper, I study one dimension of human capital that may be particularly impor- +tant for knowledge workers: cognitive endurance, that is, the ability to sustain performance +on a cognitively-demanding task for an extended duration. I first document that the per- +formance of individuals on a college admission exam tends to decline, which allows me to +measure cognitive endurance. Specifically, I develop a method to decompose test scores +into fatigue-adjusted ability and endurance. I use the decomposition to investigate the re- +lationship between endurance and long-run outcomes. I show that endurance has a sizable +wage return in the labor market, comparable to the wage return to ability. I also show +that, due to systematic differences in endurance across students, seemingly neutral exam +design choices, such as the exam length, can have equity and efficiency consequences by +affecting the sorting of students across colleges. +Psychologists and self-help books have long hypothesized that cognitive endurance is +an important productivity determinant. Research on the nature of expertise—popularized +in influential books like Focus (Goleman, 2013) or Deep Work (Newport, 2016)—often +identifies this skill as a key driver of performance.1 Relatedly, biographers of extraordinary +achievers often ascribe their accomplishments to unusually-high endurance.2 Consistent +with this, researchers have documented the negative consequences of limited endurance +for task performance in many settings.3 The hypothesized link between endurance and +1Psychologists have identified cognitive fatigue effects and highlighted the importance of mental en- +durance for high performance at least since the early 20th century (e.g., James, 1907; Dodge, 1917). +2For example, in describing Newton’s accomplishments, Keynes (1956) noted that his greatest skill was +“the power of holding continuously in his mind a purely mental problem until he had seen straight through +it.” See Lykken (2005) for many other examples. +3Specifically, researchers have shown that individual-level job performance tends to deteriorate over +relatively short time spans. For example, over the course of a day: nurses are less likely to wash their +hands (Dai et al., 2015; Steiny Wellsjo, 2022); doctors make more diagnostic mistakes (Chan et al., 2009; +2 + +productivity is also consistent with the large markets for endurance enhancers like coffee +or nootropics (e.g., Adderall).4 +These observations suggest that cognitive endurance and task performance are inti- +mately linked. Yet, despite this popular perception, empirical economists have had little +to say about the role of endurance in the labor market, possibly because of a lack of data +on this variable. I address this problem by using data from the college admission exam in +Brazil (called “ENEM”) to create an individual-level measure of endurance that is based +on performance declines throughout the exam (Borghans and Schils, 2018; Brown et al., +2022). +The ENEM is an ideal setting to study cognitive endurance for several reasons. First, +the exam is administered under uniform conditions, and the scoring is standardized—two +crucial properties for generating measures that are comparable across individuals (Almlund +et al., 2011). Second, it is a high-stakes environment. Test scores largely determine the +college options of the millions of high school students who take the ENEM every year. Since +test-takers have incentives to exert maximal effort, limits to cognitive endurance are more +likely to drive systematic declines in performance rather than low motivation (Duckworth +et al., 2011; Gneezy et al., 2019). Third, the exam is grueling. The ENEM is ten hours long +and is conducted over two consecutive days of testing. Thus, we might expect cognitive +endurance to be an especially valuable skill in this setting and cross-person differences in +endurance to be reflected in test performance. +My analysis takes advantage of three features of the ENEM. First, the dataset con- +tains students’ responses to each exam question, which enables me to measure student +performance throughout the exam. Second, students are randomly assigned different test +booklets. Each booklet has the same set of questions (or “items”) but in a different or- +der, which enables me to study how students perform on a given question when they are +relatively “fresh” versus mentally fatigued. Third, the ENEM can be linked to other admin- +istrative datasets to measure students’ long-run outcomes. Specifically, I link the ENEM +records to a census of all Brazilian college students and an employee-employer matched +dataset that covers the universe of formal-sector workers in Brazil. +Linder et al., 2014; Kim et al., 2018); financial analysts make less accurate forecasts (Hirshleifer et al., +2019); and umpires make more incorrect calls in baseball games (Archsmith et al., 2021). +4For example, in the US, 65% of adults drink coffee daily (Lampkin, 2012), and about 20% of college +students report using nootropics without a prescription to enhance focus and cognition (Benson et al., +2015). Relatedly, over-the-counter focus-enhancing drugs have entire sections in chain drug stores (e.g., +Appendix Figure A1), and there is a growing variety of products marketed as endurance training (e.g., +brain-training games like “Lumosity” or interval-based training technologies like “Pomodoros”). +3 + +I measure cognitive endurance as the impact of a one-position increase in the order of a +given question on the likelihood of correctly answering the question. A potential-outcomes +framework reveals that this measure captures the combined impact of two structural pa- +rameters: how cognitively fatigued an individual becomes throughout the exam and how +an increase in fatigue affects test performance. These two parameters, and thus, my en- +durance measure, likely capture a variety of psychological mechanisms, including intrinsic +motivation, grit, and attention capacity. +Applying this framework, I first estimate mean cognitive endurance across all students +using two empirical strategies. The first research design compares average student perfor- +mance on a given question as a function of its position on each booklet, which I implement +by regressing the fraction of students who correctly answer a question on its position on +the exam, controlling for question fixed effects. This approach provides the more credi- +ble estimates of mean cognitive endurance; however, since each student only receives one +exam booklet, it cannot be used to estimate individual-level endurance. Thus, I also use +a second research design that can be used to identify both average and individual-level +endurance. The second approach consists of creating a position-adjusted measure of ques- +tion difficulty, and then using this measure as a control variable instead of the question +fixed effects. Both strategies deliver a similar-sized estimate of mean cognitive endurance. +A one-position increase in the order of a given question decreases the chances of correctly +answering the question by 0.08 percentage points. Scaled by the number of questions per +testing day, this estimate implies that daily performance decreases by 7.1 percentage points +due to limited endurance. +Next, I estimate the difficulty-adjusted regression separately for each individual. This +allows me to decompose an individual’s test score into a measure of cognitive endurance +and a measure of fatigue-adjusted academic ability. My measure of cognitive endurance is +the same as above but now estimated separately for each student. My measure of fatigue- +adjusted ability is the residual of an individual’s test score after subtracting from it the +component explained by cognitive endurance. Using a sample of students who took the +exam multiple times, I show that this measure of cognitive endurance has a test-retest +reliability comparable to that of other commonly used constructs like risk aversion (Mata +et al., 2018) or teacher value-added (Chetty et al., 2014a). +The measures generated by the decomposition enable me to investigate the importance +of cognitive endurance for success in college and the labor market. I find that, holding fixed +fatigue-adjusted ability and other student characteristics, individuals with more cognitive +4 + +endurance are more likely to attend college, enroll in higher-quality colleges, are more likely +to graduate, earn higher wages, and work for higher-paying firms. The associations are +sizable. For example, controlling for ability and other variables, a one standard deviation +(SD) increase in cognitive endurance predicts a 5.4% increase in early-career wages. The +corresponding prediction for a one SD increase in ability equals 15.4%. Hence, the wage +return to endurance is about a third of the size of the return to ability. Instrumental +variable regressions show that the association between endurance and wages is larger after +accounting for measurement error (on the order of 70% the size of the return to ability) +and also reveal that the predicted effect is not driven by a mechanical relationship between +endurance and test scores. +Heterogeneity analysis reveals substantial variation in the wage return to ability and +to endurance across college majors, occupations, and industries. On average, occupations +and industries that pay higher wages also offer a higher wage return to ability and to +endurance. +This result documents a novel type of assortative matching between high- +endurance workers and high-paying jobs. Furthermore, occupations and industries with a +high wage return to endurance also tend to have a high wage return to ability, suggesting +these two skills are complements in production. Some occupations with the highest wage +return to endurance include those where lapses in sustained attention can have high costs, +like facility operators in chemical plants or professionals in the aviation industry. This +finding suggests that the value of endurance depends on a job’s task requirements and the +role of endurance in the production function of those tasks. +Finally, I use the measure of endurance to examine how differences in this skill across +individuals affect the sorting of students to colleges. I focus on identifying the distributional +and informational effects of an exam reform that decreases the exam length by half, thereby +reducing the importance of endurance in determining test scores. The distributional effect +asks how the exam reform would impact socioeconomic status (SES) test-score gaps. The +informational effect asks how the reform would impact the exam’s “predictive validity” +(a measure of the exam’s information content), as measured by the correlation between +test scores and long-run outcomes. I derive formulas showing that test-score gaps and +predictive validity can be written as linear functions of ability and endurance, with the +weight on endurance proportional to the exam length. +The exam reform would decrease test-score gaps by 1.3–4.8 percentage points (a 26%– +29% reduction from pre-reform gaps, depending on the measure of SES) and increase the +predictive validity of the exam’s test scores for long-run outcomes by as much as 95%. In- +5 + +tuitively, the reform would reduce test-score gaps because, conditional on academic ability, +low-SES students have lower endurance than high-SES students and, thus, perform dis- +proportionally worse in questions toward the end of the exam. Similarly, the reform would +increase the predictive validity of the exam partly because differences in performance at the +beginning of the exam mainly reflect differences in ability (roughly, because most students +are “fresh”), which are highly predictive of long-run outcomes. In contrast, performance +differences towards the end of the exam disproportionally reflect the noise associated with +mental fatigue, which reduces the information content of test responses. +My findings yield three broad lessons. First, cognitive endurance matters for success in +college and the labor market. My results provide empirical evidence on the long-standing +hypothesis of endurance being a valuable skill. Thus, investing in the development of this +skill, possibly at school during early ages, may have significant societal returns. Second, dis- +tinguishing between endurance and ability can improve how talent is selected and trained. +Since the value of endurance varies among college majors, the student-major match may +improve if majors where high endurance is required to succeed screen applicants partly +based on this skill. Similarly, workers in endurance-intensive occupations may be more +productive if the training necessary to enter into these occupations includes components +aimed at building this skill. Third, seemingly neutral exam design decisions—the “choice +architecture” of the exam—such as length or number of breaks, can have equity and ef- +ficiency consequences. By influencing the importance of endurance for test performance, +the exam design can affect test-score gaps and predictive validity and, thus, the diversity +of colleges’ student bodies and the student-college match quality. +This paper relates to the literature that studies cognitive endurance and fatigue effects +in field settings. Limited cognitive endurance has been documented in a wide variety of en- +vironments (see footnote 3). Recent experimental evidence shows that cognitive endurance +can be trained in children, which leads to less pronounced performance declines (Brown +et al., 2022). I contribute by linking individual-level endurance to long-run outcomes and +establishing a novel set of associations. I do this in a high-stakes exam, which complements +previous studies documenting performance declines in the low-stakes PISA test (e.g., De- +beer et al., 2014; Borghans and Schils, 2018; Zamarro et al., 2018; Balart and Oosterveen, +2019). My findings provide a micro perspective to the results of Balart et al. (2018), who +show that the average performance decline in the PISA test among a country’s test-takers +has a sizable predictive power in cross-country growth regressions. +This paper also contributes to a growing literature documenting the importance of +6 + +different dimensions of human capital for long-run outcomes. A large body of work shows +that cognitive skills are valuable in the labor market (e.g., Hanushek and Woessmann, +2008, 2012; Fe et al., 2022; Hermo et al., 2022). This work often uses test scores as a +measure of cognitive skills. I show that, even in a high-stakes setting, test scores partly +measure cognitive endurance and provide methods to decompose test scores into fatigue- +adjusted ability and endurance. Relatedly, a growing body of work shows that skills other +than intelligence and technical skills (“noncognitive skills”) are also important predictors +of long-run outcomes (Bowles et al., 2001; Heckman et al., 2006; Borghans et al., 2008; +Almlund et al., 2011; Lindqvist and Vestman, 2011; Deming, 2017; Jackson, 2018; Buser +et al., 2021; Edin et al., 2022). I document the strong predictive power of one noncognitive +skill for college and labor-market outcomes. +Finally, this paper contributes to the literature on the design of college admission ex- +ams (Rothstein, 2004; Ackerman and Kanfer, 2009; Bettinger et al., 2013; Hoxby et al., +2013; Bulman, 2015; Goodman, 2016; Goodman et al., 2020; Riehl, 2022). These exams +are designed to rank a large number of applicants. This requires discerning small ability +differences, and as a consequence, they tend to be long and arduous. I show that perfor- +mance on college admission exams measures not only academic preparedness but also the +capacity to endure mental fatigue. Hence, there is a limit to how much information an +exam can extract about student academic achievement. A lengthier exam may not lead +to more precise measures of ability but rather to a selection mechanism that puts more +weight on endurance. This may be desirable for programs where endurance is crucial to +succeed, but it may come at the cost of screening out high-ability low-endurance students. +The rest of the paper is structured as follows. Section 2 describes the context and data. +Section 3 presents a statistical framework and describes my research designs. +Section +4 presents estimates of average cognitive endurance. +Section 5 decomposes test scores +into fatigue-adjusted ability and cognitive endurance. Section 6 examines the association +between cognitive endurance and long-run outcomes. Section 7 studies the implication of +limited endurance for the sorting of students to colleges. Section 8 concludes. +2 +Institutional Context and Data +2.1 +The ENEM exam +The High School Assessment Exam (Exame Nacional do Ensino Médio, or ENEM for +short) is an achievement test created in 1998 by the Brazilian Ministry of Education to +7 + +make high schools accountable for their students’ progress. Some universities used the +ENEM for college admissions; however, most institutions had university-specific admission +exams. In 2009, the Ministry of Education expanded the ENEM to encourage universities +to use it as their admission exam, and created a centralized admission system that uses +ENEM scores to assign students to the highly-selective federal universities. Since then, +many universities have started using the ENEM for admissions (Machado and Szerman, +2021; Otero et al., 2021). +The ENEM contains 180 multiple-choice questions equally divided across four subject +tests (language arts, math, natural sciences, and social sciences) and an essay. The exam +takes place over two consecutive days (two subjects per day, plus the essay on the second +day). Test-takers have four and a half hours to complete the test on the first day and +five and a half hours on the second day. +There are no allocated breaks. +To combat +cheating, examinees randomly receive one of four different booklets each day. The order +of the subjects and the set of questions is the same across booklets, but the order of +the questions within a subject is randomized across booklets. A score for each subject is +calculated based on item response theory (IRT), but most colleges ask applicants to submit +their average score across all subjects. +The exam is simultaneously taken across the country once a year at the end of the +year. It costs approximately $20 to take the exam, although this fee is waived for low- +income applicants. Between 2009 and 2016, over 50 million individuals signed up to take +the ENEM, making it the second-largest college admission exam globally. In Appendix C, +I describe the main changes in the ENEM over time, explain how ENEM scores are used in +the higher-education system (other than for college admissions), and compare the ENEM +to the US SAT and ACT exams. +2.2 +Data +I combine three administrative databases from Brazil. The base dataset contains exam +records from the ENEM from 2009–2016. This dataset contains both student-level and +question-level information. The student-level data includes self-reported demographic and +socioeconomic status (SES) measures, such as sex, race, high-school type (public/private), +parental education, and family income. The question-level data includes each student’s +responses to each exam question, the position of the question, skill tested, etc. +To study individuals’ trajectories through college and the labor market, I link the +ENEM records to two other administrative datasets using individuals’ national ID num- +8 + +bers (Cadastro de Pessoas Físicas).5 To measure college outcomes, I use Brazil’s higher- +education census from 2010–2019. This dataset includes information on all college enrollees’ +major, university, year of enrollment, number of credits, and year of graduation. To mea- +sure labor-market outcomes, I use an administrative employee-employer matched dataset +called RAIS (Relação Anual de Informações Sociais) from 2016–2018.6 The RAIS covers +the universe of formal-sector workers in Brazil and includes information about both the +worker and the firm. Workers’ data include educational attainment, occupation, and earn- +ings. Firms’ data include the number of employees, industry, and geographical location. +2.3 +Samples and Summary Statistics +High-school-students sample. To construct this sample, I impose several sample restrictions. +First, I only consider individuals who take the ENEM during high school. This restriction +excludes individuals who take the exam after dropping out or graduating from high school. +Second, I only include individuals with a non-zero non-missing score on each subject test. +This restriction excludes, for example, students who missed one of the days of testing. I +also exclude a small fraction of students with special accommodations, usually due to a +disability. After these restrictions, the high-school-students sample contains information +on approximately 15 million students who took the ENEM from 2009–2016. To examine +students’ long-run outcomes, I focus on 1.9 million high-school seniors in the first two +cohorts in my data (2009–2010), for whom I observe college and labor-market outcomes +6–9 years after taking the admission exam. +Retakers sample. To assess the temporal stability of my measure of cognitive endurance, +I identify students who take the ENEM more than once, usually as high-school juniors to +practice and again in their senior year to apply for college. Approximately 16% of test- +takers in the high-school-students sample take the exam more than once.7 I only include +students with a valid exam score in all the years. The retakers sample contains information +on 1.5 million students or 3.1 million student-years. +Summary Statistics. Table 1 shows summary statistics on the samples. The average +5The linkage was conducted in the secured data room at the facilities of the Ministry of Education in +Brasilia, Brazil. +6The RAIS does not contain information on workers employed in the informal sector, self-employed +individuals, or the unemployed. +7ENEM scores are only valid for one year. Thus, students cannot use their junior-year ENEM results +to apply for college. Some high-school students take the ENEM more than two times in the data, possibly +because of grade repetition. I exclude a small fraction of students who take the ENEM more than three +times. +9 + +student in the high-school-students sample is 18.2 years old, 59.8% are female, 47.6% are +white, and 22.2% went to a private high school (column 1). Over half of students (53.4%) +have a high-school-educated mother, and 38.8% live in a household that earns an income +above twice the minimum wage.8 On average, students correctly respond to only 34.3% of +exam questions, which shows that the ENEM is a hard exam. High-school seniors from the +2009–2010 cohorts are slighly older, slightly more likely to be females, and white (column +2). Students in the retakers sample are slighly younger, their parents tend to have higher +incomes, and they tend to perform better on the exam (column 3). Student characteristics +are balanced across booklet colors (Appendix Table A1). +2.4 +Definition of Main Outcomes +Test score. I define a student’s exam score as the fraction of correct responses across all +four academic subjects. The advantage of this measure is that it is intuitive and consistent +with the existing literature (e.g., Zamarro et al., 2019). However, this measure differs from +how the Brazilian testing agency calculates the ENEM score, which is based on IRT (see +Appendix C.4). Reassuringly, the correlation between the fraction of correct responses and +the IRT-based score is above 0.90 (Appendix Table C2). +College enrollment. I define college enrollment as an indicator for appearing in the +higher-education census one year after taking the ENEM. The rest of the college outcomes +are defined conditional on college enrollment. +College quality. I construct an earnings-based index of college quality. To do this, I +group all college-educated workers in the RAIS (not just the workers in my sample) based +on the university they attended and compute the average earnings of the graduates from +each university.9 +College degree quality. I create an index of college degree (or major) quality using the +average earnings of the graduates of each college degree. To allow for international com- +parisons, I classify majors based on the International Standard Classification of Education +(UNESCO, 2012). +8Students self-report their household income and other SES measures when they enroll to take the +ENEM. Household income is elicited in ranges and expressed as a multiple of the minimum wage. I divide +students into those whose household earns more than five minimum wages and those whose household +earns less than twice minimum wage. Using the Brazilian National Household Survey, I find that the +former households are in the top 30% of the national income distribution, while the latter households are +in the bottom 30%. +9This index is analogous to the college quality measure used by Chetty et al. (2011) and Chetty et al. +(2014b) to study the long-term impacts of kindergarten quality and teachers, respectively. +10 + +Degree progress. I calculate the ratio between the number of credits completed at the +end of each year and the total number of credits required to graduate. This variable is +available starting in the 2015 higher-education census. Thus, I use data from the cohort +enrolled in 2015 to measure this outcome. +Likelihood of graduating. I define an indicator for graduating one to six years after +enrolling in college. +Most students who ever graduate do so within the first six years +(Appendix Figure A2). As robustness, I define a measure of on-time graduation based on +expected degree length. The higher-education census contains information on how long a +student in good standing should take to graduate from each program. I use this information +to define an indicator for graduating within the expected number of years. +Formal employment. I define formal employment as an indicator for appearing in the +employee-employer matched dataset in any year in my sample. This variable is defined for +all test-takers. The rest of the labor-market outcomes are defined conditional on formal +employment. +If an individual has multiple jobs, I use the data from the job with the +highest number of hours. I use the job monthly earnings as a tiebreaker. +Monthly earnings. This variable represents the average salary of a worker across all +months in a given year. +To report this variable, firms have to calculate the worker’s +total earnings for the year and divide them by the number of months the firm employed +the worker. If a worker appears in multiple years in the RAIS, I calculate the inflation- +adjusted average monthly earnings across all years. I adjust earnings for inflation using +the consumer price index. +Hourly wage. I calculate the hourly rate of each worker as the ratio between a worker’s +inflation-adjusted monthly earnings and the hours worked per month.10 If a worker appears +in multiple years in the RAIS, I calculate the average hourly wage across all years. +Firm, industry, and occupation mean wage. I calculate the average hourly wage at +each firm, industry, and occupation. I use leave-one-out measures so that an individual’s +own employment outcomes do not affect the mean wage. +I define firms using the 14- +digit CNPJ,11 industries using the Brazilian National Classification of Economic Activities +(CNAE), and occupations using the Brazilian Occupational Code Classification (CBO). I +calculate the wage indices separately for each year and use the average value across years. +I measure labor-market outcomes for the 2009–2010 cohort using employment data +10Firms do not record the number of hours individuals actually work each week. Instead, the data on +hours indicates the number of hours per week that the worker is expected to work based on her contract. +11The CNPJ is a tax identifier for legally incorporated identities. The first eight digits identify the +company. The rest of the digits identify the branch or subsidiary of the company. +11 + +from 2016–2018. This means that, for the 2009 cohort, I measure outcomes 7–9 years after +taking the ENEM, and for the 2010 cohort, 6–8 years after taking the ENEM. I account for +this variation by controlling for an individual’s potential years of experience throughout +the analysis. I measure potential experience as the individual’s age minus the years of +schooling minus six. +3 +Empirical Framework +This section lays out a simple potential-outcomes framework. +I use the framework to +formally define cognitive endurance in terms of empirical estimands and to clarify the +identification assumptions. +3.1 +Statistical Model +Let Cij be the probability of individual i correctly answering question j. I model Cij as +a function of the student’s level of cognitive fatigue, fij. Fatigue can affect performance +by impairing cognitive functions such as attention, memory, or reasoning. The effects can +be manifested in many ways, including students forgetting a crucial formula, making a +computation mistake, misinterpreting or ignoring an important aspect of a question, and +filling in the wrong bubble in the multiple-choice sheet. +To build intuition, first consider an environment in which fatigue is binary: individuals +can be either mentally “fresh” (fij = 0) or “fatigued” (fij = 1). Let Cij(0) be the likelihood +of individual i correctly answering question j if she is fresh and Cij(1) the likelihood if she +is fatigued. These two probabilities denote potential outcomes for different fatigue levels, +but only one of the two outcomes is observed. The observed performance, Cij(fij), can be +written in terms of these potential outcomes as +Cij(fij) = Cij(0) + +� +Cij(1) − Cij(0) +� +� +�� +� +“Fatigue effect” (κi) +fij, +(1) +where Cij(1)−Cij(0) ≡ κi measures the effect of fatigue on performance, or “fatigue effect,” +for short. I allow the fatigue effect to be heterogeneous across individuals, although for +simplicity I assume that it is constant across types of questions. Suppose for the moment +that we observed whether the individual was fresh or fatigued when she answered each exam +question. Then, one could compare i’s average performance in questions she answered while +12 + +fatigued (E[Cij|fij = 1]) to her average performance in questions she answered while rested +(E[Cij|fij = 0]). This comparison can be written as +E[Cij|fij = 1] − E[Cij|fij = 0] = (E[Cij(1)|fij = 1] − E[Cij(0)|fij = 1]) +� +�� +� +Term 1: Fatigue effect ++ (E[Cij(0)|fij = 1] − E[Cij(0)|fij = 0]) +� +�� +� +Term 2: Selection bias +, +(2) +Equation (2) shows that a comparison of average performance would yield the sum of +two terms. The first one is the fatigue effect for questions answered while fatigued. The +second term is a selection bias that arises when comparing performance across different +questions. For example, if individuals become fatigued over time, a selection bias might +arise if questions become increasingly hard over the course of the exam. In this case, i’s +average performance may deteriorate even if she had not experience fatigued. +In practice, cognitive fatigue is not binary; rather, an individual can have different +gradations of “tiredness.” In what follows, I assume fij is continuous and interpret κi as +the impact of a unit change of cognitive fatigue on performance. Because cognitive fatigue +cannot be directly observed, estimating κi is not feasible. In the empirical analysis, I use +the position of question j on the version of the exam answered by i (Positionij), under +the reasoning that students become increasingly fatigued over the course of the exam.12 +To understand how cognitive fatigue relates to question position, consider a hypothetical +linear projection of fij on Positionij: +fij = ωi + πiPositionij + ηij. +(3) +The intercept of the projection, ωi, measures i’s cognitive fatigue at the beginning of +the test. The slope of the projection, πi, measures the change in cognitive fatigue due to a +one-position increase in the order of a given question. ηij is a mean-zero projection error, +uncorrelated with Positionij by definition. If student i answers the exam in chronological +order and finds the exam mentally taxing, we would expect πi > 0. Using equation (3), +it is possible to re-write equation (1) as a regression equation that can be estimated in +12This idea is supported by research showing that time-on-task is a strong determinant of cognitive +fatigue. For a review of the literature on the determinants of cognitive fatigue, see Ackerman (2011). +13 + +observational data: +Cij = αi + βiPositionij + εij. +(4) +The intercept of the regression, αi ≡ E[Cij(0)]+κiωi, measures i’s expected performance +on the test if she were fresh (E[Cij(0)]), plus the impact of her initial level of fatigue on +performance (κiωi). Henceforth, I interpret αi as a measure of i’s academic ability. The +slope of the regression, βi ≡ κiπi, is the estimand of interest. This reduced-form measure +is the product of two structural parameters, κi and πi, that are likely determined by +several psychological mechanisms. For example, the performance of some individuals may +be less impaired by cognitive fatigue (captured by κi) due to, for example, high intrinsic +motivation or grit. Similarly, students may not become cognitively fatigued over the course +of the exam (captured by πi) due to, for example, high attention capacity. Henceforth, I +interpret βi as i’s cognitive endurance. +The random part of performance, εij ≡ Cij(0)−E[Cij(0)]+ηij, measures deviations of i’s +potential performance on question j from her average potential performance. Comparing +i’s performance across exam questions in different positions yields the sum of cognitive +endurance plus a selection bias: +E[Cij|Posij = p] − E[Cij|Posij = p − 1] = βi + E[Cij(0)|Posij = p] − E[Cij(0)|Posij = p − 1] +� +�� +� +Selection bias +. +Next, I describe the two research designs that I use to deal with the selection bias. +3.2 +Identifying Cognitive Endurance +In the empirical analysis, I first estimate the mean cognitive endurance across all students, +β ≡ E[βi]. This parameter represents the causal effect of increasing a question’s position +on average student performance, ¯Cj ≡ E[Cij]. Rejecting the null hypothesis of β = 0 would +demonstrate that average student performance partly depends on cognitive endurance (i.e., +this would show that κiπi ̸= 0 for some i). +To identify β, I use two research designs. The first research design consists of assessing +how average student performance on a given question varies as a function of the question’s +position. This approach is enabled by the fact that a given question is located in a different +position across booklets. To illustrate this approach, Appendix Figure D1 displays student +performance in a natural science question (Appendix Figure C2 shows the text of the +14 + +question). This question appears as early as position 46 in the gray booklet and as late as +position 87 in the blue booklet. Accordingly, the fraction of correct responses declines from +40.8% in the gray booklet to 29.9% in the blue booklet. Comparing student performance +in these two booklets reveals that an increase of 41 positions reduces performance on this +question by 10.9 percentage points. Analogous pairwise comparisons can be made for any +two booklets.13 I exploit this information using the following fixed effects specification: +¯Cjb = αj + βPositionjb + ξjb, +(5) +where ¯Cjb is the fraction of students who correctly answered question j in booklet b and αj +are question fixed effects. Appendix Figure A4 illustrates the mechanics of identification by +plotting average student performance on selected questions as a function of their position +on the four exam booklets and the corresponding best-fit lines. β is identified by first +estimating the effect of question position on average student performance separately for +each question and then aggregating these question-specific best-fit lines (like the ones +plotted in the figure) using the OLS weights. +The advantage of this approach is that +it relies on a weak identification assumption—the random allocation of booklets across +students. However, since each student only receives one exam booklet, I cannot compare +a student’s performance across different booklets to identify βi. Thus, I also use a second +empirical strategy that can be used to identify both β and βi. +The second empirical approach consists of controlling for question difficulty (Difficultyj) +in equation (5) instead of the question fixed effects. To estimate β, I assess how average +student performance changes throughout the exam in regressions of the form: +¯Cjb = α + βPositionjb + δDifficultyj + µjb. +(6) +One challenge in implementing this approach is measuring question difficulty. An in- +tuitive and often used measure of a question’s difficulty is the fraction of students who +correctly answered the question. However, a given question has a different fraction of cor- +rect responses depending on where it is located on the booklet. Thus, a question might +appear to be more difficult simply because it is located later in the exam on average across +booklets. To deal with this, I exploit the within-question position variation to construct a +“position-adjusted” measure of a question’s difficulty. This measure of question difficulty +13Not all questions appear in a different position across all booklets. Appendix Figure A3 shows the +variation in question position across all questions for every pairwise booklet combination. +15 + +represents the fraction of correct responses we would expect to observe if question j ap- +peared in the first position of the exam (see Appendix D for details). To avoid a spurious +correlation, I calculate question difficulty using data from test-takers outside my sample.14 +This strategy yields a consistent estimate of β under the assumption that unobserved +question characteristics are conditionally independent of average student performance. Be- +low, I provide evidence in support of this assumption. Importantly, as I describe in Section +5, this second empirical strategy can also be used to identify the cognitive endurance of +each individual. In this case, the identification assumption is stronger, requiring that un- +observed question characteristics are conditionally independent of i’s performance. In the +following two sections, I present estimates of mean cognitive endurance (Section 4) and +individual-level endurance (Section 5). +4 +Cognitive Endurance and Test Performance +This section presents estimates of average cognitive endurance using two research designs. +4.1 +Student Performance over the Course of the ENEM +To motivate the analysis, I begin by studying student performance over the duration of +the exam without controlling for question difficulty or any other performance determinant +that may be changing throughout the exam. Figure 1, plots the fraction of students who +correctly responded to each exam question (y-axis) against the position of the question in +the test (x-axis). As a benchmark, the red dashed line shows the expected performance if +students randomly guessed the answer to each question. +There is a strong negative relationship between student performance and question po- +sition. Average performance decreases from about 45% at the beginning of the exam to +about 24% at the end of the exam. A bivariate regression of the fraction of correct re- +sponses on question position indicates that average student performance declines by 21.4 +percentage points over the course of each testing day (p < 0.01), as shown in Table 2, +column 1. Interestingly, Figure 1 shows that average performance increases from about +30% at the end of the first day to about 45% at the beginning of the second day.15 +14These are mainly individuals who took the ENEM after graduating from high school. The results are +very similar if I use my sample to generate the measures of question difficulty. The correlation between +the measure of question difficulty estimated with test-takers in my sample and outside my sample is 0.98. +15Another interesting feature of Figure 1 is that student performance seems to increase towards the end +of each testing day. This pattern is not unique to the ENEM; a similar pattern has been found in the +SAT (Mandinach et al., 2005) and the PISA test (Borghans and Schils, 2018). One possible explanation +16 + +Limited cognitive endurance can provide a parsimonious explanation of these patterns. +As students advance through the exam, their mental resources may become increasingly +taxed, and thus they become more prone to committing mistakes. Cognitive resources are +replenished after taking a break (Sievertsen et al., 2016) and overnight via sleep (Baumeis- +ter, 2002; Lim and Dinges, 2008), which may explain why performance increases between +the end of the first day and the beginning of the second day. Next, I implement the research +designs described in Section 3.2 to identify mean cognitive endurance. +4.2 +Estimates of Mean Cognitive Endurance +Table 2 presents the regression estimates from the two research designs. To facilitate the +interpretation of the coefficients, I scale β so that it can be interpreted as decrease in +student performance due to limited endurance over the course of each testing day. +Estimating the question-fixed-effects specification (equation 5) yields an average cogni- +tive endurance β = −0.072 (p < 0.01), as shown in column 2. This estimate indicates that +student daily performance decreases, on average, by 7.2 percentage points due to limited +cognitive endurance. The difficulty-adjusted regression specification (equation 6) yields an +estimate of average cognitive endurance β = −0.058 (p < 0.01), as shown in column 3. +The similarity of this estimate relative to that obtained from the fixed effects specification +suggests that controlling for question difficulty is adequate to account for differences in +question characteristics. Moreover, the R-squared indicates that 97% of the variation in +¯Cj is explained by a question’s position and difficulty. This high R-squared shows that +there is little scope for unobservable variables to affect ¯Cj, further providing supporting +evidence for the selection-on-observables assumption (Oster, 2019). +Figures 2 and 3 provide visual evidence on the effect of limited cognitive endurance on +student performance. Figure 2 plots average student performance over the course of the +exam after removing the influence of question difficulty on performance. To construct this +figure, I first regress ¯Cjb, the fraction of students who correctly answered question j in +booklet b, on question difficulty, Difficultyj, and estimate the residual from this regression, +¯Cr +jb = ¯Cjb − E[ ¯Cjb|Difficultyj]. I add back the sample mean to ¯Cr +jb to facilitate interpre- +tation of units. Finally, I plot the mean value of ¯Cr +jb across the exam. The figure shows +that difficulty-adjusted performance tends to decline linearly throughout the exam. Daily +is what Mullainathan and Shafir (2013) refer to as the “the focus dividend,” that is, the notion that when +a resource is scarce (in this case, the time left to finish the exam), the mind becomes better at focusing +and blocking distractions. Another explanation is that some students answer the exam in reverse order. +17 + +performance decreases by about 5.2 percentage points each day, an effect consistent with +the regression estimates. +Figure 3 plots the average percentage point change in the probability of correctly an- +swering a question (y-axis) against the change in question position (x-axis) across all ques- +tions. The line is the predicted value from a linear regression estimated on the micro data. +Its intercept is statistically equal to zero, indicating that a given question is, on average, +equally likely to be answered if it appears in the same position in two different booklets. +The slope indicates that, on average, a given question is 0.08 percentage points less likely +to be correctly answered if it appears one position later in the test (p < 0.01). Thus, due to +limited endurance, performance decreases by about one percentage point roughly every 12 +questions (or 36 minutes if students spend the exam time uniformly across questions). The +implied daily change in performance due to limited endurance equals 7.2 percentage points +(p < 0.01), an estimate quantitatively identical to the question-fixed-effects specification. +Taken together, the evidence indicates that average student performance decreases by +about 5–7 percentage points per day due to limited cognitive endurance. This effect is +sizable. The fixed-effects-specification estimate represents a 16% decrease of the estimated +performance at the beginning of the exam (equal to 45%, Table 2, column 1) or about 60% +of the standard deviation of overall test score (equal to 11.6 percentage points). The effect +is comparable to that of a decrease of half a standard deviation in teacher quality (Chetty +et al., 2014a), an increase in the class size of about 16 pupils (Angrist and Lavy, 1999), or +taking the exam under 66 degrees Fahrenheit hotter conditions (Park, 2022). +4.3 +Limited Cognitive Endurance or Time Pressure? +Throughout this section, I have interpreted the causal effect of an increase in question +position on performance as a manifestation of limited cognitive endurance. This interpre- +tation is in line with the framework in Section 3. However, an estimate of β < 0 could also +potentially be generated by students running out of time toward the end of the exam. +In Appendix B.1, I provide two pieces of evidence against this alternative interpretation. +First, very few students leave any responses unanswered. Second, performance declines are +present even when students respond to questions while they are likely not time-pressured +(such as when responding to questions in the first half of each testing day). This evidence +supports the interpretation of β < 0 as a consequence of limited cognitive endurance. +18 + +5 +Decomposing Test Scores into Ability and Cognitive Endurance +The results in Section 4 demonstrate that test scores reflect not only students’ academic +preparedness (“ability”) but also their capacity to endure mental fatigue (“cognitive en- +durance”). This section decomposes individuals’ test scores into these two skills and ex- +amines the test-retest reliability of the generated measures. +5.1 +Linear Decomposition +To quantify the relative influence of ability and endurance on a student’s test score, I +estimate the difficulty-adjusted regression specification separately for each student: +Cij = αi + βiPosNormij + δiDifficultyj + εij +for i = 1, ..., N, +(7) +where Cij equals one if student i answered question j correctly, PosNormij is question po- +sition normalized such that the first question of each day equals zero and the last question +equals one, and Difficultyj is the position-adjusted measure of question difficulty, nor- +malized to have mean zero. In the baseline specification, I estimate equation (7) pooling +student responses from both testing days and all academic subjects and show robustness to +including day and subject fixed effects, as well as to estimating the parameters separately +by day and subject. +Without further assumptions, ˆαi and ˆβi simply describe how i’s performance changes +throughout the test. The intercept of each regression, ˆαi, measures the predicted perfor- +mance of student i in the first question of the test for a question of average difficulty. Thus, +ˆαi represents i’s performance after accounting for the effect of a question’s position and +difficulty on performance. The slope of each regression, ˆβi, measures the predicted perfor- +mance change between the first and last question of each testing day after accounting for +question difficulty.16 Importantly, equation (7) can be interpreted as an observational ana- +log of the model (4). Under this model, ˆαi measures i’s academic ability and ˆβi measures +i’s cognitive endurance. +16In Appendix B.2, I derive the OLS estimate of βi. The formula shows that ˆβi is calculated as a weighted +average of deviations of i’s performance on each exam question from i’s average performance. Thus, ˆβi +captures the intuition that a student who tends to do worse in the latter parts of the exam—relative to +her average— has low endurance. +19 + +5.2 +Limitations of Measuring Endurance using Standardized Tests +This approach to measuring cognitive endurance has advantages but also important limita- +tions. The main advantage is that it is based on observed behavior (“revealed preference”). +This deals with some of the well-known biases of measures based on self-reports (“stated +preferences”). +Examples include social-desirability bias (i.e., respondents want to look +good in front of the interviewer), reference-group bias (i.e., respondents judge their behav- +ior using different standards), and framing effects (i.e., slightly different ways of asking the +same question cause large changes in respondents’ answers). +However, there are at least three important concerns with the measure. +First, es- +timating individual-level endurance requires a large number of orthogonality conditions. +My research design requires any unobserved determinants of test performance to be un- +correlated with question position (conditional on question difficulty). This assumption is +unlikely to hold exactly for all students. For example, some students may happen to be +unprepared for the questions that appear at the end of the exam, which would lead to +biased estimates of endurance for these students. If the departures of the identification +assumption are not systematic (e.g., some students are unprepared for questions at the +end, but others are unprepared for questions at the beginning), then this issue is equiv- +alent to measurement error, which would attenuate the effects documented below. Using +the sample of retakers, I provide evidence consistent with this interpretation. In addition, +I show that the results are similar using several alternative measures of endurance (e.g., +calculated separately for each academic subject and using the average) +Second, my endurance measure hinges on the assumption that students answer the +exam in chronological order. However, some students might respond in a different order +(or strategically skip some questions).17 While I do not have data on the order in which +students answered the exam, below I show that the results are robust to excluding indi- +viduals with positive estimated endurance (i.e., those students who possibly answered the +exam in reverse order). +Finally, my measure of endurance is biased in the presence of floor or ceiling effects. +For example, individuals with extremely low ability or endurance may randomize their +responses throughout the entire exam and show up in the data as having high endurance +due to their stable performance. While this issue is not specific to my measure of endurance, +17For example, students with limited endurance that answer the exam in reverse chronological order +will appear in the data as exhibiting a performance increase. My estimate of endurance is biased for these +students. +20 + +it may be a concern for the empirical analysis. Below, I show that the results are robust to +excluding students in the tails of the ability and the endurance distributions (i.e., students +for whom floor and ceiling effects are more likely to be binding). +5.3 +Assessing the Reliability of the Cognitive Endurance Measure +Are the measures of academic ability and cognitive endurance generated by the decom- +position reliable? To assess the reliability of a construct, researchers typically measure +the construct multiple times and calculate the “temporal stability” or correlation between +these measures (Miller et al., 2009). The size of the correlation is a measure of construct +reliability. The higher the correlation, the more reliable the construct is said to be.18 +I compute two measures of test-retest reliability. First, I estimate ability and endurance +separately for each testing day and calculate the correlation between consecutive days. The +advantage of this approach is that it can be implemented in my main sample. The draw- +back is that the academic subjects tested vary each day, which could affect the reliability +estimates.19 Second, I estimate the temporal stability of ability and endurance between +consecutive years. This analysis produces more comparable estimates, but it can only be +done using the smaller sample of retakers. +The test-retest reliability of academic ability and cognitive endurance is comparable +to that of other well-known constructs. +Figure 4 show a series of binned scatterplots +plotting the average t+1 estimate of ability/endurance as a function of the time t estimate. +The temporal stability of ability ranges from 0.61 (between consecutive days) to 0.77 +(between consecutive years). The temporal stability of cognitive endurance ranges from +0.14 (between consecutive days) to 0.30 (between consecutive years). These results suggest +that the ability and endurance measures are reliable for use in economic analysis. +5.4 +Summary Statistics on Ability and Cognitive Endurance +Average cognitive endurance is ˆβ = −0.058, meaning that, due to limited endurance, the +performance of the average student decreases by 5.8 percentage points over the course of +18Reliability estimates vary significantly across constructs. Appendix Table A2 includes examples of +reliability estimates for some well-known economic and psychological constructs. IQ is the construct with +the highest known reliability, with correlations on the order of 0.80 (Hopkins and Bracht, 1975; Schuerger +and Witt, 1989). Other commonly used constructs have lower temporal stability. For example, reliability +estimates of risk aversion range 0.20–0.40 (Mata et al., 2018); big five personality range 0.49–0.70 (Wooden, +2012); and teacher value-added range 0.23–0.47 (Chetty et al., 2014a). +19For example, students who are good at natural science (a subject test on the first day) might not be as +good at math (a subject test on the second day). This would lead to an imperfect between-day correlation. +21 + +the exam. This estimate is consistent with the quasi-experimental results shown in Section +4. The standard deviation of ˆβi is σˆβ = 14.4 percentage points.20 Because of sampling error +in ˆβi, this raw standard deviation overstates the variability of true latent βi, σβ. Following +Angrist et al. (2017), I estimate σ2 +β as +ˆσ2 +β = σ2 +ˆβ − E[SE2 +ˆβ], +(8) +where E[SE2 +ˆβ] is the average squared standard error of ˆβi. I construct an analogous estimate +for the standard deviation of latent ability, ˆσα (see Appendix B.3 for details). +The standard deviation (SD) of βi is ˆσβ = 0.088. This means that an increase of one +SD in cognitive endurance predicts a 8.8 percentage point increase in test score. The cor- +responding estimate for ability is ˆσα = 0.132. Hence, ˆσβ is about two-thirds the magnitude +of ˆσα, meaning that ability is more dispersed than endurance across students. These es- +timates can be translated into percentage effects by dividing by the average test score of +0.344 (Table 1, Panel D). Under this rescaling, the estimates imply that a one SD increase +in endurance leads to a 25.6% increase in test score. The corresponding impact of ability +equals 38.3%. +Figure 5 shows the joint distribution of estimated ability and endurance. The red dia- +monds show a binned scatterplot of mean endurance as a function of ability, calculated by +dividing students into 100 equally-sized ability bins. The gray circles display a scatterplot +of ˆβi against ˆαi for a randomly-selected one percent of my sample. +Figure 5 reveals two important patterns. First, there is substantial variation in individ- +uals’ ability-endurance combination.21 Second, there is a negative relationship between ˆα +and ˆβ. On average, individuals with low values of ˆα tend to have higher values of ˆβ. This +relationship is largely mechanical and it is driven by floor and ceiling effects. Low-ability +individuals have a limited margin to decrease their performance throughout the exam be- +cause test scores are bounded. A similar argument holds for high-ability individuals. This +generates a “missing mass” of individuals with low-ability low-endurance and high-ability +high-endurance, inducing a negative correlation between the two variables.22 In the analysis +20Appendix Figure A6 shows the distribution of estimated ability (Panel A) and endurance (Panel B). +21For example, for individuals with ˆα ≃ 0.50, their estimates of endurance ranges from ˆβ = −0.50 (a +value roughly in the bottom one percent of the endurance distribution) to ˆβ = 0.50 (a value in the top one +percent). +22For individuals with intermediate values of ability (for whom ceiling and floor effects are less likely to +be binding), the correlation is negligible. For example, the correlation between the two measures is -0.08 +for individuals with estimated ability between 0.50 and 0.60. +22 + +below, I always control for both variables to account for their mechanical relationship and +show robustness to excluding individuals in the tails of the ability/endurance distribution. +In the following two sections, I use the estimates of ability and endurance to (i) revisit +the association between test scores and long-run outcomes through the lens of the ability- +endurance decomposition and (ii) characterize how systematic differences in endurance +across students affect test-score gaps and the information contained by test scores. +6 +Cognitive Endurance and Student Outcomes in Adulthood +In this section, I use the decomposition to separately quantify the contribution of ability +and endurance to the well-known association between test scores and long-run outcomes +(e.g., Bishop, 1989; Hanushek and Woessmann, 2008, 2012). +6.1 +Estimating the Return to Academic Ability and Cognitive Endurance +To assess how test scores and their component skills relate to college and labor-market +outcomes, I estimate regressions of the form: +Yi = φ + λXi + ψTTestScorei + νi +(9) +Yi = ˜φ + ˜λXi + ψAAbilityi + ψEEndurancei + ˜νi, +(10) +where Yi is an outcome of student i (e.g., earnings); Abilityi and Endurancei are the +measures of academic ability and cognitive endurance estimated in Section 5; and Xi +is a vector that contains demographic variables and socioeconomic status.23 For labor- +market outcomes, I additionally control for educational attainment and potential years +of experience. Because students can enroll in multiple college degrees, each observation +denotes a student–degree combination. I account for the fact that an individual can appear +multiple times in the dataset by clustering the standard errors at the individual level. +To compare the magnitude of the predicted effect of endurance on a given outcome +with the corresponding effect of academic ability, I normalize both variables such that +their coefficients represent the effect of a one standard-deviation (SD) increase on a given +outcome. +23For students with a missing value for a control variable, I define the missing value as equal to the +sample mean value and include a dummy for missing student characteristics in the regressions. +23 + +6.2 +Baseline Estimates +I first discuss college outcomes and then turn to labor-market outcomes. +6.2.1 +College outcomes. Table 3, Panel A displays estimates of the relationship be- +tween test scores, its component skills (ability and endurance), and college outcomes. The +first row shows estimates of equation (9). Consistent with a sizable literature on the strong +predictive power of test scores, I find that students with higher test scores tend to have +better college outcomes. Students with a one SD higher test score are 8.8 percentage points +more likely to enroll in college (relative to a mean of 24.4%, column 1). Conditional on +enrolling in college, the quality of their institution and college major—as measured by the +average earnings of previous graduates—is 8.2%–11.7% higher (columns 2–3), the share of +total credits they complete by the end of their first year is 1.4 percentage points higher (an +8.8% increase relative to the mean of 15.8%, column 4), and they are 6.0 percentage points +more likely to graduate (column 5). Conditional on graduating, they take 0.12 fewer years +to graduate (a 3.1% decrease relative to the mean of 3.4 years, column 6). These estimates +are comparable to those in the literature.24 +The second and third rows in Panel A show estimates of equation 10. There are two +things to notice. First, controlling for endurance produces associations between ability and +outcomes that are stronger than the associations between test scores and outcomes. Second, +endurance has an economically and statistically significant effect on college outcomes. A +one SD increase in endurance predicts a 2.9 percentage points increase in the likelihood of +enrolling in college (p < 0.01); a 8.2% increase in the college quality (p < 0.01), and a 6.0 +percentage point increase in the six-year graduation rate (p < 0.01). To benchmark the +size of these associations, I compute the ratio between the predicted effect of endurance +on an outcome and the predicted effect ability ( ˆψE/ ˆψA). This estimate is shown in the +third-to-last row in Panel A. The effect of endurance as a percent of the effect of ability +ranges from 31.6%–36.2%, depending on the outcome. +Figure 6, Panels A–C present binned scatterplots of selected college outcomes against +cognitive endurance. To construct each panel, I first regress Yi and Endurancei on student- +level characteristics and ability, and estimate the residuals from these regressions, Y r +i and +Endurancer +i (adding back the unconditional sample mean to facilitate the interpretation of +24For example, Chetty et al. (2014b) estimates that a one-standard-deviation increase in test scores is +associated with a 5.5 percentage point increase in college enrollment at age 20, a 7.8% increase in college +quality as measured by the earnings of previous graduates, and an 11.9% increase in earnings at age 28 +(see their Appendix Table 3, row 2). +24 + +units). Then, I group individuals into 10 equally-sized bins (deciles) based on Endurancer +i. +Finally, I plot the mean value of Y r +i for each bin. Consistent with the regression results, +there is a strong relationship between cognitive endurance and college enrollment (Panel +A), college quality (Panel B), and the six-year graduation rate (Panel C). +These results suggest that both ability and endurance are crucial for college suc- +cess. While the importance of academic ability had been widely documented, the results +show that traditional estimates of ability—usually measured through test scores—are con- +founded with the effect of cognitive endurance due to fatigue effects. More importantly, +the results suggest that endurance plays a commensurate role in college success.25 +6.2.2 +Labor-market outcomes. Table 3, Panel B displays the results for labor-market +outcomes. On average, students with higher test scores face better prospects in the labor +market. Students with a one SD higher test scores are 0.1 percentage points more likely to +have a formal-sector job (column 1), have a 12.7% higher hourly wage (column 2), earn a +10.9% higher monthly salary (column 3), work in firms that pay 9.1% higher wages (column +4), choose occupations that pay 4.1% higher wages (column 5), and work in industries that +pay 1.3% higher wages (column 6). +These associations reflect both the influence of academic ability and cognitive en- +durance, both of which have statistically and economically significant effects on all labor- +market outcomes. For example, a one SD increase in endurance predicts a 5.4% increase +in hourly wages (p < 0.01), a 5.2% increase in monthly earnings (p < 0.01), and a 3.6% +increase in the average firm wage (p < 0.01). The strong relationship between cognitive +endurance and these three labor-market outcomes is illustrated in binned scatterplots in +Figure 6, Panels D–F. These figures show that mean wages and earnings increase roughly +linearly with endurance. For labor-market outcomes, the predicted effect of cognitive en- +durance as a percent of the predicted effect of ability ranges from 25.5%–38.7%, depending +on the outcome. +These results indicate that endurance has a sizable wage return in the labor market. +Under complete information and frictionless markets, the price of a skill equals the present +value of the future returns generated by the skill (Abraham and Mallatt, 2022). Thus, the +sizable wage return to endurance suggests that this skill is a key productivity determinant. +The positive wage return to ability and endurance is consistent with models in which firms +25The positive association between endurance and college outcomes is consistent with Brown et al. (2022), +who show that a cognitive-endurance-enhancing intervention improves student performance in elementary +school. +25 + +pay workers according to their productivity, and output is generated by combining ability +with cognitive effort. Cognitive endurance enables workers to sustain effort for a longer +time, allowing them to produce a higher total output. The results also reveal a novel type +of assortative matching in the labor market: workers with high cognitive endurance are +more likely to work for high-paying firms. This is relevant given that the sorting between +workers and firms is an important driver of labor-market outcomes (Card et al., 2018). +6.3 +Robustness and IV Estimates +Appendix B.6 presents a series of robustness and specification checks. The baseline results +are robust to computing the effects nonparametrically, estimating ability and endurance +with alternative specifications (e.g., with day or subject fixed effects), and imposing several +sample restrictions (e.g., excluding the tails of the ability or endurance distribution). +Appendix Tables A3–A4 display instrumental variables (IV) estimates of the effect of +ability and endurance on long-run outcomes, estimated on the retakers sample. I instru- +ment the year t measure of ability/endurance with the year t − 1 measure. Using repeated +measures of a skill as an instrument is a common strategy to deal with measurement error +in the literature (e.g., Gronqvist et al., 2017; Edin et al., 2022). In addition, by using the +year t − 1 measures as instruments, this strategy eliminates the mechanical relationship +between year t ability/endurance and year t test scores. +Panel A report OLS estimates on the retakers sample. The effects are comparable to +those estimated on the main sample. Panel B reports the IV estimates. In general, these +tend to be larger than the OLS estimates. For example, the OLS estimate of the effect of +a one SD increase of endurance [ability] on wages is 12.1% [23.1%], while the IV estimate +is 18.8% [25.0%]. Relative to the OLS estimates, the IV estimates of the endurance effects +tend to increase more than the ability effects, consistent with the endurance measure +containing more measurement error than ability. Hence, the IV estimates suggest that the +wage return to endurance—as a fraction of the return ability—is significantly higher, on +the order of 75%. +6.4 +The Value of Endurance across Degrees, Occupations, and Industries +Does the value of cognitive endurance vary across degrees, occupations, and industries? +The task-based approach to labor markets highlights that workers produce output by +performing job tasks, and tasks differ in their skill requirements (Acemoglu and Autor, +2011). Consequently, the value of endurance should vary according to the tasks individuals +26 + +have to accomplish in a given job and the importance of endurance in the production +function of those tasks. For example, endurance may be particularly important for some +jobs because mistakes due to attentional lapses can dramatically reduce the output value, +as in “O-ring” production functions (Kremer, 1993). +To assess this, I estimate the wage return to endurance separately for each degree, +occupation, and industry. +Intuitively, the wage return to endurance should reflect the +increase in productivity due to an increase in this skill. +Thus, a high wage return to +endurance in a given occupation may indicate that this skill is particularly valuable in the +production function of the tasks required by such an occupation.26 +Figure 7 plots the distribution of wage returns across degrees (Panel A), occupations +(Panel C), and industries (Panel E). There is substantial heterogeneity in the wage return +to ability and to endurance. For example, while the average return to endurance across +degrees is 4.9%, the return across degrees in the bottom decile of the return distribution is +0.1% and in the top decile is 9.8%. This suggests that cognitive endurance is more valuable +for success in some college degrees. Occupations and industries also exhibit substantial +heterogeneity in wage returns. +Figure 7 also show that degrees, occupations, and industries that tend to pay higher +average wages tend to offer higher returns to ability and endurance (Panels B, D, and F). +For example, the return to endurance among the top ten percent highest-paying occupa- +tions is about three times higher than the return to endurance among the bottom-ten- +percent-paying occupations (4.9% vs. 1.6%, respectively). This finding is consistent with +high-paying jobs requiring high-endurance workers, suggesting that the value of this skill +is higher in high-paying jobs. +Figure 8 shows the joint distribution of the wage return to ability and the wage return to +endurance across college degrees (Panel A), occupations (Panel B), and industries (Panel +C). The figure reveals a strong association between the wage return to ability and the +wage return to endurance across degrees, occupations, and industries. For example, on +average, a 10%-increase in the wage return to endurance across occupations predicts a +22.1% increase in the wage return to ability (p < 0.01). This finding suggests that ability +and endurance are complementary skills in production. +To make tangible some of the real-world tasks for which endurance may be partic- +26There are two important caveats with this approach to measuring the value of endurance. The first one +is that individuals may select into degrees, occupations, and industries partly based on their endurance. +The second one is that an increase in productivity may not lead to a corresponding increase in wages in +some occupations or industries due to institutional factors (e.g., collective bargaining). +27 + +ularly valuable, Table 4 list the top-five degrees, occupations, and industries with the +highest wage return to endurance. The list includes occupations where attentional lapses +may be extremely costly—such as facility operators in petrochemical plants or air naviga- +tion professionals—but also academically-oriented occupations, like mathematicians and +statisticians (Panel B). The list also includes degrees conducive to these occupations (e.g., +aeronautics, Panel A) and related industries (e.g., oil extraction, Panel C). While sugges- +tive, this list is consistent with the proposition that the value of endurance depends on +the type of tasks required by a job and the importance of endurance in the production +function of those tasks. +7 +Endurance and the Sorting of Students to Colleges +The sorting of students to colleges has important implications for the education and labor- +market outcomes of these students (MacLeod et al., 2017). In Brazil, as in many other +countries, this sorting is largely mediated by admission exam scores. My results indicate +that test scores reflect two valuable but distinct skills: ability and endurance. An important +question is how these two skills contribute to the sorting of students to colleges. +In this section, I estimate the effects of an exam reform that reduces the exam length +by half. Such a reform would decrease the relative weight of endurance for determining test +scores and increase the relative weight of ability. I focus on two channels through which +the reform could affect the sorting of students to colleges. First, I study the distributional +effects of the reform, that is, how the reform would affect test-score gaps due to systematic +differences in average endurance across types of students. Second, I study the informational +effects of the reform, that is, how the reform would affect the information on the quality +of each applicant contained in test scores due to a change in the skills being measured by +the exam. +7.1 +Cognitive Endurance and Test-Score Gaps +Standardized tests often exhibit large racial and income test-score gaps (e.g., Fryer Jr and +Levitt, 2006; Card and Rothstein, 2007; Riehl, 2022). In the context of college admission +exams, these gaps lead to inequitable college access and amplify earnings disparities (Chetty +et al., 2020). An important question is what explains those test-score gaps. Next, I examine +the contribution of differences in cognitive endurance to these gaps. +28 + +7.1.1 +Decomposing Test-Score Gaps. To begin with, notice that the linear de- +composition (7) can be used to parsimoniously summarize an individual’s test score, +TestScorei ≡ E[Cij], as a linear combination of her academic ability and endurance: +TestScorei = ˆαi + ˆβiPosition. +(11) +Let X ∈ {0, 1} be a student observable characteristic. For example, X = 1 may denote +high-income students and X = 0 low-income students. The average test score of students +with characteristic x can be written as +E[TestScorei|Xi = x] = E[ˆαi|Xi = x] + E[ˆβi|Xi = x]Position. +(12) +Using this expression, the test-score gap, ScoreGap, can be decomposed into differences +in average academic ability and differences in average cognitive endurance as follows: +ScoreGap = +α1 − α0 +� +�� +� +Difference in average +academic ability +between groups ++ (β1 − β0)Position +� +�� +� +Difference in average +cognitive endurance +between groups +, +(13) +where αx ≡ E[ˆαi|Xi = x] and βx ≡ E[ˆβi|Xi = x]. Equation (13) shows that, in the absence +of systematic differences in limited endurance (β1 = β0), test scores gaps would be purely +a reflection of gaps in academic ability. Thus, exam design features that put a higher or +lower weight on endurance, such as the length of the exam or the number of breaks, should +not affect test-score gaps. This is no longer true in the presence of systematic differences +in endurance. If student-level characteristics are associated with endurance, then an exam +design that puts more weight on endurance will affect test-score gaps. +I focus on estimating the impact of an exam reform that decreases the length of the +test by half on test-score gaps.27 This reform would decrease the average question position +(from Position to Position/2), thereby decreasing the influence of endurance gaps on test- +score gaps.28 While I focus on test length, other exam features can also affect the influence +27Such a reform would be equivalent to changing the ENEM from its current length to roughly the +length of the ACT exam. +28An important concern is that, by reducing the number of questions, the exam would determine the +place in the score distribution of any one student with less precision. However, the reform could be achieved +without sacrificing much precision by using an adaptive exam that selects questions based on the student’s +ability level. +29 + +of endurance for test-score gaps. For example, Figures 1–2 show that student performance +starkly increases between the end of the first day and the beginning of the second day, +suggesting that giving students more breaks would decrease the importance of endurance +for test-scores gaps. Similarly, in Appendix E, I show that the type of exam questions +impacts cognitive fatigue, thereby influencing the importance of endurance for test-score +gaps. Thus, the reform can also be interpreted as, for example, introducing a long break +in the middle of each testing day. +Using equation (11), I estimate the effects of the reform on test-score gaps between: +1. Male and female students, +2. White and non-white (Black, Brown, and Indigenous) students, +3. Students in households in the top 30% and bottom 30% of the income distribution, +4. Students with a college-educated mother and non-college-educated mother, +5. Students enrolled in a private high school and public high school. +7.1.2 +The Impact of an Exam Reform on Test-Score Gaps. Table 5 shows es- +timates of the contribution of gaps in ability and endurance to test-score gaps. Column +1 shows the difference in average test scores between the groups of students listed in the +row header, column 2 shows the difference in average academic ability (in a regression that +controls for endurance), and column 3 shows the difference in average cognitive endurance +(controlling for ability). +By reducing the contribution of endurance gaps to test-score gaps by half, the reform +would: (i) Reduce the gender test-score gap by 0.85 percentage points (a 32% decrease +from the pre-reform gap of 2.6 percentage points); (ii) Reduce the racial test-score gap by +0.08 percentage points (a 14% decrease from the pre-reform gap of 5.7 percentage points); +and (iii) Reduce the SES test-score gap by 1.3–3.1 percentage points (a 13%–16% decrease +from pre-reform gaps), depending on the SES measure. +The predicted impact of the exam reform is robust to (i) measuring the gaps in per- +centiles (Appendix Table A5); (ii) Estimating ability and endurance with alternative spec- +ifications (Appendix Table A6); (iii) Using alternative measures of question difficulty when +estimating ability and endurance (Appendix Table A7); (iv) Excluding individuals in the +tails of the ability or endurance distributions (Appendix Table A8); and (v) Using precision- +weighted estimates (Appendix Table A9). +30 + +7.2 +Cognitive Endurance and the Predictive Validity of Test Scores +Admission officers use test scores to screen applicants because they are informative about +which applicants will succeed in college. The standard approach to assess the informative +content of an exam test is to calculate the cross-individual correlation between test scores +and a long-run outcome that colleges want to screen their applicants based on (such as +first-year college GPA or on-time graduation). This correlation is known as the predictive +validity of an exam (Rothstein, 2004). Next, I study how an exam’s predictive validity +depends on cognitive endurance. +7.2.1 +Decomposing Predictive Validity. In the presence of limited endurance, fea- +tures of the exam that affect the weight of endurance will affect the exam’s predictive +validity. To see this, notice that the predictive validity of test scores for outcome Y , ρY , +can be written as: +ρY ≡ Corr(Yi, TestScorei) += Corr(Yi, αi + βiPosition) += σα +σT +Corr(Yi, αi) + σβ +σT +Corr(Yi, βi)Position, +(14) +where σα, σβ, σT are the standard deviations of ability, endurance, and test scores. Equation +(14) shows that the predictive validity of an exam can be expressed as a linear combination +of the correlation between the outcome and the skills measured by the exam. The weight +of each skill depends on its dispersion and the exam’s length. Unfortunately, equation (14) +cannot be directly used to predict how an exam reform that changes the test length would +affect its predictive validity, i.e., ∂ρY /∂Position. This is because, as shown in Section 7.1, +such a reform would change the ranking of students, thereby affecting Corr(Yi, αi) and +Corr(Yi, βi). +I sidetrack this problem by studying how predictive validity varies throughout the exam. +In particular, I ask how a given question’s predictive validity ρY +j ≡ Corr(Yi, Cij), changes +when its position changes. Notice that the predictive validity of the overall exam can be +written as a weighted average of the predictive validity of each exam question j ∈ {1, ..., J}: +ρY = 1 +J +J +� +j=1 +σCij +σT +ρY +j . +(15) +Equation (15) is helpful because it allows me to exploit the random variation in whether +31 + +a given question is presented when students are relatively fresh or cognitively fatigued. To +build intuition on the mechanics of this analysis, notice that ρY +j is given by the difference +in average outcomes between students who correctly and incorrectly responded to question +j, multiplied by the ratio of standard deviations: +ρY +j = +� +E[Yi|Cij = 1] − E[Yi|Cij = 0] +�σCij +σYi +. +(16) +Equation (16) indicates that limited endurance affects the predictive validity of a ques- +tion by changing the composition of students who correctly answer the question. Loosely +speaking, correct responses at the beginning of the exam are driven by high-ability students +(regardless of their endurance level since all students are “fresh”) and low-ability students +who guessed the answer. Toward the end of the exam, correct responses are driven by stu- +dents with high ability and high cognitive endurance and students with either low ability +or low endurance who guessed the answer. +How this compositional change affects a question’s predictive power for an outcome +is theoretically ambiguous. It depends on how the outcome correlates to academic ability +relative to cognitive endurance, the distribution of ability and endurance in the population, +and how difficult the question is. Thus, I empirically assess this by estimating regressions +of the form: +ρY +jb = αj + γY Positionjb + ηjb. +(17) +where ρY +jb is the predictive validity of question j in booklet b, αj are question fixed effects, +and Positionjb is the position of question j in booklet b. The coefficient of interest is γY , +which measures the impact of a one-position increase in the order of a given question on +the question’s predictive validity for outcome Y . I scale γY so that it represents the change +in predictive validity due to a reform that decreases the average question position by half. +I estimate the effect of the reform for eight main outcomes: test score (calculated +without the contribution of question j to avoid mechanical effects), college enrollment, +college quality, degree progress, six-year graduation rate, hourly wage, monthly earnings, +and firm leave-individual-out mean earnings. Since the dependent variable is an estimate, +I weight each observation using the inverse square of its standard error. I cluster standard +errors at the question position level. +32 + +7.2.2 +The Impact of an Exam Reform on the Test’s Predictive Validity. Table 6 +presents the results. Panel A shows the average predictive validity across all test questions. +I find that individual questions are predictive of student long-run outcomes, although the +size of the correlations tends to be small. For example, on average across all questions, +correctly responding to a question has a 0.05 positive correlation with enrolling in college +(column 2, p < 0.01), 0.10 correlation with college quality (column 3, p < 0.01), and 0.10 +correlation with wages and earnings (columns 6–7, p < 0.01). +Panel B reports the estimates of equation (17). The exam reform would generate a +sizable increase in the predictive validity of the exam for the majority of outcomes. For +example, the exam reform would increase the average predictive validity of test responses +for college enrollment by 0.05 points (a 95.2% increase relative to the pre-reform mean, +p < 0.01), for college quality by 0.09 points (a 91.1% increase relative to the pre-reform +mean), and for earnings by 0.07–0.08 points (a 75.7%–79.6% increase relative to the pre- +reform mean, p < 0.01). +The predicted effect for the six-year graduation rate is also +positive but not statistically different from zero. The reform would decrease the predictive +validity for degree progress. +These estimated effects of the reform are driven by the fact that a given question tends +to be less predictive of long-run outcomes if it appears later in the exam. This can be seen +visually in Appendix Figure 9, which shows binned scatterplots plotting the change in the +predictive ability of a question (y-axis) against the change in the question position (x-axis) +for selected outcomes. In all cases, the average predictive validity of test questions tends +to decrease if the question appears later in the test.29 +These results can help explain puzzling empirical findings in the literature. Kobrin et al. +(2008) study how the predictive validity of the SAT changed after the exam increased the +number of questions in 2005. Intuitively, more test questions should lead to more precise +student ability estimates and thus to more predictive test scores. Yet, the predictive validity +of the exam did not change. This finding can be explained by cognitive fatigue eroding the +predictive power of test responses at the end of the exam. Bettinger et al. (2013) show that +performance on the English and Math sections of the ACT predict college outcomes, but +not performance on the Science and Reading sections. Based on this finding, the authors +propose eliminating the Science and Reading sections. Notably, the Science and Reading +questions are the last to appear in the ACT. Hence, the null predictive power of these two +29The negative association can also be seen in Appendix Figure A7, which plots the predictive validity +of a question (y-axis) against its position on the exam (x-axis). There is an evident decline in predictive +validity between the exam’s beginning and end. +33 + +subjects may be driven by students being cognitively fatigued by the time they reach those +sections—and not by the skills assessed by Science and Reading questions being irrelevant +for long-run outcomes.30 +7.3 +Discussion +In summary, this section shows that, due to heterogeneity in cognitive endurance, the +design of college admission exams can have equity and efficiency consequences. I estimate +that a reform that halves the exam length would reduce SES gaps by 26%–29%, possibly +leading to a more diverse college student body. In addition, the shorter exam would be more +informative about the quality of each applicant (as measured by its predictive validity), +possibly leading to a better allocation of students to colleges. The first result is driven +by the fact that, conditional on academic ability, low-SES students have lower endurance +than high-SES students; thus, their performance declines at a steeper rate throughout the +exam. The second result is driven by the fact that differences in student performance at the +beginning of the exam mainly reflect differences in ability (roughly, because most students +are “fresh”), whereas performance differences towards the end of the exam increasingly +reflect differences in endurance. Since ability is a stronger predictor of long-run outcomes +than endurance, the predictive validity of a given question decreases if it appears later on +the exam. +8 +Conclusion +Cognitive effort underlies most, if not all, productive activities. Just like individuals differ +in preferences and personality traits, they also differ in their ability to endure mental +fatigue. This paper shows that cognitive endurance affects student performance in college +admission exams and has a substantial earnings return in the labor market. +My findings have implications for investments in different types of human capital. I +find that endurance has a substantial return in the labor market. Yet, a typical school +curriculum does not include any material directly aimed at building this dimension of +human capital. Policymakers should consider investing in the development of cognitive +30If the goal is to maximize the exam’s predictive power, an alternative reform that might be more desir- +able is to reduce the number of questions in all sections (instead of eliminating some sections). Cognitive +fatigue plays a smaller role in shorter tests, allowing students to reveal their academic preparedness across +all questions. By not removing any subjects, colleges would have a measure of academic preparedness for +all topics. I discuss the implications of my findings for exam design in Section 8. +34 + +endurance, possibly during early ages when neuroplasticity is higher. While research in this +area is still in its infancy, some examples of protocols that build cognitive endurance include +mindfulness meditation (Levy et al., 2012; Goleman and Davidson, 2017), noninvasive brain +stimulation (Rubia, 2018), and the restriction of smartphones in learning environments +(Thornton et al., 2014).31 +An important caveat is the lack of exogenous variation in +cognitive endurance in my analysis. While my findings provide evidence of a positive link +between endurance and earnings, these estimates may be misleading if the available control +variables are inadequate to provide meaningful estimates of the return to this skill. Future +work should establish if this link is causal. +The findings also have implications for the design of standardized tests. In a typical +test, all questions contribute the same to an individual’s score. However, the results show +that questions that appear early in the exam are more predictive of long-run outcomes. +An aggregation mechanism of individuals’ test responses that takes into account students’ +varying fatigue levels throughout the exam may lead to more informative test scores. For +example, testing agencies can weight each question based on the position in which it was +answered, assigning more weight to questions students responded to earlier. +The ability-endurance score decomposition developed in this paper generates directions +for future research. Test scores are commonly used in economics research, for example, +as measures of cognitive skills (Hanushek and Woessmann, 2008, 2012); as a “surrogate” +variable to measure the impact of an intervention on long-run outcomes (Athey et al., +2019); and to measure the effectiveness of educational inputs (Chetty et al., 2011; Dobbie +and Fryer Jr, 2015; Angrist et al., 2016). The decomposition allows researchers to explore +the role of cognitive endurance in these and other applications. For example, researchers +can use conventional value-added methods to identify teachers who might be particularly +effective at building cognitive endurance. +31Some of these protocols are already being implemented in the private sector. For example, meditation +practices are commonly used among tech companies in Silicon Valley to enhance worker productivity +(Shachtman, 2013). +35 + +Figures and Tables +Figure 1: Average student performance over the course of the ENEM +Day 1 of the exam +Day 2 of the exam +(Correlation = -0.84) +(Correlation = -0.88) +Random chance +0.20 +0.25 +0.30 +0.35 +0.40 +0.45 +0.50 +0.55 +Fraction of students who answered correctly +1 +30 +60 +90 +120 +150 +180 +Position of the question in the exam +Notes: This figure shows student performance over the course of each testing day in the ENEM. The y-axis +displays the fraction of students who correctly responded to each question, averaged across all years in my +sample. The x-axis displays the position of each question in the exam. The dashed lines are predicted +values from a linear regression estimated separately for each testing day. The horizontal red dashed line +shows the expected performance if students randomly guessed the answer to each question. +36 + +Figure 2: Performance residuals after controlling for question difficulty +Random chance +Social science +Natural science +Language arts +Mathematics +(Correlation = -0.88) +(Correlation = -0.84) +(Correlation = -0.91) +(Correlation = -0.96) +0.20 +0.25 +0.30 +0.35 +0.40 +0.45 +0.50 +0.55 +Fraction of correct responses (residualized) +1 +30 +60 +90 +120 +150 +180 +Position of the question in the exam +Notes: This figure shows student performance over the course of each testing day after removing the +influence of question difficulty on performance. The y-axis displays the residuals of a regression of (i) +¯Cjb, the fraction of students who correctly answered question j in booklet b on (ii) Difficultyj, a position- +adjusted measure of question difficulty (adding back the sample mean to facilitate interpretation of units). +The x-axis displays the position of each question in the exam. Marker colors denote each academic subject +tested. Appendix D describes how I construct the measure of question difficulty. The dashed lines are +predicted values from a linear regression estimated separately for each academic subject. The horizontal +red dashed line shows the expected performance if students randomly guessed the answer to each question. +37 + +Figure 3: The effect of an increase in the order of a given question on student performance +Intercept: 0.000 pp +Slope: -0.080 pp +Slope x 90: -7.23 pp +-5 +-4 +-3 +-2 +-1 +0 +Average pp change in prob. of correct answer +0 +5 +10 +15 +20 +25 +30 +≥35 +Change in question position +Notes: This figure shows estimates of the impact of an increase in the order of a given question on the +fraction of students who correcly answer the question. The y-axis plots the average change (in percentage +points) in the fraction of students who correctly respond to a question. The x-axis displays changes in a +question position between each possible booklet pair. See Appendix Figure A3, Panel A for a histogram +of the values in the x-axis. To construct this figure, I first compute the change in student performance +and the distance in a question’s position between each possible booklet pair. Then, I calculate the average +change in performance for each observed distance. The solid line denotes predicted values from a linear +regression estimated on the plotted points, using as weights the number of questions used to estimate each +point. The vertical dashed lines denote 95% confidence intervals, estimated with heteroskedasticity-robust +standard errors. +38 + +Figure 4: The temporal stability of ability and endurance estimates +Panel A. Ability in day d and day d + 1 +Correlation = 0.610 +(0.000) +0.2 +0.4 +0.6 +0.8 +Average academic ability in day 2 (αi) +0.0 +0.2 +0.4 +0.6 +0.8 +Academic ability in day 1 (αi) +Panel B. Endurance in day d and day d + 1 +Correlation = 0.140 +(0.000) +-0.3 +-0.2 +-0.1 +0.0 +0.1 +Average cognitive endurance in day 2 +-0.6 +-0.4 +-0.2 +0.0 +0.2 +0.4 +Cognitive endurance in day 1 (βi) +Panel C. Ability in year t and year t + 1 +Correlation = 0.767 +(0.001) +0.2 +0.4 +0.6 +0.8 +Average academic ability in year t + 1 +0.0 +0.2 +0.4 +0.6 +0.8 +Academic ability in year t (αi) +Panel D. Endurance in year t and year t + 1 +Correlation = 0.303 +(0.001) +-0.3 +-0.2 +-0.1 +0.0 +0.1 +Average cognitive endurance in year t + 1 +-0.6 +-0.4 +-0.2 +0.0 +0.2 +0.4 +Cognitive endurance in year t (βi) +Panel E. Ability in year t and year t + 2 +Correlation = 0.752 +(0.002) +0.2 +0.4 +0.6 +0.8 +Average academic ability in year t + 1 +0.0 +0.2 +0.4 +0.6 +0.8 +Academic ability in year t (αi) +Panel F. Endurance in year t and year t + 2 +Correlation = 0.291 +(0.003) +-0.3 +-0.2 +-0.1 +0.0 +0.1 +Average cognitive endurance in year t + 2 +-0.6 +-0.4 +-0.2 +0.0 +0.2 +0.4 +Cognitive endurance in year t (βi) +Notes: This figure shows the correlation between the measures of academic ability and cognitive endurance +measured at two different points in time. Each panel shows a binned scatterplot plotting the estimates of +ability/endurance at two different times. To construct this figure, I first divide students into 100 equally- +sized bins based on their ability/endurance at time t. Then, I calculate the average ability/endurance at +time t′ > t for students in each bin. The panel title indicates the two time periods in which I measure +ability and endurance. +39 + +Figure 5: Joint distribution of ability and endurance estimates +Notes: This figure shows estimates of the relationship between academic ability and cognitive endurance. +Gray circles display a scatterplot of ˆβi against ˆαi for a randomly-selected one percent of my sample. +The red diamonds show a binned scatterplot of average endurance as a function of ability. To construct +the binned scatterplot, I first divide students into 100 equally-sized bins based on their ability. Then, I +calculate the average endurance for students in each bin. Finally, I plot average endurance against ability +in each bin. +40 + +0.7- +Raw data +Binned scatterplot +0.5 +0.3 +Cognitive endurance (β:) +0.1 - +-0.1 - +-0.3 +-0.5 +-0.7. +O +O +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Academic ability (a;)Figure 6: The relationship between cognitive endurance and long-run outcomes +Panel A. College enrollment +-0.50 +0.00 +0.50 +1.00 +College enrollment (residualized) +-0.08 +-0.07 +-0.06 +-0.05 +-0.04 +Average cognitive endurance (in pp, residualized) +Panel B. College quality +3.0 +3.2 +3.4 +3.6 +3.8 +College quality (residualized) +-0.08 +-0.06 +-0.04 +-0.02 +Average cognitive endurance (in pp, residualized) +Panel C. Six-year graduation rate +-0.5 +0.0 +0.5 +1.0 +1.5 +Six-year graduation rate (residualized) +-.07 +-.065 +-.06 +-.055 +-.05 +Average cognitive endurance (in pp, residualized) +Panel D. Log hourly wage +3.00 +3.50 +4.00 +4.50 +5.00 +Mean log hourly wage (residualized) +-0.10 +-0.08 +-0.06 +-0.04 +-0.02 +Average cognitive endurance (in pp, residualized) +Panel E. Log monthly earnings +7.0 +7.5 +8.0 +8.5 +Mean log monthly earnings (residualized) +-0.08 +-0.06 +-0.04 +-0.02 +Average cognitive endurance (in pp, residualized) +Panel F. Firm mean wage (leave-one-out) +3.0 +3.5 +4.0 +4.5 +5.0 +Mean log firm wage (residualized) +-0.08 +-0.07 +-0.06 +-0.05 +-0.04 +Average cognitive endurance (in pp, residualized) +Notes: This figure shows the relationship between cognitive endurance and selected college and labor- +market outcomes. Each panel shows a binned scatterplot plotting the average value of the outcome (y-axis) +against cognitive endurance (x-axis). To construct this figure, I first residualize cognitive endurance and +each outcome on student-level characteristics and academic ability. I add back the unconditional sample +mean to facilitate interpretation. Then, I divide students into 10 equally-sized bins (deciles) based on +their residualized endurance and plot the average outcome for students of each bin. The red dashed lines +are predicted values from a linear regression on the plotted points. Each panel shows the results for the +outcome listed in the panel title. See Section 2.4 for variable definitions. +41 + +Figure 7: Heterogeneity in the wage return to ability and cognitive endurance +Panel A. Distribution of wage returns +across college degrees +0 +4 +8 +12 +16 +20 +Density +-0.05 +0.00 +0.05 +0.10 +0.15 +0.20 +0.25 +Return to skill (in hourly wage log points) +Academic ability +Cognitive endurance +Panel B. Return to ability/endurance vs. +average wage across college degrees +0.00 +0.05 +0.10 +0.15 +0.20 +Return to skill (in hourly wage log points) +3.50 +3.90 +4.30 +4.70 +Mean log hourly wage +Academic ability +Cognitive endurance +Panel C. Distribution of wage returns +across occupations +0 +4 +8 +12 +16 +20 +Density +-0.05 +0.00 +0.05 +0.10 +0.15 +0.20 +0.25 +Return to skill (in hourly wage log points) +Academic ability +Cognitive endurance +Panel D. Return to ability/endurance vs. +average wage across occupations +0.00 +0.05 +0.10 +0.15 +0.20 +Return to skill (in hourly wage log points) +3.50 +3.90 +4.30 +4.70 +Mean log hourly wage +Academic ability +Cognitive endurance +Panel E. Distribution of wage returns +across industries +0 +4 +8 +12 +16 +20 +Density +-0.05 +0.00 +0.05 +0.10 +0.15 +0.20 +0.25 +Return to skill (in hourly wage log points) +Academic ability +Cognitive endurance +Panel F. Return to ability/endurance vs. +average wage across across industries +0.00 +0.05 +0.10 +0.15 +0.20 +Return to skill (in hourly wage log points) +3.50 +3.90 +4.30 +4.70 +Mean log hourly wage +Academic ability +Cognitive endurance +Notes: Panels A, C, and E show nonparametric estimates of the distribution of the wage return to ability +(red line) and the wage return to endurance (green line) across degrees, occupations, and industries. The +wage return to ability and endurance are the coefficients ψA and ψE in equation (10) using log hourly wage +as outcome, estimated separately for each degree, occupation, and industry. The figure excludes outliers +(i.e., estimates of the returns below -0.05 or above 0.25). +Panels B, D, and F display a series of binned scatterplots plotting the wage return to ability/endurance +(y-axis) against the mean hourly wage in bins (x-axis). To construct this figure, I first divide degrees, +occupations, and industries into 10 equally-sized bins based on their mean wage. Then, I estimate the +average return to ability/endurance in each bin. Finally, I plot the average return to ability/endurance +against the mean wage in each bin. +42 + +Figure 8: The relationship between the wage return to ability and endurance +Panel A. Across college degrees +0.00 +0.05 +0.10 +0.15 +0.20 +0.25 +0.30 +Wage return to ability +0.00 +0.05 +0.10 +Wage return to cognitive endurance +Panel B. Across occupations +0.00 +0.05 +0.10 +0.15 +0.20 +0.25 +0.30 +Wage return to ability +0.00 +0.05 +0.10 +Wage return to cognitive endurance +Panel C. Across industries +0.00 +0.05 +0.10 +0.15 +0.20 +0.25 +0.30 +Wage return to ability +0.00 +0.05 +0.10 +Wage return to cognitive endurance +Panel D. Binned scatterplot +0.00 +0.05 +0.10 +0.15 +0.20 +0.25 +0.30 +Average wage return to ability +0.00 +0.05 +0.10 +Wage return to cognitive endurance +Degrees +Occupations +Industries +Notes: This figure shows the relationship between the wage return to ability (y-axis) against the wage +return to endurance (x-axis). Panels A–C show scatterplots of the wage return to ability in a given college +degree (Panel A), occupation (Panel B), and industry (Panel C), against the wage return to endurance. The +scatterplots exclude outliers (wage returns in the bottom 5% or top 5% of the distribution). The solid lines +denote predicted values from linear regressions estimated on the microdata (including all observations). +Panel D shows a binned scatterplot plotting the mean wage return to ability against the wage return +to endurance. To construct this figure, I first divide degrees (blue circles), occupations (red triangles), and +industries (green diamonds) into 10 equally-sized bins based on their wage return to endurance. Then, I +calculate the average wage return to ability in each bin, using the number of individuals in each bin as +weights. The solid lines denote predicted values from linear regressions estimated on the plotted points. +43 + +Figure 9: Change in a question’s position and change in predictive validity +Panel A. Test score (leave-question-out) +-1.50 +-1.00 +-0.50 +0.00 +0.50 +Average change in predictive validity +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +Change in question position +Panel B. College enrollment +-0.30 +-0.20 +-0.10 +0.00 +Average change in predictive validity +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +Change in question position +Panel C. College quality +-1.00 +-0.80 +-0.60 +-0.40 +-0.20 +0.00 +Average change in predictive validity +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +Change in question position +Panel D. Hourly wage +-0.60 +-0.40 +-0.20 +0.00 +0.20 +Average change in predictive validity +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +Change in question position +Panel E. Monthly earnings +-0.60 +-0.40 +-0.20 +0.00 +0.20 +Average change in predictive validity +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +Change in question position +Panel F. Firm mean wage (leave-one-out) +-0.60 +-0.40 +-0.20 +0.00 +0.20 +Average change in predictive validity +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +Change in question position +Notes: This figure displays estimates of the effect of an increase in the order of a given question on the +question’s predictive validity. Each panel shows a binned scatterplot plotting the average change in the +predictive validity of a test question on a given outcome (y-axis) against the change in the position of the +question on the exam (x-axis). Each panel shows the results for the outcome listed in the panel title. See +Section 2.4 for variable definitions. The red dashed lines are predicted values from a linear regression on +the microdata. See Appendix Figure A3, Panel B for a histogram of the values in the x-axis. +44 + +Table 1: Summary statistics of the samples +High-school-students sample +Retakers sample +All +2009-2010 +All +(1) +(2) +(3) +Panel A. Demographic characteristics and race +Age +18.204 +19.151 +18.062 +Female +0.598 +0.611 +0.618 +White +0.476 +0.510 +0.504 +Black/Brown +0.505 +0.450 +0.483 +Panel B. SES and household characteristics +Attends a private HS +0.222 +0.222 +0.342 +Mom completed high school +0.534 +0.506 +0.606 +Mom completed college +0.205 +0.186 +0.270 +Family earns above 2x M.W. +0.388 +0.379 +0.432 +Family earns above 5x M.W. +0.062 +0.071 +0.087 +Panel C. Exam preparation +Took a foreign lang. course +0.241 +0.269 +0.263 +Took a test prep course +0.119 +0.167 +0.160 +Panel D. Fraction of correct responses +Natural Science +0.283 +0.333 +0.317 +Social Science +0.398 +0.388 +0.446 +Language +0.408 +0.449 +0.468 +Math +0.283 +0.287 +0.320 +Average +0.343 +0.364 +0.388 +Panel E. Geographical location +Lives in the North +0.089 +0.081 +0.082 +Lives in the Northeast +0.305 +0.261 +0.354 +Lives in the Southeast +0.389 +0.426 +0.365 +Lives in the South +0.131 +0.150 +0.113 +Lives in the Midwest +0.086 +0.081 +0.085 +Number of test-takers +14,941,156 +1,910,502 +1,519,842 +Notes: This table shows summary statistics on all test-takers in the high-school-students sample (column +1), those who took the exam in 2009–2010 as high-school seniors (column 2), and students in the retakers +sample (column 3). For students who took the exam multiple times, I compute the summary statistics +using data from the last year in which I observe them in my sample. See Section 2.3 for sample definitions. +45 + +Table 2: The effect of question position on test performance +Outcome: Correctly responded the question +(1) +(2) +(3) +Question position (normalized) +−0.214∗∗∗ +−0.071∗∗∗ +−0.058∗∗∗ +(0.013) +(0.004) +(0.002) +Constant +0.450∗∗∗ +(0.008) +N (Item−Booklets) +5,896 +5,896 +5,896 +N (Students) +14,940,464 +14,940,464 +14,940,464 +N (Question responses) +2,689,345,707 +2,689,345,707 +2,689,345,707 +R−squared +0.85 +0.99 +0.97 +Question fixed effects +No +Yes +No +Controls for question difficulty +No +No +Yes +Notes: This table displays estimates of the effect of a question position on the likelihood of correctly +answering the question. +Each column displays an estimate from a different specification. Column 1 presents estimates from +a bivariate regression of average student performance on question position. Column 2 presents estimates +from equation (5), which includes question fixed effects. Column 3 presents estimates from equation (6), +which controls for question difficulty. I normalize question position such that the first question in each +testing day is equal to zero and the last question is equal to one. +Heteroskedasticity-robust standard errors clustered at the question level in parentheses. ∗∗∗, ∗∗ and ∗ +denote significance at 10%, 5% and 1% levels, respectively. +46 + +Table 3: The effect of academic ability and cognitive endurance on long-run outcomes +Panel A. College outcomes +Dependent variable +Enrolled +College +Degree +1st-year +Grad. +Time to +college +quality +quality +credits +rate +grad. +(1) +(2) +(3) +(4) +(5) +(6) +Test score +0.088∗∗∗ +0.082∗∗∗ +0.117∗∗∗ +0.014∗∗∗ +0.060∗∗∗ +−0.119∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +(0.002) +Endurance +0.032∗∗∗ +0.030∗∗∗ +0.051∗∗∗ +0.006∗∗∗ +0.026∗∗∗ +−0.048∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +Ability +0.102∗∗∗ +0.095∗∗∗ +0.140∗∗∗ +0.016∗∗∗ +0.072∗∗∗ +−0.140∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +(0.002) +Ratio coef. +0.310∗∗∗ +0.319∗∗∗ +0.365∗∗∗ +0.358∗∗∗ +0.361∗∗∗ +0.342∗∗∗ +(0.002) +(0.001) +(0.001) +(0.004) +(0.003) +(0.005) +Mean DV +0.244 +3.326 +3.244 +0.158 +0.418 +3.817 +N +2,501,519 +1,800,546 +1,768,707 +1,124,972 +1,472,916 +793,822 +Panel B. Labor-market outcomes +Dependent variable +Formal +Hourly +Monthly +Firm +Occup. +Industry +sector +wage +earnings +wage +wage +wage +(1) +(2) +(3) +(4) +(5) +(6) +Test score +0.001∗∗∗ +0.129∗∗∗ +0.111∗∗∗ +0.092∗∗∗ +0.041∗∗∗ +0.013∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Endurance +0.000∗∗∗ +0.054∗∗∗ +0.052∗∗∗ +0.036∗∗∗ +0.017∗∗∗ +0.004∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.000) +(0.000) +Ability +0.002∗∗∗ +0.154∗∗∗ +0.135∗∗∗ +0.108∗∗∗ +0.049∗∗∗ +0.014∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Ratio coef. +0.276∗∗∗ +0.351∗∗∗ +0.387∗∗∗ +0.330∗∗∗ +0.346∗∗∗ +0.255∗∗∗ +(0.015) +(0.003) +(0.003) +(0.004) +(0.006) +(0.010) +Mean DV +0.326 +3.865 +7.551 +3.885 +3.886 +3.858 +N +2,523,029 +818,590 +818,590 +692,880 +818,374 +818,590 +Notes: This table displays estimates of the relationship between ability/endurance and college outcomes +(Panel A) and labor market-outcomes (Panel B). +The first row of each panel shows estimates of the association between test scores and the outcome +listed in the column header (coefficient ψT in equation (9)). The following rows show estimates of the asso- +ciation between ability and cognitive endurance and a given outcome (coefficients ψA and ψE in equation +(10)). All regressions control for age, gender, race, high school type, parental income, cohort fixed effects, +and municipality fixed effects. In addition to the baseline controls, the regressions in Panel A, columns 4–6, +include college-degree fixed effects to remove the influence of a student’s program choice, while the regres- +sions in Panel B control for potential years of experience and years of education. Heteroskedasticity-robust +standard errors clustered at the individual level in parentheses. See Section 2.4 for outcome definitions. +The third-to-last row in each panel shows the ratio between the predicted effect of academic ability +and the effect of cognitive endurance on a given outcome. Standard errors estimated through the delta +method in parentheses. ∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels. +47 + +Table 4: Degrees, occupations, and industries with the largest return to endurance +Return +Return +Ratio +Wage +Sample +ability +endur. +returns +pctil. +size +(1) +(2) +(3) +(4) +(5) +Panel A. Top five degrees +1. Aeronautics and related degrees +0.173 +0.106 +0.613 +69.7 +670 +(0.026) +(0.015) +(0.077) +2. Music and performing arts +0.221 +0.093 +0.420 +59.3 +502 +(0.060) +(0.035) +(0.110) +3. Religion +0.186 +0.088 +0.471 +49.0 +356 +(0.047) +(0.031) +(0.097) +4. History and archeology +0.211 +0.087 +0.414 +60.0 +988 +(0.043) +(0.022) +(0.064) +5. Forestry engineering +0.154 +0.084 +0.543 +52.3 +397 +(0.045) +(0.024) +(0.115) +Panel B. Top five occupations +1. Public tax auditors +0.454 +0.168 +0.369 +49.2 +255 +(0.106) +(0.057) +(0.084) +2. Professionals in air +0.278 +0.114 +0.412 +88.3 +347 +navigation, sea and fluvial +(0.049) +(0.028) +(0.072) +3. Technicians in operation of radio, +0.200 +0.112 +0.558 +66.3 +658 +TV systems and video producers +(0.047) +(0.027) +(0.091) +4. Plant operators in chemical, +0.267 +0.109 +0.409 +62.8 +1,221 +petrochemical and related occup. +(0.031) +(0.020) +(0.057) +5. Instrument and precision +0.180 +0.092 +0.511 +70.8 +203 +equipment repairers +(0.068) +(0.040) +(0.194) +Panel C. Top five industries +1. Oil extraction and +0.276 +0.135 +0.488 +91.5 +948 +related services +(0.034) +(0.021) +(0.052) +2. Financial intermediation and +0.215 +0.087 +0.402 +54.7 +6,177 +and insurance (aux. services) +(0.013) +(0.007) +(0.024) +3. Research and development +0.198 +0.084 +0.426 +73.7 +1,323 +(0.024) +(0.015) +(0.052) +4. Electricity, gas and hot water +0.223 +0.083 +0.373 +78.1 +1,966 +(0.020) +(0.011) +(0.036) +5. Manufacture of office machinery +0.132 +0.073 +0.553 +54.7 +920 +(0.033) +(0.019) +(0.095) +Notes: This table lists the top five 3-digit academic degrees (Panel A), 3-digit occupations (Panel B), and +2-digit industries (Panel C) with the highest wage return to cognitive endurance (column 2). +Column 1 shows the wage return to ability. Column 3 shows the ratio between the wage return to +endurance and the wage return to ability. Column 4 shows the average wage percentile of workers in each +degree, occupation, or industry. Column 5 shows the sample size used to estimate each wage return. +The wage return to ability and endurance are the coefficients ψA and ψE in equation (10) using as +outcome log hourly wage, estimated separately for each degree, occupation, and industry. +Heteroskedasticity-robust standard errors clustered at the individual level in parentheses. +48 + +Table 5: The contribution of gaps in ability and endurance to test-score gaps +Gap between +Male / +White / +Priv HS / +Mom coll / +High-inc / +Female +Non-white +Public HS +No coll +Low-inc +(1) +(2) +(3) +(4) +(5) +Panel A. Difference in average test score +Test-score gap +0.026∗∗∗ +0.057∗∗∗ +0.130∗∗∗ +0.098∗∗∗ +0.192∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Panel B. Contribution of gaps in ability and endurance to test-score gaps +Ability gap +0.030∗∗∗ +0.056∗∗∗ +0.127∗∗∗ +0.095∗∗∗ +0.188∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Endurance gap +0.017∗∗∗ +0.016∗∗∗ +0.038∗∗∗ +0.026∗∗∗ +0.063∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Panel C. Impact of a reform that halves the exam length on test-score gaps +P.p. change gap +-0.008∗∗∗ +-0.008∗∗∗ +-0.019∗∗∗ +-0.013∗∗∗ +-0.031∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Pct. change gap +-0.322∗∗∗ +-0.137∗∗∗ +-0.144∗∗∗ +-0.130∗∗∗ +-0.163∗∗∗ +(0.001) +(0.000) +(0.000) +(0.000) +(0.000) +N (Students) +14,941,097 +14,565,550 +9,924,652 +14,290,759 +9,996,959 +Notes: This table shows test-score gaps in the ENEM and the contribution of differences in ability and +endurance to those gaps. +Each column shows the result for a different test-score gap. Column 1 shows gaps between male and +female students. Column 2 shows gaps between white and non-white (Black, Brown, and Indigenous) +students. Column 3 shows gaps between students enrolled in a private high school and public high school. +Column 4 shows gaps between students with a college-educated mother and non-college-educated mother. +Column 5 shows gaps between students in households in the top 30% and bottom 30% of the income +distribution. +Panel A shows the average test score difference between the two groups displayed in the column header, +E[TestScorei|Xi = 1] − E[TestScorei|Xi = 0]. +Panel B shows the contribution of differences in ability and differences in endurance to the test- +score gap. +The ability gap is the average difference in ability, controlling for endurance, E[ˆαi|Xi = +1, ˆβi] − E[ˆαi|Xi = 0, ˆβi]. The endurance gap is the average difference in endurance, controlling for ability +and scaled by the average question position, +� +E[ˆβi|Xi = 1, ˆαi] − E[ˆβi|Xi = 0, ˆαi] +� +× Position. +Panel C shows estimates of the impact of a reform that changes the length of the exam from Position to +Position/2. The first row shows the percentage point change in the test-score gap due to the reform, which +is equal to − +� +E[ˆβi|Xi = 1, ˆαi] − E[ˆβi|Xi = 0, ˆαi] +� +× Position/2. The second row shows the percentage +change in the test-score gap, which equals the percentage point change in the gap divided by the pre-reform +test-score gap (shown in Panel A). Standard errors estimated through the delta method in parentheses. +∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively. +49 + +Table 6: The effect of an exam reform that halves the exam length on its predictive validity +Outcome: Predictive validity of question j for +Test +College +College +Degree +Grad. +Hourly +Monthly +Firm +score +enrol. +quality +progress +rate +wage +earnings +wage +(1) +(2) +(3) +(4) +(5) +(6) +(7) +(8) +Panel A. Average predictive validity +Constant +0.285∗∗∗ +0.057∗∗∗ +0.109∗∗∗ +0.003∗∗∗ +0.016∗∗∗ +0.106∗∗∗ +0.101∗∗∗ +0.084∗∗∗ +(0.007) +(0.002) +(0.003) +(0.001) +(0.001) +(0.003) +(0.003) +(0.002) +Panel B. Effect of the exam reform +Change in Pred. Val. +0.115∗ +0.055∗∗∗ +0.099∗∗∗ +−0.005∗∗ +0.003 +0.084∗∗ +0.077∗∗ +0.072∗∗ +(0.069) +(0.018) +(0.032) +(0.002) +(0.013) +(0.034) +(0.032) +(0.030) +Chg. Val./Mean +0.404∗∗∗ +0.952∗∗∗ +0.911∗∗∗ +−1.500∗∗∗ +0.201 +0.796∗∗∗ +0.757∗∗∗ +0.855∗∗∗ +(0.110) +(0.191) +(0.144) +(0.494) +(0.662) +(0.193) +(0.194) +(0.239) +N (Item−Booklets) +1,416 +1,416 +1,416 +700 +1,416 +1,416 +1,416 +1,416 +Notes: This table displays the estimated effect of an exam reform that changes the exam length from Position to Position/2 on the predictive +validity of the exam questions for long-run outcomes. +Each column displays the estimates of equation (17) for a different outcome. In Panel A, the regression only includes a constant. In Panel +B, the regression includes question fixed effects. I the coefficients so that they can be interpreted as the effect of decreasing the exam length +by half. See Section 2.4 for outcome definitions. +Heteroskedasticity-robust standard errors clustered at the question level in parentheses. ∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and +1% levels, respectively. +50 + +References +Abraham, K. G. and Mallatt, J. (2022). 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Publisher: The University of Chicago Press. +57 + +Appendix +A +Appendix Figures and Tables +Figure A1: Examples of “focus support” products in a local CVS +Notes: These pictures show examples of over-the-counter products aimed at enhancing focus and cognition. +The pictures were taken at a local pharmacy by the author. +58 + +/36 +2 +Your brain +does so +ARD +much. +Help treat +Rritual +roomadaptogen +enhanced elixir +it right. +reishi relax +with ashwagandha +cucao +atress+sleepaupport +prebiotic superloods +bne peppeou +By adding some brain supporting +nutrients,you may support +overall cognitive skills,including +.Memory +5.29 +UPAY +·Focus +9.99 +·Concentrationmemory +17 +brain support +vitamins +&focus +man +eckout +liquid +workout +MAXFocus +CLINICALLYTI +Support your +FORMUL +Brain & Vision +concentration levels +FOCUSFOCU +to help get stuff done. +Extra Strength +fact +factor +Gummies +FOCUS +FOCUS +Nutrition for the +Nutrition for the +factor. +factor +. Clinically Shown fo +Brain &Eyes +·Improves Memory +Nutrition +Concentration &Focu +·Plus Complete Multivit +·Plus Complete +Multivitamir +Before taking, consult with your health care professional +With Lutein +&Zeaxanthin +IAL +LFTTGUMMIES +FOCFCTGUMMIES +380482 +$14.79 +FF XS TABS +$29.99 +652541 +FF NUTRI BN TABS +A032 +$49.99 +FFCAPS +082821 +377611 +$29.99 +$43.emory,Concen +appliednutrition +andFocus +WNatureWell +FORCE +MENTAL FOCUS +COCONUT +FACTOR +MCT+ +HEALTHY BRAIN +COCOA +FOREBRAIN +Dietary Supplement Powder +ALL-DAY FOCUS +745mg of Coconut MCT +1220mg of Cocoa Powder per serving +Kalsuplemenit +POTEnT NOOTROPIC FORMULa HELPS +• supports enhanced mental focus4 +Have You Nourished +Powerful 3-in-1 Brain Booster +· improves energy +Your Brain ody? +Plus Turmeric Extract +IMPROVE MEMORY +: natural cocoa flavor +BOOST COGNiTIVE PERFORMAnCE' +BRAIN BOOST 1: +ENHANCE SHARPNESS G CLARITY +Attention&Concentration +BRAINBOOST2: +Memory&Mental Clarity +BRAINBOOST3: +Calm&Focus +CONTAINS 10 INDIVIDUALPACKETS +INDIVIDUALNETWT023OZ16.4.a +focus support products +STRGTH 60CT +FF FOREBRAIN15CT 30CT +NATUREWELL COCONUT EACH +NATUREWELL COCONUT +353031YOU PAY +03304567083YOUPAY +03303595594YOU +57594 +546416YOUPAY +01403 +0965 +$15. +$29.99 +$23.99 +A03 +$17.99 +A03 +$16.79 +A03 +A03 +08/28/21 +08/28/21 +08/28/21 +08/28/21 +13 10/23-11/20 +A03353031 +300Figure A2: Fraction of students who graduate from college by years since enrollment +0.00 +0.10 +0.20 +0.30 +0.40 +0.50 +Fraction of enrollees who graduated +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +Years since enrolling in college +Notes: This figure shows the empirical cumulative distribution function of the graduation rate of individuals +in the high-school-students sample. +59 + +Figure A3: Histogram of the change in a question’s position across exam booklets +Panel A. All years (2009–2016) +0 +5 +10 +15 +Percent of questions +0 +10 +20 +30 +40 +Change in a question's position between two different booklets +Panel B. First two cohorts (2009–2010) +0 +10 +20 +30 +40 +50 +Percent of questions +0 +5 +10 +15 +Change in a question's position between two different booklets +Notes: This figure shows the amount of variation available in a given question’s position between different +exam booklets. To construct this figure, I first calculate the difference (in absolute value) in a question’s +position in two exam booklets. This difference ranges from zero (if a question is in the same position in +two different booklets) to 44 (if a question is in the first position of a section in one booklet and the last +position of a section in another booklet). I repeat this process for each question and each possible booklet +pair. The figure plots the resulting histogram of position differences. +60 + +Figure A4: Average student performance on selected questions by question position +Random chance +0.20 +0.40 +0.60 +0.80 +Fraction of students who answered correctly +1 +10 +20 +30 +40 +50 +60 +70 +80 +90 +Position of the question in the exam +Slope x10: -0.014 +Slope x10: -0.028 +Slope x10: -0.020 +Slope x10: -0.020 +Slope x10: -0.020 +Slope x10: -0.023 +Slope x10: -0.062 +Notes: This figure plots the fraction of correct responses on seven selected exam questions as a function +of their position on the four different exam booklets. +Solid lines denote predicted values from linear +regressions estimated on the plotted points. +61 + +Figure A5: Histogram of question-level position effects +Share negative = 0.69 +Share positive = 0.31 +Mean = -0.074 pp +0 +2 +4 +6 +8 +Percent of questions +-0.50 +-0.25 +0.00 +0.25 +0.50 +Effect of a one position increase on item performance (in pp) +Notes: This figure plots the distribution of item-level position effects. To construct this figure, I estimate +the impact of an increase in the position of a given question on student performance separately for each +question. The figure displays the distribution of estimated β’s (one for each item). The figure excludes +outliers (i.e., questions for which the effect is below -0.50 or above 0.50 percentage points). +62 + +Figure A6: Distribution of academic ability and cognitive endurance +Panel A. Academic ability (αi) +0 +1 +2 +3 +Percent of students +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Academic ability (αi) +Panel B. Cognitive endurance (βi) +Share negative = 0.65 +Share positive = 0.35 +Mean β = -0.058 +0 +1 +2 +3 +Percent of students +-0.6 +-0.4 +-0.2 +0.0 +0.2 +0.4 +0.6 +Cognitive endurance (βi) +Notes: This figure shows the distribution of my estimates of academic ability (Panel A) and cognitive +endurance (Panel B) among individuals in the high-school-students sample. The measure of an individual’s +ability is the estimated intercept (αi) in equation (7). The measure of an individual’s cognitive endurance +is the estimated slope (βi) in equation (7). +63 + +Figure A7: The relationship between a question’s predictive validity and its position +Panel A. Test score (leave-question-out) +0.10 +0.20 +0.30 +0.40 +Predictive validity for average score +1 +30 +60 +90 +Position of the question in the exam +Panel B. College enrollment +0.02 +0.04 +0.06 +0.08 +0.10 +Predictive validity for college enrollment +1 +30 +60 +90 +Position of the question in the exam +Panel C. College quality +0.05 +0.10 +0.15 +0.20 +Predictive validity for college quality +1 +30 +60 +90 +Position of the question in the exam +Panel D. Hourly wage +0.00 +0.05 +0.10 +0.15 +Predictive validity for log hourly wage +1 +30 +60 +90 +Position of the question in the exam +Panel E. Monthly earnings +0.00 +0.05 +0.10 +0.15 +Predictive validity for monthly earnings +1 +30 +60 +90 +Position of the question in the exam +Panel F. Firm leave-one-out mean wage +0.02 +0.04 +0.06 +0.08 +0.10 +0.12 +Predictive validity for log firm hourly wage +1 +30 +60 +90 +Position of the question in the exam +Notes: This figure shows the relationship between (i) the predictive validity of an exam question for a +given outcome and (ii) the position of the question on the exam. The y-axis plots the correlation between +correctly responding to the question in position j and a given outcome Y . The x-axis show the position +of the question on the exam. Each plot shows the results for the outcome listed in the panel title. See +Section 2.4 for outcome definitions. The red dashed lines are predicted values from a linear regression on +the plotted points. +64 + +Table A1: Summary statistics of the high-school-student sample by booklet color +Day 1 booklet color +All +Yellow +Blue +Pink +White +(1) +(2) +(3) +(4) +(5) +Panel A. Demographic characteristics and race +Age +18.204 +18.201 +18.210 +18.209 +18.196 +Female +0.598 +0.595 +0.600 +0.595 +0.599 +White +0.476 +0.478 +0.476 +0.476 +0.474 +Black/Brown +0.505 +0.503 +0.505 +0.505 +0.507 +Panel B. Household characteristics +Attends a private HS +0.222 +0.225 +0.220 +0.223 +0.220 +Mom completed high school +0.534 +0.538 +0.532 +0.535 +0.531 +Mom completed college +0.205 +0.208 +0.203 +0.207 +0.203 +Family earns above 2x M.W. +0.388 +0.392 +0.386 +0.390 +0.385 +Family earns above 5x M.W. +0.062 +0.064 +0.061 +0.063 +0.061 +Panel C. Exam preparation +Took a foreign lang. course +0.241 +0.241 +0.241 +0.240 +0.241 +Took a test prep course +0.119 +0.121 +0.119 +0.119 +0.118 +Panel D. Fraction of correct responses +Natural Science +0.283 +0.284 +0.283 +0.283 +0.283 +Social Science +0.398 +0.398 +0.398 +0.398 +0.398 +Language +0.408 +0.410 +0.408 +0.408 +0.407 +Math +0.283 +0.284 +0.283 +0.283 +0.282 +Average +0.343 +0.344 +0.343 +0.343 +0.343 +Panel E. Geographical location +Lives in the North +0.089 +0.089 +0.089 +0.090 +0.089 +Lives in the Northeast +0.305 +0.305 +0.303 +0.306 +0.305 +Lives in the Southeast +0.389 +0.388 +0.390 +0.388 +0.389 +Lives in the South +0.131 +0.131 +0.132 +0.130 +0.131 +Lives in the Midwest +0.086 +0.086 +0.086 +0.086 +0.086 +F-statistic +– +0.875 +1.051 +0.857 +0.887 +p-value F-statistic +– +0.599 +0.452 +0.614 +0.588 +Number of test-takers +14,941,156 +3,655,807 +3,903,653 +3,590,977 +3,790,719 +Notes: This table shows summary statistics on all test-takers in the high-school-students sample (column +1) and based on the booklet color they received on the first day of testing (columns 2–5). The last panel +reports the F-statistics and p-values from F-tests that the coefficients on all pre-determined covariates +(Panels A, B, C, and E) are jointly equal across booklet colors. +65 + +Table A2: Examples of reliability estimates in economics and psychology +Construct +Reliability estimate +Reference +(1) +(2) +(3) +IQ +0.80 +Schuerger and Witt (1989) +Risk aversion +0.20–0.40 +Mata et al. (2018) +Big 5 personality traits +0.60–0.73 +Wooden (2012) +Present bias +0.36 +Meier and Sprenger (2015) +Loss aversion +0.88 +Stango and Zinman (2020) +Teacher value added +0.23–0.47 +Chetty et al. (2014a) +Life satisfaction +0.67 +Anusic and Schimmack (2016) +Self-esteem +0.71 +Anusic and Schimmack (2016) +Academic ability +0.61–0.77 +This paper +Cognitive endurance +0.14–0.30 +This paper +Notes: This table displays examples of reliability estimates from the economics and psychology litera- +ture. The last two rows show the test-retest reliability of the measures of academic ability and cognitive +endurance estimated in Section 5. +66 + +Table A3: IV estimates of the relationship between ability/endurance and college +outcomes +Dependent variable +Enrolled +College +Degree +1st-year +Grad. +Time to +college +quality +quality +credits +on time +grad. +(1) +(2) +(3) +(4) +(5) +(6) +Panel A. OLS estimates on retakers sample +Endurance +0.048∗∗∗ +0.057∗∗∗ +0.110∗∗∗ +0.010∗∗∗ +0.026∗∗∗ +−0.082∗∗∗ +(0.001) +(0.001) +(0.002) +(0.000) +(0.002) +(0.006) +Ability +0.110∗∗∗ +0.129∗∗∗ +0.217∗∗∗ +0.018∗∗∗ +0.049∗∗∗ +−0.154∗∗∗ +(0.002) +(0.001) +(0.002) +(0.000) +(0.003) +(0.009) +Ratio coef. +0.441∗∗∗ +0.443∗∗∗ +0.509∗∗∗ +0.571∗∗∗ +0.543∗∗∗ +0.533∗∗∗ +(0.011) +(0.006) +(0.007) +(0.008) +(0.037) +(0.032) +Mean DV +0.367 +3.420 +3.390 +0.146 +0.808 +4.191 +N +132,634 +111,409 +109,390 +339,727 +51,066 +51,066 +Panel B. IV estimates on retakers sample +Endurance +0.046∗∗∗ +0.067∗∗∗ +0.141∗∗∗ +0.016∗∗∗ +0.041∗∗∗ +−0.120∗∗∗ +(0.006) +(0.004) +(0.007) +(0.001) +(0.010) +(0.028) +Ability +0.107∗∗∗ +0.140∗∗∗ +0.239∗∗∗ +0.022∗∗∗ +0.057∗∗∗ +−0.169∗∗∗ +(0.002) +(0.001) +(0.003) +(0.000) +(0.005) +(0.013) +Ratio coef. +0.430∗∗∗ +0.479∗∗∗ +0.590∗∗∗ +0.738∗∗∗ +0.722∗∗∗ +0.711∗∗∗ +(0.053) +(0.025) +(0.028) +(0.026) +(0.156) +(0.145) +Mean DV +0.367 +3.420 +3.390 +0.146 +0.808 +4.191 +N +132,614 +111,394 +109,375 +339,725 +51,056 +51,056 +Notes: This table displays OLS and IV estimates of the relationship between ability/endurance and college +outcomes. +The OLS estimates are analogous to Table 3 but estimated on the sample of retakers. See notes to +Table 3 for details. The IV estimates instrument the year t measure of ability and cognitive endurance +with the t − 1 measures of these skills. +Heteroskedasticity-robust standard errors clustered at the individual level in parentheses. ∗∗∗, ∗∗ and +∗ denote significance at 10%, 5% and 1% levels, respectively. +67 + +Table A4: IV estimates of the relationship between ability/endurance and labor-market +outcomes +Dependent variable +Formal +Hourly +Monthly +Firm +Occup. +Industry +sector +wage +earnings +wage +wage +wage +(1) +(2) +(3) +(4) +(5) +(6) +Panel A. OLS estimates on retakers sample +Endurance +0.001∗∗∗ +0.121∗∗∗ +0.124∗∗∗ +0.081∗∗∗ +0.030∗∗∗ +0.008∗∗∗ +(0.000) +(0.005) +(0.005) +(0.005) +(0.003) +(0.001) +Ability +0.002∗∗∗ +0.231∗∗∗ +0.201∗∗∗ +0.163∗∗∗ +0.057∗∗∗ +0.018∗∗∗ +(0.000) +(0.006) +(0.006) +(0.005) +(0.003) +(0.002) +Ratio coef. +0.518∗∗∗ +0.525∗∗∗ +0.615∗∗∗ +0.496∗∗∗ +0.518∗∗∗ +0.413∗∗∗ +(0.072) +(0.018) +(0.020) +(0.024) +(0.040) +(0.057) +Mean DV +0.286 +4.049 +7.702 +4.014 +3.992 +3.875 +N +133,904 +37,814 +37,814 +32,908 +37,798 +37,814 +Panel B. IV estimates on retakers sample +Endurance +0.003∗∗∗ +0.188∗∗∗ +0.232∗∗∗ +0.120∗∗∗ +0.052∗∗∗ +0.001 +(0.001) +(0.018) +(0.017) +(0.015) +(0.009) +(0.004) +Ability +0.002∗∗∗ +0.250∗∗∗ +0.215∗∗∗ +0.180∗∗∗ +0.061∗∗∗ +0.018∗∗∗ +(0.000) +(0.008) +(0.007) +(0.007) +(0.004) +(0.002) +Ratio coef. +1.171∗∗∗ +0.753∗∗∗ +1.077∗∗∗ +0.670∗∗∗ +0.845∗∗∗ +0.050 +(0.323) +(0.069) +(0.079) +(0.081) +(0.150) +(0.241) +Mean DV +0.286 +4.049 +7.702 +4.014 +3.992 +3.875 +N +133,884 +37,801 +37,801 +32,902 +37,785 +37,801 +Notes: This table displays OLS and IV estimates of the relationship between ability/endurance and labor- +market outcomes. +The OLS estimates are analogous to Table 3 but estimated on the sample of retakers. See notes to +Table 3 for details. The IV estimates instrument the year t measure of ability and cognitive endurance +with the t − 1 measures of these skills. +Heteroskedasticity-robust standard errors clustered at the individual level in parentheses. ∗∗∗, ∗∗ and +∗ denote significance at 10%, 5% and 1% levels, respectively. +68 + +Table A5: Robustness of baseline test-score-gaps decomposition to measuring variables in +percentiles +Gap between +Male / +White / +Priv HS / +Mom coll / +High-inc / +Female +Non-white +Public HS +No coll +Low-inc +(1) +(2) +(3) +(4) +(5) +Panel A. Difference in average test-score percentile +Score pctil gap +5.871∗∗∗ +14.127∗∗∗ +27.826∗∗∗ +21.609∗∗∗ +39.838∗∗∗ +(0.015) +(0.015) +(0.019) +(0.018) +(0.023) +Panel B. Contribution of gaps in ability and endurance percentiles to test-score gaps +Ability pctil gap +5.599∗∗∗ +10.618∗∗∗ +21.952∗∗∗ +16.728∗∗∗ +31.775∗∗∗ +(0.012) +(0.011) +(0.017) +(0.015) +(0.024) +Endurance pctil gap +3.205∗∗∗ +3.097∗∗∗ +6.628∗∗∗ +4.596∗∗∗ +10.381∗∗∗ +(0.006) +(0.006) +(0.010) +(0.008) +(0.015) +Panel C. Impact of a reform that halves the exam length on test-score percentile gaps +Pctil. change gap +-1.603∗∗∗ +-1.548∗∗∗ +-3.314∗∗∗ +-2.298∗∗∗ +-5.190∗∗∗ +(0.003) +(0.003) +(0.005) +(0.004) +(0.008) +Pct. change gap +-0.546∗∗∗ +-0.219∗∗∗ +-0.238∗∗∗ +-0.213∗∗∗ +-0.261∗∗∗ +(0.001) +(0.000) +(0.000) +(0.000) +(0.000) +N (Students) +14,941,097 +14,565,550 +9,924,652 +14,290,759 +9,996,959 +Notes: This table is analogous to Table 5, but the variables and effects are measured in percentiles. I +construct the percentiles separately for each cohort. See notes to Table 5 for details. +69 + +Table A6: Robustness of baseline test-score-gaps decomposition to alternative ways of +measuring ability and endurance +Gap between +Male / +White / +Priv HS / +Mom coll / +High-inc / +Female +Non-white +Public HS +No coll +Low-inc +(1) +(2) +(3) +(4) +(5) +Panel A. Estimating ability/endurance separately by day and using the average +Ability gap +0.030∗∗∗ +0.056∗∗∗ +0.127∗∗∗ +0.095∗∗∗ +0.188∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Endurance gap +0.034∗∗∗ +0.032∗∗∗ +0.075∗∗∗ +0.051∗∗∗ +0.126∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Panel B. Estimating ability/endurance separately by subject and using the average +Ability gap +0.027∗∗∗ +0.061∗∗∗ +0.140∗∗∗ +0.104∗∗∗ +0.206∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Endurance gap +0.004∗∗∗ +0.042∗∗∗ +0.099∗∗∗ +0.069∗∗∗ +0.163∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Panel C. Including day fixed effects +Ability gap +0.030∗∗∗ +0.056∗∗∗ +0.128∗∗∗ +0.096∗∗∗ +0.189∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Endurance gap +0.034∗∗∗ +0.031∗∗∗ +0.075∗∗∗ +0.051∗∗∗ +0.125∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Panel D. Including subject fixed effects +Ability gap +0.026∗∗∗ +0.061∗∗∗ +0.141∗∗∗ +0.104∗∗∗ +0.207∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Endurance gap +0.002∗∗∗ +0.039∗∗∗ +0.095∗∗∗ +0.066∗∗∗ +0.158∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Panel E. Using linear correlation as an alternative measure of endurance +Ability gap +0.030∗∗∗ +0.057∗∗∗ +0.129∗∗∗ +0.097∗∗∗ +0.191∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Endurance gap +0.021∗∗∗ +0.020∗∗∗ +0.047∗∗∗ +0.032∗∗∗ +0.079∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +N (Students) +14,941,097 +14,565,550 +9,924,652 +14,290,759 +9,996,959 +Notes: This table shows estimates of the contribution of gaps in ability and endurance to test-score gaps +using alternative specifications to estimate ability and endurance. +Each column shows the result for a different test-score gap. Each panel shows the result from estimating +ability and endurance with a different specification. In Panels A–B, I estimate a student’s ability/endurance +separately for each testing day (Panel A) and academic subject (Panel B) and then average the estimates +across days or subjects. In Panels C–D, I estimate endurance in a regression that controls for day fixed +effects (Panel C) or subject fixed effects (Panel D). Finally, in Panel E, I use the correlation between +question position and a dummy for correctly answering a question as an alternative measure of endurance. +Heteroskedasticity-robust standard errors clustered at the question level in parentheses. ∗∗∗, ∗∗ and ∗ +denote significance at 10%, 5% and 1% levels, respectively. +70 + +Table A7: Robustness of baseline test-score-gaps decomposition to alternative ways of +controlling for question difficulty when estimating ability/endurance +Gap between +Male / +White / +Priv HS / +Mom coll / +High-inc / +Female +Non-white +Public HS +No coll +Low-inc +(1) +(2) +(3) +(4) +(5) +Panel A. Not controlling for question difficulty +Ability gap +0.032∗∗∗ +0.049∗∗∗ +0.118∗∗∗ +0.087∗∗∗ +0.175∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Endurance gap +0.033∗∗∗ +0.026∗∗∗ +0.074∗∗∗ +0.050∗∗∗ +0.128∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Panel B. Estimating difficulty without adjusting for average position +Ability gap +0.028∗∗∗ +0.057∗∗∗ +0.130∗∗∗ +0.097∗∗∗ +0.191∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Endurance gap +0.034∗∗∗ +0.036∗∗∗ +0.080∗∗∗ +0.055∗∗∗ +0.131∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Panel C. Estimating difficulty using question-specific position effects +Ability gap +0.032∗∗∗ +0.055∗∗∗ +0.126∗∗∗ +0.095∗∗∗ +0.186∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Endurance gap +0.036∗∗∗ +0.031∗∗∗ +0.082∗∗∗ +0.058∗∗∗ +0.135∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Panel D. Estimating difficulty using shrunk question-specific position effects +Ability gap +0.031∗∗∗ +0.056∗∗∗ +0.127∗∗∗ +0.095∗∗∗ +0.187∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Endurance gap +0.036∗∗∗ +0.032∗∗∗ +0.080∗∗∗ +0.057∗∗∗ +0.131∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Panel E. Estimating position effects separately by fraction of correct responses +Ability gap +0.030∗∗∗ +0.056∗∗∗ +0.128∗∗∗ +0.096∗∗∗ +0.189∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Endurance gap +0.035∗∗∗ +0.032∗∗∗ +0.078∗∗∗ +0.053∗∗∗ +0.130∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Panel F. Estimating position effects separately by subject +Ability gap +0.029∗∗∗ +0.057∗∗∗ +0.128∗∗∗ +0.096∗∗∗ +0.190∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Endurance gap +0.034∗∗∗ +0.034∗∗∗ +0.077∗∗∗ +0.053∗∗∗ +0.128∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +N (Students) +14,941,097 +14,565,550 +9,924,652 +14,290,759 +9,996,959 +Notes: This table shows estimates of the contribution of gaps in ability and endurance to test-score gaps +using alternative measures of difficulty in the specification used to estimate ability and endurance. +Each column shows the result for a different test-score gap. Each panel shows the result from a different +way of controlling for question difficulty in equation (7). In Panel A, I compute the estimate equation +(7) without controlling for question difficulty. In Panel B, I measure question difficulty as the fraction of +students who incorrectly answer to the question across all booklets. In Panels C–F, I adjust for average +question position by estimating the positon effects with alternative specifications. In column C, I compute +question-specific position effects. In Panel D, I compute a shrinkage estimator of the position effects. In +Panel E, I compute the position effects separately for questions with a below/above fraction of correct +responses. In Panel F, I compute the position effects separately by subject. See Appendix D for details +on each measure of question difficulty. +Heteroskedasticity-robust standard errors clustered at the question level in parentheses. ∗∗∗, ∗∗ and ∗ +denote significance at 10%, 5% and 1% levels, respectively. +71 + +Table A8: Robustness of baseline test-score-gaps decomposition to alternative sample +restrictions +Gap between +Male / +White / +Priv HS / +Mom coll / +High-inc / +Female +Non-white +Public HS +No coll +Low-inc +(1) +(2) +(3) +(4) +(5) +Panel A. Excluding students in the bottom or top 10% of the ability distribution +Ability gap +0.018∗∗∗ +0.036∗∗∗ +0.076∗∗∗ +0.055∗∗∗ +0.116∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Endurance gap +0.032∗∗∗ +0.031∗∗∗ +0.067∗∗∗ +0.045∗∗∗ +0.107∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Panel B. Excluding students in the bottom or top 10% of the endurance distribution +Ability gap +0.027∗∗∗ +0.054∗∗∗ +0.125∗∗∗ +0.094∗∗∗ +0.190∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Endurance gap +0.017∗∗∗ +0.017∗∗∗ +0.041∗∗∗ +0.028∗∗∗ +0.078∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Panel C. Excluding students in the bottom or top 10% of either distribution +Ability gap +0.016∗∗∗ +0.036∗∗∗ +0.073∗∗∗ +0.053∗∗∗ +0.113∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Endurance gap +0.017∗∗∗ +0.018∗∗∗ +0.037∗∗∗ +0.025∗∗∗ +0.062∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Panel D. Excluding students in the bottom or top 20% of either distribution +Ability gap +0.009∗∗∗ +0.023∗∗∗ +0.042∗∗∗ +0.030∗∗∗ +0.066∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Endurance gap +0.009∗∗∗ +0.011∗∗∗ +0.019∗∗∗ +0.013∗∗∗ +0.032∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Panel E. Excluding individuals with positive estimated endurance +Ability gap +0.021∗∗∗ +0.050∗∗∗ +0.112∗∗∗ +0.084∗∗∗ +0.165∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Endurance gap +0.013∗∗∗ +0.017∗∗∗ +0.037∗∗∗ +0.025∗∗∗ +0.063∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Notes: This table shows estimates of the contribution of gaps in ability and endurance to test-score gaps +using alternative sample restrictions. +Each column shows the result for a different test-score gap. Each panel shows the result for a different +sample of students. In Panel A, I exclude students in the bottom and top deciles of the ability distribution. +In Panel B, I exclude students in the bottom and top deciles of the endurance distribution. In Panel C, +I exclude students in the bottom and top deciles of the distribution of either skill. In Panel D, I exclude +students in the bottom and top quintiles of the distribution of either skill. In Panel E, I exclude students +with positive estimated endurance. +I construct the deciles and quintiles using all the students in the +high-school-students sample. +Heteroskedasticity-robust standard errors clustered at the question level in parentheses. ∗∗∗, ∗∗ and ∗ +denote significance at 10%, 5% and 1% levels, respectively. +72 + +Table A9: Robustness of baseline test-score-gaps decomposition to accounting for +measurement error +Gap between +Male / +White / +Priv HS / +Mom coll / +High-inc / +Female +Non-white +Public HS +No coll +Low-inc +(1) +(2) +(3) +(4) +(5) +Panel A. Weighting each observation by its precision +Ability gap +0.030∗∗∗ +0.056∗∗∗ +0.127∗∗∗ +0.095∗∗∗ +0.188∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Endurance gap +0.034∗∗∗ +0.031∗∗∗ +0.075∗∗∗ +0.051∗∗∗ +0.126∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Panel B. Shrunk estimator of ability and endurance +Ability gap +0.021∗∗∗ +0.040∗∗∗ +0.091∗∗∗ +0.067∗∗∗ +0.136∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Endurance gap +0.009∗∗∗ +0.010∗∗∗ +0.023∗∗∗ +0.016∗∗∗ +0.040∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +N (Students) +14,941,097 +14,565,550 +9,924,652 +14,290,759 +9,996,959 +Notes: This table shows estimates of the contribution of gaps in ability and endurance to test-score gaps +accounting for measurement error in the estimates of ability and endurance. +Each column shows the result for a different test-score gap. In Panel A, I weight each observation by +the inverse of the standard error of the ability and endurance estimates. Specifically, the weight of each +observation is w = 1/(SE2 +ˆαi + SE2 +ˆβi), where SEˆαi and SE2 +ˆβi are the standard errors of ˆαi and ˆβi. In Panel +B, I estimate the baseline regression using a shrunk estimator of ability and endurance. I compute the +shrunk estimator of endurance as βs +i = ωi ˆβi + (1 − ωj)¯β, where ¯β is the average cognitive endurance in +my sample. The individual-specific weight is ωi = +Var[βi]−E[SE2 +ˆ +βi] +Var[βi]−E[SE2 +ˆ +βi]+SE2 +ˆ +βi +. The shrunk estimator, βs +i , puts +more weight on estimates of βi that are more precisely estimated, as measured by a low standard error. I +compute the shrunk estimator of ability analgously. +Heteroskedasticity-robust standard errors clustered at the question level in parentheses. ∗∗∗, ∗∗ and ∗ +denote significance at 10%, 5% and 1% levels, respectively. +73 + +B +Empirical Appendix +B.1 +Limited Cognitive Endurance and Time Pressure +Is the causal effect of an increase in the order of a given question on student performance +a manifestation of limited cognitive endurance or is it driven by students running out of +time? Two pieces of evidence suggest that time pressure does not explain the estimated +β < 0. +First, very few students leave responses unanswered. Appendix Figure B1 plots the +fraction of students who left a question unanswered (possibly, because they ran out of +time) against the question position. Questions that appear later in the test are more likely +to be left unanswered. However, only a small fraction of students leave any questions +unanswered. Thus, missing responses cannot account for the large change in performance +observed throughout the exam.32 +Figure B1: Fraction of question left unanswered throughout the ENEM +Day 1 of the exam +Day 2 of the exam +(Correlation = 0.84) +(Correlation = 0.74) +0.000 +0.001 +0.002 +0.003 +0.004 +Fraction of students who did not answer question +1 +30 +60 +90 +120 +150 +180 +Position of the question in the exam +Notes: This figure shows the fraction of questions left unanswered over the course of each testing day. The +y-axis displays the fraction of students who did not select any of the multiple-choice answers to a given +question. The x-axis displays the position of each question in the exam. The dashed lines are predicted +values from a linear regression estimated separately for each testing day. +Second, student performance declines even in questions that students answer when they +32There is no penalty for incorrectly answering a question. Therefore, this evidence is only suggestive +since leaving a question unanswered is a weakly dominated strategy. +74 + +are likely not time-pressured. Appendix Table E1 estimates the fatigue effect separately +for questions that appear in the first half (column 1) and the second half of each testing +day (column 2). Presumably, students should have plenty of time to answer the first half of +the exam. Yet, I still find fatigue effects that are quantitatively similar—or even larger—to +those estimated on the second half of each day or with all questions (see also Appendix +Figure B2). This result is consistent with visual evidence in Figure 2, which shows that +student performance tends to decline shortly after the exam starts and with the declines in +performance exhibited by the example questions that appear at the beginning of the exam +in Appendix Figure A4. +In summary, the evidence indicates that the effect of a question position on student +performance is not driven by students running out of time. +Figure B2: The heterogeneous effect of fatigue on performance by question position +Panel A. First half of each testing day +Intercept: -0.02 pp +Slope: -0.11 pp +Slope x 90: -9.58 pp +Percent change: -27.8% +-7 +-6 +-5 +-4 +-3 +-2 +-1 +0 +1 +Average pp change in prob. of correct answer +0 +5 +10 +15 +20 +25 +30 +35 +≥40 +Change in question position +Panel B. Second half of each testing day +Intercept: 0.04 pp +Slope: -0.06 pp +Slope x 90: -5.33 pp +Percent change: -15.5% +-6 +-5 +-4 +-3 +-2 +-1 +0 +1 +-7 +Average pp change in prob. of correct answer +0 +5 +10 +15 +20 +25 +30 +35 +≥40 +Change in question position +Notes: This figure shows heterogeneity in the effect of limited endurance on performance by question +position. Panels A and B are analogous to Figure 3, but the effect is estimated separately for questions +that appear on the first half of each testing day (Panel A) or the second half of each testing day (Panel B). +The y-axis shows the average change (in percentage points) in the fraction of students correctly responding +to a question. The x-axis plots the difference in the question position between each possible booklet pair. +The dashed line denotes predicted values from a linear regression estimated on the plotted points, using +the number of questions used to estimate each point as weights. +75 + +B.2 +OLS Formulas of Academic Ability and Cognitive Endurance +My measure of cognitive endurance is βi in equation (7). Ignoring controls for question +difficulty, the OLS estimator of βi is +ˆβi = +� +j(Posij − Pos)(Cij − ¯Ci) +� +j(Posij − Pos)2 += +� +j +wj +���� +Weight of +question j +× +(Cij − ¯Ci), +� +�� +� +Performance on +question j relative to +i’s average performance +(B1) +where ¯Ci is the fraction of questions correctly answered by student i, Pos is the average +question position (which is constant across test-takers), and wj ≡ +Posj−Pos +� +j(Posj−Pos)2 is the +weight of question j. +Equation (B1) shows that ˆβi is a weighted average of deviations from i’s average score. +The weight of each question depends on the location of the question on the test. Appendix +Figure B3 plots the weight OLS places on each question. The questions with the largest +weights (in absolute value) are the ones at the beginning and the end of the test. +Figure B3: Weight of each question in a test with 90 questions +-.001 +-.0005 +0 +.0005 +.001 +wq +1 +10 +20 +30 +40 +50 +60 +70 +80 +90 +Position of the question +Notes: This figure displays the weight put by the ordinary least squares (OLS) estimator of βi (equation +(7)) on each question of the test. +76 + +My measure of academic ability is αi in equation (7). The OLS estimator of αi is +ˆαi = ¯Ci − ˆβiPos +(B2) +Equation (B2) shows that αi can be estimated by the difference between i’s test score +( ¯Ci) and the part of her test score that is explained by limited endurance, ˆβiPos. +B.3 +Estimating the Standard Deviation of Ability and Endurance +The estimate of cognitive endurance, ˆβi, can be decomposed into latent cognitive en- +durance, βi, and a sampling error ei independent of βi and with variance σ2 +e: +ˆβi = βi + ei +(B3) +Calculating the variance on each side of equation (B3) yields: +σ2 +ˆβ = σ2 +β + σ2 +e, +(B4) +where σ2 +ˆβ and σ2 +β are the variances of ˆβ and β, respectively. Equation (B4) shows that the +raw standard deviation of ˆβ overstates the variability of β since it includes variability in +the sampling error. Let SEˆβ be the standard error of ˆβ. The variance of the sampling error +can be estimated as σ2 +e = E[SE2 +ˆβ]. Thus, an estimate of the variance of β is given by +ˆσ2 +β = σ2 +ˆβ − E[SE2 +ˆβ]. +(B5) +I use an analogous derivation to estimate the variance of latent ability, σ2 +α. +B.4 +Estimating the Predictive Validity of a Question +Let πj be the fraction of students who correctly responded to question j. Note that the +standard deviation of Cij is σCij = +� +πj(1 − πj). The predictive ability of question j for +77 + +outcome Y is given by +ρY +j ≡ Corr(Yi, Cij) = Cov(Yi, Cij) +σY σCij += +� +E[Yi|Cij = 1] − E[Yi|Cij = 0] +� +πj(1 − πj) +σY σCij += +� +E[Yi|Cij = 1] − E[Yi|Cij = 0] +�σCij +σY +. +(B6) +Equation (B6) shows that the predictive validity of a question partly depends on the +difference between the average outcome of students who correctly responded to the ques- +tion and the average outcome of students who did not, E[Yi|Cij = 1] − E[Yi|Cij = 0]. The +predictive validity also depends on the variability of correct responses relative to variabil- +ity in the outcome, σCij/σY . Thus, holding the rest of the variables constant, the more +dispersion there is in the distribution of correct responses, the more predictive the question +will be for future outcomes.33 +B.5 +Non-parametric Estimates +I assess nonparametrically the predicted effects of endurance on long-run outcomes by +estimating how a movement from the bottom decile to the top decile in the endurance +distribution affects a given outcome: +E[Yi|i ∈ Top decile Endurance] − E[Yi|i ∈ Bottom decile Endurance]. +(B7) +As a benchmark, I compare the size of a decile movement in the endurance distribution +to an equivalent decile movement in the ability distribution. I compute these effects in a +regression framework by estimating equations of the form: +Yi = φ + λXi + +10 +� +d=2 +1{i ∈ TestScore decile d} + ζi +(B8) +Yi = ˜φ1 + ˜λ1Xi + +10 +� +d=2 +1{i ∈ Ability decile d} + +10 +� +d=2 +1{i ∈ Endurance decile d} + ˜ζi, +(B9) +where the omitted category is the bottom decile. +33For example, for a question with two possible responses, the variance is maximized when πj = 0.50, +that is, when half students correctly answer the question. +78 + +B.6 +Robustness of the Relationship between Endurance and Long-Run Out- +comes +Appendix Table B1 shows non-parametric estimates of the effect of ability and endurance +on each outcome based on the slope of percentile changes on outcomes (Heckman et al., +2006). Specifically, I estimate how a movement from the bottom decile to the top decile +in the endurance distribution affects a given outcome (see Appendix B.5 for details). The +first row of each panel shows that moving higher in the distribution of test scores tends +to improve college and labor-market outcomes. Subsequent rows show that both cognitive +endurance and ability contribute to this effect. Depending on the outcome, the predicted +effect of a movement from decile 1 to decile 10 in the endurance distribution represents +32.6%–53.0% of the corresponding effect of a movement in the ability distribution. +Appendix Tables B2–B3 show that the results are robust to estimating ability and en- +durance with alternative specifications. First, I compute the estimates of ability/endurance +separately for each testing day and for each academic subject, and use the average estimate +across days/subjects as regressors in equation (10). Second, I compute the estimates of +endurance controlling for day fixed effects and subject fixed effects; thus accounting for +possible differences in preparation across subjects. Finally, I use the correlation between +question position and a dummy for correctly answering a question as an alternative mea- +sure of endurance. Across specifications, I find effects that are quantitatively similar and +qualitatively identical to those of the baseline specification. +Appendix Tables B4–B5 show that the results are robust to controlling for question +difficulty in alternative ways when estimating ability and endurance. First, I compute +the estimates of ability and endurance in equation (7) without controlling for question +difficulty. Second, I calculate question difficulty without adjusting for the average position +of the question across booklets. Finally, I compute question difficulty adjusting for average +question position in several alternative ways (see Appendix D). Consistent with the baseline +results, I find that the estimates are remarkably robust across specifications. +Appendix Tables B6–B7 shows that the results are robust to different sample restric- +tions. Specifically, I estimate the baseline specification excluding students in the tails of +the ability and the endurance distributions. These are students for whom floor and ceil- +ing effects may be binding and, thus, for whom estimates may be biased. I also exclude +students with a positive estimate of endurance. These are students who, for example, may +answer the exam in reverse order. I find little impact of these sample restrictions on the +estimates. +79 + +Appendix Tables B8–B9 show robustness of the baseline regressions to accounting for +measurement error. First, I weight each observation by the inverse of the standard error +of the ability and endurance estimates, thus giving more weight to students for which I +estimate more precise measures. Second, I estimate the baseline regressions using shrunk +estimates of ability and endurance. The shrunk estimators of ability and endurance put +more weight on measures estimated with more precision, as measured by a low standard +error. The results are very similar to the baseline results. +80 + +Table B1: The effect of a movement from decile 1 to decile 10 in the ability/endurance +distribution on long-run outcomes +Panel A. College outcomes +Dependent variable +Enrolled +College +Degree +1st-year +Grad. +Time to +college +quality +quality +credits +on time +grad. +(1) +(2) +(3) +(4) +(5) +(6) +Test score +0.300∗∗∗ +0.275∗∗∗ +0.389∗∗∗ +0.046∗∗∗ +0.215∗∗∗ +−0.397∗∗∗ +(0.001) +(0.001) +(0.002) +(0.001) +(0.002) +(0.008) +Endurance +0.136∗∗∗ +0.139∗∗∗ +0.232∗∗∗ +0.030∗∗∗ +0.132∗∗∗ +−0.224∗∗∗ +(0.002) +(0.001) +(0.002) +(0.001) +(0.002) +(0.007) +Ability +0.319∗∗∗ +0.338∗∗∗ +0.488∗∗∗ +0.057∗∗∗ +0.272∗∗∗ +−0.486∗∗∗ +(0.002) +(0.001) +(0.002) +(0.001) +(0.003) +(0.009) +Ratio coef. +0.426∗∗∗ +0.412∗∗∗ +0.474∗∗∗ +0.530∗∗∗ +0.485∗∗∗ +0.462∗∗∗ +(0.005) +(0.003) +(0.003) +(0.009) +(0.007) +(0.012) +Mean DV +0.329 +3.327 +3.244 +0.158 +0.418 +3.842 +N +1,850,938 +1,711,475 +1,681,214 +1,124,972 +1,471,569 +786,391 +Panel B. Labor-market outcomes +Dependent variable +Formal +Hourly +Monthly +Firm +Occup. +Industry +sector +wage +earnings +wage +wage +wage +(1) +(2) +(3) +(4) +(5) +(6) +Test score +0.005∗∗∗ +0.457∗∗∗ +0.395∗∗∗ +0.320∗∗∗ +0.141∗∗∗ +0.046∗∗∗ +(0.000) +(0.004) +(0.004) +(0.004) +(0.002) +(0.001) +Endurance +0.002∗∗∗ +0.241∗∗∗ +0.240∗∗∗ +0.159∗∗∗ +0.084∗∗∗ +0.018∗∗∗ +(0.000) +(0.005) +(0.004) +(0.004) +(0.003) +(0.001) +Ability +0.006∗∗∗ +0.543∗∗∗ +0.475∗∗∗ +0.387∗∗∗ +0.177∗∗∗ +0.055∗∗∗ +(0.000) +(0.005) +(0.005) +(0.005) +(0.003) +(0.001) +Ratio coef. +0.337∗∗∗ +0.443∗∗∗ +0.506∗∗∗ +0.410∗∗∗ +0.472∗∗∗ +0.326∗∗∗ +(0.034) +(0.007) +(0.007) +(0.009) +(0.012) +(0.020) +Mean DV +0.326 +3.865 +7.551 +3.885 +3.886 +3.858 +N +2,523,032 +818,590 +818,590 +692,880 +818,374 +818,590 +Notes: This table displays estimates of the relationship between ability/endurance and college outcomes +(Panel A) and labor-market outcomes (Panel B). +The first row of each panel shows estimates of the mean outcome difference between individuals in the +tenth and first decile of the test score distribution (the coefficient on the decile ten dummy in equation +(B8)). The following rows show estimates of the mean outcome difference between individuals in the tenth +and first decile of the ability/endurance distribution (the coefficients on the decile ten dummies in equation +(B9)). See Section 5 for a description of the measures of ability and endurance. See Section 2.4 for outcome +definitions. Heteroskedasticity-robust standard errors clustered at the individual level in parentheses. +The third-to-last row in each panel shows the ratio between the effect of ability and endurance on a +given outcome. Standard errors estimated through the delta method in parentheses. ∗∗∗, ∗∗ and ∗ denote +significance at 10%, 5% and 1% levels, respectively. +81 + +Table B2: Robustness of baseline regressions to alternative ways of measuring ability and +endurance: College outcomes +Dependent variable: +Enrolled +College +Degree +1st-year +Grad. +Time to +college +quality +quality +credits +on time +grad. +(1) +(2) +(3) +(4) +(5) +(6) +Panel A. Estimating ability/endurance separately by day and using the average +Endurance +0.053∗∗∗ +0.050∗∗∗ +0.084∗∗∗ +0.010∗∗∗ +0.043∗∗∗ +−0.079∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +(0.002) +Ability +0.114∗∗∗ +0.107∗∗∗ +0.157∗∗∗ +0.018∗∗∗ +0.081∗∗∗ +−0.158∗∗∗ +(0.000) +(0.000) +(0.001) +(0.000) +(0.001) +(0.002) +Panel B. Estimating ability/endurance separately by subject and using the average +Endurance +0.060∗∗∗ +0.055∗∗∗ +0.080∗∗∗ +0.009∗∗∗ +0.043∗∗∗ +−0.079∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +(0.002) +Ability +0.103∗∗∗ +0.097∗∗∗ +0.140∗∗∗ +0.016∗∗∗ +0.067∗∗∗ +−0.130∗∗∗ +(0.000) +(0.000) +(0.001) +(0.000) +(0.001) +(0.002) +Panel C. Including day fixed effects +Endurance +0.031∗∗∗ +0.030∗∗∗ +0.050∗∗∗ +0.006∗∗∗ +0.025∗∗∗ +−0.047∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +Ability +0.110∗∗∗ +0.104∗∗∗ +0.152∗∗∗ +0.018∗∗∗ +0.077∗∗∗ +−0.151∗∗∗ +(0.000) +(0.000) +(0.001) +(0.000) +(0.001) +(0.002) +Panel D. Including subject fixed effects +Endurance +0.019∗∗∗ +0.018∗∗∗ +0.026∗∗∗ +0.003∗∗∗ +0.014∗∗∗ +−0.025∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +Ability +0.097∗∗∗ +0.092∗∗∗ +0.133∗∗∗ +0.015∗∗∗ +0.062∗∗∗ +−0.119∗∗∗ +(0.000) +(0.000) +(0.001) +(0.000) +(0.001) +(0.002) +Panel E. Using linear correlation as an alternative measure of endurance +Endurance +0.030∗∗∗ +0.030∗∗∗ +0.049∗∗∗ +0.006∗∗∗ +0.025∗∗∗ +−0.047∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +Ability +0.101∗∗∗ +0.095∗∗∗ +0.138∗∗∗ +0.016∗∗∗ +0.072∗∗∗ +−0.139∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +(0.002) +Mean DV +0.244 +3.326 +3.244 +0.158 +0.418 +3.817 +N +2,501,519 +1,800,546 +1,768,707 +1,124,972 +1,472,916 +793,822 +Notes: This table shows estimates of the relationship between ability/endurance and college outcomes +using alternative specifications to estimate ability and endurance. +Each column shows the result for a different dependent variable. Each panel shows the result from +estimating ability and endurance with a different specification. In Panels A–B, I estimate a student’s +ability/endurance separately for each testing day (Panel A) and academic subject (Panel B) and then +average the estimates across days or subjects. In Panels C–D, I estimate endurance in a regression that +controls for day fixed effects (Panel C) or subject fixed effects (Panel D). Finally, in Panel E, I use the +correlation between question position and a dummy for correctly answering a question as an alternative +measure of endurance. +Heteroskedasticity-robust standard errors clustered at the individual level in parentheses.∗∗∗, ∗∗ and ∗ +denote significance at 10%, 5% and 1% levels, respectively. +82 + +Table B3: Robustness of baseline regressions to alternative ways of measuring ability and +endurance: Labor-market outcomes +Dependent variable: +Formal +Hourly +Monthly +Firm +Occup. +Industry +sector +wage +earnings +wage +wage +wage +(1) +(2) +(3) +(4) +(5) +(6) +Panel A. Estimating ability/endurance separately by day and using the average +Endurance +0.001∗∗∗ +0.088∗∗∗ +0.085∗∗∗ +0.058∗∗∗ +0.028∗∗∗ +0.006∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Ability +0.002∗∗∗ +0.172∗∗∗ +0.152∗∗∗ +0.121∗∗∗ +0.055∗∗∗ +0.016∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Panel B. Estimating ability/endurance separately by subject and using the average +Endurance +0.001∗∗∗ +0.088∗∗∗ +0.076∗∗∗ +0.061∗∗∗ +0.026∗∗∗ +0.008∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Ability +0.002∗∗∗ +0.156∗∗∗ +0.135∗∗∗ +0.110∗∗∗ +0.048∗∗∗ +0.014∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Panel C. Including day fixed effects +Endurance +0.000∗∗∗ +0.053∗∗∗ +0.051∗∗∗ +0.035∗∗∗ +0.017∗∗∗ +0.004∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.000) +(0.000) +Ability +0.002∗∗∗ +0.167∗∗∗ +0.147∗∗∗ +0.117∗∗∗ +0.053∗∗∗ +0.016∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Panel D. Including subject fixed effects +Endurance +0.000∗∗∗ +0.029∗∗∗ +0.025∗∗∗ +0.020∗∗∗ +0.008∗∗∗ +0.003∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +Ability +0.002∗∗∗ +0.147∗∗∗ +0.127∗∗∗ +0.104∗∗∗ +0.045∗∗∗ +0.013∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Panel E. Using linear correlation as an alternative measure of endurance +Endurance +0.000∗∗∗ +0.052∗∗∗ +0.050∗∗∗ +0.035∗∗∗ +0.016∗∗∗ +0.004∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.000) +(0.000) +Ability +0.002∗∗∗ +0.151∗∗∗ +0.132∗∗∗ +0.107∗∗∗ +0.048∗∗∗ +0.014∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Mean DV +0.326 +3.865 +7.551 +3.885 +3.886 +3.858 +N +2,523,029 +818,590 +818,590 +692,880 +818,374 +818,590 +Notes: This table shows estimates of the relationship between ability/endurance and labor-market out- +comes using alternative specifications to estimate ability and endurance. +Each column shows the result for a different dependent variable. Each panel shows the result from +estimating ability and endurance with a different specification. In Panels A–B, I estimate a student’s +ability/endurance separately for each testing day (Panel A) and academic subject (Panel B) and then +average the estimates across days or subjects. In Panels C–D, I estimate endurance in a regression that +controls for day fixed effects (Panel C) or subject fixed effects (Panel D). Finally, in Panel E, I use the +correlation between question position and a dummy for correctly answering a question as an alternative +measure of endurance. +Heteroskedasticity-robust standard errors clustered at the individual level in parentheses. ∗∗∗, ∗∗ and +∗ denote significance at 10%, 5% and 1% levels, respectively. +83 + +Table B4: Robustness of the baseline regressions to alternative ways of controlling for +question difficulty when estimating ability/endurance: College outcomes +Dependent variable: +Enrolled +College +Degree +1st-year +Grad. +Time to +college +quality +quality +credits +on time +grad. +(1) +(2) +(3) +(4) +(5) +(6) +Panel A. Not controlling for question difficulty +Endurance +0.040∗∗∗ +0.045∗∗∗ +0.080∗∗∗ +0.007∗∗∗ +0.028∗∗∗ +−0.061∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +(0.002) +Ability +0.114∗∗∗ +0.112∗∗∗ +0.169∗∗∗ +0.018∗∗∗ +0.079∗∗∗ +−0.159∗∗∗ +(0.000) +(0.000) +(0.001) +(0.000) +(0.001) +(0.002) +Panel B. Estimating difficulty without adjusting for average position +Endurance +0.030∗∗∗ +0.028∗∗∗ +0.045∗∗∗ +0.006∗∗∗ +0.026∗∗∗ +−0.046∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +Ability +0.097∗∗∗ +0.090∗∗∗ +0.130∗∗∗ +0.016∗∗∗ +0.068∗∗∗ +−0.133∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +(0.002) +Panel C. Estimating difficulty using question-specific position effects +Endurance +0.035∗∗∗ +0.038∗∗∗ +0.065∗∗∗ +0.007∗∗∗ +0.027∗∗∗ +−0.054∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +Ability +0.106∗∗∗ +0.102∗∗∗ +0.152∗∗∗ +0.017∗∗∗ +0.074∗∗∗ +−0.147∗∗∗ +(0.000) +(0.000) +(0.001) +(0.000) +(0.001) +(0.002) +Panel D. Estimating difficulty using shrunk question-specific position effects +Endurance +0.034∗∗∗ +0.035∗∗∗ +0.059∗∗∗ +0.006∗∗∗ +0.026∗∗∗ +−0.052∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +Ability +0.104∗∗∗ +0.098∗∗∗ +0.146∗∗∗ +0.017∗∗∗ +0.073∗∗∗ +−0.144∗∗∗ +(0.000) +(0.000) +(0.001) +(0.000) +(0.001) +(0.002) +Panel E. Estimating position effects separately by fraction of correct responses +Endurance +0.031∗∗∗ +0.030∗∗∗ +0.049∗∗∗ +0.006∗∗∗ +0.026∗∗∗ +−0.047∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +Ability +0.101∗∗∗ +0.094∗∗∗ +0.138∗∗∗ +0.016∗∗∗ +0.071∗∗∗ +−0.139∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +(0.002) +Panel F. Estimating position effects separately by subject +Endurance +0.031∗∗∗ +0.029∗∗∗ +0.048∗∗∗ +0.006∗∗∗ +0.026∗∗∗ +−0.047∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +Ability +0.099∗∗∗ +0.093∗∗∗ +0.135∗∗∗ +0.016∗∗∗ +0.071∗∗∗ +−0.137∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +(0.002) +Mean DV +0.244 +3.326 +3.244 +0.158 +0.418 +3.817 +N +2,501,519 +1,800,546 +1,768,707 +1,124,972 +1,472,916 +793,822 +Notes: This table shows estimates of the relationship between ability/endurance and college outcomes +using alternative measures of difficulty in the specification used to estimate ability and endurance. +Each panel shows the result using a different measure of question difficulty in equation (7). In Panel A, +I estimate equation (7) without controlling for question difficulty. In Panel B, I measure question difficulty +as the fraction of students who incorrectly answer the question across all booklets. +In Panels C–F, I +adjust for differences in average position across questions by estimating the position effects with alternative +specifications. In column C, I compute question-specific position effects. In Panel D, I compute a shrinkage +estimator of the position effects. In Panel E, I compute the position effects separately for questions with +a below/above fraction of correct responses. In Panel F, I compute the position effects separately by +subject. See Appendix D for details on each measure of question difficulty. Heteroskedasticity-robust +standard errors clustered at the individual level in parentheses.∗∗∗, ∗∗ and ∗ denote significance at 10%, +5% and 1% levels, respectively. +84 + +Table B5: Robustness of the baseline regressions to alternative ways of controlling for +question difficulty when estimating ability/endurance: Labor-market outcomes +Dependent variable: +Formal +Hourly +Monthly +Firm +Occup. +Industry +sector +wage +earnings +wage +wage +wage +(1) +(2) +(3) +(4) +(5) +(6) +Panel A. Not controlling for question difficulty +Endurance +0.001∗∗∗ +0.080∗∗∗ +0.077∗∗∗ +0.053∗∗∗ +0.022∗∗∗ +0.004∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Ability +0.002∗∗∗ +0.183∗∗∗ +0.163∗∗∗ +0.127∗∗∗ +0.056∗∗∗ +0.015∗∗∗ +(0.000) +(0.002) +(0.001) +(0.001) +(0.001) +(0.000) +Panel B. Estimating difficulty without adjusting for average position +Endurance +0.000∗∗∗ +0.048∗∗∗ +0.047∗∗∗ +0.032∗∗∗ +0.016∗∗∗ +0.004∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.000) +(0.000) +Ability +0.001∗∗∗ +0.143∗∗∗ +0.125∗∗∗ +0.101∗∗∗ +0.046∗∗∗ +0.014∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Panel C. Estimating difficulty using question-specific position effects +Endurance +0.001∗∗∗ +0.066∗∗∗ +0.064∗∗∗ +0.044∗∗∗ +0.019∗∗∗ +0.004∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.000) +(0.000) +Ability +0.002∗∗∗ +0.165∗∗∗ +0.146∗∗∗ +0.115∗∗∗ +0.051∗∗∗ +0.015∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Panel D. Estimating difficulty using shrunk question-specific position effects +Endurance +0.000∗∗∗ +0.061∗∗∗ +0.059∗∗∗ +0.040∗∗∗ +0.018∗∗∗ +0.004∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.000) +(0.000) +Ability +0.002∗∗∗ +0.159∗∗∗ +0.140∗∗∗ +0.111∗∗∗ +0.050∗∗∗ +0.014∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Panel E. Estimating position effects separately by fraction of correct responses +Endurance +0.000∗∗∗ +0.053∗∗∗ +0.051∗∗∗ +0.035∗∗∗ +0.017∗∗∗ +0.004∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.000) +(0.000) +Ability +0.002∗∗∗ +0.152∗∗∗ +0.133∗∗∗ +0.107∗∗∗ +0.048∗∗∗ +0.014∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Panel F. Estimating position effects separately by subject +Endurance +0.000∗∗∗ +0.051∗∗∗ +0.049∗∗∗ +0.034∗∗∗ +0.016∗∗∗ +0.004∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.000) +(0.000) +Ability +0.002∗∗∗ +0.149∗∗∗ +0.130∗∗∗ +0.105∗∗∗ +0.048∗∗∗ +0.014∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Mean DV +0.326 +3.865 +7.551 +3.885 +3.886 +3.858 +N +2,523,029 +818,590 +818,590 +692,880 +818,374 +818,590 +Notes: This table shows estimates of the relationship between ability/endurance and labor-market out- +comes using alternative measures of difficulty in the specification used to estimate ability and endurance. +Each panel shows the result using a different measure of question difficulty in equation (7). In Panel A, +I estimate equation (7) without controlling for question difficulty. In Panel B, I measure question difficulty +as the fraction of students who incorrectly answer the question across all booklets. +In Panels C–F, I +adjust for differences in average position across questions by estimating the position effects with alternative +specifications. In column C, I compute question-specific position effects. In Panel D, I compute a shrinkage +estimator of the position effects. In Panel E, I compute the position effects separately for questions with +a below/above fraction of correct responses. In Panel F, I compute the position effects separately by +subject. See Appendix D for details on each measure of question difficulty. Heteroskedasticity-robust +standard errors clustered at the individual level in parentheses.∗∗∗, ∗∗ and ∗ denote significance at 10%, +5% and 1% levels, respectively. +85 + +Table B6: Robustness of the baseline regressions to sample selection: College outcomes +Dependent variable: +Enrolled +College +Degree +1st-year +Grad. +Time to +college +quality +quality +credits +on time +grad. +(1) +(2) +(3) +(4) +(5) +(6) +Panel A. Excluding students in the bottom or top 10% of the ability distribution +Endurance +0.032∗∗∗ +0.027∗∗∗ +0.039∗∗∗ +0.007∗∗∗ +0.030∗∗∗ +−0.047∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +Ability +0.102∗∗∗ +0.085∗∗∗ +0.107∗∗∗ +0.019∗∗∗ +0.087∗∗∗ +−0.146∗∗∗ +(0.000) +(0.000) +(0.001) +(0.000) +(0.001) +(0.003) +Panel B. Excluding students in the bottom or top 10% of the endurance distribution +Endurance +0.030∗∗∗ +0.030∗∗∗ +0.050∗∗∗ +0.006∗∗∗ +0.025∗∗∗ +−0.044∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +(0.002) +Ability +0.100∗∗∗ +0.093∗∗∗ +0.135∗∗∗ +0.016∗∗∗ +0.075∗∗∗ +−0.138∗∗∗ +(0.000) +(0.000) +(0.001) +(0.000) +(0.001) +(0.002) +Panel C. Excluding students in the bottom or top 10% of either distribution +Endurance +0.031∗∗∗ +0.026∗∗∗ +0.037∗∗∗ +0.007∗∗∗ +0.030∗∗∗ +−0.046∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +(0.002) +Ability +0.102∗∗∗ +0.083∗∗∗ +0.102∗∗∗ +0.020∗∗∗ +0.089∗∗∗ +−0.146∗∗∗ +(0.001) +(0.000) +(0.001) +(0.000) +(0.001) +(0.003) +Panel D. Excluding students in the bottom or top 20% of either distribution +Endurance +0.030∗∗∗ +0.023∗∗∗ +0.030∗∗∗ +0.008∗∗∗ +0.034∗∗∗ +−0.044∗∗∗ +(0.001) +(0.000) +(0.001) +(0.000) +(0.001) +(0.003) +Ability +0.099∗∗∗ +0.074∗∗∗ +0.086∗∗∗ +0.022∗∗∗ +0.100∗∗∗ +−0.152∗∗∗ +(0.001) +(0.001) +(0.001) +(0.000) +(0.001) +(0.004) +Panel E. Excluding individuals with positive estimated endurance +Endurance +0.033∗∗∗ +0.028∗∗∗ +0.048∗∗∗ +0.005∗∗∗ +0.026∗∗∗ +−0.047∗∗∗ +(0.000) +(0.000) +(0.001) +(0.000) +(0.001) +(0.002) +Ability +0.107∗∗∗ +0.097∗∗∗ +0.143∗∗∗ +0.016∗∗∗ +0.065∗∗∗ +−0.133∗∗∗ +(0.001) +(0.000) +(0.001) +(0.000) +(0.001) +(0.003) +Notes: This table shows estimates of the relationship between ability/endurance and college outcomes +using alternative sample restrictions. +Each column shows the result for a different dependent variable. Each panel shows the result for a +different sample of students. In Panel A, I exclude students in the bottom and top deciles of the ability +distribution. In Panel B, I exclude students in the bottom and top deciles of the endurance distribution. +In Panel C, I exclude students in the bottom and top deciles of the distribution of either skill. In Panel D, +I exclude students in the bottom and top quintiles of the distribution of either skill. In Panel E, I exclude +students with a positive estimate of endurance (ˆβ > 0). I construct the deciles and quintiles using all the +students in the high-school-students sample. +Heteroskedasticity-robust standard errors clustered at the individual level in parentheses.∗∗∗, ∗∗ and ∗ +denote significance at 10%, 5% and 1% levels, respectively. +86 + +Table B7: Robustness of the baseline regressions to sample selection: Labor-market +outcomes +Dependent variable: +Formal +Hourly +Monthly +Firm +Occup. +Industry +sector +wage +earnings +wage +wage +wage +(1) +(2) +(3) +(4) +(5) +(6) +Panel A. Excluding students in the bottom or top 10% of the ability distribution +Endurance +0.000∗∗∗ +0.046∗∗∗ +0.044∗∗∗ +0.031∗∗∗ +0.017∗∗∗ +0.004∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.000) +(0.000) +Ability +0.001∗∗∗ +0.130∗∗∗ +0.113∗∗∗ +0.092∗∗∗ +0.051∗∗∗ +0.016∗∗∗ +(0.000) +(0.002) +(0.001) +(0.001) +(0.001) +(0.000) +Panel B. Excluding students in the bottom or top 10% of the endurance distribution +Endurance +0.000∗∗∗ +0.053∗∗∗ +0.050∗∗∗ +0.035∗∗∗ +0.016∗∗∗ +0.004∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Ability +0.001∗∗∗ +0.149∗∗∗ +0.131∗∗∗ +0.103∗∗∗ +0.049∗∗∗ +0.014∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Panel C. Excluding students in the bottom or top 10% of either distribution +Endurance +0.000∗∗∗ +0.044∗∗∗ +0.042∗∗∗ +0.029∗∗∗ +0.017∗∗∗ +0.004∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Ability +0.001∗∗∗ +0.127∗∗∗ +0.112∗∗∗ +0.089∗∗∗ +0.050∗∗∗ +0.015∗∗∗ +(0.000) +(0.002) +(0.001) +(0.001) +(0.001) +(0.000) +Panel D. Excluding students in the bottom or top 20% of either distribution +Endurance +0.000∗∗∗ +0.039∗∗∗ +0.037∗∗∗ +0.025∗∗∗ +0.016∗∗∗ +0.004∗∗∗ +(0.000) +(0.002) +(0.001) +(0.001) +(0.001) +(0.001) +Ability +0.001∗∗∗ +0.117∗∗∗ +0.105∗∗∗ +0.083∗∗∗ +0.052∗∗∗ +0.016∗∗∗ +(0.000) +(0.002) +(0.002) +(0.002) +(0.001) +(0.001) +Panel E. Excluding individuals with positive estimated endurance +Endurance +0.001∗∗∗ +0.054∗∗∗ +0.055∗∗∗ +0.033∗∗∗ +0.017∗∗∗ +0.003∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Ability +0.002∗∗∗ +0.158∗∗∗ +0.137∗∗∗ +0.112∗∗∗ +0.049∗∗∗ +0.014∗∗∗ +(0.000) +(0.002) +(0.002) +(0.002) +(0.001) +(0.000) +Notes: This table shows estimates of the relationship between ability/endurance and labor-market out- +comes using alternative sample restrictions. +Each column shows the result for a different dependent variable. Each panel shows the result for a +different sample of students. In Panel A, I exclude students in the bottom and top deciles of the ability +distribution. In Panel B, I exclude students in the bottom and top deciles of the endurance distribution. +In Panel C, I exclude students in the bottom and top deciles of the distribution of either skill. In Panel D, +I exclude students in the bottom and top quintiles of the distribution of either skill. In Panel E, I exclude +students with a positive estimate of endurance (ˆβ > 0). I construct the deciles and quintiles using all the +students in the high-school-students sample. +Heteroskedasticity-robust standard errors clustered at the individual level in parentheses.∗∗∗, ∗∗ and ∗ +denote significance at 10%, 5% and 1% levels, respectively. +87 + +Table B8: Robustness of the baseline regressions to accounting for measurement error: +College outcomes +Dependent variable +Enrolled +College +Degree +1st-year +Grad. +Time to +college +quality +quality +credits +on time +grad. +(1) +(2) +(3) +(4) +(5) +(6) +Panel A. Weighting each observation by its precision +Endurance +0.031∗∗∗ +0.030∗∗∗ +0.051∗∗∗ +0.006∗∗∗ +0.026∗∗∗ +−0.048∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +Ability +0.100∗∗∗ +0.094∗∗∗ +0.139∗∗∗ +0.016∗∗∗ +0.073∗∗∗ +−0.140∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +(0.002) +Panel B. Shrunk estimator of ability and endurance +Endurance +0.045∗∗∗ +0.043∗∗∗ +0.073∗∗∗ +0.012∗∗∗ +0.037∗∗∗ +−0.067∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.001) +(0.002) +Ability +0.105∗∗∗ +0.099∗∗∗ +0.145∗∗∗ +0.023∗∗∗ +0.074∗∗∗ +−0.143∗∗∗ +(0.000) +(0.000) +(0.001) +(0.000) +(0.001) +(0.002) +Mean DV +0.244 +3.326 +3.244 +0.158 +0.418 +3.817 +N +2,501,519 +1,800,546 +1,768,707 +1,124,972 +1,472,916 +793,822 +Notes: This table displays estimates of the relationship between ability/endurance and college outcomes +accounting for measurement error in the estimates of ability and endurance. +Each column shows the result for a different dependent variable. In Panel A, I weight each observation +by the inverse of the standard error of the ability and endurance estimates. Specifically, the weight of +each observation is w = 1/(SE2 +ˆαi + SE2 +ˆβi), where SEˆαi and SE2 +ˆβi are the standard errors of ˆαi and ˆβi. In +Panel B, I estimate the baseline regression using a shrunk estimator of ability and endurance. I compute +the shrunk estimator of endurance as βs +i = ωi ˆβi + (1 − ωj)¯β, where ¯β is the average cognitive endurance +in my sample. The individual-specific weight is ωi = +Var[βi]−E[SE2 +ˆ +βi] +Var[βi]−E[SE2 +ˆ +βi]+SE2 +ˆ +βi +. The shrunk estimator, βs +i , puts +more weight on estimates of βi that are more precisely estimated, as measured by a low standard error. I +compute the shrunk estimator of ability analogously. +Heteroskedasticity-robust standard errors clustered at the individual level in parentheses.∗∗∗, ∗∗ and ∗ +denote significance at 10%, 5% and 1% levels, respectively. +88 + +Table B9: Robustness of the baseline regressions to accounting for measurement error: +Labor-market outcomes +Dependent variable +Formal +Hourly +Monthly +Firm +Occup. +Industry +sector +wage +earnings +wage +wage +wage +(1) +(2) +(3) +(4) +(5) +(6) +Panel A. Weighting each observation by its precision +Endurance +0.000∗∗∗ +0.053∗∗∗ +0.051∗∗∗ +0.035∗∗∗ +0.017∗∗∗ +0.004∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.000) +(0.000) +Ability +0.001∗∗∗ +0.151∗∗∗ +0.133∗∗∗ +0.107∗∗∗ +0.048∗∗∗ +0.014∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Panel B. Shrunk estimator of ability and endurance +Endurance +0.001∗∗∗ +0.076∗∗∗ +0.074∗∗∗ +0.050∗∗∗ +0.024∗∗∗ +0.005∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Ability +0.002∗∗∗ +0.157∗∗∗ +0.138∗∗∗ +0.111∗∗∗ +0.050∗∗∗ +0.015∗∗∗ +(0.000) +(0.001) +(0.001) +(0.001) +(0.001) +(0.000) +Mean DV +0.326 +3.865 +7.551 +3.885 +3.886 +3.858 +N +2,523,029 +818,590 +818,590 +692,880 +818,374 +818,590 +Notes: This table displays estimates of the relationship between ability/endurance and labor-market out- +comes accounting for measurement error in the estimates of ability and endurance. +Each column shows the result for a different dependent variable. In Panel A, I weight each observation +by the inverse of the standard error of the ability and endurance estimates. Specifically, the weight of +each observation is w = 1/(SE2 +ˆαi + SE2 +ˆβi), where SEˆαi and SE2 +ˆβi are the standard errors of ˆαi and ˆβi. In +Panel B, I estimate the baseline regression using a shrunk estimator of ability and endurance. I compute +the shrunk estimator of endurance as βs +i = ωi ˆβi + (1 − ωj)¯β, where ¯β is the average cognitive endurance +in my sample. The individual-specific weight is ωi = +Var[βi]−E[SE2 +ˆ +βi] +Var[βi]−E[SE2 +ˆ +βi]+SE2 +ˆ +βi +. The shrunk estimator, βs +i , puts +more weight on estimates of βi that are more precisely estimated, as measured by a low standard error. I +compute the shrunk estimator of ability analogously. +Heteroskedasticity-robust standard errors clustered at the individual level in parentheses.∗∗∗, ∗∗ and ∗ +denote significance at 10%, 5% and 1% levels, respectively. +89 + +C +The ENEM +In this Appendix, I describe the changing role of the ENEM in the higher-education system +over time, compare the ENEM to the US SAT and ACT exams, and describe the IRT +grading system used by the Ministry of Education to generate ENEM test scores. +C.1 +The Role of the ENEM in the Higher-education System +The ENEM was created in 1998 by the National Institute of Educational Studies (INEP), a +unit of the Brazilian Ministry of Education, with the goal of evaluating student performance +at the end of high school (Appendix Figure C1). The ENEM is an achievement test, that +is, it was designed to test for mastery of material individuals should learn by the end of +high school.34 +The first ENEM contained 63 multiple-choice interdisciplinary questions and was con- +ducted over a five-hour testing block. The test score was calculated as the fraction of +correct responses. In its first edition, fewer than 200,000 individuals enrolled to take the +ENEM. +Figure C1: Timeline of the ENEM +1998 +First edition: HS +accountability test +(non-mandatory) +2004 +PROUNI program: +scholarships to +low-income students +2009 +Expansion: Federal +college admission exam +& HS certification +2017 +New +schedule +2020 +Online +option +Unique test (1 day, 5 hours) +63 interdisciplinary questions +180 q’s divided into 4 subjects: +Day 1: Soc. sci., Nat. sci. (4.5h) +Day 2: Essay, Lang., Math (5.5h) +2 consecutive Sundays: +Day 1: Lang., Essay, S. sci. (5.5h) +Day 2: Nat. sci., Math (5h) +In 2004, the government created a college scholarship program for low-income students +called ProUni (Programa Universidade para Todos). ProUni used ENEM scores to allocate +the scholarships to applicants, with program-specific score cutoffs based on the number of +seats available in each program. After ProUni was implemented, the number of individuals +who signed up to take the ENEM doubled from 1.5 million in 2004 to 3.0 million in 2005. +In 2009, the Ministry of Education reformed the ENEM with the aim of encouraging +colleges to use it as an admission exam. The new ENEM consists of 180 multiple-choice +34Researchers often divide standardized tests into two types: reasoning tests and achievement tests. +Reasoning tests measure a student’s verbal reasoning, critical reading, and skills. +Achievement tests +measure a student’s mastery of specific subjects, like biology or physics. In practice, performance on both +types of tests is highly correlated (Soares, 2015). +90 + +questions conducted over two consecutive days of testing during a weekend. +The new +exam contains questions in four subjects: mathematics, natural sciences (which includes +biology, physics, and chemistry questions), social sciences (which includes history, geog- +raphy, philosophy, and sociology questions), and language arts (which includes questions +on Portuguese language, literature, foreign language, arts, physical education, and infor- +mation and communication technologies). On the first day of testing, individuals had five +and a half hours to take the social science test, the natural science test, and the essay. +On the second day of testing, individuals had five hours to take math and language arts +tests. The new ENEM is graded according to Item Response Theory (IRT), which enables +colleges to compare test scores over time (see Appendix C.4). +In 2010, the Ministry of Education introduced a centralized admission system called +SISU (Sistema de Seleção Unificada) with the goal of simplifying the college application +process for federal universities. +The centralized system used ENEM scores to allocate +students to participating colleges. All federal universities are part of the system, but other +universities (including state and municipal universities) are not mandated to be part of it. +Also in 2010, the Government started using ENEM scores to allocate student loans through +a program called FIES (Fundo de Financiamento ao Estudante do Ensino Superior). In +addition, starting in 2010 (and finishing in 2016), ENEM scores could be used to certify +the attainment of high-school-level skills (analogously to the GED in the US). By 2010, +over 4.6 million individuals enrolled to take the ENEM. +In 2017, INEP changed the schedule of the ENEM. The exam started being conducted +over two consecutive Sundays. On the first Sunday, individuals have five and a half hours +to answer the language arts test, the social science test, and the essay. On the second +Sunday, individuals have five hours to answer the natural science and math tests. The +other features of the exam remained constant. +In 2020, individuals had the option to take the ENEM through a computer without +internet access. Over 5.7 million individuals enrolled to take the ENEM this year. +C.2 +ENEM Sample Questions +Appendix Figures C2–C5 present sample questions from the natural science, social science, +language arts, and math components of the ENEM. The questions come from the 2016 +ENEM. The questions are average in terms of their difficulty. +91 + +Figure C2: Natural Science sample question (item #11898) +Panel A. Original (in portuguese) +Portadores de diabetes insipidus reclamam da confusão feita pelos profissionais da saúde +quanto aos dois tipos de diabetes: mellitus e insipidus. Enquanto o primeiro tipo está +associado aos níveis ou à ação da insulina, o segundo não está ligado à deficiência desse +hormônio. +O diabetes insipidus é caracterizado por um distúrbio na produção ou no +funcionamento do hormônio antidiurético (na sigla em inglés, ADH), secretado pela +neuro-hipófise para controlar a reabsorção de água pelos túbulos renais. +Tendo em vista o papel funcional do ADH, qual é um sintoma clássico de um paciente +acometido por diabetes insipidus? +A +Alta taxa de glicose no sangue. +B +Aumento da pressão arterial. +C +Ganho de massa corporal. +D +Anemia crônica. +E +Desidratação. +Panel B. Translation +Patients with diabetes insipidus complain about the confusion made by health profes- +sionals about the two types of diabetes: mellitus and insipidus. While the first type is +associated with insulin levels or action, the second is not linked to insulin deficiency. +Diabetes insipidus is characterized by a disturbance in the production or functioning of the +antidiuretic hormone (ADH), secreted by the neurohypophysis to control the reabsorption +of water by the renal tubules. +In view of the functional role of ADH, what is a classic symptom of a patient with diabetes +insipidus? +A +High blood glucose. +B +Increase in blood pressure. +C +Body mass gain. +D +Chronic anemia. +E +Dehydration. +Notes: The correct answer is underlined. +92 + +Figure C3: Social Science sample question (item #97290) +Panel A. Original (in portuguese) +Parceria Transpacífica +Dentro das atuais redes produtivas, o referido bloco apresenta composição estratégica por +se tratar de um conjunto de países com +A +Elevado padrão social. +B +Sistema monetário integrado. +C +Alto desenvolvimento tecnológico. +D +Identidades culturais semelhantes. +E +Vantagens locacionais complementares. +Panel B. Translation +Trans-Pacific Partnership +Within the current production networks, the aforementioned bloc has a strategic +composition because it is a group of countries with: +A +High social standard. +B +Integrated monetary system. +C +High technological development. +D +Similar cultural identities. +E +Complementary locational advantages. +Notes: The correct answer is underlined. +93 + +Canada +Estados Unidos +Japao +México +Vietna +Cingapura +BruneiDarussalam +Malasia +Peru +Australia +Chile +Nova ZelandiaFigure C4: Language Arts sample question (item #86509) +Panel A. Original (in portuguese) +O último longa de Carlão acompanha a operária Silmara, que vive com o pai, um ex- +presidiário, numa casa da periferia paulistana. Ciente de sua beleza, o que lhe dá certa +soberba, a jovem acredita que terá um destino diferente do de suas colegas. +Cruza o +caminho de dois cantores por quem é apaixonada. E constata, na prática, que o romantismo +dos contos de fada tem perna curta. +VOMERO, M. F. Romantismo de araque. Vida Simples, n. 121, ago. 2012. +Reconhece-se, nesse trecho, uma posição crítica aos ideais de amor e felicidade +encontrados nos contos de fada. Essa crítica é traduzida +A +Pela descrição da dura realidade da vida das operárias. +B +Pelas decepções semelhantes às encontradas nos contos de fada. +C +Pela ilusão de que a beleza garantiria melhor sorte na vida e no amor. +D +Pelas fantasias existentes apenas na imaginação de pessoas apaixonadas. +E +Pelos sentimentos intensos dos apaixonados enquanto vivem o romantismo. +Panel B. Translation +Carlão’s latest feature follows the worker Silmara, who lives with her father, an ex-convict, +in a house on the outskirts of São Paulo. Aware of her beauty, which gives her a certain +arrogance, the young woman believes that she will have a different destiny from her col- +leagues. She crosses paths with two singers she is in love with. And she finds, in practice, +that the romanticism of fairy tales has short legs. +VOMERO, M. F. Romanticism of arak. Simple Life, n. 121, Aug. 2012. +This passage recognizes a critical position on the ideals of love and happiness found in +fairy tales. This criticism is translated +A +For the description of the harsh reality of the workers’ lives. +B +For disappointments similar to those found in fairy tales. +C +For the illusion that beauty would guarantee better luck in life and in love. +D +For the fantasies that exist only in the imagination of people in love. +E +For the intense feelings of those in love while living romanticism. +Notes: The correct answer is underlined. +94 + +Figure C5: Math sample question (item #37515) +Panel A. Original (in portuguese) +Para evitar uma epidemia, a Secretaria de Saúde de uma cidade dedetizou todos os +bairros, de modo a evitar a proliferação do mosquito da dengue. Sabe-se que o número f +de infectados é dado pela função f(t) = −2t2 + 120t (em que t é expresso em dia e t = 0 é +o dia anterior à primeira infecção) e que tal expressão é válida para os 60 primeiros dias +da epidemia. +A Secretaria de Saúde decidiu que uma segunda dedetização deveria ser feita no dia em +que o número de infectados chegasse à marca de 1600 pessoas, e uma segunda dedetização +precisou acontecer. +A segunda dedetização começou no +A +19° dia. +B +20° dia. +C +29° dia. +D +30° dia. +E +60° dia. +Panel B. Translation +To prevent an epidemic, the Health Department of a city sprayed all neighborhoods, in +order to prevent the proliferation of the dengue mosquito. It is known that the number f +of infected people is given by the function f(t) = −2t2 + 120t (where t is expressed in day +and t = 0 is the day before the first infection) and that this expression is valid for the first +60 days of the epidemic. +The Health Department decided that a second extermination should be carried out on the +day when the number of infected people reached the mark of 1,600 people, and a second +extermination had to take place. +The second extermination started in +A +19th day. +B +20th day. +C +29th day. +D +30th day. +E +60th day. +Notes: The correct answer is underlined. +95 + +C.3 +Comparison of the ENEM to the ACT and SAT exams +Appendix Table C1 compares important features of the SAT, ACT, and ENEM. The SAT +contains 154 multiple-choice questions divided into three sections: reading, writing and +language, and math, plus an optional essay. Including the essay, individuals have 3 hours +and 50 minutes to take the test. On average across sections, test-takers have about 1 +minute and 10 seconds to answer each question. Raw scores are converted into scaled +scores through a score conversion table. +The ACT contains 215 multiple-choice questions divided into four sections: English, +math, reading, and science, plus an optional essay. Including the essay, individuals have +3 hours and 35 minutes to take the test. +On average across sections, test-takers have +less than 1 minute to answer each question. Raw scores are converted into scaled scores +through a score conversion table. +There are some notable differences between the SAT/ACT and the ENEM. First, the +ENEM is conducted over two days of testing. Second, individuals in the ENEM have no +assigned breaks. Third, the booklet ENEM test-takers receive contains all the questions +they have to answer during the testing day. Thus, they may allocate time disproportionally +across sections. In contrast, in the SAT and ACT, each section has an assigned amount of +time. Finally, in the ENEM, each question is associated with a different text passage or +prompt (in some cases, two questions share a prompt or passage). In contrast, in the SAT +and ACT, a given passage is associated with multiple questions. This partly explains why +the time per question is higher in the ENEM than in the ACT/SAT. +96 + +Table C1: Comparison of the SAT, ACT, and ENEM college admission exams +SAT +ACT +ENEM +Cost +∼$60 +∼$88 +∼$17 +Grading +Score conversion chart using raw scores +Score conversion chart using raw scores +Item Response Theory (IRT) +Starting time +Between 8:30 and 9am +Between 8:30 and 9am +1pm Brasilia time +Number of items +154 questions +215 questions +180 questions +Total length +3 hours and 50 mins over 1 testing day +3 hours and 35 mins over 1 testing day +10 hours over 2 testing days +Time per question +1 minute and 10 seconds +50 seconds +3 minutes +Breaks +10 mins break after reading section +10 min break after math section +N/A +5 min break between math sections +5 min break before essay +2 min break before the essay +Sections +Reading (65 mins, 52 items) +English (45 mins, 75 items) +Social science (day 1, 45 items) +Writing and Language (35 mins, 44 items) +Math (60 mins, 60 items) +Natural science (day 1, 45 items) +Math w/o calculator (25 mins, 20 items) +Reading (35 mins, 40 items) +Language arts (day 2, 45 items) +Math w/ calculator (55 mins, 38 items) +Science (35 mins, 40 items) +Math (day 2, 45 items) +Optional essay (50 mins) +Optional essay (40 mins) +Mandatory essay (day 2) +Notes: The SAT refers to the post-2016 version of the SAT, which includes an optional essay. This optional essay was eliminated in 2021. The +ENEM refers to the 2009–2016 version of the exam (see Section C.1 for information on the pre-2009 and post-2016 versions). The exam length +was computed excluding breaks and including the essay. The time per question does not account for the essay. +97 + +C.4 +IRT Grading +The Brazilian Testing Agency grades the ENEM exam based on the three-parameter item +response theory (IRT). According to IRT, the probability that an individual i with ability +θi correctly answers question j is: +Pr(Cij = 1|θi) = pj(θi) = cj + +1 − cj +1 + e−aj(θi−bi), +(C1) +where aj, bj, and cj are three question-level parameters that represent, respectively, a +question’s “discrimination,” “difficulty,” and “pseudo-guess.” A question’s discrimination +refers to its ability to discriminate between low- and high-ability individuals; the difficulty +represents the value of θ at which pj(θi) has the maximum slope, and the pseudo-guess +parameter indicates the likelihood that a student with an infinitely negative ability has to +correctly respond to the question. Notice that in equation (C1), the probability of correctly +answering a question does not depend on its position. Thus, the type of position effects +documented above suggests that the IRT estimates of individual-level ability are biased. +Modern IRT approaches (e.g., Debeer and Janssen, 2013) include item position into the +framework. +Each question’s parameters are known from pre-testing. The testing agency estimates +the θi that maximizes the empirical likelihood of the entire sequence of responses. They +do this separately for each student and academic subject. ENEM scores are normalized to +have a mean of 500 and a standard deviation of 100. +Despite its complexity, most of the variation in IRT-estimated ENEM scores is driven +by variation in the fraction of correct responses in the exam. A regression of IRT-estimated +ENEM scores on the fraction of correct responses yields an R-squared of 0.88 (the rank +correlation between the two variables is 0.93). Consistent with this, Appendix Figure C6 +shows that the relationship between these two variables is linear in both levels (Panel A) +and percentiles (Panel B). The strong relationship between IRT-estimated scores and the +fraction of correct responses holds not just for the overall score but also for the score in +each academic subject (Appendix Table C2). +98 + +Figure C6: Comparison of IRT-estimated ENEM score and fraction of correct responses +Panel A. In levels +300 +400 +500 +600 +700 +800 +Average IRT-estimated ENEM score +0.10 +0.20 +0.30 +0.40 +0.50 +0.60 +0.70 +0.80 +Fraction of correct responses +Panel B. In percentiles +0 +20 +40 +60 +80 +100 +Average percentile IRT-estimated score +0 +20 +40 +60 +80 +100 +Percentile fraction of correct responses +Notes: This figure shows binned scatterplots plotting the average IRT-estimated ENEM score across all +four academic subjects (y-axis) against the fraction of correct responses on the exam (x-axis). Panel A +shows the results in levels and Panel B in percentiles. I first group students into 100 equally-sized bins +based on their fraction of correct responses. Then, I calculate the average IRT-estimated ENEM score or +score percentile in each bin. The vertical lines denote the 10th and 90th percentiles of the ENEM score +distribution. The solid red line shows the predicted values from a linear regression on the plotted points. +Table C2: Correlation between IRT-estimated ENEM score and fraction of correct +responses on each subject +Academic subject +Social +Natural +Language +Math +Average +science +science +arts +score +(1) +(2) +(3) +(4) +(5) +Panel A. Variables measured in levels +Fraction correct resp. +0.892∗∗∗ +0.880∗∗∗ +0.907∗∗∗ +0.885∗∗∗ +0.937∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +N +14,936,699 +14,936,699 +14,936,699 +14,936,699 +14,936,699 +R−squared +0.79 +0.77 +0.82 +0.78 +0.88 +Panel B. Variables measured in percentiles +Fraction correct resp. +0.904∗∗∗ +0.858∗∗∗ +0.917∗∗∗ +0.845∗∗∗ +0.931∗∗∗ +(0.000) +(0.000) +(0.000) +(0.000) +(0.000) +N +14,936,699 +14,936,699 +14,936,699 +14,936,699 +14,936,699 +R−squared +0.82 +0.74 +0.84 +0.71 +0.87 +Notes: This table displays the correlation between the IRT-estimated ENEM score and the fraction of +correct responses. Columns 1–4 present the correlations separately for each academic subject. Column 5 +presents the correlation between the average score across all subjects and the fraction of correct responses +in the entire exam. Heteroskedasticity-robust standard errors clustered at the question level in parentheses. +∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively. +99 + +D +Measuring Question Difficulty +In this Appendix, I describe my measures of question difficulty. Instead of taking a strong +stance on what the right measure of difficulty is, I show that the results are robust to +measuring question difficulty in several ways. +An intuitive measure of a question’s difficulty is the fraction of students who correctly +answer the question. This measure is problematic in the presence of fatigue effects since +a given question has a different fraction of correct responses depending on its location. +To illustrate this problem, Appendix Figure D1 plots students’ performance on a natural +science question in each booklet. The position of this item ranged from position 46 in the +gray booklet to position 87 in the blue booklet. Correspondingly, student performance +varied from 40.7% in the gray booklet to 29.9% in the blue booklet. +Figure D1: Performance on a natural science question (item #11898) +0.407 +0.359 +0.339 +0.299 +0.00 +0.10 +0.20 +0.30 +0.40 +0.50 +Fraction of correct responses +Gray Booklet +Position = 46 +Yellow Booklet +Position = 63 +Pink Booklet +Position = 66 +Blue Booklet +Position = 87 +Notes: This figure shows the fraction of individuals who correctly responded to item #11898 in each of +the four booklets. See Appendix Figure C2 for the question’s text. +The fact that performance on a question varies according to its position raises an +important challenge for measuring question difficulty. It is hard to know whether questions +that appear later in the exam are less likely to be correctly answered because they test +more difficult material or because students are more fatigued by the time they get to these +questions. +To account for fatigue effects, I estimate measures of question difficulty that represent +100 + +the fraction of students who would correctly answer a question if the question appeared in +the first position of the exam. To estimate this fraction, I follow a three-step process. First, +I compute the average position of each question across all booklets. Second, I estimate +the effect of a one-position increase of a question position on performance on the question +(“position effect”). Third, I multiply the average question position calculated in the first +step by the position effect estimated in the second step and subtract this figure from the +fraction of correct responses across all booklets. This yields a position-adjusted estimate of +question difficulty. Appendix Table D1 illustrates these steps in calculating the difficulty +of item #11898. +The measures of question difficulty differ in how I estimate the position effect in the +second step. My baseline measure of question difficulty uses the position effect estimated +by pooling all questions (Table 2, column 3). This measure assumes that the effect of a +one-position increase on performance is homogeneous across questions. +The second measure of question difficulty uses a question-specific position effect. +I +estimate equation (4) separately for each question and use the intercept from the regression +as the measure of difficulty. This does not assume homogeneity in position effects; however, +for some questions the position effect is imprecisely estimated. +The third measure of question difficulty combines the first two by shrinking the question- +specific position effect to the average effect by its signal-to-noise ratio. Specifically, let βj +be the position effect estimating using data only from question j and ¯β be the average +position effect across all questions. The shrunk position effect of question j, βs +j, is a convex +combination of βj and ¯β: +βs +j = ωjβj + (1 − ωj)¯β, +where the question-specific weight, ωj, is +ωj = +Var[ˆβj] − E[SE2 +ˆβj] +Var[ˆβj] − E[SE2 +ˆβj] + SE2 +ˆβj +. +The shrunk estimator puts more weight on position effects that are more precisely +estimated, as measured by a low standard error of ˆβj, SE2 +ˆβj. +The fourth measure estimates the position effect separately for questions with a be- +low/above median fraction of correct responses. The fifth measure estimates the effect +separately for each academic subject. These measures assume that the effect of a one- +101 + +position increase on performance is homogeneous within a type of question. +Table D1: Alternative measures of the difficulty of item #11898 +Position effect +Average fraction +Fatigue effect (in pp) +Question +estimation method +correct responses +× average position +difficulty +(1) +(2) +(3) +(4) +None +0.36 +0 × 64 = 0 +0.36 +Pooling all items +0.36 +-0.08 × 64 = -5.1 +0.41 +Item-specific effect +0.36 +-0.24 × 64 = -15.3 +0.51 +Shrinkage estimator +0.36 +-0.24 × 64 = -15.3 +0.51 +By fraction corr. resp. +0.36 +-0.15 × 64 = -9.6 +0.45 +By academic subject +0.36 +-0.03 × 64 = -1.6 +0.37 +Notes: This table illustrates how the six measures of a question’s difficulty are calculated. The average +fraction of correct responses and the average question position are calculated using the number of students +with each booklet as weights. +Appendix Figure D2 shows the cross-question correlation between the measures of ques- +tion difficulty. Reassuringly, all difficulty measures are highly correlated, with coefficients +ranging from 0.77 to 0.99. +Figure D2: Cross-question correlation matrix of item difficulty measures +No position +adjustment +0.774 +Item-specific +adjustment +0.992 +0.778 +Adjustment using +mean effect +0.848 0.976 0.851 +Adjustment using +shrunk effect +0.985 +0.780 0.990 0.853 +Adjustment by +below/above +median fraction +of correct resp. +0.991 +0.780 0.993 0.852 0.984 +Adjustment by +academic subject +Notes: This figure shows the relationship between the different measures of question difficulty. Each cell +shows the cross-question linear correlation between two measures of question difficulty. The sample size is +N = 1, 842 across all cells. +102 + +E +Exam Content and Cognitive Endurance +In this Appendix, I assess whether the type of questions of an exam can influence the effect +of limited endurance on performance. For this, I estimate heterogeneity in the effect of +limited endurance on student performance based on two question characteristics: difficulty +and length. +First, I explore heterogeneity based on question difficulty. Previous research has identi- +fied task difficulty as a moderator of cognitive fatigue (Ackerman, 2011). We might expect +cognitive endurance to matter only for questions in a certain difficulty range. Students +should be able to answer very easy questions regardless of how tired they are. Similarly, +some questions might be too difficult for students to answer regardless of how rested they +are. The ENEM contains very difficult questions. On average, students only answer 34.3% +of questions correctly (random chance would imply 20%). Individuals who answer 50% of +questions correctly are in the top 10% of the score distribution. Thus, we might expect +limited endurance to affect performance in the relatively-easier questions. +In Appendix Table E1, I estimate equation (5) separately for below/above median- +difficulty questions.35 Appendix Figure E1, Panel A, plots corresponding binned scatter- +plots. The effect of limited endurance is driven by relatively easier questions (columns 3–4). +The estimated coefficient is thirteen times larger for below-median-difficulty questions than +for above-median-difficulty questions (-13.2 vs. -1.0 percentage points, respectively). More +broadly, there is a negative—although non-monotonic—relationship between a question’s +difficulty and the magnitude of the limited endurance effect (Appendix Figure E1, Panel +B). The performance of students only declines when responding to questions below a cer- +tain difficulty, possibly because they do not have the preparation required to respond to +the hardest questions regardless of their location. +Second, I explore heterogeneity based on question length. Previous research has shown +that time-on-task is one of the main predictors of cognitive fatigue (Ackerman, 2011). We +might expect fatigue effects to be larger for lengthy questions if students are more likely +to have an attentional lapse in long questions. To measure question length, I compute the +number of words in each question using text-scraped data. Appendix Table E1 estimates +equation (5) separately for relatively long questions (above-median number of words) and +short questions (below-median number of words).36 I find that limited endurance effects +are about twice as large for longer questions (-10.2 vs. -5.3 percentage points, respectively). +35Above [below] median difficulty questions are responded correctly 22% [48%] of the time. +36Above [below] median length questions have 209 [100] words. +103 + +Overall, there seems to be a negative relationship between a question’s length and the size +of the limited endurance effect (Appendix Figure E1, Panels C–D). +Figure E1: The effect of cognitive endurance on performance by question characteristics +Panel A. Change in performance vs. change +in question position by question difficulty +-8 +-6 +-4 +-2 +0 +2 +Average pp change in prob. of correct answer +0 +5 +10 +15 +20 +25 +30 +35 +≥40 +Change in question position +Below median difficulty (mean correct: 49.1%) +Above median difficulty (mean correct: 22.4%) +Panel B. Binned scatterplot: +Endurance effect vs. question difficulty +-0.30 +-0.20 +-0.10 +0.00 +0.10 +Average position effect (in pp) +0.20 +0.40 +0.60 +0.80 +1.00 +Question difficulty (fraction of incorrect responses) +Panel C. Change in performance vs. change +in question position by question length +-8 +-6 +-4 +-2 +0 +Average pp change in prob. of correct answer +0 +5 +10 +15 +20 +25 +30 +35 +≥40 +Change in question position +Below median length (mean # words: 100.7) +Above median length (mean # words: 209.9) +Panel D. Binned scatterplot: +Endurance effect vs. question length +-0.40 +-0.30 +-0.20 +-0.10 +0.00 +0.10 +Average position effect (in pp) +50 +100 +150 +200 +250 +300 +Question length (average number of words) +Notes: This figure shows heterogeneity in the effect of limited endurance on student performance by +question difficulty and length. Panels A and C are analogous to Figure 3, but the fatigue effect is estimated +separately for below/above median difficulty questions (Panel A) and below/above median length questions +(Panel C). The y-axis shows the average change (in percentage points) in the fraction of students who +correctly respond to a question. The x-axis plots the change in the question position between each possible +booklet pair. The dashed line denotes predicted values from a linear regression estimated on the plotted +points, using the number of questions used to estimate each point as weights. Panels B and D show a +series of binned scatterplots plotting the average endurance effect among questions in a given difficulty +bin (Panel B) or length bin (Panel B). To construct this figure, I divide questions into ten equally-sized +bins based on their difficulty or length. Then, I calculate the effect of limited endurance on performance +on questions in each bin. +104 + +Table E1: The heterogeneous effect of limited cognitive endurance on performance by question characteristics +Outcome: Fraction of correct responses +Question position +Question difficulty +Question length +1st half +2nd half +Below +Above +Below +Above +each day +each day +median +median +median +median +(1) +(2) +(3) +(4) +(5) +(6) +Position (normalized) +−0.097∗∗∗ +−0.051∗∗∗ +−0.132∗∗∗ +−0.010∗∗∗ +−0.053∗∗∗ +−0.102∗∗∗ +(0.006) +(0.006) +(0.006) +(0.003) +(0.005) +(0.007) +Question fixed effects +Yes +Yes +Yes +Yes +Yes +Yes +N (Item−Booklets) +3,016 +2,880 +2,935 +2,911 +2,940 +2,956 +Notes: This table shows the heterogeneous effect of limited cognitive endurance on daily student performance based on question characteristics. +Each column displays the estimate of β in equation (5) estimated on the sample listed in the column header. I normalize question position +such that the first question in each testing day is equal to zero and the last question is equal to one. +Heteroskedasticity-robust standard errors clustered at the question level in parentheses. ∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and +1% levels, respectively. +105 + diff --git a/udE0T4oBgHgl3EQfsQEM/content/tmp_files/load_file.txt b/udE0T4oBgHgl3EQfsQEM/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..5df41c7acd2d89b8bc2dd42c506f9402e4427ce9 --- /dev/null +++ b/udE0T4oBgHgl3EQfsQEM/content/tmp_files/load_file.txt @@ -0,0 +1,5317 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf,len=5316 +page_content='Cognitive Endurance, Talent Selection, and the Labor Market Returns to Human Capital Germán Reyes∗ January 2023 Abstract Cognitive endurance—the ability to sustain performance on a cognitively-demanding task over time—is thought to be a crucial productivity determinant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' However, a lack of data on this variable has limited researchers’ ability to understand its role for suc- cess in college and the labor market.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This paper uses college-admission-exam records from 15 million Brazilian high school students to measure cognitive endurance based on changes in performance throughout the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' By exploiting exogenous variation in the order of exam questions, I show that students are 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 percentage points more likely to correctly answer a given question when it appears at the beginning of the day versus the end (relative to a sample mean of 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I develop a method to decompose test scores into fatigue-adjusted ability and cognitive endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I then merge these measures into a higher-education census and the earnings records of the universe of Brazilian formal-sector workers to quantify the association between en- durance and long-run outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I find that cognitive endurance has a statistically and economically significant wage return.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Controlling for fatigue-adjusted ability and other student characteristics, a one-standard-deviation higher endurance predicts a 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4% wage increase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This wage return to endurance is sizable, equivalent to a third of the wage return to ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I also document positive associations between endurance and college attendance, college quality, college graduation, firm quality, and other outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Finally, I show how systematic differences in endurance across students interact with the exam design to determine the sorting of students to colleges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I dis- cuss the implications of these findings for the use of cognitive assessments for talent selection and investments in interventions that build cognitive endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' ∗Department of Economics, Cornell University, 457 Uris Hall, Ithaca, NY 14853, United States (e- mail: gjr66@cornell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='edu).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I thank especially my advisor Ted O’Donoghue for invaluable guidance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For helpful discussions and comments,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I thank Ned Augenblick,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Michèle Belot,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Nicolas Bottan,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Emily Breza,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Aviv Caspi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Zoë Cullen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Neel Datta,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Stefano DellaVigna,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Josh Dean,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Christa Deneault,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Rebecca Dera- nian,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Gary Fields,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thomas Graeber,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Ori Heffetz,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Alex Imas,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Guy Ishai,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Judd Kessler,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Yizhou (Kyle) Kuang,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Shengwu Li,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Yucheng Liang,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' George Loewenstein,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Michael Lovenheim,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Suraj Malladi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Alejan- dro Martínez-Marquina,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Francesca Molinari,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Kevin Ng,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Muriel Niederle,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Ricardo Perez-Truglia,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Grace Phillips,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Alex Rees-Jones,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Evan Riehl,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Seth Sanders,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Paola Sapienza,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Frank Schilbach,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heather Schofield,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Peter Schwardmann,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Dmitry Taubinsky,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' participants in the Cornell behavioral economics group,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' partic- ipants in the UC Berkeley psychology and economics group,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' and numerous seminar participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I also thank Marco Pereira and other members of SEDAP for invaluable help using the secured data room.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Financial support from the National Science Foundation is gratefully acknowledged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='02575v1 [econ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='GN] 6 Jan 2023 1 Introduction The human capital framework posits that individuals’ skills and knowledge act as a form of capital that improves productivity and, thus, labor earnings (Becker, 1962).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The positive relationship between human capital and earnings is one of the most robust findings in the social sciences (Deming, 2022), and is supported by a large body of work (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', Mincer, 1958;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Griliches, 1977;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Card, 1999, 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' While early studies focused on aggregate measures of human capital—like years of schooling—more recent work has focused on estimating the economic returns to specific skills, such as social skills (Deming, 2017) or cognitive skills (Hermo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Identifying skills that foster productivity is essential for the design of effective education and labor-market policies (Almlund et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Kautz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In this paper, I study one dimension of human capital that may be particularly impor- tant for knowledge workers: cognitive endurance, that is, the ability to sustain performance on a cognitively-demanding task for an extended duration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I first document that the per- formance of individuals on a college admission exam tends to decline, which allows me to measure cognitive endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Specifically, I develop a method to decompose test scores into fatigue-adjusted ability and endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I use the decomposition to investigate the re- lationship between endurance and long-run outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I show that endurance has a sizable wage return in the labor market, comparable to the wage return to ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I also show that, due to systematic differences in endurance across students, seemingly neutral exam design choices, such as the exam length, can have equity and efficiency consequences by affecting the sorting of students across colleges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Psychologists and self-help books have long hypothesized that cognitive endurance is an important productivity determinant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Research on the nature of expertise—popularized in influential books like Focus (Goleman, 2013) or Deep Work (Newport, 2016)—often identifies this skill as a key driver of performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 Relatedly, biographers of extraordinary achievers often ascribe their accomplishments to unusually-high endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 Consistent with this, researchers have documented the negative consequences of limited endurance for task performance in many settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 The hypothesized link between endurance and 1Psychologists have identified cognitive fatigue effects and highlighted the importance of mental en- durance for high performance at least since the early 20th century (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', James, 1907;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Dodge, 1917).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 2For example, in describing Newton’s accomplishments, Keynes (1956) noted that his greatest skill was “the power of holding continuously in his mind a purely mental problem until he had seen straight through it.” See Lykken (2005) for many other examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 3Specifically, researchers have shown that individual-level job performance tends to deteriorate over relatively short time spans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For example, over the course of a day: nurses are less likely to wash their hands (Dai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Steiny Wellsjo, 2022);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' doctors make more diagnostic mistakes (Chan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 2 productivity is also consistent with the large markets for endurance enhancers like coffee or nootropics (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', Adderall).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 These observations suggest that cognitive endurance and task performance are inti- mately linked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Yet, despite this popular perception, empirical economists have had little to say about the role of endurance in the labor market, possibly because of a lack of data on this variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I address this problem by using data from the college admission exam in Brazil (called “ENEM”) to create an individual-level measure of endurance that is based on performance declines throughout the exam (Borghans and Schils, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Brown et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The ENEM is an ideal setting to study cognitive endurance for several reasons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' First, the exam is administered under uniform conditions, and the scoring is standardized—two crucial properties for generating measures that are comparable across individuals (Almlund et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Second, it is a high-stakes environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Test scores largely determine the college options of the millions of high school students who take the ENEM every year.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Since test-takers have incentives to exert maximal effort, limits to cognitive endurance are more likely to drive systematic declines in performance rather than low motivation (Duckworth et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Gneezy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Third, the exam is grueling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The ENEM is ten hours long and is conducted over two consecutive days of testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thus, we might expect cognitive endurance to be an especially valuable skill in this setting and cross-person differences in endurance to be reflected in test performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' My analysis takes advantage of three features of the ENEM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' First, the dataset con- tains students’ responses to each exam question, which enables me to measure student performance throughout the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Second, students are randomly assigned different test booklets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each booklet has the same set of questions (or “items”) but in a different or- der, which enables me to study how students perform on a given question when they are relatively “fresh” versus mentally fatigued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Third, the ENEM can be linked to other admin- istrative datasets to measure students’ long-run outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Specifically, I link the ENEM records to a census of all Brazilian college students and an employee-employer matched dataset that covers the universe of formal-sector workers in Brazil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Linder et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Kim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' financial analysts make less accurate forecasts (Hirshleifer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' and umpires make more incorrect calls in baseball games (Archsmith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 4For example, in the US, 65% of adults drink coffee daily (Lampkin, 2012), and about 20% of college students report using nootropics without a prescription to enhance focus and cognition (Benson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Relatedly, over-the-counter focus-enhancing drugs have entire sections in chain drug stores (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', Appendix Figure A1), and there is a growing variety of products marketed as endurance training (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', brain-training games like “Lumosity” or interval-based training technologies like “Pomodoros”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 3 I measure cognitive endurance as the impact of a one-position increase in the order of a given question on the likelihood of correctly answering the question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' A potential-outcomes framework reveals that this measure captures the combined impact of two structural pa- rameters: how cognitively fatigued an individual becomes throughout the exam and how an increase in fatigue affects test performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' These two parameters, and thus, my en- durance measure, likely capture a variety of psychological mechanisms, including intrinsic motivation, grit, and attention capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Applying this framework, I first estimate mean cognitive endurance across all students using two empirical strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The first research design compares average student perfor- mance on a given question as a function of its position on each booklet, which I implement by regressing the fraction of students who correctly answer a question on its position on the exam, controlling for question fixed effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This approach provides the more credi- ble estimates of mean cognitive endurance;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' however, since each student only receives one exam booklet, it cannot be used to estimate individual-level endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thus, I also use a second research design that can be used to identify both average and individual-level endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The second approach consists of creating a position-adjusted measure of ques- tion difficulty, and then using this measure as a control variable instead of the question fixed effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Both strategies deliver a similar-sized estimate of mean cognitive endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' A one-position increase in the order of a given question decreases the chances of correctly answering the question by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='08 percentage points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Scaled by the number of questions per testing day, this estimate implies that daily performance decreases by 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 percentage points due to limited endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Next, I estimate the difficulty-adjusted regression separately for each individual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This allows me to decompose an individual’s test score into a measure of cognitive endurance and a measure of fatigue-adjusted academic ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' My measure of cognitive endurance is the same as above but now estimated separately for each student.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' My measure of fatigue- adjusted ability is the residual of an individual’s test score after subtracting from it the component explained by cognitive endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Using a sample of students who took the exam multiple times, I show that this measure of cognitive endurance has a test-retest reliability comparable to that of other commonly used constructs like risk aversion (Mata et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2018) or teacher value-added (Chetty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2014a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The measures generated by the decomposition enable me to investigate the importance of cognitive endurance for success in college and the labor market.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I find that, holding fixed fatigue-adjusted ability and other student characteristics, individuals with more cognitive 4 endurance are more likely to attend college, enroll in higher-quality colleges, are more likely to graduate, earn higher wages, and work for higher-paying firms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The associations are sizable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For example, controlling for ability and other variables, a one standard deviation (SD) increase in cognitive endurance predicts a 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4% increase in early-career wages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The corresponding prediction for a one SD increase in ability equals 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Hence, the wage return to endurance is about a third of the size of the return to ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Instrumental variable regressions show that the association between endurance and wages is larger after accounting for measurement error (on the order of 70% the size of the return to ability) and also reveal that the predicted effect is not driven by a mechanical relationship between endurance and test scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heterogeneity analysis reveals substantial variation in the wage return to ability and to endurance across college majors, occupations, and industries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' On average, occupations and industries that pay higher wages also offer a higher wage return to ability and to endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This result documents a novel type of assortative matching between high- endurance workers and high-paying jobs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Furthermore, occupations and industries with a high wage return to endurance also tend to have a high wage return to ability, suggesting these two skills are complements in production.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Some occupations with the highest wage return to endurance include those where lapses in sustained attention can have high costs, like facility operators in chemical plants or professionals in the aviation industry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This finding suggests that the value of endurance depends on a job’s task requirements and the role of endurance in the production function of those tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Finally, I use the measure of endurance to examine how differences in this skill across individuals affect the sorting of students to colleges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I focus on identifying the distributional and informational effects of an exam reform that decreases the exam length by half, thereby reducing the importance of endurance in determining test scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The distributional effect asks how the exam reform would impact socioeconomic status (SES) test-score gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The informational effect asks how the reform would impact the exam’s “predictive validity” (a measure of the exam’s information content), as measured by the correlation between test scores and long-run outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I derive formulas showing that test-score gaps and predictive validity can be written as linear functions of ability and endurance, with the weight on endurance proportional to the exam length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The exam reform would decrease test-score gaps by 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8 percentage points (a 26%– 29% reduction from pre-reform gaps, depending on the measure of SES) and increase the predictive validity of the exam’s test scores for long-run outcomes by as much as 95%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In- 5 tuitively, the reform would reduce test-score gaps because, conditional on academic ability, low-SES students have lower endurance than high-SES students and, thus, perform dis- proportionally worse in questions toward the end of the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Similarly, the reform would increase the predictive validity of the exam partly because differences in performance at the beginning of the exam mainly reflect differences in ability (roughly, because most students are “fresh”), which are highly predictive of long-run outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In contrast, performance differences towards the end of the exam disproportionally reflect the noise associated with mental fatigue, which reduces the information content of test responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' My findings yield three broad lessons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' First, cognitive endurance matters for success in college and the labor market.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' My results provide empirical evidence on the long-standing hypothesis of endurance being a valuable skill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thus, investing in the development of this skill, possibly at school during early ages, may have significant societal returns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Second, dis- tinguishing between endurance and ability can improve how talent is selected and trained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Since the value of endurance varies among college majors, the student-major match may improve if majors where high endurance is required to succeed screen applicants partly based on this skill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Similarly, workers in endurance-intensive occupations may be more productive if the training necessary to enter into these occupations includes components aimed at building this skill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Third, seemingly neutral exam design decisions—the “choice architecture” of the exam—such as length or number of breaks, can have equity and ef- ficiency consequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' By influencing the importance of endurance for test performance, the exam design can affect test-score gaps and predictive validity and, thus, the diversity of colleges’ student bodies and the student-college match quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This paper relates to the literature that studies cognitive endurance and fatigue effects in field settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Limited cognitive endurance has been documented in a wide variety of en- vironments (see footnote 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Recent experimental evidence shows that cognitive endurance can be trained in children, which leads to less pronounced performance declines (Brown et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I contribute by linking individual-level endurance to long-run outcomes and establishing a novel set of associations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I do this in a high-stakes exam, which complements previous studies documenting performance declines in the low-stakes PISA test (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', De- beer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Borghans and Schils, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Zamarro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Balart and Oosterveen, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' My findings provide a micro perspective to the results of Balart et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (2018), who show that the average performance decline in the PISA test among a country’s test-takers has a sizable predictive power in cross-country growth regressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This paper also contributes to a growing literature documenting the importance of 6 different dimensions of human capital for long-run outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' A large body of work shows that cognitive skills are valuable in the labor market (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', Hanushek and Woessmann, 2008, 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Fe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Hermo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This work often uses test scores as a measure of cognitive skills.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I show that, even in a high-stakes setting, test scores partly measure cognitive endurance and provide methods to decompose test scores into fatigue- adjusted ability and endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Relatedly, a growing body of work shows that skills other than intelligence and technical skills (“noncognitive skills”) are also important predictors of long-run outcomes (Bowles et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heckman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Borghans et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Almlund et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Lindqvist and Vestman, 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Deming, 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Jackson, 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Buser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Edin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I document the strong predictive power of one noncognitive skill for college and labor-market outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Finally, this paper contributes to the literature on the design of college admission ex- ams (Rothstein, 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Ackerman and Kanfer, 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Bettinger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Hoxby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Bulman, 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Goodman, 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Goodman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Riehl, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' These exams are designed to rank a large number of applicants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This requires discerning small ability differences, and as a consequence, they tend to be long and arduous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I show that perfor- mance on college admission exams measures not only academic preparedness but also the capacity to endure mental fatigue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Hence, there is a limit to how much information an exam can extract about student academic achievement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' A lengthier exam may not lead to more precise measures of ability but rather to a selection mechanism that puts more weight on endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This may be desirable for programs where endurance is crucial to succeed, but it may come at the cost of screening out high-ability low-endurance students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The rest of the paper is structured as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Section 2 describes the context and data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Section 3 presents a statistical framework and describes my research designs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Section 4 presents estimates of average cognitive endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Section 5 decomposes test scores into fatigue-adjusted ability and cognitive endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Section 6 examines the association between cognitive endurance and long-run outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Section 7 studies the implication of limited endurance for the sorting of students to colleges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Section 8 concludes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 2 Institutional Context and Data 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 The ENEM exam The High School Assessment Exam (Exame Nacional do Ensino Médio, or ENEM for short) is an achievement test created in 1998 by the Brazilian Ministry of Education to 7 make high schools accountable for their students’ progress.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Some universities used the ENEM for college admissions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' however, most institutions had university-specific admission exams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In 2009, the Ministry of Education expanded the ENEM to encourage universities to use it as their admission exam, and created a centralized admission system that uses ENEM scores to assign students to the highly-selective federal universities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Since then, many universities have started using the ENEM for admissions (Machado and Szerman, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Otero et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The ENEM contains 180 multiple-choice questions equally divided across four subject tests (language arts, math, natural sciences, and social sciences) and an essay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The exam takes place over two consecutive days (two subjects per day, plus the essay on the second day).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Test-takers have four and a half hours to complete the test on the first day and five and a half hours on the second day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' There are no allocated breaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To combat cheating, examinees randomly receive one of four different booklets each day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The order of the subjects and the set of questions is the same across booklets, but the order of the questions within a subject is randomized across booklets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' A score for each subject is calculated based on item response theory (IRT), but most colleges ask applicants to submit their average score across all subjects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The exam is simultaneously taken across the country once a year at the end of the year.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' It costs approximately $20 to take the exam, although this fee is waived for low- income applicants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Between 2009 and 2016, over 50 million individuals signed up to take the ENEM, making it the second-largest college admission exam globally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Appendix C, I describe the main changes in the ENEM over time, explain how ENEM scores are used in the higher-education system (other than for college admissions), and compare the ENEM to the US SAT and ACT exams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 Data I combine three administrative databases from Brazil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The base dataset contains exam records from the ENEM from 2009–2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This dataset contains both student-level and question-level information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The student-level data includes self-reported demographic and socioeconomic status (SES) measures, such as sex, race, high-school type (public/private), parental education, and family income.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The question-level data includes each student’s responses to each exam question, the position of the question, skill tested, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To study individuals’ trajectories through college and the labor market, I link the ENEM records to two other administrative datasets using individuals’ national ID num- 8 bers (Cadastro de Pessoas Físicas).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5 To measure college outcomes, I use Brazil’s higher- education census from 2010–2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This dataset includes information on all college enrollees’ major, university, year of enrollment, number of credits, and year of graduation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To mea- sure labor-market outcomes, I use an administrative employee-employer matched dataset called RAIS (Relação Anual de Informações Sociais) from 2016–2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 The RAIS covers the universe of formal-sector workers in Brazil and includes information about both the worker and the firm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Workers’ data include educational attainment, occupation, and earn- ings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Firms’ data include the number of employees, industry, and geographical location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 Samples and Summary Statistics High-school-students sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To construct this sample, I impose several sample restrictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' First, I only consider individuals who take the ENEM during high school.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This restriction excludes individuals who take the exam after dropping out or graduating from high school.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Second, I only include individuals with a non-zero non-missing score on each subject test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This restriction excludes, for example, students who missed one of the days of testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I also exclude a small fraction of students with special accommodations, usually due to a disability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' After these restrictions, the high-school-students sample contains information on approximately 15 million students who took the ENEM from 2009–2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To examine students’ long-run outcomes, I focus on 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='9 million high-school seniors in the first two cohorts in my data (2009–2010), for whom I observe college and labor-market outcomes 6–9 years after taking the admission exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Retakers sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To assess the temporal stability of my measure of cognitive endurance, I identify students who take the ENEM more than once, usually as high-school juniors to practice and again in their senior year to apply for college.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Approximately 16% of test- takers in the high-school-students sample take the exam more than once.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='7 I only include students with a valid exam score in all the years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The retakers sample contains information on 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5 million students or 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 million student-years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Summary Statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Table 1 shows summary statistics on the samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The average 5The linkage was conducted in the secured data room at the facilities of the Ministry of Education in Brasilia, Brazil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 6The RAIS does not contain information on workers employed in the informal sector, self-employed individuals, or the unemployed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 7ENEM scores are only valid for one year.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thus, students cannot use their junior-year ENEM results to apply for college.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Some high-school students take the ENEM more than two times in the data, possibly because of grade repetition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I exclude a small fraction of students who take the ENEM more than three times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 9 student in the high-school-students sample is 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 years old, 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8% are female, 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6% are white, and 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2% went to a private high school (column 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Over half of students (53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4%) have a high-school-educated mother, and 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8% live in a household that earns an income above twice the minimum wage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8 On average, students correctly respond to only 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3% of exam questions, which shows that the ENEM is a hard exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' High-school seniors from the 2009–2010 cohorts are slighly older, slightly more likely to be females, and white (column 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Students in the retakers sample are slighly younger, their parents tend to have higher incomes, and they tend to perform better on the exam (column 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Student characteristics are balanced across booklet colors (Appendix Table A1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 Definition of Main Outcomes Test score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I define a student’s exam score as the fraction of correct responses across all four academic subjects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The advantage of this measure is that it is intuitive and consistent with the existing literature (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', Zamarro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' However, this measure differs from how the Brazilian testing agency calculates the ENEM score, which is based on IRT (see Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Reassuringly, the correlation between the fraction of correct responses and the IRT-based score is above 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='90 (Appendix Table C2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' College enrollment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I define college enrollment as an indicator for appearing in the higher-education census one year after taking the ENEM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The rest of the college outcomes are defined conditional on college enrollment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' College quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I construct an earnings-based index of college quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To do this, I group all college-educated workers in the RAIS (not just the workers in my sample) based on the university they attended and compute the average earnings of the graduates from each university.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='9 College degree quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I create an index of college degree (or major) quality using the average earnings of the graduates of each college degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To allow for international com- parisons, I classify majors based on the International Standard Classification of Education (UNESCO, 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 8Students self-report their household income and other SES measures when they enroll to take the ENEM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Household income is elicited in ranges and expressed as a multiple of the minimum wage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I divide students into those whose household earns more than five minimum wages and those whose household earns less than twice minimum wage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Using the Brazilian National Household Survey, I find that the former households are in the top 30% of the national income distribution, while the latter households are in the bottom 30%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 9This index is analogous to the college quality measure used by Chetty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (2011) and Chetty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (2014b) to study the long-term impacts of kindergarten quality and teachers, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 10 Degree progress.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I calculate the ratio between the number of credits completed at the end of each year and the total number of credits required to graduate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This variable is available starting in the 2015 higher-education census.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thus, I use data from the cohort enrolled in 2015 to measure this outcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Likelihood of graduating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I define an indicator for graduating one to six years after enrolling in college.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Most students who ever graduate do so within the first six years (Appendix Figure A2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' As robustness, I define a measure of on-time graduation based on expected degree length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The higher-education census contains information on how long a student in good standing should take to graduate from each program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I use this information to define an indicator for graduating within the expected number of years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Formal employment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I define formal employment as an indicator for appearing in the employee-employer matched dataset in any year in my sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This variable is defined for all test-takers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The rest of the labor-market outcomes are defined conditional on formal employment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' If an individual has multiple jobs, I use the data from the job with the highest number of hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I use the job monthly earnings as a tiebreaker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Monthly earnings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This variable represents the average salary of a worker across all months in a given year.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To report this variable, firms have to calculate the worker’s total earnings for the year and divide them by the number of months the firm employed the worker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' If a worker appears in multiple years in the RAIS, I calculate the inflation- adjusted average monthly earnings across all years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I adjust earnings for inflation using the consumer price index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Hourly wage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I calculate the hourly rate of each worker as the ratio between a worker’s inflation-adjusted monthly earnings and the hours worked per month.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 If a worker appears in multiple years in the RAIS, I calculate the average hourly wage across all years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Firm, industry, and occupation mean wage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I calculate the average hourly wage at each firm, industry, and occupation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I use leave-one-out measures so that an individual’s own employment outcomes do not affect the mean wage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I define firms using the 14- digit CNPJ,11 industries using the Brazilian National Classification of Economic Activities (CNAE), and occupations using the Brazilian Occupational Code Classification (CBO).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I calculate the wage indices separately for each year and use the average value across years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I measure labor-market outcomes for the 2009–2010 cohort using employment data 10Firms do not record the number of hours individuals actually work each week.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Instead, the data on hours indicates the number of hours per week that the worker is expected to work based on her contract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 11The CNPJ is a tax identifier for legally incorporated identities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The first eight digits identify the company.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The rest of the digits identify the branch or subsidiary of the company.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 11 from 2016–2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This means that, for the 2009 cohort, I measure outcomes 7–9 years after taking the ENEM, and for the 2010 cohort, 6–8 years after taking the ENEM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I account for this variation by controlling for an individual’s potential years of experience throughout the analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I measure potential experience as the individual’s age minus the years of schooling minus six.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 3 Empirical Framework This section lays out a simple potential-outcomes framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I use the framework to formally define cognitive endurance in terms of empirical estimands and to clarify the identification assumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 Statistical Model Let Cij be the probability of individual i correctly answering question j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I model Cij as a function of the student’s level of cognitive fatigue, fij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Fatigue can affect performance by impairing cognitive functions such as attention, memory, or reasoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The effects can be manifested in many ways, including students forgetting a crucial formula, making a computation mistake, misinterpreting or ignoring an important aspect of a question, and filling in the wrong bubble in the multiple-choice sheet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To build intuition, first consider an environment in which fatigue is binary: individuals can be either mentally “fresh” (fij = 0) or “fatigued” (fij = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Let Cij(0) be the likelihood of individual i correctly answering question j if she is fresh and Cij(1) the likelihood if she is fatigued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' These two probabilities denote potential outcomes for different fatigue levels, but only one of the two outcomes is observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The observed performance, Cij(fij), can be written in terms of these potential outcomes as Cij(fij) = Cij(0) + � Cij(1) − Cij(0) � � �� � “Fatigue effect” (κi) fij, (1) where Cij(1)−Cij(0) ≡ κi measures the effect of fatigue on performance, or “fatigue effect,” for short.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I allow the fatigue effect to be heterogeneous across individuals, although for simplicity I assume that it is constant across types of questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Suppose for the moment that we observed whether the individual was fresh or fatigued when she answered each exam question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Then, one could compare i’s average performance in questions she answered while 12 fatigued (E[Cij|fij = 1]) to her average performance in questions she answered while rested (E[Cij|fij = 0]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This comparison can be written as E[Cij|fij = 1] − E[Cij|fij = 0] = (E[Cij(1)|fij = 1] − E[Cij(0)|fij = 1]) � �� � Term 1: Fatigue effect + (E[Cij(0)|fij = 1] − E[Cij(0)|fij = 0]) � �� � Term 2: Selection bias , (2) Equation (2) shows that a comparison of average performance would yield the sum of two terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The first one is the fatigue effect for questions answered while fatigued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The second term is a selection bias that arises when comparing performance across different questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For example, if individuals become fatigued over time, a selection bias might arise if questions become increasingly hard over the course of the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In this case, i’s average performance may deteriorate even if she had not experience fatigued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In practice, cognitive fatigue is not binary;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' rather, an individual can have different gradations of “tiredness.” In what follows, I assume fij is continuous and interpret κi as the impact of a unit change of cognitive fatigue on performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Because cognitive fatigue cannot be directly observed, estimating κi is not feasible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In the empirical analysis, I use the position of question j on the version of the exam answered by i (Positionij), under the reasoning that students become increasingly fatigued over the course of the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='12 To understand how cognitive fatigue relates to question position, consider a hypothetical linear projection of fij on Positionij: fij = ωi + πiPositionij + ηij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (3) The intercept of the projection, ωi, measures i’s cognitive fatigue at the beginning of the test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The slope of the projection, πi, measures the change in cognitive fatigue due to a one-position increase in the order of a given question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' ηij is a mean-zero projection error, uncorrelated with Positionij by definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' If student i answers the exam in chronological order and finds the exam mentally taxing, we would expect πi > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Using equation (3), it is possible to re-write equation (1) as a regression equation that can be estimated in 12This idea is supported by research showing that time-on-task is a strong determinant of cognitive fatigue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For a review of the literature on the determinants of cognitive fatigue, see Ackerman (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 13 observational data: Cij = αi + βiPositionij + εij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (4) The intercept of the regression, αi ≡ E[Cij(0)]+κiωi, measures i’s expected performance on the test if she were fresh (E[Cij(0)]), plus the impact of her initial level of fatigue on performance (κiωi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Henceforth, I interpret αi as a measure of i’s academic ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The slope of the regression, βi ≡ κiπi, is the estimand of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This reduced-form measure is the product of two structural parameters, κi and πi, that are likely determined by several psychological mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For example, the performance of some individuals may be less impaired by cognitive fatigue (captured by κi) due to, for example, high intrinsic motivation or grit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Similarly, students may not become cognitively fatigued over the course of the exam (captured by πi) due to, for example, high attention capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Henceforth, I interpret βi as i’s cognitive endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The random part of performance, εij ≡ Cij(0)−E[Cij(0)]+ηij, measures deviations of i’s potential performance on question j from her average potential performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Comparing i’s performance across exam questions in different positions yields the sum of cognitive endurance plus a selection bias: E[Cij|Posij = p] − E[Cij|Posij = p − 1] = βi + E[Cij(0)|Posij = p] − E[Cij(0)|Posij = p − 1] � �� � Selection bias .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Next, I describe the two research designs that I use to deal with the selection bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 Identifying Cognitive Endurance In the empirical analysis, I first estimate the mean cognitive endurance across all students, β ≡ E[βi].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This parameter represents the causal effect of increasing a question’s position on average student performance, ¯Cj ≡ E[Cij].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Rejecting the null hypothesis of β = 0 would demonstrate that average student performance partly depends on cognitive endurance (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', this would show that κiπi ̸= 0 for some i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To identify β, I use two research designs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The first research design consists of assessing how average student performance on a given question varies as a function of the question’s position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This approach is enabled by the fact that a given question is located in a different position across booklets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To illustrate this approach, Appendix Figure D1 displays student performance in a natural science question (Appendix Figure C2 shows the text of the 14 question).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This question appears as early as position 46 in the gray booklet and as late as position 87 in the blue booklet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Accordingly, the fraction of correct responses declines from 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8% in the gray booklet to 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='9% in the blue booklet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Comparing student performance in these two booklets reveals that an increase of 41 positions reduces performance on this question by 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='9 percentage points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Analogous pairwise comparisons can be made for any two booklets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='13 I exploit this information using the following fixed effects specification: ¯Cjb = αj + βPositionjb + ξjb, (5) where ¯Cjb is the fraction of students who correctly answered question j in booklet b and αj are question fixed effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Appendix Figure A4 illustrates the mechanics of identification by plotting average student performance on selected questions as a function of their position on the four exam booklets and the corresponding best-fit lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' β is identified by first estimating the effect of question position on average student performance separately for each question and then aggregating these question-specific best-fit lines (like the ones plotted in the figure) using the OLS weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The advantage of this approach is that it relies on a weak identification assumption—the random allocation of booklets across students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' However, since each student only receives one exam booklet, I cannot compare a student’s performance across different booklets to identify βi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thus, I also use a second empirical strategy that can be used to identify both β and βi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The second empirical approach consists of controlling for question difficulty (Difficultyj) in equation (5) instead of the question fixed effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To estimate β, I assess how average student performance changes throughout the exam in regressions of the form: ¯Cjb = α + βPositionjb + δDifficultyj + µjb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (6) One challenge in implementing this approach is measuring question difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' An in- tuitive and often used measure of a question’s difficulty is the fraction of students who correctly answered the question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' However, a given question has a different fraction of cor- rect responses depending on where it is located on the booklet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thus, a question might appear to be more difficult simply because it is located later in the exam on average across booklets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To deal with this, I exploit the within-question position variation to construct a “position-adjusted” measure of a question’s difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This measure of question difficulty 13Not all questions appear in a different position across all booklets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Appendix Figure A3 shows the variation in question position across all questions for every pairwise booklet combination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 15 represents the fraction of correct responses we would expect to observe if question j ap- peared in the first position of the exam (see Appendix D for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To avoid a spurious correlation, I calculate question difficulty using data from test-takers outside my sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='14 This strategy yields a consistent estimate of β under the assumption that unobserved question characteristics are conditionally independent of average student performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Be- low, I provide evidence in support of this assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Importantly, as I describe in Section 5, this second empirical strategy can also be used to identify the cognitive endurance of each individual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In this case, the identification assumption is stronger, requiring that un- observed question characteristics are conditionally independent of i’s performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In the following two sections, I present estimates of mean cognitive endurance (Section 4) and individual-level endurance (Section 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 4 Cognitive Endurance and Test Performance This section presents estimates of average cognitive endurance using two research designs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 Student Performance over the Course of the ENEM To motivate the analysis, I begin by studying student performance over the duration of the exam without controlling for question difficulty or any other performance determinant that may be changing throughout the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Figure 1, plots the fraction of students who correctly responded to each exam question (y-axis) against the position of the question in the test (x-axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' As a benchmark, the red dashed line shows the expected performance if students randomly guessed the answer to each question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' There is a strong negative relationship between student performance and question po- sition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Average performance decreases from about 45% at the beginning of the exam to about 24% at the end of the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' A bivariate regression of the fraction of correct re- sponses on question position indicates that average student performance declines by 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 percentage points over the course of each testing day (p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='01), as shown in Table 2, column 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Interestingly, Figure 1 shows that average performance increases from about 30% at the end of the first day to about 45% at the beginning of the second day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='15 14These are mainly individuals who took the ENEM after graduating from high school.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The results are very similar if I use my sample to generate the measures of question difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The correlation between the measure of question difficulty estimated with test-takers in my sample and outside my sample is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 15Another interesting feature of Figure 1 is that student performance seems to increase towards the end of each testing day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This pattern is not unique to the ENEM;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' a similar pattern has been found in the SAT (Mandinach et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2005) and the PISA test (Borghans and Schils, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' One possible explanation 16 Limited cognitive endurance can provide a parsimonious explanation of these patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' As students advance through the exam, their mental resources may become increasingly taxed, and thus they become more prone to committing mistakes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Cognitive resources are replenished after taking a break (Sievertsen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2016) and overnight via sleep (Baumeis- ter, 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Lim and Dinges, 2008), which may explain why performance increases between the end of the first day and the beginning of the second day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Next, I implement the research designs described in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 to identify mean cognitive endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 Estimates of Mean Cognitive Endurance Table 2 presents the regression estimates from the two research designs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To facilitate the interpretation of the coefficients, I scale β so that it can be interpreted as decrease in student performance due to limited endurance over the course of each testing day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating the question-fixed-effects specification (equation 5) yields an average cogni- tive endurance β = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='072 (p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='01), as shown in column 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This estimate indicates that student daily performance decreases, on average, by 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 percentage points due to limited cognitive endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The difficulty-adjusted regression specification (equation 6) yields an estimate of average cognitive endurance β = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='058 (p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='01), as shown in column 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The similarity of this estimate relative to that obtained from the fixed effects specification suggests that controlling for question difficulty is adequate to account for differences in question characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Moreover, the R-squared indicates that 97% of the variation in ¯Cj is explained by a question’s position and difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This high R-squared shows that there is little scope for unobservable variables to affect ¯Cj, further providing supporting evidence for the selection-on-observables assumption (Oster, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Figures 2 and 3 provide visual evidence on the effect of limited cognitive endurance on student performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Figure 2 plots average student performance over the course of the exam after removing the influence of question difficulty on performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To construct this figure, I first regress ¯Cjb, the fraction of students who correctly answered question j in booklet b, on question difficulty, Difficultyj, and estimate the residual from this regression, ¯Cr jb = ¯Cjb − E[ ¯Cjb|Difficultyj].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I add back the sample mean to ¯Cr jb to facilitate interpre- tation of units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Finally, I plot the mean value of ¯Cr jb across the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The figure shows that difficulty-adjusted performance tends to decline linearly throughout the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Daily is what Mullainathan and Shafir (2013) refer to as the “the focus dividend,” that is, the notion that when a resource is scarce (in this case, the time left to finish the exam), the mind becomes better at focusing and blocking distractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Another explanation is that some students answer the exam in reverse order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 17 performance decreases by about 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 percentage points each day, an effect consistent with the regression estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Figure 3 plots the average percentage point change in the probability of correctly an- swering a question (y-axis) against the change in question position (x-axis) across all ques- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The line is the predicted value from a linear regression estimated on the micro data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Its intercept is statistically equal to zero, indicating that a given question is, on average, equally likely to be answered if it appears in the same position in two different booklets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The slope indicates that, on average, a given question is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='08 percentage points less likely to be correctly answered if it appears one position later in the test (p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='01).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thus, due to limited endurance, performance decreases by about one percentage point roughly every 12 questions (or 36 minutes if students spend the exam time uniformly across questions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The implied daily change in performance due to limited endurance equals 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 percentage points (p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='01), an estimate quantitatively identical to the question-fixed-effects specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Taken together, the evidence indicates that average student performance decreases by about 5–7 percentage points per day due to limited cognitive endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This effect is sizable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The fixed-effects-specification estimate represents a 16% decrease of the estimated performance at the beginning of the exam (equal to 45%, Table 2, column 1) or about 60% of the standard deviation of overall test score (equal to 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 percentage points).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The effect is comparable to that of a decrease of half a standard deviation in teacher quality (Chetty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2014a), an increase in the class size of about 16 pupils (Angrist and Lavy, 1999), or taking the exam under 66 degrees Fahrenheit hotter conditions (Park, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 Limited Cognitive Endurance or Time Pressure?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Throughout this section, I have interpreted the causal effect of an increase in question position on performance as a manifestation of limited cognitive endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This interpre- tation is in line with the framework in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' However, an estimate of β < 0 could also potentially be generated by students running out of time toward the end of the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1, I provide two pieces of evidence against this alternative interpretation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' First, very few students leave any responses unanswered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Second, performance declines are present even when students respond to questions while they are likely not time-pressured (such as when responding to questions in the first half of each testing day).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This evidence supports the interpretation of β < 0 as a consequence of limited cognitive endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 18 5 Decomposing Test Scores into Ability and Cognitive Endurance The results in Section 4 demonstrate that test scores reflect not only students’ academic preparedness (“ability”) but also their capacity to endure mental fatigue (“cognitive en- durance”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This section decomposes individuals’ test scores into these two skills and ex- amines the test-retest reliability of the generated measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 Linear Decomposition To quantify the relative influence of ability and endurance on a student’s test score, I estimate the difficulty-adjusted regression specification separately for each student: Cij = αi + βiPosNormij + δiDifficultyj + εij for i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', N, (7) where Cij equals one if student i answered question j correctly, PosNormij is question po- sition normalized such that the first question of each day equals zero and the last question equals one, and Difficultyj is the position-adjusted measure of question difficulty, nor- malized to have mean zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In the baseline specification, I estimate equation (7) pooling student responses from both testing days and all academic subjects and show robustness to including day and subject fixed effects, as well as to estimating the parameters separately by day and subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Without further assumptions, ˆαi and ˆβi simply describe how i’s performance changes throughout the test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The intercept of each regression, ˆαi, measures the predicted perfor- mance of student i in the first question of the test for a question of average difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thus, ˆαi represents i’s performance after accounting for the effect of a question’s position and difficulty on performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The slope of each regression, ˆβi, measures the predicted perfor- mance change between the first and last question of each testing day after accounting for question difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='16 Importantly, equation (7) can be interpreted as an observational ana- log of the model (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Under this model, ˆαi measures i’s academic ability and ˆβi measures i’s cognitive endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 16In Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2, I derive the OLS estimate of βi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The formula shows that ˆβi is calculated as a weighted average of deviations of i’s performance on each exam question from i’s average performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thus, ˆβi captures the intuition that a student who tends to do worse in the latter parts of the exam—relative to her average— has low endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 19 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 Limitations of Measuring Endurance using Standardized Tests This approach to measuring cognitive endurance has advantages but also important limita- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The main advantage is that it is based on observed behavior (“revealed preference”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This deals with some of the well-known biases of measures based on self-reports (“stated preferences”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Examples include social-desirability bias (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', respondents want to look good in front of the interviewer), reference-group bias (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', respondents judge their behav- ior using different standards), and framing effects (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', slightly different ways of asking the same question cause large changes in respondents’ answers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' However, there are at least three important concerns with the measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' First, es- timating individual-level endurance requires a large number of orthogonality conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' My research design requires any unobserved determinants of test performance to be un- correlated with question position (conditional on question difficulty).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This assumption is unlikely to hold exactly for all students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For example, some students may happen to be unprepared for the questions that appear at the end of the exam, which would lead to biased estimates of endurance for these students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' If the departures of the identification assumption are not systematic (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', some students are unprepared for questions at the end, but others are unprepared for questions at the beginning), then this issue is equiv- alent to measurement error, which would attenuate the effects documented below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Using the sample of retakers, I provide evidence consistent with this interpretation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In addition, I show that the results are similar using several alternative measures of endurance (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', calculated separately for each academic subject and using the average) Second, my endurance measure hinges on the assumption that students answer the exam in chronological order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' However, some students might respond in a different order (or strategically skip some questions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='17 While I do not have data on the order in which students answered the exam, below I show that the results are robust to excluding indi- viduals with positive estimated endurance (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', those students who possibly answered the exam in reverse order).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Finally, my measure of endurance is biased in the presence of floor or ceiling effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For example, individuals with extremely low ability or endurance may randomize their responses throughout the entire exam and show up in the data as having high endurance due to their stable performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' While this issue is not specific to my measure of endurance, 17For example, students with limited endurance that answer the exam in reverse chronological order will appear in the data as exhibiting a performance increase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' My estimate of endurance is biased for these students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 20 it may be a concern for the empirical analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Below, I show that the results are robust to excluding students in the tails of the ability and the endurance distributions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', students for whom floor and ceiling effects are more likely to be binding).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 Assessing the Reliability of the Cognitive Endurance Measure Are the measures of academic ability and cognitive endurance generated by the decom- position reliable?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To assess the reliability of a construct, researchers typically measure the construct multiple times and calculate the “temporal stability” or correlation between these measures (Miller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The size of the correlation is a measure of construct reliability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The higher the correlation, the more reliable the construct is said to be.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='18 I compute two measures of test-retest reliability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' First, I estimate ability and endurance separately for each testing day and calculate the correlation between consecutive days.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The advantage of this approach is that it can be implemented in my main sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The draw- back is that the academic subjects tested vary each day, which could affect the reliability estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='19 Second, I estimate the temporal stability of ability and endurance between consecutive years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This analysis produces more comparable estimates, but it can only be done using the smaller sample of retakers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The test-retest reliability of academic ability and cognitive endurance is comparable to that of other well-known constructs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Figure 4 show a series of binned scatterplots plotting the average t+1 estimate of ability/endurance as a function of the time t estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The temporal stability of ability ranges from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='61 (between consecutive days) to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='77 (between consecutive years).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The temporal stability of cognitive endurance ranges from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='14 (between consecutive days) to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='30 (between consecutive years).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' These results suggest that the ability and endurance measures are reliable for use in economic analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 Summary Statistics on Ability and Cognitive Endurance Average cognitive endurance is ˆβ = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='058, meaning that, due to limited endurance, the performance of the average student decreases by 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8 percentage points over the course of 18Reliability estimates vary significantly across constructs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Appendix Table A2 includes examples of reliability estimates for some well-known economic and psychological constructs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' IQ is the construct with the highest known reliability, with correlations on the order of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='80 (Hopkins and Bracht, 1975;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Schuerger and Witt, 1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Other commonly used constructs have lower temporal stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For example, reliability estimates of risk aversion range 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='40 (Mata et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' big five personality range 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='49–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='70 (Wooden, 2012);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' and teacher value-added range 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='23–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='47 (Chetty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2014a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 19For example, students who are good at natural science (a subject test on the first day) might not be as good at math (a subject test on the second day).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This would lead to an imperfect between-day correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 21 the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This estimate is consistent with the quasi-experimental results shown in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The standard deviation of ˆβi is σˆβ = 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 percentage points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 Because of sampling error in ˆβi, this raw standard deviation overstates the variability of true latent βi, σβ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Following Angrist et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (2017), I estimate σ2 β as ˆσ2 β = σ2 ˆβ − E[SE2 ˆβ], (8) where E[SE2 ˆβ] is the average squared standard error of ˆβi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I construct an analogous estimate for the standard deviation of latent ability, ˆσα (see Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The standard deviation (SD) of βi is ˆσβ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='088.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This means that an increase of one SD in cognitive endurance predicts a 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8 percentage point increase in test score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The cor- responding estimate for ability is ˆσα = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='132.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Hence, ˆσβ is about two-thirds the magnitude of ˆσα, meaning that ability is more dispersed than endurance across students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' These es- timates can be translated into percentage effects by dividing by the average test score of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='344 (Table 1, Panel D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Under this rescaling, the estimates imply that a one SD increase in endurance leads to a 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6% increase in test score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The corresponding impact of ability equals 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Figure 5 shows the joint distribution of estimated ability and endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The red dia- monds show a binned scatterplot of mean endurance as a function of ability, calculated by dividing students into 100 equally-sized ability bins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The gray circles display a scatterplot of ˆβi against ˆαi for a randomly-selected one percent of my sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Figure 5 reveals two important patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' First, there is substantial variation in individ- uals’ ability-endurance combination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='21 Second, there is a negative relationship between ˆα and ˆβ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' On average, individuals with low values of ˆα tend to have higher values of ˆβ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This relationship is largely mechanical and it is driven by floor and ceiling effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Low-ability individuals have a limited margin to decrease their performance throughout the exam be- cause test scores are bounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' A similar argument holds for high-ability individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This generates a “missing mass” of individuals with low-ability low-endurance and high-ability high-endurance, inducing a negative correlation between the two variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='22 In the analysis 20Appendix Figure A6 shows the distribution of estimated ability (Panel A) and endurance (Panel B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 21For example, for individuals with ˆα ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50, their estimates of endurance ranges from ˆβ = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 (a value roughly in the bottom one percent of the endurance distribution) to ˆβ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 (a value in the top one percent).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 22For individuals with intermediate values of ability (for whom ceiling and floor effects are less likely to be binding), the correlation is negligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For example, the correlation between the two measures is -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='08 for individuals with estimated ability between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 22 below, I always control for both variables to account for their mechanical relationship and show robustness to excluding individuals in the tails of the ability/endurance distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In the following two sections, I use the estimates of ability and endurance to (i) revisit the association between test scores and long-run outcomes through the lens of the ability- endurance decomposition and (ii) characterize how systematic differences in endurance across students affect test-score gaps and the information contained by test scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 6 Cognitive Endurance and Student Outcomes in Adulthood In this section, I use the decomposition to separately quantify the contribution of ability and endurance to the well-known association between test scores and long-run outcomes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', Bishop, 1989;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Hanushek and Woessmann, 2008, 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 Estimating the Return to Academic Ability and Cognitive Endurance To assess how test scores and their component skills relate to college and labor-market outcomes, I estimate regressions of the form: Yi = φ + λXi + ψTTestScorei + νi (9) Yi = ˜φ + ˜λXi + ψAAbilityi + ψEEndurancei + ˜νi, (10) where Yi is an outcome of student i (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', earnings);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Abilityi and Endurancei are the measures of academic ability and cognitive endurance estimated in Section 5;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' and Xi is a vector that contains demographic variables and socioeconomic status.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='23 For labor- market outcomes, I additionally control for educational attainment and potential years of experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Because students can enroll in multiple college degrees, each observation denotes a student–degree combination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I account for the fact that an individual can appear multiple times in the dataset by clustering the standard errors at the individual level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To compare the magnitude of the predicted effect of endurance on a given outcome with the corresponding effect of academic ability, I normalize both variables such that their coefficients represent the effect of a one standard-deviation (SD) increase on a given outcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 23For students with a missing value for a control variable, I define the missing value as equal to the sample mean value and include a dummy for missing student characteristics in the regressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 23 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 Baseline Estimates I first discuss college outcomes and then turn to labor-market outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 College outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Table 3, Panel A displays estimates of the relationship be- tween test scores, its component skills (ability and endurance), and college outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The first row shows estimates of equation (9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Consistent with a sizable literature on the strong predictive power of test scores, I find that students with higher test scores tend to have better college outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Students with a one SD higher test score are 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8 percentage points more likely to enroll in college (relative to a mean of 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4%, column 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Conditional on enrolling in college, the quality of their institution and college major—as measured by the average earnings of previous graduates—is 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2%–11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='7% higher (columns 2–3), the share of total credits they complete by the end of their first year is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 percentage points higher (an 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8% increase relative to the mean of 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8%, column 4), and they are 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 percentage points more likely to graduate (column 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Conditional on graduating, they take 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='12 fewer years to graduate (a 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1% decrease relative to the mean of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 years, column 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' These estimates are comparable to those in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='24 The second and third rows in Panel A show estimates of equation 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' There are two things to notice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' First, controlling for endurance produces associations between ability and outcomes that are stronger than the associations between test scores and outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Second, endurance has an economically and statistically significant effect on college outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' A one SD increase in endurance predicts a 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='9 percentage points increase in the likelihood of enrolling in college (p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='01);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' a 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2% increase in the college quality (p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='01), and a 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 percentage point increase in the six-year graduation rate (p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='01).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To benchmark the size of these associations, I compute the ratio between the predicted effect of endurance on an outcome and the predicted effect ability ( ˆψE/ ˆψA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This estimate is shown in the third-to-last row in Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The effect of endurance as a percent of the effect of ability ranges from 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6%–36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2%, depending on the outcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Figure 6, Panels A–C present binned scatterplots of selected college outcomes against cognitive endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To construct each panel, I first regress Yi and Endurancei on student- level characteristics and ability, and estimate the residuals from these regressions, Y r i and Endurancer i (adding back the unconditional sample mean to facilitate the interpretation of 24For example, Chetty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (2014b) estimates that a one-standard-deviation increase in test scores is associated with a 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5 percentage point increase in college enrollment at age 20, a 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8% increase in college quality as measured by the earnings of previous graduates, and an 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='9% increase in earnings at age 28 (see their Appendix Table 3, row 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 24 units).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Then, I group individuals into 10 equally-sized bins (deciles) based on Endurancer i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Finally, I plot the mean value of Y r i for each bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Consistent with the regression results, there is a strong relationship between cognitive endurance and college enrollment (Panel A), college quality (Panel B), and the six-year graduation rate (Panel C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' These results suggest that both ability and endurance are crucial for college suc- cess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' While the importance of academic ability had been widely documented, the results show that traditional estimates of ability—usually measured through test scores—are con- founded with the effect of cognitive endurance due to fatigue effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' More importantly, the results suggest that endurance plays a commensurate role in college success.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='25 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 Labor-market outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Table 3, Panel B displays the results for labor-market outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' On average, students with higher test scores face better prospects in the labor market.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Students with a one SD higher test scores are 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 percentage points more likely to have a formal-sector job (column 1), have a 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='7% higher hourly wage (column 2), earn a 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='9% higher monthly salary (column 3), work in firms that pay 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1% higher wages (column 4), choose occupations that pay 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1% higher wages (column 5), and work in industries that pay 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3% higher wages (column 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' These associations reflect both the influence of academic ability and cognitive en- durance, both of which have statistically and economically significant effects on all labor- market outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For example, a one SD increase in endurance predicts a 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4% increase in hourly wages (p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='01), a 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2% increase in monthly earnings (p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='01), and a 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6% increase in the average firm wage (p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='01).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The strong relationship between cognitive endurance and these three labor-market outcomes is illustrated in binned scatterplots in Figure 6, Panels D–F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' These figures show that mean wages and earnings increase roughly linearly with endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For labor-market outcomes, the predicted effect of cognitive en- durance as a percent of the predicted effect of ability ranges from 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5%–38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='7%, depending on the outcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' These results indicate that endurance has a sizable wage return in the labor market.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Under complete information and frictionless markets, the price of a skill equals the present value of the future returns generated by the skill (Abraham and Mallatt, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thus, the sizable wage return to endurance suggests that this skill is a key productivity determinant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The positive wage return to ability and endurance is consistent with models in which firms 25The positive association between endurance and college outcomes is consistent with Brown et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (2022), who show that a cognitive-endurance-enhancing intervention improves student performance in elementary school.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 25 pay workers according to their productivity, and output is generated by combining ability with cognitive effort.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Cognitive endurance enables workers to sustain effort for a longer time, allowing them to produce a higher total output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The results also reveal a novel type of assortative matching in the labor market: workers with high cognitive endurance are more likely to work for high-paying firms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This is relevant given that the sorting between workers and firms is an important driver of labor-market outcomes (Card et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 Robustness and IV Estimates Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 presents a series of robustness and specification checks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The baseline results are robust to computing the effects nonparametrically, estimating ability and endurance with alternative specifications (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', with day or subject fixed effects), and imposing several sample restrictions (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', excluding the tails of the ability or endurance distribution).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Appendix Tables A3–A4 display instrumental variables (IV) estimates of the effect of ability and endurance on long-run outcomes, estimated on the retakers sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I instru- ment the year t measure of ability/endurance with the year t − 1 measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Using repeated measures of a skill as an instrument is a common strategy to deal with measurement error in the literature (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', Gronqvist et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Edin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In addition, by using the year t − 1 measures as instruments, this strategy eliminates the mechanical relationship between year t ability/endurance and year t test scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Panel A report OLS estimates on the retakers sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The effects are comparable to those estimated on the main sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Panel B reports the IV estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In general, these tend to be larger than the OLS estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For example, the OLS estimate of the effect of a one SD increase of endurance [ability] on wages is 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1% [23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1%], while the IV estimate is 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8% [25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0%].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Relative to the OLS estimates, the IV estimates of the endurance effects tend to increase more than the ability effects, consistent with the endurance measure containing more measurement error than ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Hence, the IV estimates suggest that the wage return to endurance—as a fraction of the return ability—is significantly higher, on the order of 75%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 The Value of Endurance across Degrees, Occupations, and Industries Does the value of cognitive endurance vary across degrees, occupations, and industries?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The task-based approach to labor markets highlights that workers produce output by performing job tasks, and tasks differ in their skill requirements (Acemoglu and Autor, 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Consequently, the value of endurance should vary according to the tasks individuals 26 have to accomplish in a given job and the importance of endurance in the production function of those tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For example, endurance may be particularly important for some jobs because mistakes due to attentional lapses can dramatically reduce the output value, as in “O-ring” production functions (Kremer, 1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To assess this, I estimate the wage return to endurance separately for each degree, occupation, and industry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Intuitively, the wage return to endurance should reflect the increase in productivity due to an increase in this skill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thus, a high wage return to endurance in a given occupation may indicate that this skill is particularly valuable in the production function of the tasks required by such an occupation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='26 Figure 7 plots the distribution of wage returns across degrees (Panel A), occupations (Panel C), and industries (Panel E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' There is substantial heterogeneity in the wage return to ability and to endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For example, while the average return to endurance across degrees is 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='9%, the return across degrees in the bottom decile of the return distribution is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1% and in the top decile is 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This suggests that cognitive endurance is more valuable for success in some college degrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Occupations and industries also exhibit substantial heterogeneity in wage returns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Figure 7 also show that degrees, occupations, and industries that tend to pay higher average wages tend to offer higher returns to ability and endurance (Panels B, D, and F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For example, the return to endurance among the top ten percent highest-paying occupa- tions is about three times higher than the return to endurance among the bottom-ten- percent-paying occupations (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='9% vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6%, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This finding is consistent with high-paying jobs requiring high-endurance workers, suggesting that the value of this skill is higher in high-paying jobs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Figure 8 shows the joint distribution of the wage return to ability and the wage return to endurance across college degrees (Panel A), occupations (Panel B), and industries (Panel C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The figure reveals a strong association between the wage return to ability and the wage return to endurance across degrees, occupations, and industries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For example, on average, a 10%-increase in the wage return to endurance across occupations predicts a 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1% increase in the wage return to ability (p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='01).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This finding suggests that ability and endurance are complementary skills in production.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To make tangible some of the real-world tasks for which endurance may be partic- 26There are two important caveats with this approach to measuring the value of endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The first one is that individuals may select into degrees, occupations, and industries partly based on their endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The second one is that an increase in productivity may not lead to a corresponding increase in wages in some occupations or industries due to institutional factors (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', collective bargaining).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 27 ularly valuable, Table 4 list the top-five degrees, occupations, and industries with the highest wage return to endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The list includes occupations where attentional lapses may be extremely costly—such as facility operators in petrochemical plants or air naviga- tion professionals—but also academically-oriented occupations, like mathematicians and statisticians (Panel B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The list also includes degrees conducive to these occupations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', aeronautics, Panel A) and related industries (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', oil extraction, Panel C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' While sugges- tive, this list is consistent with the proposition that the value of endurance depends on the type of tasks required by a job and the importance of endurance in the production function of those tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 7 Endurance and the Sorting of Students to Colleges The sorting of students to colleges has important implications for the education and labor- market outcomes of these students (MacLeod et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Brazil, as in many other countries, this sorting is largely mediated by admission exam scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' My results indicate that test scores reflect two valuable but distinct skills: ability and endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' An important question is how these two skills contribute to the sorting of students to colleges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In this section, I estimate the effects of an exam reform that reduces the exam length by half.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Such a reform would decrease the relative weight of endurance for determining test scores and increase the relative weight of ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I focus on two channels through which the reform could affect the sorting of students to colleges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' First, I study the distributional effects of the reform, that is, how the reform would affect test-score gaps due to systematic differences in average endurance across types of students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Second, I study the informational effects of the reform, that is, how the reform would affect the information on the quality of each applicant contained in test scores due to a change in the skills being measured by the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 Cognitive Endurance and Test-Score Gaps Standardized tests often exhibit large racial and income test-score gaps (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', Fryer Jr and Levitt, 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Card and Rothstein, 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Riehl, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In the context of college admission exams, these gaps lead to inequitable college access and amplify earnings disparities (Chetty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' An important question is what explains those test-score gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Next, I examine the contribution of differences in cognitive endurance to these gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 28 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 Decomposing Test-Score Gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To begin with, notice that the linear de- composition (7) can be used to parsimoniously summarize an individual’s test score, TestScorei ≡ E[Cij], as a linear combination of her academic ability and endurance: TestScorei = ˆαi + ˆβiPosition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (11) Let X ∈ {0, 1} be a student observable characteristic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For example, X = 1 may denote high-income students and X = 0 low-income students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The average test score of students with characteristic x can be written as E[TestScorei|Xi = x] = E[ˆαi|Xi = x] + E[ˆβi|Xi = x]Position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (12) Using this expression, the test-score gap, ScoreGap, can be decomposed into differences in average academic ability and differences in average cognitive endurance as follows: ScoreGap = α1 − α0 � �� � Difference in average academic ability between groups + (β1 − β0)Position � �� � Difference in average cognitive endurance between groups , (13) where αx ≡ E[ˆαi|Xi = x] and βx ≡ E[ˆβi|Xi = x].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Equation (13) shows that, in the absence of systematic differences in limited endurance (β1 = β0), test scores gaps would be purely a reflection of gaps in academic ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thus, exam design features that put a higher or lower weight on endurance, such as the length of the exam or the number of breaks, should not affect test-score gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This is no longer true in the presence of systematic differences in endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' If student-level characteristics are associated with endurance, then an exam design that puts more weight on endurance will affect test-score gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I focus on estimating the impact of an exam reform that decreases the length of the test by half on test-score gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='27 This reform would decrease the average question position (from Position to Position/2), thereby decreasing the influence of endurance gaps on test- score gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='28 While I focus on test length, other exam features can also affect the influence 27Such a reform would be equivalent to changing the ENEM from its current length to roughly the length of the ACT exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 28An important concern is that, by reducing the number of questions, the exam would determine the place in the score distribution of any one student with less precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' However, the reform could be achieved without sacrificing much precision by using an adaptive exam that selects questions based on the student’s ability level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 29 of endurance for test-score gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For example, Figures 1–2 show that student performance starkly increases between the end of the first day and the beginning of the second day, suggesting that giving students more breaks would decrease the importance of endurance for test-scores gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Similarly, in Appendix E, I show that the type of exam questions impacts cognitive fatigue, thereby influencing the importance of endurance for test-score gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thus, the reform can also be interpreted as, for example, introducing a long break in the middle of each testing day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Using equation (11), I estimate the effects of the reform on test-score gaps between: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Male and female students, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' White and non-white (Black, Brown, and Indigenous) students, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Students in households in the top 30% and bottom 30% of the income distribution, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Students with a college-educated mother and non-college-educated mother, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Students enrolled in a private high school and public high school.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 The Impact of an Exam Reform on Test-Score Gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Table 5 shows es- timates of the contribution of gaps in ability and endurance to test-score gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Column 1 shows the difference in average test scores between the groups of students listed in the row header, column 2 shows the difference in average academic ability (in a regression that controls for endurance), and column 3 shows the difference in average cognitive endurance (controlling for ability).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' By reducing the contribution of endurance gaps to test-score gaps by half, the reform would: (i) Reduce the gender test-score gap by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='85 percentage points (a 32% decrease from the pre-reform gap of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 percentage points);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (ii) Reduce the racial test-score gap by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='08 percentage points (a 14% decrease from the pre-reform gap of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='7 percentage points);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' and (iii) Reduce the SES test-score gap by 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3–3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 percentage points (a 13%–16% decrease from pre-reform gaps), depending on the SES measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The predicted impact of the exam reform is robust to (i) measuring the gaps in per- centiles (Appendix Table A5);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (ii) Estimating ability and endurance with alternative spec- ifications (Appendix Table A6);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (iii) Using alternative measures of question difficulty when estimating ability and endurance (Appendix Table A7);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (iv) Excluding individuals in the tails of the ability or endurance distributions (Appendix Table A8);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' and (v) Using precision- weighted estimates (Appendix Table A9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 30 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 Cognitive Endurance and the Predictive Validity of Test Scores Admission officers use test scores to screen applicants because they are informative about which applicants will succeed in college.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The standard approach to assess the informative content of an exam test is to calculate the cross-individual correlation between test scores and a long-run outcome that colleges want to screen their applicants based on (such as first-year college GPA or on-time graduation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This correlation is known as the predictive validity of an exam (Rothstein, 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Next, I study how an exam’s predictive validity depends on cognitive endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 Decomposing Predictive Validity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In the presence of limited endurance, fea- tures of the exam that affect the weight of endurance will affect the exam’s predictive validity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To see this, notice that the predictive validity of test scores for outcome Y , ρY , can be written as: ρY ≡ Corr(Yi, TestScorei) = Corr(Yi, αi + βiPosition) = σα σT Corr(Yi, αi) + σβ σT Corr(Yi, βi)Position, (14) where σα, σβ, σT are the standard deviations of ability, endurance, and test scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Equation (14) shows that the predictive validity of an exam can be expressed as a linear combination of the correlation between the outcome and the skills measured by the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The weight of each skill depends on its dispersion and the exam’s length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Unfortunately, equation (14) cannot be directly used to predict how an exam reform that changes the test length would affect its predictive validity, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', ∂ρY /∂Position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This is because, as shown in Section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1, such a reform would change the ranking of students, thereby affecting Corr(Yi, αi) and Corr(Yi, βi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I sidetrack this problem by studying how predictive validity varies throughout the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In particular, I ask how a given question’s predictive validity ρY j ≡ Corr(Yi, Cij), changes when its position changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Notice that the predictive validity of the overall exam can be written as a weighted average of the predictive validity of each exam question j ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', J}: ρY = 1 J J � j=1 σCij σT ρY j .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (15) Equation (15) is helpful because it allows me to exploit the random variation in whether 31 a given question is presented when students are relatively fresh or cognitively fatigued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To build intuition on the mechanics of this analysis, notice that ρY j is given by the difference in average outcomes between students who correctly and incorrectly responded to question j, multiplied by the ratio of standard deviations: ρY j = � E[Yi|Cij = 1] − E[Yi|Cij = 0] �σCij σYi .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (16) Equation (16) indicates that limited endurance affects the predictive validity of a ques- tion by changing the composition of students who correctly answer the question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Loosely speaking, correct responses at the beginning of the exam are driven by high-ability students (regardless of their endurance level since all students are “fresh”) and low-ability students who guessed the answer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Toward the end of the exam, correct responses are driven by stu- dents with high ability and high cognitive endurance and students with either low ability or low endurance who guessed the answer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' How this compositional change affects a question’s predictive power for an outcome is theoretically ambiguous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' It depends on how the outcome correlates to academic ability relative to cognitive endurance, the distribution of ability and endurance in the population, and how difficult the question is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thus, I empirically assess this by estimating regressions of the form: ρY jb = αj + γY Positionjb + ηjb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (17) where ρY jb is the predictive validity of question j in booklet b, αj are question fixed effects, and Positionjb is the position of question j in booklet b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The coefficient of interest is γY , which measures the impact of a one-position increase in the order of a given question on the question’s predictive validity for outcome Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I scale γY so that it represents the change in predictive validity due to a reform that decreases the average question position by half.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I estimate the effect of the reform for eight main outcomes: test score (calculated without the contribution of question j to avoid mechanical effects), college enrollment, college quality, degree progress, six-year graduation rate, hourly wage, monthly earnings, and firm leave-individual-out mean earnings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Since the dependent variable is an estimate, I weight each observation using the inverse square of its standard error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I cluster standard errors at the question position level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 32 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 The Impact of an Exam Reform on the Test’s Predictive Validity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Table 6 presents the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Panel A shows the average predictive validity across all test questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I find that individual questions are predictive of student long-run outcomes, although the size of the correlations tends to be small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For example, on average across all questions, correctly responding to a question has a 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 positive correlation with enrolling in college (column 2, p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='01), 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 correlation with college quality (column 3, p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='01), and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 correlation with wages and earnings (columns 6–7, p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='01).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Panel B reports the estimates of equation (17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The exam reform would generate a sizable increase in the predictive validity of the exam for the majority of outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For example, the exam reform would increase the average predictive validity of test responses for college enrollment by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 points (a 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2% increase relative to the pre-reform mean, p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='01), for college quality by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='09 points (a 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1% increase relative to the pre-reform mean), and for earnings by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='07–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='08 points (a 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='7%–79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6% increase relative to the pre- reform mean, p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='01).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The predicted effect for the six-year graduation rate is also positive but not statistically different from zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The reform would decrease the predictive validity for degree progress.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' These estimated effects of the reform are driven by the fact that a given question tends to be less predictive of long-run outcomes if it appears later in the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This can be seen visually in Appendix Figure 9, which shows binned scatterplots plotting the change in the predictive ability of a question (y-axis) against the change in the question position (x-axis) for selected outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In all cases, the average predictive validity of test questions tends to decrease if the question appears later in the test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='29 These results can help explain puzzling empirical findings in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Kobrin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (2008) study how the predictive validity of the SAT changed after the exam increased the number of questions in 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Intuitively, more test questions should lead to more precise student ability estimates and thus to more predictive test scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Yet, the predictive validity of the exam did not change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This finding can be explained by cognitive fatigue eroding the predictive power of test responses at the end of the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Bettinger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (2013) show that performance on the English and Math sections of the ACT predict college outcomes, but not performance on the Science and Reading sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Based on this finding, the authors propose eliminating the Science and Reading sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Notably, the Science and Reading questions are the last to appear in the ACT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Hence, the null predictive power of these two 29The negative association can also be seen in Appendix Figure A7, which plots the predictive validity of a question (y-axis) against its position on the exam (x-axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' There is an evident decline in predictive validity between the exam’s beginning and end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 33 subjects may be driven by students being cognitively fatigued by the time they reach those sections—and not by the skills assessed by Science and Reading questions being irrelevant for long-run outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='30 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 Discussion In summary, this section shows that, due to heterogeneity in cognitive endurance, the design of college admission exams can have equity and efficiency consequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I estimate that a reform that halves the exam length would reduce SES gaps by 26%–29%, possibly leading to a more diverse college student body.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In addition, the shorter exam would be more informative about the quality of each applicant (as measured by its predictive validity), possibly leading to a better allocation of students to colleges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The first result is driven by the fact that, conditional on academic ability, low-SES students have lower endurance than high-SES students;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' thus, their performance declines at a steeper rate throughout the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The second result is driven by the fact that differences in student performance at the beginning of the exam mainly reflect differences in ability (roughly, because most students are “fresh”), whereas performance differences towards the end of the exam increasingly reflect differences in endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Since ability is a stronger predictor of long-run outcomes than endurance, the predictive validity of a given question decreases if it appears later on the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 8 Conclusion Cognitive effort underlies most, if not all, productive activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Just like individuals differ in preferences and personality traits, they also differ in their ability to endure mental fatigue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This paper shows that cognitive endurance affects student performance in college admission exams and has a substantial earnings return in the labor market.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' My findings have implications for investments in different types of human capital.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I find that endurance has a substantial return in the labor market.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Yet, a typical school curriculum does not include any material directly aimed at building this dimension of human capital.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Policymakers should consider investing in the development of cognitive 30If the goal is to maximize the exam’s predictive power, an alternative reform that might be more desir- able is to reduce the number of questions in all sections (instead of eliminating some sections).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Cognitive fatigue plays a smaller role in shorter tests, allowing students to reveal their academic preparedness across all questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' By not removing any subjects, colleges would have a measure of academic preparedness for all topics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I discuss the implications of my findings for exam design in Section 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 34 endurance, possibly during early ages when neuroplasticity is higher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' While research in this area is still in its infancy, some examples of protocols that build cognitive endurance include mindfulness meditation (Levy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Goleman and Davidson, 2017), noninvasive brain stimulation (Rubia, 2018), and the restriction of smartphones in learning environments (Thornton et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='31 An important caveat is the lack of exogenous variation in cognitive endurance in my analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' While my findings provide evidence of a positive link between endurance and earnings, these estimates may be misleading if the available control variables are inadequate to provide meaningful estimates of the return to this skill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Future work should establish if this link is causal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The findings also have implications for the design of standardized tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In a typical test, all questions contribute the same to an individual’s score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' However, the results show that questions that appear early in the exam are more predictive of long-run outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' An aggregation mechanism of individuals’ test responses that takes into account students’ varying fatigue levels throughout the exam may lead to more informative test scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For example, testing agencies can weight each question based on the position in which it was answered, assigning more weight to questions students responded to earlier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The ability-endurance score decomposition developed in this paper generates directions for future research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Test scores are commonly used in economics research, for example, as measures of cognitive skills (Hanushek and Woessmann, 2008, 2012);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' as a “surrogate” variable to measure the impact of an intervention on long-run outcomes (Athey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' and to measure the effectiveness of educational inputs (Chetty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Dobbie and Fryer Jr, 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Angrist et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The decomposition allows researchers to explore the role of cognitive endurance in these and other applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For example, researchers can use conventional value-added methods to identify teachers who might be particularly effective at building cognitive endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 31Some of these protocols are already being implemented in the private sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For example, meditation practices are commonly used among tech companies in Silicon Valley to enhance worker productivity (Shachtman, 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 35 Figures and Tables Figure 1: Average student performance over the course of the ENEM Day 1 of the exam Day 2 of the exam (Correlation = -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='84) (Correlation = -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='88) Random chance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='35 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='45 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='55 Fraction of students who answered correctly 1 30 60 90 120 150 180 Position of the question in the exam Notes: This figure shows student performance over the course of each testing day in the ENEM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The y-axis displays the fraction of students who correctly responded to each question, averaged across all years in my sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The x-axis displays the position of each question in the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The dashed lines are predicted values from a linear regression estimated separately for each testing day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The horizontal red dashed line shows the expected performance if students randomly guessed the answer to each question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 36 Figure 2: Performance residuals after controlling for question difficulty Random chance Social science Natural science Language arts Mathematics (Correlation = -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='88) (Correlation = -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='84) (Correlation = -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='91) (Correlation = -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='96) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='35 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='45 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='55 Fraction of correct responses (residualized) 1 30 60 90 120 150 180 Position of the question in the exam Notes: This figure shows student performance over the course of each testing day after removing the influence of question difficulty on performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The y-axis displays the residuals of a regression of (i) ¯Cjb, the fraction of students who correctly answered question j in booklet b on (ii) Difficultyj, a position- adjusted measure of question difficulty (adding back the sample mean to facilitate interpretation of units).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The x-axis displays the position of each question in the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Marker colors denote each academic subject tested.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Appendix D describes how I construct the measure of question difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The dashed lines are predicted values from a linear regression estimated separately for each academic subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The horizontal red dashed line shows the expected performance if students randomly guessed the answer to each question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 37 Figure 3: The effect of an increase in the order of a given question on student performance Intercept: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000 pp Slope: -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='080 pp Slope x 90: -7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='23 pp 5 4 3 2 1 0 Average pp change in prob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' of correct answer 0 5 10 15 20 25 30 ≥35 Change in question position Notes: This figure shows estimates of the impact of an increase in the order of a given question on the fraction of students who correcly answer the question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The y-axis plots the average change (in percentage points) in the fraction of students who correctly respond to a question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The x-axis displays changes in a question position between each possible booklet pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' See Appendix Figure A3, Panel A for a histogram of the values in the x-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To construct this figure, I first compute the change in student performance and the distance in a question’s position between each possible booklet pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Then, I calculate the average change in performance for each observed distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The solid line denotes predicted values from a linear regression estimated on the plotted points, using as weights the number of questions used to estimate each point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The vertical dashed lines denote 95% confidence intervals, estimated with heteroskedasticity-robust standard errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 38 Figure 4: The temporal stability of ability and endurance estimates Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Ability in day d and day d + 1 Correlation = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='610 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8 Average academic ability in day 2 (αi) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8 Academic ability in day 1 (αi) Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Endurance in day d and day d + 1 Correlation = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='140 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 Average cognitive endurance in day 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 Cognitive endurance in day 1 (βi) Panel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Ability in year t and year t + 1 Correlation = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='767 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8 Average academic ability in year t + 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8 Academic ability in year t (αi) Panel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Endurance in year t and year t + 1 Correlation = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='303 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 Average cognitive endurance in year t + 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 Cognitive endurance in year t (βi) Panel E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Ability in year t and year t + 2 Correlation = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='752 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8 Average academic ability in year t + 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8 Academic ability in year t (αi) Panel F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Endurance in year t and year t + 2 Correlation = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='291 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 Average cognitive endurance in year t + 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 Cognitive endurance in year t (βi) Notes: This figure shows the correlation between the measures of academic ability and cognitive endurance measured at two different points in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each panel shows a binned scatterplot plotting the estimates of ability/endurance at two different times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To construct this figure, I first divide students into 100 equally- sized bins based on their ability/endurance at time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Then, I calculate the average ability/endurance at time t′ > t for students in each bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The panel title indicates the two time periods in which I measure ability and endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 39 Figure 5: Joint distribution of ability and endurance estimates Notes: This figure shows estimates of the relationship between academic ability and cognitive endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Gray circles display a scatterplot of ˆβi against ˆαi for a randomly-selected one percent of my sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The red diamonds show a binned scatterplot of average endurance as a function of ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To construct the binned scatterplot, I first divide students into 100 equally-sized bins based on their ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Then, I calculate the average endurance for students in each bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Finally, I plot average endurance against ability in each bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='7- Raw data Binned scatterplot 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 Cognitive endurance (β:) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 - 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' O O 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 Academic ability (a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=')Figure 6: The relationship between cognitive endurance and long-run outcomes Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' College enrollment 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 College enrollment (residualized) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='04 Average cognitive endurance (in pp, residualized) Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' College quality 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8 College quality (residualized) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='02 Average cognitive endurance (in pp, residualized) Panel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Six-year graduation rate 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5 Six-year graduation rate (residualized) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='07 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='065 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='06 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='055 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 Average cognitive endurance (in pp, residualized) Panel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Log hourly wage 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 Mean log hourly wage (residualized) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='02 Average cognitive endurance (in pp, residualized) Panel E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Log monthly earnings 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5 Mean log monthly earnings (residualized) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='02 Average cognitive endurance (in pp, residualized) Panel F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Firm mean wage (leave-one-out) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 Mean log firm wage (residualized) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='04 Average cognitive endurance (in pp, residualized) Notes: This figure shows the relationship between cognitive endurance and selected college and labor- market outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each panel shows a binned scatterplot plotting the average value of the outcome (y-axis) against cognitive endurance (x-axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To construct this figure, I first residualize cognitive endurance and each outcome on student-level characteristics and academic ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I add back the unconditional sample mean to facilitate interpretation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Then, I divide students into 10 equally-sized bins (deciles) based on their residualized endurance and plot the average outcome for students of each bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The red dashed lines are predicted values from a linear regression on the plotted points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each panel shows the results for the outcome listed in the panel title.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' See Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 for variable definitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 41 Figure 7: Heterogeneity in the wage return to ability and cognitive endurance Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Distribution of wage returns across college degrees 0 4 8 12 16 20 Density 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='25 Return to skill (in hourly wage log points) Academic ability Cognitive endurance Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Return to ability/endurance vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' average wage across college degrees 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 Return to skill (in hourly wage log points) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='90 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='30 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='70 Mean log hourly wage Academic ability Cognitive endurance Panel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Distribution of wage returns across occupations 0 4 8 12 16 20 Density 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='25 Return to skill (in hourly wage log points) Academic ability Cognitive endurance Panel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Return to ability/endurance vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' average wage across occupations 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 Return to skill (in hourly wage log points) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='90 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='30 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='70 Mean log hourly wage Academic ability Cognitive endurance Panel E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Distribution of wage returns across industries 0 4 8 12 16 20 Density 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='25 Return to skill (in hourly wage log points) Academic ability Cognitive endurance Panel F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Return to ability/endurance vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' average wage across across industries 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 Return to skill (in hourly wage log points) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='90 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='30 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='70 Mean log hourly wage Academic ability Cognitive endurance Notes: Panels A, C, and E show nonparametric estimates of the distribution of the wage return to ability (red line) and the wage return to endurance (green line) across degrees, occupations, and industries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The wage return to ability and endurance are the coefficients ψA and ψE in equation (10) using log hourly wage as outcome, estimated separately for each degree, occupation, and industry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The figure excludes outliers (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', estimates of the returns below -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 or above 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Panels B, D, and F display a series of binned scatterplots plotting the wage return to ability/endurance (y-axis) against the mean hourly wage in bins (x-axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To construct this figure, I first divide degrees, occupations, and industries into 10 equally-sized bins based on their mean wage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Then, I estimate the average return to ability/endurance in each bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Finally, I plot the average return to ability/endurance against the mean wage in each bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 42 Figure 8: The relationship between the wage return to ability and endurance Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Across college degrees 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='30 Wage return to ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 Wage return to cognitive endurance Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Across occupations 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='30 Wage return to ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 Wage return to cognitive endurance Panel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Across industries 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='30 Wage return to ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 Wage return to cognitive endurance Panel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Binned scatterplot 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='30 Average wage return to ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 Wage return to cognitive endurance Degrees Occupations Industries Notes: This figure shows the relationship between the wage return to ability (y-axis) against the wage return to endurance (x-axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Panels A–C show scatterplots of the wage return to ability in a given college degree (Panel A), occupation (Panel B), and industry (Panel C), against the wage return to endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The scatterplots exclude outliers (wage returns in the bottom 5% or top 5% of the distribution).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The solid lines denote predicted values from linear regressions estimated on the microdata (including all observations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Panel D shows a binned scatterplot plotting the mean wage return to ability against the wage return to endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To construct this figure, I first divide degrees (blue circles), occupations (red triangles), and industries (green diamonds) into 10 equally-sized bins based on their wage return to endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Then, I calculate the average wage return to ability in each bin, using the number of individuals in each bin as weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The solid lines denote predicted values from linear regressions estimated on the plotted points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 43 Figure 9: Change in a question’s position and change in predictive validity Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Test score (leave-question-out) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 Average change in predictive validity 0 1 2 3 4 5 6 7 8 9 Change in question position Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' College enrollment 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 Average change in predictive validity 0 1 2 3 4 5 6 7 8 9 Change in question position Panel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' College quality 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='80 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 Average change in predictive validity 0 1 2 3 4 5 6 7 8 9 Change in question position Panel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Hourly wage 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 Average change in predictive validity 0 1 2 3 4 5 6 7 8 9 Change in question position Panel E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Monthly earnings 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 Average change in predictive validity 0 1 2 3 4 5 6 7 8 9 Change in question position Panel F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Firm mean wage (leave-one-out) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 Average change in predictive validity 0 1 2 3 4 5 6 7 8 9 Change in question position Notes: This figure displays estimates of the effect of an increase in the order of a given question on the question’s predictive validity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each panel shows a binned scatterplot plotting the average change in the predictive validity of a test question on a given outcome (y-axis) against the change in the position of the question on the exam (x-axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each panel shows the results for the outcome listed in the panel title.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' See Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 for variable definitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The red dashed lines are predicted values from a linear regression on the microdata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' See Appendix Figure A3, Panel B for a histogram of the values in the x-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 44 Table 1: Summary statistics of the samples High-school-students sample Retakers sample All 2009-2010 All (1) (2) (3) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Demographic characteristics and race Age 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='204 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='151 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='062 Female 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='598 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='611 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='618 White 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='476 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='510 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='504 Black/Brown 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='505 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='450 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='483 Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' SES and household characteristics Attends a private HS 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='222 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='222 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='342 Mom completed high school 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='534 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='506 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='606 Mom completed college 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='205 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='186 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='270 Family earns above 2x M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='388 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='379 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='432 Family earns above 5x M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='062 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='071 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='087 Panel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Exam preparation Took a foreign lang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' course 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='241 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='269 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='263 Took a test prep course 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='119 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='167 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='160 Panel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Fraction of correct responses Natural Science 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='283 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='333 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='317 Social Science 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='398 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='388 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='446 Language 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='408 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='449 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='468 Math 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='283 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='287 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='320 Average 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='343 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='364 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='388 Panel E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Geographical location Lives in the North 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='089 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='081 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='082 Lives in the Northeast 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='305 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='261 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='354 Lives in the Southeast 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='389 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='426 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='365 Lives in the South 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='131 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='150 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='113 Lives in the Midwest 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='086 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='081 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='085 Number of test-takers 14,941,156 1,910,502 1,519,842 Notes: This table shows summary statistics on all test-takers in the high-school-students sample (column 1), those who took the exam in 2009–2010 as high-school seniors (column 2), and students in the retakers sample (column 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For students who took the exam multiple times, I compute the summary statistics using data from the last year in which I observe them in my sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' See Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 for sample definitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 45 Table 2: The effect of question position on test performance Outcome: Correctly responded the question (1) (2) (3) Question position (normalized) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='214∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='071∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='058∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='013) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Constant 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='450∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='008) N (Item−Booklets) 5,896 5,896 5,896 N (Students) 14,940,464 14,940,464 14,940,464 N (Question responses) 2,689,345,707 2,689,345,707 2,689,345,707 R−squared 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='85 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='99 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='97 Question fixed effects No Yes No Controls for question difficulty No No Yes Notes: This table displays estimates of the effect of a question position on the likelihood of correctly answering the question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each column displays an estimate from a different specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Column 1 presents estimates from a bivariate regression of average student performance on question position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Column 2 presents estimates from equation (5), which includes question fixed effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Column 3 presents estimates from equation (6), which controls for question difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I normalize question position such that the first question in each testing day is equal to zero and the last question is equal to one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heteroskedasticity-robust standard errors clustered at the question level in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' ∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 46 Table 3: The effect of academic ability and cognitive endurance on long-run outcomes Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' College outcomes Dependent variable Enrolled College Degree 1st-year Grad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Time to college quality quality credits rate grad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (1) (2) (3) (4) (5) (6) Test score 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='088∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='082∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='117∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='014∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='060∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='119∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='032∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='051∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='026∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='048∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='102∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='095∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='140∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='072∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='140∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Ratio coef.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='310∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='319∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='365∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='358∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='361∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='342∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='005) Mean DV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='244 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='326 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='244 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='158 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='418 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='817 N 2,501,519 1,800,546 1,768,707 1,124,972 1,472,916 793,822 Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Labor-market outcomes Dependent variable Formal Hourly Monthly Firm Occup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Industry sector wage earnings wage wage wage (1) (2) (3) (4) (5) (6) Test score 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='129∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='111∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='092∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='041∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='013∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='054∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='052∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='036∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='017∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='154∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='135∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='108∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='049∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='014∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Ratio coef.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='276∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='351∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='387∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='330∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='346∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='255∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='015) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='010) Mean DV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='326 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='865 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='551 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='885 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='886 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='858 N 2,523,029 818,590 818,590 692,880 818,374 818,590 Notes: This table displays estimates of the relationship between ability/endurance and college outcomes (Panel A) and labor market-outcomes (Panel B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The first row of each panel shows estimates of the association between test scores and the outcome listed in the column header (coefficient ψT in equation (9)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The following rows show estimates of the asso- ciation between ability and cognitive endurance and a given outcome (coefficients ψA and ψE in equation (10)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' All regressions control for age, gender, race, high school type, parental income, cohort fixed effects, and municipality fixed effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In addition to the baseline controls, the regressions in Panel A, columns 4–6, include college-degree fixed effects to remove the influence of a student’s program choice, while the regres- sions in Panel B control for potential years of experience and years of education.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heteroskedasticity-robust standard errors clustered at the individual level in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' See Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 for outcome definitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The third-to-last row in each panel shows the ratio between the predicted effect of academic ability and the effect of cognitive endurance on a given outcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Standard errors estimated through the delta method in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' ∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 47 Table 4: Degrees, occupations, and industries with the largest return to endurance Return Return Ratio Wage Sample ability endur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' returns pctil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' size (1) (2) (3) (4) (5) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Top five degrees 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Aeronautics and related degrees 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='173 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='106 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='613 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='7 670 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='026) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='015) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='077) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Music and performing arts 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='221 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='093 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='420 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 502 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='060) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='035) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='110) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Religion 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='186 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='088 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='471 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 356 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='047) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='031) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='097) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' History and archeology 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='211 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='087 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='414 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 988 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='043) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='022) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='064) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Forestry engineering 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='154 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='084 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='543 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 397 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='045) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='024) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='115) Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Top five occupations 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Public tax auditors 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='454 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='168 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='369 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 255 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='106) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='057) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='084) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Professionals in air 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='278 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='114 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='412 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 347 navigation, sea and fluvial (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='049) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='028) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='072) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Technicians in operation of radio, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='200 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='112 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='558 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 658 TV systems and video producers (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='047) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='027) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='091) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Plant operators in chemical, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='267 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='109 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='409 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8 1,221 petrochemical and related occup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='031) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='020) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='057) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Instrument and precision 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='180 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='092 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='511 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8 203 equipment repairers (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='068) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='040) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='194) Panel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Top five industries 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Oil extraction and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='276 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='135 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='488 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5 948 related services (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='034) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='021) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='052) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Financial intermediation and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='215 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='087 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='402 54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='7 6,177 and insurance (aux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' services) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='013) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='007) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='024) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Research and development 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='198 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='084 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='426 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='7 1,323 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='024) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='015) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='052) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Electricity, gas and hot water 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='223 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='083 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='373 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 1,966 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='020) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='011) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='036) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Manufacture of office machinery 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='132 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='073 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='553 54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='7 920 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='033) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='019) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='095) Notes: This table lists the top five 3-digit academic degrees (Panel A), 3-digit occupations (Panel B), and 2-digit industries (Panel C) with the highest wage return to cognitive endurance (column 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Column 1 shows the wage return to ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Column 3 shows the ratio between the wage return to endurance and the wage return to ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Column 4 shows the average wage percentile of workers in each degree, occupation, or industry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Column 5 shows the sample size used to estimate each wage return.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The wage return to ability and endurance are the coefficients ψA and ψE in equation (10) using as outcome log hourly wage, estimated separately for each degree, occupation, and industry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heteroskedasticity-robust standard errors clustered at the individual level in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 48 Table 5: The contribution of gaps in ability and endurance to test-score gaps Gap between Male / White / Priv HS / Mom coll / High-inc / Female Non-white Public HS No coll Low-inc (1) (2) (3) (4) (5) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Difference in average test score Test-score gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='026∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='057∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='130∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='098∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='192∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Contribution of gaps in ability and endurance to test-score gaps Ability gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='056∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='127∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='095∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='188∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Endurance gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='017∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='038∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='026∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='063∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Impact of a reform that halves the exam length on test-score gaps P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' change gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='008∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='008∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='019∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='013∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='031∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Pct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' change gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='322∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='137∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='144∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='130∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='163∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) N (Students) 14,941,097 14,565,550 9,924,652 14,290,759 9,996,959 Notes: This table shows test-score gaps in the ENEM and the contribution of differences in ability and endurance to those gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each column shows the result for a different test-score gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Column 1 shows gaps between male and female students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Column 2 shows gaps between white and non-white (Black, Brown, and Indigenous) students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Column 3 shows gaps between students enrolled in a private high school and public high school.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Column 4 shows gaps between students with a college-educated mother and non-college-educated mother.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Column 5 shows gaps between students in households in the top 30% and bottom 30% of the income distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Panel A shows the average test score difference between the two groups displayed in the column header, E[TestScorei|Xi = 1] − E[TestScorei|Xi = 0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Panel B shows the contribution of differences in ability and differences in endurance to the test- score gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The ability gap is the average difference in ability, controlling for endurance, E[ˆαi|Xi = 1, ˆβi] − E[ˆαi|Xi = 0, ˆβi].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The endurance gap is the average difference in endurance, controlling for ability and scaled by the average question position, � E[ˆβi|Xi = 1, ˆαi] − E[ˆβi|Xi = 0, ˆαi] � × Position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Panel C shows estimates of the impact of a reform that changes the length of the exam from Position to Position/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The first row shows the percentage point change in the test-score gap due to the reform, which is equal to − � E[ˆβi|Xi = 1, ˆαi] − E[ˆβi|Xi = 0, ˆαi] � × Position/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The second row shows the percentage change in the test-score gap, which equals the percentage point change in the gap divided by the pre-reform test-score gap (shown in Panel A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Standard errors estimated through the delta method in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' ∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 49 Table 6: The effect of an exam reform that halves the exam length on its predictive validity Outcome: Predictive validity of question j for Test College College Degree Grad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Hourly Monthly Firm score enrol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' quality progress rate wage earnings wage (1) (2) (3) (4) (5) (6) (7) (8) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Average predictive validity Constant 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='285∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='057∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='109∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='106∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='101∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='084∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='007) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Effect of the exam reform Change in Pred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Val.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='115∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='055∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='099∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='005∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='084∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='077∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='072∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='069) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='018) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='032) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='013) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='034) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='032) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030) Chg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Val.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='/Mean 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='404∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='952∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='911∗∗∗ −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='500∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='201 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='796∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='757∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='855∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='110) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='191) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='144) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='494) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='662) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='193) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='194) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='239) N (Item−Booklets) 1,416 1,416 1,416 700 1,416 1,416 1,416 1,416 Notes: This table displays the estimated effect of an exam reform that changes the exam length from Position to Position/2 on the predictive validity of the exam questions for long-run outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each column displays the estimates of equation (17) for a different outcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel A, the regression only includes a constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel B, the regression includes question fixed effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I the coefficients so that they can be interpreted as the effect of decreasing the exam length by half.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' See Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 for outcome definitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heteroskedasticity-robust standard errors clustered at the question level in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' ∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 50 References Abraham, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' and Mallatt, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (2022).' 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+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Comparing and validating measures of non-cognitive traits: Performance task measures and self-reports from a nationally representative internet panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Journal of Behavioral and Experimental Eco- nomics, 72:51–60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Zamarro, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', Hitt, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', and Mendez, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' When Students Don’t Care: Reexamining International Differences in Achievement and Student Effort.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Journal of Human Capital, 13(4):519–552.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Publisher: The University of Chicago Press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 57 Appendix A Appendix Figures and Tables Figure A1: Examples of “focus support” products in a local CVS Notes: These pictures show examples of over-the-counter products aimed at enhancing focus and cognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The pictures were taken at a local pharmacy by the author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 58 /36 2 Your brain does so ARD much.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Help treat Rritual roomadaptogen enhanced elixir it right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' reishi relax with ashwagandha cucao atress+sleepaupport prebiotic superloods bne peppeou By adding some brain supporting nutrients,you may support overall cognitive skills,including .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='Memory 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='29 UPAY Focus 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='99 Concentrationmemory 17 brain support vitamins &focus man eckout liquid workout MAXFocus CLINICALLYTI Support your FORMUL Brain & Vision concentration levels FOCUSFOCU to help get stuff done.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Extra Strength fact factor Gummies FOCUS FOCUS Nutrition for the Nutrition for the factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' factor .' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='emory,Concen appliednutrition andFocus WNatureWell FORCE MENTAL FOCUS COCONUT FACTOR MCT+ HEALTHY BRAIN COCOA FOREBRAIN Dietary Supplement Powder ALL-DAY FOCUS 745mg of Coconut MCT 1220mg of Cocoa Powder per serving Kalsuplemenit POTEnT NOOTROPIC FORMULa HELPS supports enhanced mental focus4 Have You Nourished Powerful 3-in-1 Brain Booster improves energy Your Brain ody?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=" Plus Turmeric Extract IMPROVE MEMORY : natural cocoa flavor BOOST COGNiTIVE PERFORMAnCE' BRAIN BOOST 1: ENHANCE SHARPNESS G CLARITY Attention&Concentration BRAINBOOST2: Memory&Mental Clarity BRAINBOOST3: Calm&Focus CONTAINS 10 INDIVIDUALPACKETS INDIVIDUALNETWT023OZ16." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='a focus support products STRGTH 60CT FF FOREBRAIN15CT 30CT NATUREWELL COCONUT EACH NATUREWELL COCONUT 353031YOU PAY 03304567083YOUPAY 03303595594YOU 57594 546416YOUPAY 01403 0965 $15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' $29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='99 $23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='99 A03 $17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='99 A03 $16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='79 A03 A03 08/28/21 08/28/21 08/28/21 08/28/21 13 10/23-11/20 A03353031 300Figure A2: Fraction of students who graduate from college by years since enrollment 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 Fraction of enrollees who graduated 0 1 2 3 4 5 6 7 8 9 Years since enrolling in college Notes: This figure shows the empirical cumulative distribution function of the graduation rate of individuals in the high-school-students sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 59 Figure A3: Histogram of the change in a question’s position across exam booklets Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=" All years (2009–2016) 0 5 10 15 Percent of questions 0 10 20 30 40 Change in a question's position between two different booklets Panel B." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=" First two cohorts (2009–2010) 0 10 20 30 40 50 Percent of questions 0 5 10 15 Change in a question's position between two different booklets Notes: This figure shows the amount of variation available in a given question’s position between different exam booklets." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To construct this figure, I first calculate the difference (in absolute value) in a question’s position in two exam booklets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This difference ranges from zero (if a question is in the same position in two different booklets) to 44 (if a question is in the first position of a section in one booklet and the last position of a section in another booklet).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I repeat this process for each question and each possible booklet pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The figure plots the resulting histogram of position differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 60 Figure A4: Average student performance on selected questions by question position Random chance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='80 Fraction of students who answered correctly 1 10 20 30 40 50 60 70 80 90 Position of the question in the exam Slope x10: -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='014 Slope x10: -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='028 Slope x10: -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='020 Slope x10: -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='020 Slope x10: -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='020 Slope x10: -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='023 Slope x10: -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='062 Notes: This figure plots the fraction of correct responses on seven selected exam questions as a function of their position on the four different exam booklets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Solid lines denote predicted values from linear regressions estimated on the plotted points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 61 Figure A5: Histogram of question-level position effects Share negative = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='69 Share positive = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='31 Mean = -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='074 pp 0 2 4 6 8 Percent of questions 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 Effect of a one position increase on item performance (in pp) Notes: This figure plots the distribution of item-level position effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To construct this figure, I estimate the impact of an increase in the position of a given question on student performance separately for each question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The figure displays the distribution of estimated β’s (one for each item).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The figure excludes outliers (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', questions for which the effect is below -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 or above 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 percentage points).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 62 Figure A6: Distribution of academic ability and cognitive endurance Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Academic ability (αi) 0 1 2 3 Percent of students 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 Academic ability (αi) Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Cognitive endurance (βi) Share negative = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='65 Share positive = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='35 Mean β = -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='058 0 1 2 3 Percent of students 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 Cognitive endurance (βi) Notes: This figure shows the distribution of my estimates of academic ability (Panel A) and cognitive endurance (Panel B) among individuals in the high-school-students sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The measure of an individual’s ability is the estimated intercept (αi) in equation (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The measure of an individual’s cognitive endurance is the estimated slope (βi) in equation (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 63 Figure A7: The relationship between a question’s predictive validity and its position Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Test score (leave-question-out) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='40 Predictive validity for average score 1 30 60 90 Position of the question in the exam Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' College enrollment 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 Predictive validity for college enrollment 1 30 60 90 Position of the question in the exam Panel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' College quality 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 Predictive validity for college quality 1 30 60 90 Position of the question in the exam Panel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Hourly wage 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='15 Predictive validity for log hourly wage 1 30 60 90 Position of the question in the exam Panel E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Monthly earnings 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='15 Predictive validity for monthly earnings 1 30 60 90 Position of the question in the exam Panel F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Firm leave-one-out mean wage 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='12 Predictive validity for log firm hourly wage 1 30 60 90 Position of the question in the exam Notes: This figure shows the relationship between (i) the predictive validity of an exam question for a given outcome and (ii) the position of the question on the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The y-axis plots the correlation between correctly responding to the question in position j and a given outcome Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The x-axis show the position of the question on the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each plot shows the results for the outcome listed in the panel title.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' See Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 for outcome definitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The red dashed lines are predicted values from a linear regression on the plotted points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 64 Table A1: Summary statistics of the high-school-student sample by booklet color Day 1 booklet color All Yellow Blue Pink White (1) (2) (3) (4) (5) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Demographic characteristics and race Age 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='204 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='201 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='210 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='209 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='196 Female 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='598 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='595 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='600 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='595 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='599 White 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='476 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='478 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='476 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='476 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='474 Black/Brown 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='505 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='503 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='505 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='505 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='507 Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Household characteristics Attends a private HS 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='222 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='225 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='220 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='223 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='220 Mom completed high school 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='534 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='538 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='532 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='535 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='531 Mom completed college 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='205 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='208 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='203 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='207 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='203 Family earns above 2x M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='388 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='392 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='386 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='390 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='385 Family earns above 5x M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='062 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='064 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='061 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='063 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='061 Panel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Exam preparation Took a foreign lang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' course 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='241 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='241 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='241 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='240 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='241 Took a test prep course 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='119 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='121 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='119 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='119 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='118 Panel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Fraction of correct responses Natural Science 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='283 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='284 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='283 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='283 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='283 Social Science 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='398 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='398 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='398 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='398 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='398 Language 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='408 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='410 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='408 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='408 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='407 Math 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='283 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='284 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='283 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='283 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='282 Average 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='343 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='344 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='343 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='343 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='343 Panel E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Geographical location Lives in the North 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='089 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='089 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='089 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='090 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='089 Lives in the Northeast 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='305 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='305 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='303 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='306 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='305 Lives in the Southeast 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='389 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='388 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='390 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='388 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='389 Lives in the South 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='131 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='131 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='132 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='130 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='131 Lives in the Midwest 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='086 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='086 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='086 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='086 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='086 F-statistic – 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='875 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='051 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='857 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='887 p-value F-statistic – 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='599 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='452 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='614 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='588 Number of test-takers 14,941,156 3,655,807 3,903,653 3,590,977 3,790,719 Notes: This table shows summary statistics on all test-takers in the high-school-students sample (column 1) and based on the booklet color they received on the first day of testing (columns 2–5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The last panel reports the F-statistics and p-values from F-tests that the coefficients on all pre-determined covariates (Panels A, B, C, and E) are jointly equal across booklet colors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 65 Table A2: Examples of reliability estimates in economics and psychology Construct Reliability estimate Reference (1) (2) (3) IQ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='80 Schuerger and Witt (1989) Risk aversion 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='40 Mata et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (2018) Big 5 personality traits 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='60–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='73 Wooden (2012) Present bias 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='36 Meier and Sprenger (2015) Loss aversion 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='88 Stango and Zinman (2020) Teacher value added 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='23–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='47 Chetty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (2014a) Life satisfaction 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='67 Anusic and Schimmack (2016) Self-esteem 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='71 Anusic and Schimmack (2016) Academic ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='61–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='77 This paper Cognitive endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='14–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='30 This paper Notes: This table displays examples of reliability estimates from the economics and psychology litera- ture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The last two rows show the test-retest reliability of the measures of academic ability and cognitive endurance estimated in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 66 Table A3: IV estimates of the relationship between ability/endurance and college outcomes Dependent variable Enrolled College Degree 1st-year Grad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Time to college quality quality credits on time grad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (1) (2) (3) (4) (5) (6) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' OLS estimates on retakers sample Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='048∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='057∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='110∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='010∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='026∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='082∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='110∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='129∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='217∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='018∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='049∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='154∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='009) Ratio coef.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='441∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='443∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='509∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='571∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='543∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='533∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='011) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='007) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='008) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='037) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='032) Mean DV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='367 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='420 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='390 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='146 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='808 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='191 N 132,634 111,409 109,390 339,727 51,066 51,066 Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' IV estimates on retakers sample Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='046∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='067∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='141∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='041∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='120∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='007) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='010) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='028) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='107∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='140∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='239∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='022∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='057∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='169∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='005) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='013) Ratio coef.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='430∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='479∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='590∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='738∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='722∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='711∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='053) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='025) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='028) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='026) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='156) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='145) Mean DV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='367 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='420 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='390 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='146 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='808 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='191 N 132,614 111,394 109,375 339,725 51,056 51,056 Notes: This table displays OLS and IV estimates of the relationship between ability/endurance and college outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The OLS estimates are analogous to Table 3 but estimated on the sample of retakers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' See notes to Table 3 for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The IV estimates instrument the year t measure of ability and cognitive endurance with the t − 1 measures of these skills.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heteroskedasticity-robust standard errors clustered at the individual level in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' ∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 67 Table A4: IV estimates of the relationship between ability/endurance and labor-market outcomes Dependent variable Formal Hourly Monthly Firm Occup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Industry sector wage earnings wage wage wage (1) (2) (3) (4) (5) (6) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' OLS estimates on retakers sample Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='121∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='124∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='081∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='008∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='005) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='005) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='005) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='231∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='201∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='163∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='057∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='018∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='005) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Ratio coef.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='518∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='525∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='615∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='496∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='518∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='413∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='072) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='018) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='020) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='024) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='040) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='057) Mean DV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='286 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='049 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='702 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='014 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='992 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='875 N 133,904 37,814 37,814 32,908 37,798 37,814 Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' IV estimates on retakers sample Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='188∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='232∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='120∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='052∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='018) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='017) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='015) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='009) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='250∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='215∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='180∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='061∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='018∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='008) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='007) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='007) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Ratio coef.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='171∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='753∗∗∗ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='077∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='670∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='845∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='050 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='323) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='069) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='079) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='081) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='150) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='241) Mean DV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='286 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='049 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='702 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='014 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='992 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='875 N 133,884 37,801 37,801 32,902 37,785 37,801 Notes: This table displays OLS and IV estimates of the relationship between ability/endurance and labor- market outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The OLS estimates are analogous to Table 3 but estimated on the sample of retakers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' See notes to Table 3 for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The IV estimates instrument the year t measure of ability and cognitive endurance with the t − 1 measures of these skills.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heteroskedasticity-robust standard errors clustered at the individual level in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' ∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 68 Table A5: Robustness of baseline test-score-gaps decomposition to measuring variables in percentiles Gap between Male / White / Priv HS / Mom coll / High-inc / Female Non-white Public HS No coll Low-inc (1) (2) (3) (4) (5) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Difference in average test-score percentile Score pctil gap 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='871∗∗∗ 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='127∗∗∗ 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='826∗∗∗ 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='609∗∗∗ 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='838∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='015) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='015) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='019) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='018) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='023) Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Contribution of gaps in ability and endurance percentiles to test-score gaps Ability pctil gap 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='599∗∗∗ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='618∗∗∗ 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='952∗∗∗ 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='728∗∗∗ 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='775∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='012) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='011) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='017) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='015) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='024) Endurance pctil gap 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='205∗∗∗ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='097∗∗∗ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='628∗∗∗ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='596∗∗∗ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='381∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='010) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='008) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='015) Panel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Impact of a reform that halves the exam length on test-score percentile gaps Pctil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' change gap 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='603∗∗∗ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='548∗∗∗ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='314∗∗∗ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='298∗∗∗ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='190∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='005) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='008) Pct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' change gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='546∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='219∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='238∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='213∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='261∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) N (Students) 14,941,097 14,565,550 9,924,652 14,290,759 9,996,959 Notes: This table is analogous to Table 5, but the variables and effects are measured in percentiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I construct the percentiles separately for each cohort.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' See notes to Table 5 for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 69 Table A6: Robustness of baseline test-score-gaps decomposition to alternative ways of measuring ability and endurance Gap between Male / White / Priv HS / Mom coll / High-inc / Female Non-white Public HS No coll Low-inc (1) (2) (3) (4) (5) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating ability/endurance separately by day and using the average Ability gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='056∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='127∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='095∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='188∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Endurance gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='034∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='032∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='075∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='051∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='126∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating ability/endurance separately by subject and using the average Ability gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='027∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='061∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='140∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='104∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='206∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Endurance gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='042∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='099∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='069∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='163∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Including day fixed effects Ability gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='056∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='128∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='096∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='189∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Endurance gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='034∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='031∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='075∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='051∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='125∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Including subject fixed effects Ability gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='026∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='061∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='141∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='104∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='207∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Endurance gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='039∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='095∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='066∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='158∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Using linear correlation as an alternative measure of endurance Ability gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='057∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='129∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='097∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='191∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Endurance gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='021∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='020∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='047∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='032∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='079∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) N (Students) 14,941,097 14,565,550 9,924,652 14,290,759 9,996,959 Notes: This table shows estimates of the contribution of gaps in ability and endurance to test-score gaps using alternative specifications to estimate ability and endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each column shows the result for a different test-score gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each panel shows the result from estimating ability and endurance with a different specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panels A–B, I estimate a student’s ability/endurance separately for each testing day (Panel A) and academic subject (Panel B) and then average the estimates across days or subjects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panels C–D, I estimate endurance in a regression that controls for day fixed effects (Panel C) or subject fixed effects (Panel D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Finally, in Panel E, I use the correlation between question position and a dummy for correctly answering a question as an alternative measure of endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heteroskedasticity-robust standard errors clustered at the question level in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' ∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 70 Table A7: Robustness of baseline test-score-gaps decomposition to alternative ways of controlling for question difficulty when estimating ability/endurance Gap between Male / White / Priv HS / Mom coll / High-inc / Female Non-white Public HS No coll Low-inc (1) (2) (3) (4) (5) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Not controlling for question difficulty Ability gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='032∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='049∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='118∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='087∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='175∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Endurance gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='033∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='026∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='074∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='050∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='128∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating difficulty without adjusting for average position Ability gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='028∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='057∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='130∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='097∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='191∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Endurance gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='034∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='036∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='080∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='055∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='131∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating difficulty using question-specific position effects Ability gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='032∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='055∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='126∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='095∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='186∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Endurance gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='036∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='031∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='082∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='058∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='135∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating difficulty using shrunk question-specific position effects Ability gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='031∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='056∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='127∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='095∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='187∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Endurance gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='036∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='032∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='080∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='057∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='131∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating position effects separately by fraction of correct responses Ability gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='056∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='128∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='096∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='189∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Endurance gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='035∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='032∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='078∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='053∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='130∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating position effects separately by subject Ability gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='029∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='057∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='128∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='096∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='190∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Endurance gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='034∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='034∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='077∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='053∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='128∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) N (Students) 14,941,097 14,565,550 9,924,652 14,290,759 9,996,959 Notes: This table shows estimates of the contribution of gaps in ability and endurance to test-score gaps using alternative measures of difficulty in the specification used to estimate ability and endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each column shows the result for a different test-score gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each panel shows the result from a different way of controlling for question difficulty in equation (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel A, I compute the estimate equation (7) without controlling for question difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel B, I measure question difficulty as the fraction of students who incorrectly answer to the question across all booklets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panels C–F, I adjust for average question position by estimating the positon effects with alternative specifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In column C, I compute question-specific position effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel D, I compute a shrinkage estimator of the position effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel E, I compute the position effects separately for questions with a below/above fraction of correct responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel F, I compute the position effects separately by subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' See Appendix D for details on each measure of question difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heteroskedasticity-robust standard errors clustered at the question level in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' ∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 71 Table A8: Robustness of baseline test-score-gaps decomposition to alternative sample restrictions Gap between Male / White / Priv HS / Mom coll / High-inc / Female Non-white Public HS No coll Low-inc (1) (2) (3) (4) (5) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Excluding students in the bottom or top 10% of the ability distribution Ability gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='018∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='036∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='076∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='055∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='116∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Endurance gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='032∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='031∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='067∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='045∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='107∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Excluding students in the bottom or top 10% of the endurance distribution Ability gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='027∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='054∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='125∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='094∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='190∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Endurance gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='017∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='017∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='041∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='028∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='078∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Excluding students in the bottom or top 10% of either distribution Ability gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='036∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='073∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='053∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='113∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Endurance gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='017∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='018∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='037∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='025∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='062∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Excluding students in the bottom or top 20% of either distribution Ability gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='009∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='023∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='042∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='066∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Endurance gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='009∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='011∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='019∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='013∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='032∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Excluding individuals with positive estimated endurance Ability gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='021∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='050∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='112∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='084∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='165∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Endurance gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='013∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='017∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='037∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='025∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='063∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Notes: This table shows estimates of the contribution of gaps in ability and endurance to test-score gaps using alternative sample restrictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each column shows the result for a different test-score gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each panel shows the result for a different sample of students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel A, I exclude students in the bottom and top deciles of the ability distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel B, I exclude students in the bottom and top deciles of the endurance distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel C, I exclude students in the bottom and top deciles of the distribution of either skill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel D, I exclude students in the bottom and top quintiles of the distribution of either skill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel E, I exclude students with positive estimated endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I construct the deciles and quintiles using all the students in the high-school-students sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heteroskedasticity-robust standard errors clustered at the question level in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' ∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 72 Table A9: Robustness of baseline test-score-gaps decomposition to accounting for measurement error Gap between Male / White / Priv HS / Mom coll / High-inc / Female Non-white Public HS No coll Low-inc (1) (2) (3) (4) (5) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Weighting each observation by its precision Ability gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='056∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='127∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='095∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='188∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Endurance gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='034∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='031∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='075∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='051∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='126∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Shrunk estimator of ability and endurance Ability gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='021∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='040∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='091∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='067∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='136∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Endurance gap 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='009∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='010∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='023∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='040∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) N (Students) 14,941,097 14,565,550 9,924,652 14,290,759 9,996,959 Notes: This table shows estimates of the contribution of gaps in ability and endurance to test-score gaps accounting for measurement error in the estimates of ability and endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each column shows the result for a different test-score gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel A, I weight each observation by the inverse of the standard error of the ability and endurance estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Specifically, the weight of each observation is w = 1/(SE2 ˆαi + SE2 ˆβi), where SEˆαi and SE2 ˆβi are the standard errors of ˆαi and ˆβi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel B, I estimate the baseline regression using a shrunk estimator of ability and endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I compute the shrunk estimator of endurance as βs i = ωi ˆβi + (1 − ωj)¯β, where ¯β is the average cognitive endurance in my sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The individual-specific weight is ωi = Var[βi]−E[SE2 ˆ βi] Var[βi]−E[SE2 ˆ βi]+SE2 ˆ βi .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The shrunk estimator, βs i , puts more weight on estimates of βi that are more precisely estimated, as measured by a low standard error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I compute the shrunk estimator of ability analgously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heteroskedasticity-robust standard errors clustered at the question level in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' ∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 73 B Empirical Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 Limited Cognitive Endurance and Time Pressure Is the causal effect of an increase in the order of a given question on student performance a manifestation of limited cognitive endurance or is it driven by students running out of time?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Two pieces of evidence suggest that time pressure does not explain the estimated β < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' First, very few students leave responses unanswered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Appendix Figure B1 plots the fraction of students who left a question unanswered (possibly, because they ran out of time) against the question position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Questions that appear later in the test are more likely to be left unanswered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' However, only a small fraction of students leave any questions unanswered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thus, missing responses cannot account for the large change in performance observed throughout the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='32 Figure B1: Fraction of question left unanswered throughout the ENEM Day 1 of the exam Day 2 of the exam (Correlation = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='84) (Correlation = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='74) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004 Fraction of students who did not answer question 1 30 60 90 120 150 180 Position of the question in the exam Notes: This figure shows the fraction of questions left unanswered over the course of each testing day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The y-axis displays the fraction of students who did not select any of the multiple-choice answers to a given question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The x-axis displays the position of each question in the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The dashed lines are predicted values from a linear regression estimated separately for each testing day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Second, student performance declines even in questions that students answer when they 32There is no penalty for incorrectly answering a question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Therefore, this evidence is only suggestive since leaving a question unanswered is a weakly dominated strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 74 are likely not time-pressured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Appendix Table E1 estimates the fatigue effect separately for questions that appear in the first half (column 1) and the second half of each testing day (column 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Presumably, students should have plenty of time to answer the first half of the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Yet, I still find fatigue effects that are quantitatively similar—or even larger—to those estimated on the second half of each day or with all questions (see also Appendix Figure B2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This result is consistent with visual evidence in Figure 2, which shows that student performance tends to decline shortly after the exam starts and with the declines in performance exhibited by the example questions that appear at the beginning of the exam in Appendix Figure A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In summary, the evidence indicates that the effect of a question position on student performance is not driven by students running out of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Figure B2: The heterogeneous effect of fatigue on performance by question position Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' First half of each testing day Intercept: -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='02 pp Slope: -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='11 pp Slope x 90: -9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='58 pp Percent change: -27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='8% 7 6 5 4 3 2 1 0 1 Average pp change in prob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' of correct answer 0 5 10 15 20 25 30 35 ≥40 Change in question position Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Second half of each testing day Intercept: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='04 pp Slope: -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='06 pp Slope x 90: -5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='33 pp Percent change: -15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5% 6 5 4 3 2 1 0 1 7 Average pp change in prob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' of correct answer 0 5 10 15 20 25 30 35 ≥40 Change in question position Notes: This figure shows heterogeneity in the effect of limited endurance on performance by question position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Panels A and B are analogous to Figure 3, but the effect is estimated separately for questions that appear on the first half of each testing day (Panel A) or the second half of each testing day (Panel B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The y-axis shows the average change (in percentage points) in the fraction of students correctly responding to a question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The x-axis plots the difference in the question position between each possible booklet pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The dashed line denotes predicted values from a linear regression estimated on the plotted points, using the number of questions used to estimate each point as weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 75 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 OLS Formulas of Academic Ability and Cognitive Endurance My measure of cognitive endurance is βi in equation (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Ignoring controls for question difficulty, the OLS estimator of βi is ˆβi = � j(Posij − Pos)(Cij − ¯Ci) � j(Posij − Pos)2 = � j wj ���� Weight of question j × (Cij − ¯Ci), � �� � Performance on question j relative to i’s average performance (B1) where ¯Ci is the fraction of questions correctly answered by student i, Pos is the average question position (which is constant across test-takers), and wj ≡ Posj−Pos � j(Posj−Pos)2 is the weight of question j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Equation (B1) shows that ˆβi is a weighted average of deviations from i’s average score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The weight of each question depends on the location of the question on the test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Appendix Figure B3 plots the weight OLS places on each question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The questions with the largest weights (in absolute value) are the ones at the beginning and the end of the test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Figure B3: Weight of each question in a test with 90 questions .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0005 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0005 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001 wq 1 10 20 30 40 50 60 70 80 90 Position of the question Notes: This figure displays the weight put by the ordinary least squares (OLS) estimator of βi (equation (7)) on each question of the test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 76 My measure of academic ability is αi in equation (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The OLS estimator of αi is ˆαi = ¯Ci − ˆβiPos (B2) Equation (B2) shows that αi can be estimated by the difference between i’s test score ( ¯Ci) and the part of her test score that is explained by limited endurance, ˆβiPos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 Estimating the Standard Deviation of Ability and Endurance The estimate of cognitive endurance, ˆβi, can be decomposed into latent cognitive en- durance, βi, and a sampling error ei independent of βi and with variance σ2 e: ˆβi = βi + ei (B3) Calculating the variance on each side of equation (B3) yields: σ2 ˆβ = σ2 β + σ2 e, (B4) where σ2 ˆβ and σ2 β are the variances of ˆβ and β, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Equation (B4) shows that the raw standard deviation of ˆβ overstates the variability of β since it includes variability in the sampling error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Let SEˆβ be the standard error of ˆβ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The variance of the sampling error can be estimated as σ2 e = E[SE2 ˆβ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thus, an estimate of the variance of β is given by ˆσ2 β = σ2 ˆβ − E[SE2 ˆβ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (B5) I use an analogous derivation to estimate the variance of latent ability, σ2 α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 Estimating the Predictive Validity of a Question Let πj be the fraction of students who correctly responded to question j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Note that the standard deviation of Cij is σCij = � πj(1 − πj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The predictive ability of question j for 77 outcome Y is given by ρY j ≡ Corr(Yi, Cij) = Cov(Yi, Cij) σY σCij = � E[Yi|Cij = 1] − E[Yi|Cij = 0] � πj(1 − πj) σY σCij = � E[Yi|Cij = 1] − E[Yi|Cij = 0] �σCij σY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (B6) Equation (B6) shows that the predictive validity of a question partly depends on the difference between the average outcome of students who correctly responded to the ques- tion and the average outcome of students who did not, E[Yi|Cij = 1] − E[Yi|Cij = 0].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The predictive validity also depends on the variability of correct responses relative to variabil- ity in the outcome, σCij/σY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thus, holding the rest of the variables constant, the more dispersion there is in the distribution of correct responses, the more predictive the question will be for future outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='33 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5 Non-parametric Estimates I assess nonparametrically the predicted effects of endurance on long-run outcomes by estimating how a movement from the bottom decile to the top decile in the endurance distribution affects a given outcome: E[Yi|i ∈ Top decile Endurance] − E[Yi|i ∈ Bottom decile Endurance].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (B7) As a benchmark, I compare the size of a decile movement in the endurance distribution to an equivalent decile movement in the ability distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I compute these effects in a regression framework by estimating equations of the form: Yi = φ + λXi + 10 � d=2 1{i ∈ TestScore decile d} + ζi (B8) Yi = ˜φ1 + ˜λ1Xi + 10 � d=2 1{i ∈ Ability decile d} + 10 � d=2 1{i ∈ Endurance decile d} + ˜ζi, (B9) where the omitted category is the bottom decile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 33For example, for a question with two possible responses, the variance is maximized when πj = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50, that is, when half students correctly answer the question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 78 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 Robustness of the Relationship between Endurance and Long-Run Out- comes Appendix Table B1 shows non-parametric estimates of the effect of ability and endurance on each outcome based on the slope of percentile changes on outcomes (Heckman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Specifically, I estimate how a movement from the bottom decile to the top decile in the endurance distribution affects a given outcome (see Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5 for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The first row of each panel shows that moving higher in the distribution of test scores tends to improve college and labor-market outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Subsequent rows show that both cognitive endurance and ability contribute to this effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Depending on the outcome, the predicted effect of a movement from decile 1 to decile 10 in the endurance distribution represents 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6%–53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0% of the corresponding effect of a movement in the ability distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Appendix Tables B2–B3 show that the results are robust to estimating ability and en- durance with alternative specifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' First, I compute the estimates of ability/endurance separately for each testing day and for each academic subject, and use the average estimate across days/subjects as regressors in equation (10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Second, I compute the estimates of endurance controlling for day fixed effects and subject fixed effects;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' thus accounting for possible differences in preparation across subjects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Finally, I use the correlation between question position and a dummy for correctly answering a question as an alternative mea- sure of endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Across specifications, I find effects that are quantitatively similar and qualitatively identical to those of the baseline specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Appendix Tables B4–B5 show that the results are robust to controlling for question difficulty in alternative ways when estimating ability and endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' First, I compute the estimates of ability and endurance in equation (7) without controlling for question difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Second, I calculate question difficulty without adjusting for the average position of the question across booklets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Finally, I compute question difficulty adjusting for average question position in several alternative ways (see Appendix D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Consistent with the baseline results, I find that the estimates are remarkably robust across specifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Appendix Tables B6–B7 shows that the results are robust to different sample restric- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Specifically, I estimate the baseline specification excluding students in the tails of the ability and the endurance distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' These are students for whom floor and ceil- ing effects may be binding and, thus, for whom estimates may be biased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I also exclude students with a positive estimate of endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' These are students who, for example, may answer the exam in reverse order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I find little impact of these sample restrictions on the estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 79 Appendix Tables B8–B9 show robustness of the baseline regressions to accounting for measurement error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' First, I weight each observation by the inverse of the standard error of the ability and endurance estimates, thus giving more weight to students for which I estimate more precise measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Second, I estimate the baseline regressions using shrunk estimates of ability and endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The shrunk estimators of ability and endurance put more weight on measures estimated with more precision, as measured by a low standard error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The results are very similar to the baseline results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 80 Table B1: The effect of a movement from decile 1 to decile 10 in the ability/endurance distribution on long-run outcomes Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' College outcomes Dependent variable Enrolled College Degree 1st-year Grad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Time to college quality quality credits on time grad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (1) (2) (3) (4) (5) (6) Test score 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='300∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='275∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='389∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='046∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='215∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='397∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='008) Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='136∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='139∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='232∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='132∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='224∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='007) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='319∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='338∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='488∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='057∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='272∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='486∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='009) Ratio coef.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='426∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='412∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='474∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='530∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='485∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='462∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='005) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='009) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='007) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='012) Mean DV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='329 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='327 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='244 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='158 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='418 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='842 N 1,850,938 1,711,475 1,681,214 1,124,972 1,471,569 786,391 Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Labor-market outcomes Dependent variable Formal Hourly Monthly Firm Occup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Industry sector wage earnings wage wage wage (1) (2) (3) (4) (5) (6) Test score 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='005∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='457∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='395∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='320∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='141∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='046∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='241∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='240∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='159∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='084∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='018∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='005) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='543∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='475∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='387∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='177∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='055∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='005) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='005) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='005) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) Ratio coef.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='337∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='443∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='506∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='410∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='472∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='326∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='034) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='007) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='007) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='009) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='012) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='020) Mean DV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='326 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='865 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='551 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='885 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='886 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='858 N 2,523,032 818,590 818,590 692,880 818,374 818,590 Notes: This table displays estimates of the relationship between ability/endurance and college outcomes (Panel A) and labor-market outcomes (Panel B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The first row of each panel shows estimates of the mean outcome difference between individuals in the tenth and first decile of the test score distribution (the coefficient on the decile ten dummy in equation (B8)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The following rows show estimates of the mean outcome difference between individuals in the tenth and first decile of the ability/endurance distribution (the coefficients on the decile ten dummies in equation (B9)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' See Section 5 for a description of the measures of ability and endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' See Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 for outcome definitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heteroskedasticity-robust standard errors clustered at the individual level in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The third-to-last row in each panel shows the ratio between the effect of ability and endurance on a given outcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Standard errors estimated through the delta method in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' ∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 81 Table B2: Robustness of baseline regressions to alternative ways of measuring ability and endurance: College outcomes Dependent variable: Enrolled College Degree 1st-year Grad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Time to college quality quality credits on time grad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (1) (2) (3) (4) (5) (6) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating ability/endurance separately by day and using the average Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='053∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='050∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='084∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='010∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='043∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='079∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='114∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='107∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='157∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='018∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='081∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='158∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating ability/endurance separately by subject and using the average Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='060∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='055∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='080∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='009∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='043∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='079∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='103∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='097∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='140∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='067∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='130∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Panel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Including day fixed effects Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='031∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='050∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='025∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='047∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='110∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='104∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='152∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='018∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='077∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='151∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Panel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Including subject fixed effects Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='019∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='018∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='026∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='014∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='025∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='097∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='092∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='133∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='015∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='062∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='119∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Panel E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Using linear correlation as an alternative measure of endurance Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='049∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='025∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='047∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='101∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='095∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='138∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='072∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='139∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Mean DV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='244 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='326 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='244 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='158 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='418 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='817 N 2,501,519 1,800,546 1,768,707 1,124,972 1,472,916 793,822 Notes: This table shows estimates of the relationship between ability/endurance and college outcomes using alternative specifications to estimate ability and endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each column shows the result for a different dependent variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each panel shows the result from estimating ability and endurance with a different specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panels A–B, I estimate a student’s ability/endurance separately for each testing day (Panel A) and academic subject (Panel B) and then average the estimates across days or subjects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panels C–D, I estimate endurance in a regression that controls for day fixed effects (Panel C) or subject fixed effects (Panel D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Finally, in Panel E, I use the correlation between question position and a dummy for correctly answering a question as an alternative measure of endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heteroskedasticity-robust standard errors clustered at the individual level in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 82 Table B3: Robustness of baseline regressions to alternative ways of measuring ability and endurance: Labor-market outcomes Dependent variable: Formal Hourly Monthly Firm Occup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Industry sector wage earnings wage wage wage (1) (2) (3) (4) (5) (6) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating ability/endurance separately by day and using the average Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='088∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='085∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='058∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='028∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='172∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='152∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='121∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='055∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating ability/endurance separately by subject and using the average Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='088∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='076∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='061∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='026∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='008∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='156∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='135∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='110∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='048∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='014∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Including day fixed effects Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='053∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='051∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='035∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='017∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='167∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='147∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='117∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='053∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Including subject fixed effects Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='029∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='025∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='020∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='008∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='147∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='127∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='104∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='045∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='013∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Using linear correlation as an alternative measure of endurance Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='052∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='050∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='035∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='151∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='132∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='107∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='048∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='014∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Mean DV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='326 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='865 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='551 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='885 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='886 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='858 N 2,523,029 818,590 818,590 692,880 818,374 818,590 Notes: This table shows estimates of the relationship between ability/endurance and labor-market out- comes using alternative specifications to estimate ability and endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each column shows the result for a different dependent variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each panel shows the result from estimating ability and endurance with a different specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panels A–B, I estimate a student’s ability/endurance separately for each testing day (Panel A) and academic subject (Panel B) and then average the estimates across days or subjects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panels C–D, I estimate endurance in a regression that controls for day fixed effects (Panel C) or subject fixed effects (Panel D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Finally, in Panel E, I use the correlation between question position and a dummy for correctly answering a question as an alternative measure of endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heteroskedasticity-robust standard errors clustered at the individual level in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' ∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 83 Table B4: Robustness of the baseline regressions to alternative ways of controlling for question difficulty when estimating ability/endurance: College outcomes Dependent variable: Enrolled College Degree 1st-year Grad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Time to college quality quality credits on time grad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (1) (2) (3) (4) (5) (6) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Not controlling for question difficulty Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='040∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='045∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='080∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='007∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='028∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='061∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='114∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='112∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='169∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='018∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='079∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='159∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating difficulty without adjusting for average position Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='028∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='045∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='026∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='046∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='097∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='090∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='130∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='068∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='133∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Panel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating difficulty using question-specific position effects Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='035∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='038∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='065∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='007∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='027∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='054∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='106∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='102∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='152∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='017∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='074∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='147∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Panel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating difficulty using shrunk question-specific position effects Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='034∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='035∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='059∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='026∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='052∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='104∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='098∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='146∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='017∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='073∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='144∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Panel E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating position effects separately by fraction of correct responses Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='031∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='049∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='026∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='047∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='101∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='094∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='138∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='071∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='139∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Panel F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating position effects separately by subject Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='031∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='029∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='048∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='026∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='047∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='099∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='093∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='135∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='071∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='137∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Mean DV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='244 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='326 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='244 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='158 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='418 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='817 N 2,501,519 1,800,546 1,768,707 1,124,972 1,472,916 793,822 Notes: This table shows estimates of the relationship between ability/endurance and college outcomes using alternative measures of difficulty in the specification used to estimate ability and endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each panel shows the result using a different measure of question difficulty in equation (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel A, I estimate equation (7) without controlling for question difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel B, I measure question difficulty as the fraction of students who incorrectly answer the question across all booklets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panels C–F, I adjust for differences in average position across questions by estimating the position effects with alternative specifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In column C, I compute question-specific position effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel D, I compute a shrinkage estimator of the position effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel E, I compute the position effects separately for questions with a below/above fraction of correct responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel F, I compute the position effects separately by subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' See Appendix D for details on each measure of question difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heteroskedasticity-robust standard errors clustered at the individual level in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 84 Table B5: Robustness of the baseline regressions to alternative ways of controlling for question difficulty when estimating ability/endurance: Labor-market outcomes Dependent variable: Formal Hourly Monthly Firm Occup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Industry sector wage earnings wage wage wage (1) (2) (3) (4) (5) (6) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Not controlling for question difficulty Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='080∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='077∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='053∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='022∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='183∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='163∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='127∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='056∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='015∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating difficulty without adjusting for average position Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='048∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='047∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='032∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='143∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='125∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='101∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='046∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='014∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating difficulty using question-specific position effects Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='066∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='064∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='044∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='019∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='165∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='146∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='115∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='051∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='015∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating difficulty using shrunk question-specific position effects Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='061∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='059∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='040∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='018∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='159∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='140∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='111∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='050∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='014∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating position effects separately by fraction of correct responses Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='053∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='051∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='035∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='017∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='152∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='133∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='107∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='048∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='014∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Estimating position effects separately by subject Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='051∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='049∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='034∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='149∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='130∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='105∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='048∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='014∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Mean DV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='326 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='865 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='551 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='885 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='886 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='858 N 2,523,029 818,590 818,590 692,880 818,374 818,590 Notes: This table shows estimates of the relationship between ability/endurance and labor-market out- comes using alternative measures of difficulty in the specification used to estimate ability and endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each panel shows the result using a different measure of question difficulty in equation (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel A, I estimate equation (7) without controlling for question difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel B, I measure question difficulty as the fraction of students who incorrectly answer the question across all booklets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panels C–F, I adjust for differences in average position across questions by estimating the position effects with alternative specifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In column C, I compute question-specific position effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel D, I compute a shrinkage estimator of the position effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel E, I compute the position effects separately for questions with a below/above fraction of correct responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel F, I compute the position effects separately by subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' See Appendix D for details on each measure of question difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heteroskedasticity-robust standard errors clustered at the individual level in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 85 Table B6: Robustness of the baseline regressions to sample selection: College outcomes Dependent variable: Enrolled College Degree 1st-year Grad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Time to college quality quality credits on time grad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (1) (2) (3) (4) (5) (6) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Excluding students in the bottom or top 10% of the ability distribution Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='032∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='027∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='039∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='007∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='047∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='102∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='085∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='107∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='019∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='087∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='146∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Excluding students in the bottom or top 10% of the endurance distribution Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='050∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='025∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='044∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='100∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='093∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='135∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='075∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='138∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Panel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Excluding students in the bottom or top 10% of either distribution Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='031∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='026∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='037∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='007∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='046∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='102∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='083∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='102∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='020∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='089∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='146∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) Panel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Excluding students in the bottom or top 20% of either distribution Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='023∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='008∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='034∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='044∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='099∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='074∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='086∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='022∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='100∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='152∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004) Panel E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Excluding individuals with positive estimated endurance Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='033∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='028∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='048∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='005∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='026∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='047∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='107∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='097∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='143∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='065∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='133∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) Notes: This table shows estimates of the relationship between ability/endurance and college outcomes using alternative sample restrictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each column shows the result for a different dependent variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each panel shows the result for a different sample of students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel A, I exclude students in the bottom and top deciles of the ability distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel B, I exclude students in the bottom and top deciles of the endurance distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel C, I exclude students in the bottom and top deciles of the distribution of either skill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel D, I exclude students in the bottom and top quintiles of the distribution of either skill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel E, I exclude students with a positive estimate of endurance (ˆβ > 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I construct the deciles and quintiles using all the students in the high-school-students sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heteroskedasticity-robust standard errors clustered at the individual level in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 86 Table B7: Robustness of the baseline regressions to sample selection: Labor-market outcomes Dependent variable: Formal Hourly Monthly Firm Occup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Industry sector wage earnings wage wage wage (1) (2) (3) (4) (5) (6) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Excluding students in the bottom or top 10% of the ability distribution Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='046∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='044∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='031∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='017∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='130∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='113∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='092∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='051∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Excluding students in the bottom or top 10% of the endurance distribution Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='053∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='050∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='035∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='149∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='131∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='103∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='049∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='014∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Excluding students in the bottom or top 10% of either distribution Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='044∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='042∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='029∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='017∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='127∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='112∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='089∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='050∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='015∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Excluding students in the bottom or top 20% of either distribution Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='039∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='037∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='025∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='117∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='105∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='083∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='052∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) Panel E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Excluding individuals with positive estimated endurance Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='054∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='055∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='033∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='017∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='158∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='137∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='112∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='049∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='014∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Notes: This table shows estimates of the relationship between ability/endurance and labor-market out- comes using alternative sample restrictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each column shows the result for a different dependent variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each panel shows the result for a different sample of students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel A, I exclude students in the bottom and top deciles of the ability distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel B, I exclude students in the bottom and top deciles of the endurance distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel C, I exclude students in the bottom and top deciles of the distribution of either skill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel D, I exclude students in the bottom and top quintiles of the distribution of either skill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel E, I exclude students with a positive estimate of endurance (ˆβ > 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I construct the deciles and quintiles using all the students in the high-school-students sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heteroskedasticity-robust standard errors clustered at the individual level in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 87 Table B8: Robustness of the baseline regressions to accounting for measurement error: College outcomes Dependent variable Enrolled College Degree 1st-year Grad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Time to college quality quality credits on time grad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (1) (2) (3) (4) (5) (6) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Weighting each observation by its precision Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='031∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='030∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='051∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='026∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='048∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='100∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='094∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='139∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='016∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='073∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='140∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Shrunk estimator of ability and endurance Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='045∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='043∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='073∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='012∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='037∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='067∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='105∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='099∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='145∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='023∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='074∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='143∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002) Mean DV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='244 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='326 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='244 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='158 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='418 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='817 N 2,501,519 1,800,546 1,768,707 1,124,972 1,472,916 793,822 Notes: This table displays estimates of the relationship between ability/endurance and college outcomes accounting for measurement error in the estimates of ability and endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each column shows the result for a different dependent variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel A, I weight each observation by the inverse of the standard error of the ability and endurance estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Specifically, the weight of each observation is w = 1/(SE2 ˆαi + SE2 ˆβi), where SEˆαi and SE2 ˆβi are the standard errors of ˆαi and ˆβi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel B, I estimate the baseline regression using a shrunk estimator of ability and endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I compute the shrunk estimator of endurance as βs i = ωi ˆβi + (1 − ωj)¯β, where ¯β is the average cognitive endurance in my sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The individual-specific weight is ωi = Var[βi]−E[SE2 ˆ βi] Var[βi]−E[SE2 ˆ βi]+SE2 ˆ βi .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The shrunk estimator, βs i , puts more weight on estimates of βi that are more precisely estimated, as measured by a low standard error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I compute the shrunk estimator of ability analogously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heteroskedasticity-robust standard errors clustered at the individual level in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 88 Table B9: Robustness of the baseline regressions to accounting for measurement error: Labor-market outcomes Dependent variable Formal Hourly Monthly Firm Occup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Industry sector wage earnings wage wage wage (1) (2) (3) (4) (5) (6) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Weighting each observation by its precision Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='053∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='051∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='035∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='017∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='004∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='151∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='133∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='107∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='048∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='014∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Shrunk estimator of ability and endurance Endurance 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='076∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='074∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='050∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='024∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='005∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Ability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='002∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='157∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='138∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='111∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='050∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='015∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='001) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) Mean DV 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='326 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='865 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='551 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='885 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='886 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='858 N 2,523,029 818,590 818,590 692,880 818,374 818,590 Notes: This table displays estimates of the relationship between ability/endurance and labor-market out- comes accounting for measurement error in the estimates of ability and endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each column shows the result for a different dependent variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel A, I weight each observation by the inverse of the standard error of the ability and endurance estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Specifically, the weight of each observation is w = 1/(SE2 ˆαi + SE2 ˆβi), where SEˆαi and SE2 ˆβi are the standard errors of ˆαi and ˆβi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Panel B, I estimate the baseline regression using a shrunk estimator of ability and endurance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I compute the shrunk estimator of endurance as βs i = ωi ˆβi + (1 − ωj)¯β, where ¯β is the average cognitive endurance in my sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The individual-specific weight is ωi = Var[βi]−E[SE2 ˆ βi] Var[βi]−E[SE2 ˆ βi]+SE2 ˆ βi .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The shrunk estimator, βs i , puts more weight on estimates of βi that are more precisely estimated, as measured by a low standard error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I compute the shrunk estimator of ability analogously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heteroskedasticity-robust standard errors clustered at the individual level in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 89 C The ENEM In this Appendix, I describe the changing role of the ENEM in the higher-education system over time, compare the ENEM to the US SAT and ACT exams, and describe the IRT grading system used by the Ministry of Education to generate ENEM test scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 The Role of the ENEM in the Higher-education System The ENEM was created in 1998 by the National Institute of Educational Studies (INEP), a unit of the Brazilian Ministry of Education, with the goal of evaluating student performance at the end of high school (Appendix Figure C1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The ENEM is an achievement test, that is, it was designed to test for mastery of material individuals should learn by the end of high school.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='34 The first ENEM contained 63 multiple-choice interdisciplinary questions and was con- ducted over a five-hour testing block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The test score was calculated as the fraction of correct responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In its first edition, fewer than 200,000 individuals enrolled to take the ENEM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Figure C1: Timeline of the ENEM 1998 First edition: HS accountability test (non-mandatory) 2004 PROUNI program: scholarships to low-income students 2009 Expansion: Federal college admission exam & HS certification 2017 New schedule 2020 Online option Unique test (1 day, 5 hours) 63 interdisciplinary questions 180 q’s divided into 4 subjects: Day 1: Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5h) Day 2: Essay, Lang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', Math (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5h) 2 consecutive Sundays: Day 1: Lang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', Essay, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5h) Day 2: Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', Math (5h) In 2004, the government created a college scholarship program for low-income students called ProUni (Programa Universidade para Todos).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' ProUni used ENEM scores to allocate the scholarships to applicants, with program-specific score cutoffs based on the number of seats available in each program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' After ProUni was implemented, the number of individuals who signed up to take the ENEM doubled from 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5 million in 2004 to 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 million in 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In 2009, the Ministry of Education reformed the ENEM with the aim of encouraging colleges to use it as an admission exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The new ENEM consists of 180 multiple-choice 34Researchers often divide standardized tests into two types: reasoning tests and achievement tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Reasoning tests measure a student’s verbal reasoning, critical reading, and skills.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Achievement tests measure a student’s mastery of specific subjects, like biology or physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In practice, performance on both types of tests is highly correlated (Soares, 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 90 questions conducted over two consecutive days of testing during a weekend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The new exam contains questions in four subjects: mathematics, natural sciences (which includes biology, physics, and chemistry questions), social sciences (which includes history, geog- raphy, philosophy, and sociology questions), and language arts (which includes questions on Portuguese language, literature, foreign language, arts, physical education, and infor- mation and communication technologies).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' On the first day of testing, individuals had five and a half hours to take the social science test, the natural science test, and the essay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' On the second day of testing, individuals had five hours to take math and language arts tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The new ENEM is graded according to Item Response Theory (IRT), which enables colleges to compare test scores over time (see Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In 2010, the Ministry of Education introduced a centralized admission system called SISU (Sistema de Seleção Unificada) with the goal of simplifying the college application process for federal universities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The centralized system used ENEM scores to allocate students to participating colleges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' All federal universities are part of the system, but other universities (including state and municipal universities) are not mandated to be part of it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Also in 2010, the Government started using ENEM scores to allocate student loans through a program called FIES (Fundo de Financiamento ao Estudante do Ensino Superior).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In addition, starting in 2010 (and finishing in 2016), ENEM scores could be used to certify the attainment of high-school-level skills (analogously to the GED in the US).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' By 2010, over 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 million individuals enrolled to take the ENEM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In 2017, INEP changed the schedule of the ENEM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The exam started being conducted over two consecutive Sundays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' On the first Sunday, individuals have five and a half hours to answer the language arts test, the social science test, and the essay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' On the second Sunday, individuals have five hours to answer the natural science and math tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The other features of the exam remained constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In 2020, individuals had the option to take the ENEM through a computer without internet access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Over 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='7 million individuals enrolled to take the ENEM this year.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 ENEM Sample Questions Appendix Figures C2–C5 present sample questions from the natural science, social science, language arts, and math components of the ENEM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The questions come from the 2016 ENEM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The questions are average in terms of their difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 91 Figure C2: Natural Science sample question (item #11898) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Original (in portuguese) Portadores de diabetes insipidus reclamam da confusão feita pelos profissionais da saúde quanto aos dois tipos de diabetes: mellitus e insipidus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Enquanto o primeiro tipo está associado aos níveis ou à ação da insulina, o segundo não está ligado à deficiência desse hormônio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' O diabetes insipidus é caracterizado por um distúrbio na produção ou no funcionamento do hormônio antidiurético (na sigla em inglés, ADH), secretado pela neuro-hipófise para controlar a reabsorção de água pelos túbulos renais.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Tendo em vista o papel funcional do ADH, qual é um sintoma clássico de um paciente acometido por diabetes insipidus?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' A Alta taxa de glicose no sangue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' B Aumento da pressão arterial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' C Ganho de massa corporal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' D Anemia crônica.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' E Desidratação.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Translation Patients with diabetes insipidus complain about the confusion made by health profes- sionals about the two types of diabetes: mellitus and insipidus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' While the first type is associated with insulin levels or action, the second is not linked to insulin deficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Diabetes insipidus is characterized by a disturbance in the production or functioning of the antidiuretic hormone (ADH), secreted by the neurohypophysis to control the reabsorption of water by the renal tubules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In view of the functional role of ADH, what is a classic symptom of a patient with diabetes insipidus?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' A High blood glucose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' B Increase in blood pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' C Body mass gain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' D Chronic anemia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' E Dehydration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Notes: The correct answer is underlined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 92 Figure C3: Social Science sample question (item #97290) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Original (in portuguese) Parceria Transpacífica Dentro das atuais redes produtivas, o referido bloco apresenta composição estratégica por se tratar de um conjunto de países com A Elevado padrão social.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' B Sistema monetário integrado.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' C Alto desenvolvimento tecnológico.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' D Identidades culturais semelhantes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' E Vantagens locacionais complementares.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Translation Trans-Pacific Partnership Within the current production networks, the aforementioned bloc has a strategic composition because it is a group of countries with: A High social standard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' B Integrated monetary system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' C High technological development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' D Similar cultural identities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' E Complementary locational advantages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Notes: The correct answer is underlined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 93 Canada Estados Unidos Japao México Vietna Cingapura BruneiDarussalam Malasia Peru Australia Chile Nova ZelandiaFigure C4: Language Arts sample question (item #86509) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Original (in portuguese) O último longa de Carlão acompanha a operária Silmara, que vive com o pai, um ex- presidiário, numa casa da periferia paulistana.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Ciente de sua beleza, o que lhe dá certa soberba, a jovem acredita que terá um destino diferente do de suas colegas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Cruza o caminho de dois cantores por quem é apaixonada.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' E constata, na prática, que o romantismo dos contos de fada tem perna curta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' VOMERO, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Romantismo de araque.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Vida Simples, n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 121, ago.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Reconhece-se, nesse trecho, uma posição crítica aos ideais de amor e felicidade encontrados nos contos de fada.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Essa crítica é traduzida A Pela descrição da dura realidade da vida das operárias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' B Pelas decepções semelhantes às encontradas nos contos de fada.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' C Pela ilusão de que a beleza garantiria melhor sorte na vida e no amor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' D Pelas fantasias existentes apenas na imaginação de pessoas apaixonadas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' E Pelos sentimentos intensos dos apaixonados enquanto vivem o romantismo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Translation Carlão’s latest feature follows the worker Silmara, who lives with her father, an ex-convict, in a house on the outskirts of São Paulo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Aware of her beauty, which gives her a certain arrogance, the young woman believes that she will have a different destiny from her col- leagues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' She crosses paths with two singers she is in love with.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' And she finds, in practice, that the romanticism of fairy tales has short legs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' VOMERO, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Romanticism of arak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Simple Life, n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 121, Aug.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This passage recognizes a critical position on the ideals of love and happiness found in fairy tales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This criticism is translated A For the description of the harsh reality of the workers’ lives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' B For disappointments similar to those found in fairy tales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' C For the illusion that beauty would guarantee better luck in life and in love.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' D For the fantasies that exist only in the imagination of people in love.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' E For the intense feelings of those in love while living romanticism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Notes: The correct answer is underlined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 94 Figure C5: Math sample question (item #37515) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Original (in portuguese) Para evitar uma epidemia, a Secretaria de Saúde de uma cidade dedetizou todos os bairros, de modo a evitar a proliferação do mosquito da dengue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Sabe-se que o número f de infectados é dado pela função f(t) = −2t2 + 120t (em que t é expresso em dia e t = 0 é o dia anterior à primeira infecção) e que tal expressão é válida para os 60 primeiros dias da epidemia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' A Secretaria de Saúde decidiu que uma segunda dedetização deveria ser feita no dia em que o número de infectados chegasse à marca de 1600 pessoas, e uma segunda dedetização precisou acontecer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' A segunda dedetização começou no A 19° dia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' B 20° dia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' C 29° dia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' D 30° dia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' E 60° dia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Translation To prevent an epidemic, the Health Department of a city sprayed all neighborhoods, in order to prevent the proliferation of the dengue mosquito.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' It is known that the number f of infected people is given by the function f(t) = −2t2 + 120t (where t is expressed in day and t = 0 is the day before the first infection) and that this expression is valid for the first 60 days of the epidemic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The Health Department decided that a second extermination should be carried out on the day when the number of infected people reached the mark of 1,600 people, and a second extermination had to take place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The second extermination started in A 19th day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' B 20th day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' C 29th day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' D 30th day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' E 60th day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Notes: The correct answer is underlined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 95 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 Comparison of the ENEM to the ACT and SAT exams Appendix Table C1 compares important features of the SAT, ACT, and ENEM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The SAT contains 154 multiple-choice questions divided into three sections: reading, writing and language, and math, plus an optional essay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Including the essay, individuals have 3 hours and 50 minutes to take the test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' On average across sections, test-takers have about 1 minute and 10 seconds to answer each question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Raw scores are converted into scaled scores through a score conversion table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The ACT contains 215 multiple-choice questions divided into four sections: English, math, reading, and science, plus an optional essay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Including the essay, individuals have 3 hours and 35 minutes to take the test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' On average across sections, test-takers have less than 1 minute to answer each question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Raw scores are converted into scaled scores through a score conversion table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' There are some notable differences between the SAT/ACT and the ENEM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' First, the ENEM is conducted over two days of testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Second, individuals in the ENEM have no assigned breaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Third, the booklet ENEM test-takers receive contains all the questions they have to answer during the testing day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thus, they may allocate time disproportionally across sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In contrast, in the SAT and ACT, each section has an assigned amount of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Finally, in the ENEM, each question is associated with a different text passage or prompt (in some cases, two questions share a prompt or passage).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In contrast, in the SAT and ACT, a given passage is associated with multiple questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This partly explains why the time per question is higher in the ENEM than in the ACT/SAT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 96 Table C1: Comparison of the SAT,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' ACT,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' and ENEM college admission exams ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='SAT ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='ACT ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='ENEM ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='Cost ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='∼$60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='∼$88 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='∼$17 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='Grading ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='Score conversion chart using raw scores ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='Score conversion chart using raw scores ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='Item Response Theory (IRT) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='Starting time ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='Between 8:30 and 9am ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='Between 8:30 and 9am ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1pm Brasilia time ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='Number of items ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='154 questions ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='215 questions ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='180 questions ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='Total length ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 hours and 50 mins over 1 testing day ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 hours and 35 mins over 1 testing day ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 hours over 2 testing days ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='Time per question ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 minute and 10 seconds ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 seconds ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 minutes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='Breaks ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 mins break after reading section ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 min break after math section ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='N/A ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5 min break between math sections ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='5 min break before essay ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 min break before the essay ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='Sections ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='Reading (65 mins,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 52 items) English (45 mins,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 75 items) Social science (day 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 45 items) Writing and Language (35 mins,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 44 items) Math (60 mins,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 60 items) Natural science (day 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 45 items) Math w/o calculator (25 mins,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 20 items) Reading (35 mins,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 40 items) Language arts (day 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 45 items) Math w/ calculator (55 mins,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 38 items) Science (35 mins,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 40 items) Math (day 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 45 items) Optional essay (50 mins) Optional essay (40 mins) Mandatory essay (day 2) Notes: The SAT refers to the post-2016 version of the SAT,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' which includes an optional essay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This optional essay was eliminated in 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The ENEM refers to the 2009–2016 version of the exam (see Section C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 for information on the pre-2009 and post-2016 versions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The exam length was computed excluding breaks and including the essay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The time per question does not account for the essay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 97 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4 IRT Grading The Brazilian Testing Agency grades the ENEM exam based on the three-parameter item response theory (IRT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' According to IRT, the probability that an individual i with ability θi correctly answers question j is: Pr(Cij = 1|θi) = pj(θi) = cj + 1 − cj 1 + e−aj(θi−bi), (C1) where aj, bj, and cj are three question-level parameters that represent, respectively, a question’s “discrimination,” “difficulty,” and “pseudo-guess.” A question’s discrimination refers to its ability to discriminate between low- and high-ability individuals;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' the difficulty represents the value of θ at which pj(θi) has the maximum slope, and the pseudo-guess parameter indicates the likelihood that a student with an infinitely negative ability has to correctly respond to the question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Notice that in equation (C1), the probability of correctly answering a question does not depend on its position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thus, the type of position effects documented above suggests that the IRT estimates of individual-level ability are biased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Modern IRT approaches (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=', Debeer and Janssen, 2013) include item position into the framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each question’s parameters are known from pre-testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The testing agency estimates the θi that maximizes the empirical likelihood of the entire sequence of responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' They do this separately for each student and academic subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' ENEM scores are normalized to have a mean of 500 and a standard deviation of 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Despite its complexity, most of the variation in IRT-estimated ENEM scores is driven by variation in the fraction of correct responses in the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' A regression of IRT-estimated ENEM scores on the fraction of correct responses yields an R-squared of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='88 (the rank correlation between the two variables is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='93).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Consistent with this, Appendix Figure C6 shows that the relationship between these two variables is linear in both levels (Panel A) and percentiles (Panel B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The strong relationship between IRT-estimated scores and the fraction of correct responses holds not just for the overall score but also for the score in each academic subject (Appendix Table C2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 98 Figure C6: Comparison of IRT-estimated ENEM score and fraction of correct responses Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In levels 300 400 500 600 700 800 Average IRT-estimated ENEM score 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='70 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='80 Fraction of correct responses Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In percentiles 0 20 40 60 80 100 Average percentile IRT-estimated score 0 20 40 60 80 100 Percentile fraction of correct responses Notes: This figure shows binned scatterplots plotting the average IRT-estimated ENEM score across all four academic subjects (y-axis) against the fraction of correct responses on the exam (x-axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Panel A shows the results in levels and Panel B in percentiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I first group students into 100 equally-sized bins based on their fraction of correct responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Then, I calculate the average IRT-estimated ENEM score or score percentile in each bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The vertical lines denote the 10th and 90th percentiles of the ENEM score distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The solid red line shows the predicted values from a linear regression on the plotted points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Table C2: Correlation between IRT-estimated ENEM score and fraction of correct responses on each subject Academic subject Social Natural Language Math Average science science arts score (1) (2) (3) (4) (5) Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Variables measured in levels Fraction correct resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='892∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='880∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='907∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='885∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='937∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) N 14,936,699 14,936,699 14,936,699 14,936,699 14,936,699 R−squared 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='79 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='77 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='82 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='78 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='88 Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Variables measured in percentiles Fraction correct resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='904∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='858∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='917∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='845∗∗∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='931∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='000) N 14,936,699 14,936,699 14,936,699 14,936,699 14,936,699 R−squared 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='82 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='74 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='84 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='71 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='87 Notes: This table displays the correlation between the IRT-estimated ENEM score and the fraction of correct responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Columns 1–4 present the correlations separately for each academic subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Column 5 presents the correlation between the average score across all subjects and the fraction of correct responses in the entire exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heteroskedasticity-robust standard errors clustered at the question level in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' ∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 99 D Measuring Question Difficulty In this Appendix, I describe my measures of question difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Instead of taking a strong stance on what the right measure of difficulty is, I show that the results are robust to measuring question difficulty in several ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' An intuitive measure of a question’s difficulty is the fraction of students who correctly answer the question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This measure is problematic in the presence of fatigue effects since a given question has a different fraction of correct responses depending on its location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To illustrate this problem, Appendix Figure D1 plots students’ performance on a natural science question in each booklet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The position of this item ranged from position 46 in the gray booklet to position 87 in the blue booklet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Correspondingly, student performance varied from 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='7% in the gray booklet to 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='9% in the blue booklet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Figure D1: Performance on a natural science question (item #11898) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='407 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='359 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='339 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='299 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='50 Fraction of correct responses Gray Booklet Position = 46 Yellow Booklet Position = 63 Pink Booklet Position = 66 Blue Booklet Position = 87 Notes: This figure shows the fraction of individuals who correctly responded to item #11898 in each of the four booklets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' See Appendix Figure C2 for the question’s text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The fact that performance on a question varies according to its position raises an important challenge for measuring question difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' It is hard to know whether questions that appear later in the exam are less likely to be correctly answered because they test more difficult material or because students are more fatigued by the time they get to these questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To account for fatigue effects, I estimate measures of question difficulty that represent 100 the fraction of students who would correctly answer a question if the question appeared in the first position of the exam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To estimate this fraction, I follow a three-step process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' First, I compute the average position of each question across all booklets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Second, I estimate the effect of a one-position increase of a question position on performance on the question (“position effect”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Third, I multiply the average question position calculated in the first step by the position effect estimated in the second step and subtract this figure from the fraction of correct responses across all booklets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This yields a position-adjusted estimate of question difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Appendix Table D1 illustrates these steps in calculating the difficulty of item #11898.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The measures of question difficulty differ in how I estimate the position effect in the second step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' My baseline measure of question difficulty uses the position effect estimated by pooling all questions (Table 2, column 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This measure assumes that the effect of a one-position increase on performance is homogeneous across questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The second measure of question difficulty uses a question-specific position effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I estimate equation (4) separately for each question and use the intercept from the regression as the measure of difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' This does not assume homogeneity in position effects;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' however, for some questions the position effect is imprecisely estimated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The third measure of question difficulty combines the first two by shrinking the question- specific position effect to the average effect by its signal-to-noise ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Specifically, let βj be the position effect estimating using data only from question j and ¯β be the average position effect across all questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The shrunk position effect of question j, βs j, is a convex combination of βj and ¯β: βs j = ωjβj + (1 − ωj)¯β, where the question-specific weight, ωj, is ωj = Var[ˆβj] − E[SE2 ˆβj] Var[ˆβj] − E[SE2 ˆβj] + SE2 ˆβj .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The shrunk estimator puts more weight on position effects that are more precisely estimated, as measured by a low standard error of ˆβj, SE2 ˆβj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The fourth measure estimates the position effect separately for questions with a be- low/above median fraction of correct responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The fifth measure estimates the effect separately for each academic subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' These measures assume that the effect of a one- 101 position increase on performance is homogeneous within a type of question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Table D1: Alternative measures of the difficulty of item #11898 Position effect Average fraction Fatigue effect (in pp) Question estimation method correct responses × average position difficulty (1) (2) (3) (4) None 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='36 0 × 64 = 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='36 Pooling all items 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='08 × 64 = -5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='41 Item-specific effect 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='24 × 64 = -15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='51 Shrinkage estimator 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='24 × 64 = -15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='51 By fraction corr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='15 × 64 = -9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='45 By academic subject 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='03 × 64 = -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='37 Notes: This table illustrates how the six measures of a question’s difficulty are calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The average fraction of correct responses and the average question position are calculated using the number of students with each booklet as weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Appendix Figure D2 shows the cross-question correlation between the measures of ques- tion difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Reassuringly, all difficulty measures are highly correlated, with coefficients ranging from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='77 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Figure D2: Cross-question correlation matrix of item difficulty measures No position adjustment 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='774 Item-specific adjustment 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='992 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='778 Adjustment using mean effect 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='848 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='976 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='851 Adjustment using shrunk effect 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='985 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='780 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='990 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='853 Adjustment by below/above median fraction of correct resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='991 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='780 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='993 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='852 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='984 Adjustment by academic subject Notes: This figure shows the relationship between the different measures of question difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each cell shows the cross-question linear correlation between two measures of question difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The sample size is N = 1, 842 across all cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 102 E Exam Content and Cognitive Endurance In this Appendix, I assess whether the type of questions of an exam can influence the effect of limited endurance on performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' For this, I estimate heterogeneity in the effect of limited endurance on student performance based on two question characteristics: difficulty and length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' First, I explore heterogeneity based on question difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Previous research has identi- fied task difficulty as a moderator of cognitive fatigue (Ackerman, 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' We might expect cognitive endurance to matter only for questions in a certain difficulty range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Students should be able to answer very easy questions regardless of how tired they are.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Similarly, some questions might be too difficult for students to answer regardless of how rested they are.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The ENEM contains very difficult questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' On average, students only answer 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3% of questions correctly (random chance would imply 20%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Individuals who answer 50% of questions correctly are in the top 10% of the score distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Thus, we might expect limited endurance to affect performance in the relatively-easier questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' In Appendix Table E1, I estimate equation (5) separately for below/above median- difficulty questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='35 Appendix Figure E1, Panel A, plots corresponding binned scatter- plots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The effect of limited endurance is driven by relatively easier questions (columns 3–4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The estimated coefficient is thirteen times larger for below-median-difficulty questions than for above-median-difficulty questions (-13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='0 percentage points, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' More broadly, there is a negative—although non-monotonic—relationship between a question’s difficulty and the magnitude of the limited endurance effect (Appendix Figure E1, Panel B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The performance of students only declines when responding to questions below a cer- tain difficulty, possibly because they do not have the preparation required to respond to the hardest questions regardless of their location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Second, I explore heterogeneity based on question length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Previous research has shown that time-on-task is one of the main predictors of cognitive fatigue (Ackerman, 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' We might expect fatigue effects to be larger for lengthy questions if students are more likely to have an attentional lapse in long questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To measure question length, I compute the number of words in each question using text-scraped data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Appendix Table E1 estimates equation (5) separately for relatively long questions (above-median number of words) and short questions (below-median number of words).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='36 I find that limited endurance effects are about twice as large for longer questions (-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='2 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' -5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='3 percentage points, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 35Above [below] median difficulty questions are responded correctly 22% [48%] of the time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 36Above [below] median length questions have 209 [100] words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 103 Overall, there seems to be a negative relationship between a question’s length and the size of the limited endurance effect (Appendix Figure E1, Panels C–D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Figure E1: The effect of cognitive endurance on performance by question characteristics Panel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Change in performance vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' change in question position by question difficulty 8 6 4 2 0 2 Average pp change in prob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' of correct answer 0 5 10 15 20 25 30 35 ≥40 Change in question position Below median difficulty (mean correct: 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='1%) Above median difficulty (mean correct: 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='4%) Panel B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Binned scatterplot: Endurance effect vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' question difficulty 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 Average position effect (in pp) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='60 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='80 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 Question difficulty (fraction of incorrect responses) Panel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Change in performance vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' change in question position by question length 8 6 4 2 0 Average pp change in prob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' of correct answer 0 5 10 15 20 25 30 35 ≥40 Change in question position Below median length (mean # words: 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='7) Above median length (mean # words: 209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='9) Panel D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Binned scatterplot: Endurance effect vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' question length 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='10 Average position effect (in pp) 50 100 150 200 250 300 Question length (average number of words) Notes: This figure shows heterogeneity in the effect of limited endurance on student performance by question difficulty and length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Panels A and C are analogous to Figure 3, but the fatigue effect is estimated separately for below/above median difficulty questions (Panel A) and below/above median length questions (Panel C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The y-axis shows the average change (in percentage points) in the fraction of students who correctly respond to a question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The x-axis plots the change in the question position between each possible booklet pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' The dashed line denotes predicted values from a linear regression estimated on the plotted points, using the number of questions used to estimate each point as weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Panels B and D show a series of binned scatterplots plotting the average endurance effect among questions in a given difficulty bin (Panel B) or length bin (Panel B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' To construct this figure, I divide questions into ten equally-sized bins based on their difficulty or length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Then, I calculate the effect of limited endurance on performance on questions in each bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 104 Table E1: The heterogeneous effect of limited cognitive endurance on performance by question characteristics Outcome: Fraction of correct responses Question position Question difficulty Question length 1st half 2nd half Below Above Below Above each day each day median median median median (1) (2) (3) (4) (5) (6) Position (normalized) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='097∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='051∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='132∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='010∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='053∗∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='102∗∗∗ (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='006) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='003) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='005) (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content='007) Question fixed effects Yes Yes Yes Yes Yes Yes N (Item−Booklets) 3,016 2,880 2,935 2,911 2,940 2,956 Notes: This table shows the heterogeneous effect of limited cognitive endurance on daily student performance based on question characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Each column displays the estimate of β in equation (5) estimated on the sample listed in the column header.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' I normalize question position such that the first question in each testing day is equal to zero and the last question is equal to one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' Heteroskedasticity-robust standard errors clustered at the question level in parentheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' ∗∗∗, ∗∗ and ∗ denote significance at 10%, 5% and 1% levels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} +page_content=' 105' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE0T4oBgHgl3EQfsQEM/content/2301.02575v1.pdf'} diff --git a/vdFLT4oBgHgl3EQfjy_2/content/tmp_files/2301.12113v1.pdf.txt b/vdFLT4oBgHgl3EQfjy_2/content/tmp_files/2301.12113v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..91efac0fb9b643fc822d532abb42e3d96c259d17 --- /dev/null +++ b/vdFLT4oBgHgl3EQfjy_2/content/tmp_files/2301.12113v1.pdf.txt @@ -0,0 +1,1226 @@ +Strong quantum metrological limit from many-body physics +Yaoming Chu,1, ∗ Xiangbei Li,1, ∗ and Jianming Cai1, 2, † +1School of Physics, International Joint Laboratory on Quantum Sensing and Quantum Metrology, +Institute for Quantum Science and Engineering, Wuhan National High Magnetic Field Center, +Huazhong University of Science and Technology, Wuhan 430074, China +2Shanghai Key Laboratory of Magnetic Resonance, East China Normal University, Shanghai 200062, China +Surpassing the standard quantum limit and even reaching the Heisenberg limit using quantum entanglement, +represents the Holy Grail of quantum metrology. However, quantum entanglement is a valuable resource that +does not come without a price. The exceptional overhead for the preparation of large-scale entangled states +raises disconcerting concerns about whether the Heisenberg limit is fundamentally achievable. Here we find a +universal speed limit set by the Lieb-Robinson light cone for the quantum Fisher information growth to charac- +terize the metrological potential of quantum resource states during their preparation. Our main result establishes +a strong precision limit of quantum metrology accounting for the complexity of many-body quantum resource +state preparation and reveals a fundamental constraint for reaching the Heisenberg limit. Our result makes +it possible to identify the essential features of quantum many-body systems that are crucial for achieving the +quantum advantage of quantum metrology and brings a new perspective to understanding many-body quantum +dynamics from quantum metrology. +Quantum metrology, as part of the rapidly rising field of +quantum science and technology, is capable of achieving en- +hanced precision measurement by exploiting quantum strate- +gies and promises unprecedented applications in basic sci- +ence and technology [1–6]. Importantly, irrespective of clas- +sical accidental errors [1], quantum mechanics imposes a fun- +damental limit on the accuracy to which measurements can +be performed, called the Heisenberg limit [7–9]. The cele- +brated Heisenberg limit conventionally refers to a measure- +ment precision scaling as 1/N (where N is typically regarded +as the number of probes employed) and acts as a hallmark of +scaling improvement over the standard quantum limit (SQL), +which arises from uncorrelated measurements and is given +by 1/ +√ +N. The advantage of quantum metrology in terms of +reaching the Heisenberg limit often attribute to quantum en- +tanglement [10–13], such as the “cat” state of N probes. Al- +though the improved scaling has been unfortunately demon- +strated to be fragile when suffering from noise sources [14– +16], a number of clever noise-robust quantum metrological +schemes [17–19] have been proposed to battle against deco- +herence, making it not a fundamentally unsolvable obstacle +for reaching the Heisenberg limit. +In contrast, given that the preparation of large-scale entan- +gled states of many-body quantum systems is usually a highly +demanding and challenging task, the following intricate and +critical problem remains elusive: whether is there any funda- +mental constraint that prevents reaching the Heisenberg limit +imposed by the complexity of state preparation [20–22]? Ad- +dressing this problem and establishing a stronger precision +limit would put comparisons of entanglement-enhanced quan- +tum measurements with the SQL on a more fair footing, and +consistently consolidate the foundation of the quantum ad- +vantage offered by quantum metrology over classical counter- +parts. It also relates to another crucial problem: is there any +simple and universal principle to find quantum metrological +systems that are favorable for achieving the quantum advan- +tage of quantum metrology? +In this letter, we address these problems by quantifying the +growth of quantum Fisher information (QFI) for the metrolog- +ical state preparation in generic quantum many-body systems. +As our main result, we find a universal speed limit for the QFI +growth set by the celebrated Lieb-Robinson (LR) light cone +from many-body physics [23, 24]. This provides a versatile +tool to lower bound the minimal time required by metrological +resource state preparation, and thus establishes the precision +limit for quantum metrology explicitly involving the complex- +ity of state preparation (dubbed “strong precision limit”). Ap- +plying our result to quantum many-body systems with Ising +and dipolar interactions, we illustrate how to achieve the ad- +vantage of quantum metrology through long-range interact- +ing and higher-dimensional systems, which presents insight- +ful design principles for quantum metrological systems. The +result also connects quantum metrology with quantum infor- +mation propagation and offers a new perspective to under- +standing many-body quantum dynamics via the concept of +QFI growth. +Fundamental constraint for QFI growth.— Quantum Fisher +information, FQ, as a fundamental concept in quantum +metrology, determines the optimal measurement precision us- +ing a given quantum resource state ϱ [25]. It quantifies the +sensitivity of ϱ to a parameter-dependent unitary transforma- +tion generated by an interrogation operator K, i.e. +ϱϑ = +e−iϑKϱeiϑK with ϑ a phase to be estimated. Usually the inter- +rogation operator is local, K = �N +i=1 Ki, with Ki defined on +the i-th individual probe, see Fig. 1a. For a general resource +state, spectrally decomposed as ϱ = � +n pn|n⟩⟨n|, the QFI +takes a structure of the following form +FQ[ϱ, K] = 2 +� +n,m +(pn − pm)2 +pn + pm +|⟨n|K|m⟩|2 , +(1) +where the sum includes only terms with pn+pm > 0. A larger +QFI indicates a better distinguishability between neighboring +parametrized quantum states ϱϑ and ϱϑ+δϑ, and thus a more +sensitive ϱ to the operator K. +arXiv:2301.12113v1 [quant-ph] 28 Jan 2023 + +2 +R +i +j +U(1) +ϑ +U(2) +ϑ +ϱ +σ1 +σ2 +σN +(1) +(2) +(N) +Measurement +Preparation +U(N) +ϑ +a +b +FQ/N +RL(t) +FQ ≲ RD +L (t) +RL(t) +dij/2 +QFI by site and +i +j +0 +O(1) +FIG. 1. Metrological resource state preparation and QFI growth. +a, Conventional scheme for quantum metrology. A N-probe quan- +tum system is prepared in the resource state ϱ and is fed into N +parallel local channels (each one is described as U (i) +ϑ +≡ e−iϑKi) +to sense an unknown phase ϑ. b, Spreading of local operators in a +quantum lattice. The quasilocality implied by LR bound ensures that +Ki(t) (red region) is well approximated by an operator Ki(t, i[R]) +defined on a ball region i[R] (dashed circle) with R ≳ RL(t), where +RL(t) represents the effective light cone. The QFI collaboratively +contributed by the site i and j (red curve, Sec. 1 in Supplementary In- +formation) begins to be nonzero only when the two balls Ki(t, i[R]) +and Kj(t, j[R]) grow to touch each other. Consequently, the upper +bound of the QFI growth (green curve) would be constrained by the +effective light cone RL(t). +Quantum metrology often seeks such metrological states +ϱ (e.g. GHZ state [26], squeezed spin states [27, 28], crit- +ical ground states [29], etc.) to enhance the optimal mea- +surement precision [1]. These strongly correlated quantum +metrological states are usually prepared via coherent interac- +tions between individual probes, see e.g. [30–34]. We con- +sider generic Hamiltonians with few-body interactions on a +D-dimensional lattice, with Λ the total particle set and the +cardinality |Λ| = N. In detail, the interaction Hamiltonian +of a k-local form with bounded one-site energy [35] can be +expressed as, +H = +� +|X|≤k +hX, +max +i∈Λ +� +X:X∋i +∥hX∥ ≲ O(1), +(2) +where each interaction term hX acts on the particle subset +X ⊂ Λ, and ∥ • ∥ is the operator norm. Remarkably, in state- +of-the-art quantum platforms including trapped ions [36, 37], +Bose-Einstein condensates [38–42], Rydberg atoms [43, 44] +etc., the interaction Hamiltonians to generate unprecedented +levels of multipartite entanglement with N ≳ O(100) gener- +ally belong to this family of Hamiltonian [Eq. (2)]. +The key is to find the speed limit of the QFI growth for +a quantum metrological resource state ϱ(t) prepared by a +unitary evolution U(t) with the Hamiltonian in Eq. (2), see +Fig. 1a. Starting from a full product state σ = ⊗N +i=1σi, the +QFI of ϱ(t) = U(t)σU†(t) [cf. Eq. (1)] associated with K can +be formulated as (Sec. 1 in Supplementary Information) +FQ(t) = 2cWY +� +i,j +tr +� +[Ki(t), √σ]†[Kj(t), √σ] +� +, +(3) +with cWY ∈ [1, 2] relevant to the Wigner-Yanase skew in- +formation [45], and Ki(t) = U†(t)KiU(t). This result re- +veals an explicit connection between the evolution of QFI +and the spreading as well as interference of on-site operators, +see Fig. 1b. Such a connection will enable us to analyze the +“growth” behavior of the QFI with respect to the preparation +time. +In non-relativistic quantum mechanics, by analogy to Ein- +stein’s relativity, Lieb-Robinson bound imposes one of the +most fundamental restrictions to quantum dynamics, lead- +ing to the formation of an “effective light cone”, RL(t), that +bounds the propagation of quantum information to a finite ve- +locity (i.e. causality in a quantum many-body lattice) [23]. +Mathematically, the time-dependent commutator between two +operators Ki(t) and Kj (i.e. [Ki(t), Kj]) decrease rapidly +with the graph-theoretic distance dij separating site i and j +outside the light cone, which ensures an approximation of +Ki(t) as Ki(t) ≈ Ki(t, i[R]) (Sec. 2 in Supplementary In- +formation). Here, R ≳ RL(t) up to a constant factor, and +Ki(t, i[R]) represents a projection of Ki(t) onto the subset +i[R] ⊂ Λ that is a ball region centered at the site i with ra- +dius R, see Fig. 1b. Exploiting such a causality relation, we +establish an upper bound for the growth of QFI in many-body +quantum lattices as (Sec. 3 in Supplementary Information) +FQ(t) ≲ κcWY +� +1 + γ2DRD +L (t) +� +N, +(4) +where κ ≃ O(1) represents the maximal spectrum width of +the local interrogation operators {Ki}, and γ is a positive con- +stant determined by the geometry of a quantum lattice. There- +fore, given a state preparation time t, the maximal QFI that +can be achieved is strictly constrained by the geometry and +the light cone for a quantum many-body lattice. Such a fun- +damental constraint determines whether the metrological sys- +tem can surpass the SQL and even reach the Heisenberg limit +when accounting for the overhead of quantum resource state +preparation. +Strong precision limit of quantum metrology.— In quantum +metrology, in order to estimate a parameter λ encoded in the +phase ϑ = λτ with τ the interrogation time of single measure- +ment, the minimal uncertainty of multiple identical measure- +ments is set via the well-known quantum Cramér-Rao bound +(Sec. 4 in Supplementary Information), +δλ ≥ N −∆/2λSQL ≡ N −(1+∆)/2 +1 +√ +Tτ +(5) + +3 +Here, δλSQL ≡ 1/ +√ +NTτ represents the standard quantum +limit with T the total measurement time. The exponent ∆ +characterizes the quantum metrological enhancement to beat +the SQL; specifically, ∆ = 0 and 1 correspond to the SQL +and Heisenberg scaling respectively. For a sufficiently large +quantum many-body system, the preparation time (below de- +noted as tp) of entangled metrological resource state would +generally be much longer than the signal interrogation time +(which is limited by the system’s coherence time), namely +tp ≫ τ, and then the number of measurement repetitions is +upper bounded by T/tp. Thus, the enhancing exponent ∆ is +dominantly determined by the ratio of QFI to the state prepa- +ration time (Sec. 4 in Supplementary Information), +∆ = logN +�FQ +tp +· τ +N +� +. +(6) +Based on the QFI growth bound in Eq. (4), we are able to de- +termine the maximal exponent ∆ through the scaling behavior +of (FQ/tp), and then strengthen the ultimate precision limit of +quantum metrology in generic quantum many-body lattices. +For short-range interacting systems, namely, the decay of +interaction strength is faster than an exponential decay relative +to the distance between separated sites, Lieb and Robinson +proved in 1972 an effective linear light cone RL(t) ≃ vLRt +with vLR ∼ O(1) the so-called LR velocity [23]. By us- +ing our result in Eq. (4) that FQ ≲ NRD +L (tp) ∼ NtD +p , the +metrological enhancing exponent would be upper bounded by +(Sec. 4 in Supplementary Information) +∆ ≤ 1 − 1 +D. +(7) +Particularly, for one dimensional (1D) short-range interacting +quantum systems, the result implies that one can only achieve +a zero enhancing exponent, i.e. ∆ = 0, and thereby a sur- +prising precision scaling as δλSQL. In this scenario, even if +the system might be able to be prepared in a global multi- +partite entangled state with FQ ∼ N 2, the Heisenberg scal- +ing would not be feasible due to the required state preparation +time that scales at least linearly with the system size, namely +tp ∼ FQ/N ∼ N following Eq. (4). +For long-range interacting systems, we consider two-body +interactions of the form ∥hi,j∥ ≲ d−α +i,j , where {hij} are bi- +partite interaction operators, di,j is the distance from the site +i to j, α is the power-law decaying exponent. A strictly linear +light cone exists for sufficiently large α (i.e. α > 2D + 1) +in generic long-range interacting lattices [46], and thus the +quantum metrological enhancing exponent is also bounded by +Eq.(7). Nevertheless, as the decaying exponent α becomes +smaller, a linear light cone can be broken [47]. In the regime +of α ∈ (2D, 2D + 1], the shape of the effective light cone +becomes polynomial and is given by RL(t) ≃ ct1/ξ, where +c is a constant of O(1) and ξ = α − 2D up to an arbitrarily +small constant [48]. Therefore, our result in Eq. (4) leads to +the following metrological enhancing exponent as (Sec. 4 in +1 +1 − 1 +D +2D + 1 +2D +Heisenberg scaling +Δ = logN(FQτ/Ntp) +D +SQL +t ∼ log r +α +0 +t ∼ r +t ∼ rξ +Forbidden +FIG. 2. Bound of quantum metrological enhancement. In the +regime of α > 2D + 1, a quantum many-body lattice is governed by +a linear light cone (t ∼ r), resulting in that ∆ ≤ 1 − 1/D; while +in the regime of α ≤ 2D + 1, “supersonic” information propagation +(e.g. polynomial t ∼ rξ and logarithmic t ∼ log r light cones) is +possible, which gives rise to that ∆ ≤ 3−α/D for α ∈ (2D, 2D+1] +and ∆ ≤ 1 − logN(polylog(N)) (i.e. approaching the Heisenberg +scaling in the limit of large system size) for α ∈ (D, 2D]. +Supplementary Information) +∆ ≤ 1 − ξ +D. +(8) +As one can see, as α → 2D and ξ → 0+, the measure- +ment precision would approach the Heisenberg scaling (i.e. +∆ = 1). +While in the regime of α ∈ (D, 2D], the LR +bounds give rise to a “logarithmic light cone” (i.e. t ∼ log R), +or equivalently an exponentially growing speed of quantum +information propagation [24, 48]. +Similarly, according to +Eq. (4), this would lead to the quantum metrological enhance- +ment as (Sec. 4 in Supplementary Information) +∆ ≤ 1 − logN polylog(N). +(9) +Note that logN polylog(N) < o(1) (namely, smaller than an +arbitrarily small positive constant) for N → ∞, therefore +the Heisenberg limit becomes asymptotically achievable. In +Fig. 2, we summarize the scaling behavior of these strong pre- +cision limits of quantum metrology with respect to the system +size for α > D. For ultra long-range interacting systems with +α ∈ [0, D], the notion of quasilocality is broken [49–51]; in +other words, the causal region defined by an effective light +cone might disappear. In this scenario, even faster information +propagation and metrological state preparation are possible. +In particular, we remark that the interaction regime of α = 0 +offers very favorable systems to prepare many-body entangled +metrological resource states, especially in experimental plat- +forms of Bose-Einstein condensates [13, 38–40, 42]. +Design principles for quantum metrological systems.— Our +result suggests that long-range interaction is favorable for +achieving the quantum advantage of quantum metrology over +the SQL. Below we present an illustrative example of the Ising + +4 +0 +0.2 0.4 0.6 0.8 +1 +1.2 1.4 +0 +0.2 +0.4 +0.6 +0.8 +1 +0 +2 +4 +6 +0 +10 +20 +30 +40 +α +0 +0.2 +0.4 +0.6 +0.8 +a +FQ/N +t +Δf +Δ +b +α +FIG. 3. Metrological enhancement by Ising chain with long-range +interaction. a, QFI growth with respect to the evolution time for dif- +ferent values of α with N = 60 sites. Starting from the coherent +spin state along the x direction, we maximize the QFI at all times t +by optimizing local interrogation operators, Ki = Sˆn, with Sˆn the +spin-1/2 operator along the direction ˆn. The circles mark the opti- +mum of (FQ/tp) for tp > 0. b, Metrological enhancing exponent +{∆f = logN(FQ/N), ∆ = logN(FQτ/Ntp)} for different values +of α. We obtain each value of ∆ and ∆f by numerically fitting the +quantities (FQ/tp) and FQ with respect to the system size N (Sec. 5 +in Supplementary Information). Here, the interrogation time is set as +a unit (τ = 1). +chain (D = 1) with the Hamiltonian given by +HIsing = +1 +Nα +� +i 1 respectively to ensure system +energy an extensive quantity [52]. Despite the fact that all +terms of the Ising Hamiltonian commute, rich genuine quan- +tum features (e.g. spin squeezing [27], quantum magnetism +[36] etc.) can occur. In Fig. 3a, we investigate in detail the +growth dynamics of the QFI for different values of α, and +find the maximal point where an optimal enhancing factor +(FQ/tp) [cf. Eq.(6)] is obtained. It is worth noting that the +optimal metrological points are no more those maximizing +the QFI when taking the state preparation time into account. +As can be seen from Fig. 3b, for long-range interaction, the +metrological enhancing exponents ∆ are smaller than the ones +(denoted as ∆f) without considering the required time for re- +source state preparation (i.e. solely determined by FQ/N), +namely ∆ < ∆f ≡ logN(FQ/N). Nevertheless, it still re- +sults in an apparent quantum advantage over the SQL (i.e. +∆ ≳ 0.4) if α < 1. In contrast, the SQL can not be surpassed +for α ≳ 1.4, since the maximal QFI would only scale approx- +imately as FQ ∼ N (cf. Sec. 5 and Fig. S1 in Supplementary +Information). +Our result also hints that the quantum advantage of +quantum metrology can be achieved by exploiting higher- +dimensional systems. For a larger dimension D, local infor- +mation can propagate along more directions to spread across +the entire lattice, resulting in the speed-up of QFI growth +which is evidenced by the power exponent D of RL(t) [cf. +Eq. (4)]. Given a power-law decaying exponent α, a larger D +would change the shape of the effective light cone, and re- +sult in an improved bound for the strong precision limit (see +Fig.2). An important example is the multipartite entanglement +generation in quantum systems with U(1) symmetric dipo- +lar interactions, i.e. HXX = − � +i 0 and pm > 0, one can find that +(√pn − √pm)2 ≤ (pn − pm)2 +pn + pm +≤ 2(√pn − √pm)2. +(S2) +Based on the definition of QFI in Eq. (1) in the main text, we have +2 +� +n,m +(√pn − √pm)2 |⟨n|K|m⟩|2 ≤ FQ[ϱ, K] ≤ 4 +� +n,m +(√pn − √pm)2 |⟨n|K|m⟩|2 . +(S3) +By further introducing a coefficient cWY ∈ [1, 2], the following expression for +the QFI can be obtained, +FQ[ϱ, K] = 2cWY +� +n,m +(√pn − √pm)2 |⟨n|K|m⟩|2 . +(S4) +Therefore, the QFI of the prepared metrological state ϱ(t) at an evolution time +t can be formulated as +FQ[ϱ(t), K] = 2cWY +� +n,m +(√pn − √pm)2 |⟨n|K|m⟩|2 += 2cWY +� +n,m +⟨n|[K, +� +ϱ(t)]†|m⟩⟨m|[K, +� +ϱ(t)]|n⟩ += 2cWY tr +� +[K, +� +ϱ(t)]†[K, +� +ϱ(t)] +� += 2cWY tr +�[K(t), √σ]†[K(t), √σ] +� += 2cWY +� +i,j +tr +�[Ki(t), √σ]†[Kj(t), √σ] +� , +(S5) +2 + +Here, the interrogation operator is K(t) = U†(t)KU(t) = � +i Ki(t), where +Ki(t) ≡ U†(t)KiU(t) represents the time evolution of local interrogation oper- +ators in the Heisenberg picture. The last equality [namely Eq. (3) in the main +text] implies that the QFI dynamics to prepare a metrological resource state +is deeply related to the spreading of local operators. We define the component +of the QFI collaboratively contributed by the site i and j as +αij(t) ≡ tr +�[Ki(t), √σ]†[Kj(t), √σ] +� , +(S6) +and the QFI can then be written as +FQ[ϱ(t), K] = 2cWY +� +i,j +αij(t). +(S7) +Generally, by utilizing Cauchy–Schwarz inequality, we obtain that +|αij(t)|2 ≤ tr +�[Ki(t), √σ]†[Ki(t), √σ] +� tr +�[Kj(t), √σ]†[Kj(t), √σ] +� +≤ 1 +4FQ[ϱ, Ki]FQ[ϱ, Kj] +≤ 1 +4∥Ki∥2 +s∥Kj∥2 +s. +(S8) +The second inequality results from a similar relation as Eq. (S5) between the +QFI and the local operator Ki, namely +FQ[ϱ(t), Ki] = 2cWY tr +�[Ki(t), √σ]†[Ki(t), √σ] +� = 2cWYαii(t), +(S9) +which directly yields that +αii(t) ≤ 1 +2FQ[ϱ(t), Ki]. +(S10) +While in the third inequality, we use the fact that FQ[ϱ, Ki] ≤ ∥Ki∥2 +s (cf. +Ref. [S1]), with the semi-norm ∥ • ∥s taking the spectrum width, namely the +3 + +difference between the largest and smallest eigenvalues. By further defining +κ ≡ maxi∈Λ ∥Ki∥2 +s as the maximum spectrum width of the local interrogation +operators {Ki}, we conclude that |αij(t)| ≤ κ/2 ∼ O(1) for arbitrary i and j. +2. Causality relation for local operator spreading +In this section, we sketch the proof for the projection of the time-evolved +local operator [subject to the Hamiltonian in Eq. (2) of the main text], Ki(t) = +U†(t)KiU(t). +Mathematically, we define the projection operation onto its +neighboring ball region denoted by i[R] as +Ki(t, i[R]) ≡ +1 +tri[R]c ˆ1i[R]c tri[R]c[Ki(t)] ⊗ ˆ1i[R]c, +(S11) +where i[R]c denotes the complementary set of i[R], i.e. +i[R]c = Λ \ i[R]. +Following Ref. [S2], let U be a unitary operator acting on i[R]c and µ(U) be +the Haar measure for U, one can rewrite Ki(t, i[R]) in the following form +Ki(t, i[R]) = +� +dµ(U)UKi(t)U †, +(S12) +and therefore +∥Ki(t) − Ki(t, i[R])∥ ≤ +� +dµ(U)∥[Ki(t), U]∥ ≤ maxU ∥[Ki(t), U]∥, +(S13) +where maxU accepts all unitary operators U supported on i[R]c. By further +using the standard commutator form of Lieb-Robinson bound for generic quan- +tum many-body lattices, one can find that +∥Ki(t) − Ki(t, i[R])∥ ≤ maxU ∥[Ki(t), U]∥ ≤ C(t, R). +(S14) +Here, C(t, R) is a function that takes the forms of: (i) C(t, R) ∼ evt−R and v ≃ +O(1) for short-range interaction [S3]; (ii) C(t, R) ∼ ta/Rb (with a, b ≃ O(1) +4 + +are positive exponents) for long-range interactions with α > 2D [S4]; and (iii) +C(t, R) ∼ evt/Rα and v ≃ O(1) for long-range interactions with α ∈ (D, 2D] +[S5]. The right-hand side of Eq. (S14) would decay to zero by requiring that +R ≳ RL(t) (up to a constant factor), where RL(t) represents the effective light +cone. In this sense [S6], one obtains that +Ki(t) ≃ Ki(t, i[R]) +if +R ≳ RL(t), +(S15) +and below we further abbreviate it as Ki[R](t) ≡ Ki(t, i[R]) for simplicity. +3. Proof of the bound for QFI growth +Based on the causality relation in the above section, the component of the +QFI collaboratively contributed by the site i and j can be approximately rewrit- +ten as +αij(t) ≃ tr +�[Ki[R](t), √σ]†[Kj[R](t), √σ] +� +if +R ≳ RL(t). +(S16) +Importantly, if the distance between the site i and j is outside the light cone, +i.e. dij ≥ 2R ≳ 2RL(t), the two ball regions Ki[R](t) and Kj[R](t) would fail +to intersect with each other (see Fig. 1b in the main text), and one can derive +that +αij(t) = tr +�√σΛ\i[R][Ki[R](t), √σi[R]]†[Kj[R](t), √σj[R]]√σΛ\j[R] +� += tr +�√σi[R][Ki[R](t), √σi[R]]†[Kj[R](t), √σj[R]]√σj[R]σΛ\(i[R]∪j[R]) +� += tr +�√σi[R][Ki[R](t), √σi[R]]†� tr +�[Kj[R](t), √σj[R]]√σj[R] +� += 0, +(S17) +5 + +where σA denotes the projection of σ onto the region A ⊂ Λ. The second +equality results from that +√σΛ\i[R]√σΛ\j[R] = √σi[R]√σj[R]σΛ\(i[R]∪j[R]), +(S18) +due to the non-intersection of the two sets i[R] and j[R]. The fourth equality +in Eq. (S17) can be obtained by noticing the identity that tr([A, B]B) = 0 with +A and B arbitrary Hermitian operators. Consequently, the QFI (Eq.S7) can +be bounded as +FQ = 2cWY +� +i +� +�αii(t) + βi(t) +� +j∈i[2R]\i +1 +� +� +≤ 2cWY +� +i +�αii(t) + βi(t)γ2DRD� +(S19) +with βi(t) ≡ � +j∈i[2R]\i Re[αij(t)]/ � +j∈i[2R]\i 1 ≤ κ/2. In the second inequality +of Eq. (S19), we have used a geometry assumption that maxi∈Λ|i[R]| ≤ γRD, +where the introduced geometric parameter γ is determined based on the lattice +structure alone. By further defining that αt ≡ maxi∈Λ αii(t) as well as βt ≡ +maxi∈Λ βi(t), and taking R = RL(t), we arrive at +FQ ≲ 2cWY[αt + βt2DγRD +L (t)]N. +(S20) +This result straightforwardly gives rise to Eq. (4) in the main text using +{|αt|, |βt|} ≤ κ/2. +6 + +4. Proof of the strong precision limit of quantum metrology +The celebrated quantum Cramér-Rao bound [S7] states that the ultimate +measurement precision via local unbiased estimates is lower bounded by +δλ ≥ +1 +� +νFQτ 2, +(S21) +where ν is the number of identical measurement repetitions and is constrained +by the total measurement time T, i.e. ν ≤ T/(τ +tp). Here, tp and τ represent +the required time for single-run metrological state preparation and signal inter- +rogation respectively. As a result, the above precision limit can be reformulated +as +δλ ≥ +� +N(1 + tp/τ) +FQ +δλSQL ≡ N − ∆ +2 δλSQL, +(S22) +where δλSQL ≡ 1/ +√ +NTτ represents the standard quantum limit (SQL). By +making the natural assumption that tp ≫ τ for large many-body quantum +systems, one would obtain Eq. (5) with the metrological enhancing exponent +[Eq. (6) in the main text] defined as +∆ = −2 logN +�� +N(1 + tp/τ) +FQ +� +≈ logN +�FQ +tp +· τ +N +� +. +(S23) +Without loss of generality, we can set τ = 1 as a unit and focus on the scaling +behavior of FQ/tp with respect to N. +Next, we exploit the established bound of the QFI growth [cf. Eq. (4) in +the main text], i.e. +FQ/N ≲ RD +L (tp) (up to some constant coefficients) to +derive the strong precision limits set by Eqs. (7-9) in the main text. For short- +range interacting system, i.e. RL(tp) ∼ tp [S3, S6], using our result in Eq. (4) +of the main text, we can conclude that, in order to achieve the QFI density +7 + +of FQ/N ∼ N ∆f with the assumption that ∆f ∈ [0, 1], a metrological state +preparation time at least on the order of +tp ∼ +�FQ +N +� 1 +D +∼ N +∆f +D , +(S24) +would be required. Hence, the metrological enhancing exponent in this scenario +is given by +∆ = logN N(1− 1 +D)∆f = +� +1 − 1 +D +� +∆f ≤ 1 − 1 +D, +(S25) +namely Eq. (7) in the main text. While for long-range interacting systems: (i) +if α ∈ (2D, 2D + 1], the light cone is given by RL(tp) ∼ t1/ξ +p +[S4], and then +Eq. (4) in the main text allows us to find that the minimal state preparation +time to reach FQ/N ∼ N ∆f needs to satisfy +tp ∼ +�FQ +N +� ξ +D +∼ N +ξ +D∆f, +(S26) +which further leads to Eq. (8) in the main text, i.e. +∆ = logN +�N ∆f +tp +� += +� +1 − ξ +D +� +∆f ≤ 1 − ξ +D. +(S27) +(ii) if α ∈ (D, 2D], then RL(tp) ∼ etp [S5, S8]. Similarly, the state preparation +time shall be larger than +tp ∼ log N ∆f/D ∼ polylog(N), +(S28) +and thus we have +∆ ≤ 1 − logN polylog(N), +(S29) +namely Eq. (9) in the main text. +8 + +5. Behavior of the QFI growth of Ising model +The pure Ising model for demonstrating the metrological enhancement of +long-range interacting systems is exactly solvable. Below, we provide the an- +alytical formulas to calculate the QFI dynamics. Starting from the coherent +spin state along the x direction, the maximal QFI at a given evolution time t +(by optimizing the interrogation operator Sˆn that points along the direction ˆn) +can be obtained as follows +FQ(t) = N + maxφ +� +i̸=j +� +sin2(φ)Cy +ij(t) + 1 +2 sin(2φ)Cyz +ij (t) +� +, +(S30) +where +Cy +ij(t) = 1 +2 +� +k̸=i,j +cos [2(Jik − Jjk)t] − 1 +2 +� +k̸=i,j +cos [2(Jik + Jjk)t] , +(S31) +and +Cyz +ij (t) = − sin(2Jijt) +� +� � +k̸=i,j +cos(2Jikt) + +� +k̸=i,j +cos(2Jjkt) +� +� , +(S32) +with Jij ≡ 4/(Nα|i−j|α). For α = 0 and Jij = 4/N, the above formulas reduce +to the well-known results for spin squeezing under one-axis-twisting quantum +dynamics [S9, S10], namely +FQ(t) = N + N(N − 1) +� +A + +√ +A2 + B2 +� +/4, +(S33) +where A = 1 − [cos(2u)]N−2, and B = 4 sin(u)[cos(u)]N−2 with u = 8t/N. +Based on these analytical formulas of the QFI at any evolution time t, the +QFI dynamics for a given system size N can be determined numerically. In +Fig. S1, we depict the scaling behavior of the maximal QFI by setting the value +9 + +0 +50 +100 +150 +200 +250 +300 +0 +10 +20 +30 +40 +50 +60 +70 +0 +50 +100 +150 +200 +250 +300 +0 +1 +2 +3 +4 +5 +6 +7 +FQ/N +FQ/N +N +(a) +(b) +FIG. S1. Scaling behavior of the QFI for long-range Ising chain. Starting from the +coherent spin state along the x direction, we maximize the QFI at all times t by optimizing +local interrogation operators, Ki = Sˆn, with Sˆn the spin-1/2 operator along the direction ˆn. +Each square marks the optimum of FQ for a specific value of N. a, Polynomial increase of +the QFI at α = 0.5 as FQ/N = a + bNc with a = 1.41, b = 0.57 and c = 0.85 (red curve). +b, Saturation of the QFI for α = 1.4. The maximal QFI is well fitted by the green curve, +i.e. of the form FQ/N = a[1 − e−(N/b)c] with a ≈ 6.65, b ≈ 19.76 and c ≈ 0.37. Therefore, +for large-size systems, the QFI would saturate as FQ ∼ N. +10 + +of the interaction decaying exponent α as 0.5 and 1.4 respectively [cf. Eq. (10) +in the main text]. Importantly, our numerical result suggests that the maximal +QFI for α ≳ 1.4 would not surpass the SQL. +[S1] Boixo, S., Flammia, S. T., Caves, C. M. & Geremia, J. Generalized limits for single- +parameter quantum estimation. Phys. Rev. Lett. 98, 090401 (2007). +[S2] Bravyi, S., Hastings, M. B. & Verstraete, F. Lieb-Robinson bounds and the generation +of correlations and topological quantum order. Phys. Rev. Lett. 97, 050401 (2006). +[S3] Lieb, E. H. & Robinson, D. W. The finite group velocity of quantum spin systems. +Commun. Math. Phys. 28, 251–257 (1972). +[S4] Tran, M. C., Guo, A. Y., Baldwin, C. L., Ehrenberg, A., Gorshkov, A. V. & Lucas, +A. Lieb-Robinson light cone for power-law interactions. Phys. Rev. Lett. 127, 160401 +(2021). +[S5] Eisert, J., van den Worm, M., Manmana, S. R. & Kastner, M. Breakdown of quasilo- +cality in long-range quantum lattice models. Phys. Rev. Lett. 111, 260401 (2013). +[S6] Kuwahara, T. & Saito, K. Strictly linear light cones in long-range interacting systems +of arbitrary dimensions. Phys. Rev. X 10, 031010 (2020). +[S7] Braunstein, S. L. & Caves, C. M. Statistical distance and the geometry of quantum +states. Phys. Rev. Lett. 72, 3439–3443 (1994). +[S8] Hastings, M. B. & Koma, T. +Spectral gap and exponential decay of correlations. +Commun. Math. Phys. 265, 781–804 (2006). +[S9] Kitagawa, M. & Ueda, M. Squeezed spin states. Phys. Rev. A 47, 5138–5143 (1993). +[S10] Pezzè, L., Smerzi, A., Oberthaler, M. K., Schmied, R. & Treutlein, P. +Quantum +metrology with nonclassical states of atomic ensembles. Rev. Mod. Phys. 90, 035005 +(2018). +11 + diff --git a/vdFLT4oBgHgl3EQfjy_2/content/tmp_files/load_file.txt b/vdFLT4oBgHgl3EQfjy_2/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..c9b693c187935fc0174c6433605d5e5a6529a310 --- /dev/null +++ b/vdFLT4oBgHgl3EQfjy_2/content/tmp_files/load_file.txt @@ -0,0 +1,1090 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf,len=1089 +page_content='Strong quantum metrological limit from many-body physics Yaoming Chu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' ∗ Xiangbei Li,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' ∗ and Jianming Cai1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' † 1School of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' International Joint Laboratory on Quantum Sensing and Quantum Metrology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Institute for Quantum Science and Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Wuhan National High Magnetic Field Center,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Huazhong University of Science and Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Wuhan 430074,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' China 2Shanghai Key Laboratory of Magnetic Resonance,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' East China Normal University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Shanghai 200062,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' China Surpassing the standard quantum limit and even reaching the Heisenberg limit using quantum entanglement,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' represents the Holy Grail of quantum metrology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' However, quantum entanglement is a valuable resource that does not come without a price.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' The exceptional overhead for the preparation of large-scale entangled states raises disconcerting concerns about whether the Heisenberg limit is fundamentally achievable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Here we find a universal speed limit set by the Lieb-Robinson light cone for the quantum Fisher information growth to charac- terize the metrological potential of quantum resource states during their preparation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Our main result establishes a strong precision limit of quantum metrology accounting for the complexity of many-body quantum resource state preparation and reveals a fundamental constraint for reaching the Heisenberg limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Our result makes it possible to identify the essential features of quantum many-body systems that are crucial for achieving the quantum advantage of quantum metrology and brings a new perspective to understanding many-body quantum dynamics from quantum metrology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Quantum metrology, as part of the rapidly rising field of quantum science and technology, is capable of achieving en- hanced precision measurement by exploiting quantum strate- gies and promises unprecedented applications in basic sci- ence and technology [1–6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Importantly, irrespective of clas- sical accidental errors [1], quantum mechanics imposes a fun- damental limit on the accuracy to which measurements can be performed, called the Heisenberg limit [7–9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' The cele- brated Heisenberg limit conventionally refers to a measure- ment precision scaling as 1/N (where N is typically regarded as the number of probes employed) and acts as a hallmark of scaling improvement over the standard quantum limit (SQL), which arises from uncorrelated measurements and is given by 1/ √ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' The advantage of quantum metrology in terms of reaching the Heisenberg limit often attribute to quantum en- tanglement [10–13], such as the “cat” state of N probes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Al- though the improved scaling has been unfortunately demon- strated to be fragile when suffering from noise sources [14– 16], a number of clever noise-robust quantum metrological schemes [17–19] have been proposed to battle against deco- herence, making it not a fundamentally unsolvable obstacle for reaching the Heisenberg limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' In contrast, given that the preparation of large-scale entan- gled states of many-body quantum systems is usually a highly demanding and challenging task, the following intricate and critical problem remains elusive: whether is there any funda- mental constraint that prevents reaching the Heisenberg limit imposed by the complexity of state preparation [20–22]?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Ad- dressing this problem and establishing a stronger precision limit would put comparisons of entanglement-enhanced quan- tum measurements with the SQL on a more fair footing, and consistently consolidate the foundation of the quantum ad- vantage offered by quantum metrology over classical counter- parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' It also relates to another crucial problem: is there any simple and universal principle to find quantum metrological systems that are favorable for achieving the quantum advan- tage of quantum metrology?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' In this letter, we address these problems by quantifying the growth of quantum Fisher information (QFI) for the metrolog- ical state preparation in generic quantum many-body systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' As our main result, we find a universal speed limit for the QFI growth set by the celebrated Lieb-Robinson (LR) light cone from many-body physics [23, 24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' This provides a versatile tool to lower bound the minimal time required by metrological resource state preparation, and thus establishes the precision limit for quantum metrology explicitly involving the complex- ity of state preparation (dubbed “strong precision limit”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Ap- plying our result to quantum many-body systems with Ising and dipolar interactions, we illustrate how to achieve the ad- vantage of quantum metrology through long-range interact- ing and higher-dimensional systems, which presents insight- ful design principles for quantum metrological systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' The result also connects quantum metrology with quantum infor- mation propagation and offers a new perspective to under- standing many-body quantum dynamics via the concept of QFI growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Fundamental constraint for QFI growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='— Quantum Fisher information, FQ, as a fundamental concept in quantum metrology, determines the optimal measurement precision us- ing a given quantum resource state ϱ [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' It quantifies the sensitivity of ϱ to a parameter-dependent unitary transforma- tion generated by an interrogation operator K, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' ϱϑ = e−iϑKϱeiϑK with ϑ a phase to be estimated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Usually the inter- rogation operator is local, K = �N i=1 Ki, with Ki defined on the i-th individual probe, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 1a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' For a general resource state, spectrally decomposed as ϱ = � n pn|n⟩⟨n|, the QFI takes a structure of the following form FQ[ϱ, K] = 2 � n,m (pn − pm)2 pn + pm |⟨n|K|m⟩|2 , (1) where the sum includes only terms with pn+pm > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' A larger QFI indicates a better distinguishability between neighboring parametrized quantum states ϱϑ and ϱϑ+δϑ, and thus a more sensitive ϱ to the operator K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='12113v1 [quant-ph] 28 Jan 2023 2 R i j U(1) ϑ U(2) ϑ ϱ σ1 σ2 σN (1) (2) (N) Measurement Preparation U(N) ϑ a b FQ/N RL(t) FQ ≲ RD L (t) RL(t) dij/2 QFI by site and i j 0 O(1) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Metrological resource state preparation and QFI growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' a, Conventional scheme for quantum metrology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' A N-probe quan- tum system is prepared in the resource state ϱ and is fed into N parallel local channels (each one is described as U (i) ϑ ≡ e−iϑKi) to sense an unknown phase ϑ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' b, Spreading of local operators in a quantum lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' The quasilocality implied by LR bound ensures that Ki(t) (red region) is well approximated by an operator Ki(t, i[R]) defined on a ball region i[R] (dashed circle) with R ≳ RL(t), where RL(t) represents the effective light cone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' The QFI collaboratively contributed by the site i and j (red curve, Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 1 in Supplementary In- formation) begins to be nonzero only when the two balls Ki(t, i[R]) and Kj(t, j[R]) grow to touch each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Consequently, the upper bound of the QFI growth (green curve) would be constrained by the effective light cone RL(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Quantum metrology often seeks such metrological states ϱ (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' GHZ state [26], squeezed spin states [27, 28], crit- ical ground states [29], etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=') to enhance the optimal mea- surement precision [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' These strongly correlated quantum metrological states are usually prepared via coherent interac- tions between individual probes, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' [30–34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' We con- sider generic Hamiltonians with few-body interactions on a D-dimensional lattice, with Λ the total particle set and the cardinality |Λ| = N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' In detail, the interaction Hamiltonian of a k-local form with bounded one-site energy [35] can be expressed as, H = � |X|≤k hX, max i∈Λ � X:X∋i ∥hX∥ ≲ O(1), (2) where each interaction term hX acts on the particle subset X ⊂ Λ, and ∥ • ∥ is the operator norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Remarkably, in state- of-the-art quantum platforms including trapped ions [36, 37], Bose-Einstein condensates [38–42], Rydberg atoms [43, 44] etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=', the interaction Hamiltonians to generate unprecedented levels of multipartite entanglement with N ≳ O(100) gener- ally belong to this family of Hamiltonian [Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' (2)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' The key is to find the speed limit of the QFI growth for a quantum metrological resource state ϱ(t) prepared by a unitary evolution U(t) with the Hamiltonian in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' (2), see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 1a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Starting from a full product state σ = ⊗N i=1σi, the QFI of ϱ(t) = U(t)σU†(t) [cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' (1)] associated with K can be formulated as (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 1 in Supplementary Information) FQ(t) = 2cWY � i,j tr � [Ki(t), √σ]†[Kj(t), √σ] � , (3) with cWY ∈ [1, 2] relevant to the Wigner-Yanase skew in- formation [45], and Ki(t) = U†(t)KiU(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' This result re- veals an explicit connection between the evolution of QFI and the spreading as well as interference of on-site operators, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 1b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Such a connection will enable us to analyze the “growth” behavior of the QFI with respect to the preparation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' In non-relativistic quantum mechanics, by analogy to Ein- stein’s relativity, Lieb-Robinson bound imposes one of the most fundamental restrictions to quantum dynamics, lead- ing to the formation of an “effective light cone”, RL(t), that bounds the propagation of quantum information to a finite ve- locity (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' causality in a quantum many-body lattice) [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Mathematically, the time-dependent commutator between two operators Ki(t) and Kj (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' [Ki(t), Kj]) decrease rapidly with the graph-theoretic distance dij separating site i and j outside the light cone, which ensures an approximation of Ki(t) as Ki(t) ≈ Ki(t, i[R]) (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 2 in Supplementary In- formation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Here, R ≳ RL(t) up to a constant factor, and Ki(t, i[R]) represents a projection of Ki(t) onto the subset i[R] ⊂ Λ that is a ball region centered at the site i with ra- dius R, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 1b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Exploiting such a causality relation, we establish an upper bound for the growth of QFI in many-body quantum lattices as (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 3 in Supplementary Information) FQ(t) ≲ κcWY � 1 + γ2DRD L (t) � N, (4) where κ ≃ O(1) represents the maximal spectrum width of the local interrogation operators {Ki}, and γ is a positive con- stant determined by the geometry of a quantum lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' There- fore, given a state preparation time t, the maximal QFI that can be achieved is strictly constrained by the geometry and the light cone for a quantum many-body lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Such a fun- damental constraint determines whether the metrological sys- tem can surpass the SQL and even reach the Heisenberg limit when accounting for the overhead of quantum resource state preparation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Strong precision limit of quantum metrology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='— In quantum metrology, in order to estimate a parameter λ encoded in the phase ϑ = λτ with τ the interrogation time of single measure- ment, the minimal uncertainty of multiple identical measure- ments is set via the well-known quantum Cramér-Rao bound (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 4 in Supplementary Information), δλ ≥ N −∆/2λSQL ≡ N −(1+∆)/2 1 √ Tτ (5) 3 Here, δλSQL ≡ 1/ √ NTτ represents the standard quantum limit with T the total measurement time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' The exponent ∆ characterizes the quantum metrological enhancement to beat the SQL;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' specifically, ∆ = 0 and 1 correspond to the SQL and Heisenberg scaling respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' For a sufficiently large quantum many-body system, the preparation time (below de- noted as tp) of entangled metrological resource state would generally be much longer than the signal interrogation time (which is limited by the system’s coherence time), namely tp ≫ τ, and then the number of measurement repetitions is upper bounded by T/tp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Thus, the enhancing exponent ∆ is dominantly determined by the ratio of QFI to the state prepa- ration time (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 4 in Supplementary Information), ∆ = logN �FQ tp τ N � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' (6) Based on the QFI growth bound in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' (4), we are able to de- termine the maximal exponent ∆ through the scaling behavior of (FQ/tp), and then strengthen the ultimate precision limit of quantum metrology in generic quantum many-body lattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' For short-range interacting systems, namely, the decay of interaction strength is faster than an exponential decay relative to the distance between separated sites, Lieb and Robinson proved in 1972 an effective linear light cone RL(t) ≃ vLRt with vLR ∼ O(1) the so-called LR velocity [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' By us- ing our result in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' (4) that FQ ≲ NRD L (tp) ∼ NtD p , the metrological enhancing exponent would be upper bounded by (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 4 in Supplementary Information) ∆ ≤ 1 − 1 D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' (7) Particularly, for one dimensional (1D) short-range interacting quantum systems, the result implies that one can only achieve a zero enhancing exponent, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' ∆ = 0, and thereby a sur- prising precision scaling as δλSQL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' In this scenario, even if the system might be able to be prepared in a global multi- partite entangled state with FQ ∼ N 2, the Heisenberg scal- ing would not be feasible due to the required state preparation time that scales at least linearly with the system size, namely tp ∼ FQ/N ∼ N following Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' For long-range interacting systems, we consider two-body interactions of the form ∥hi,j∥ ≲ d−α i,j , where {hij} are bi- partite interaction operators, di,j is the distance from the site i to j, α is the power-law decaying exponent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' A strictly linear light cone exists for sufficiently large α (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' α > 2D + 1) in generic long-range interacting lattices [46], and thus the quantum metrological enhancing exponent is also bounded by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='(7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Nevertheless, as the decaying exponent α becomes smaller, a linear light cone can be broken [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' In the regime of α ∈ (2D, 2D + 1], the shape of the effective light cone becomes polynomial and is given by RL(t) ≃ ct1/ξ, where c is a constant of O(1) and ξ = α − 2D up to an arbitrarily small constant [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Therefore, our result in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' (4) leads to the following metrological enhancing exponent as (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 4 in 1 1 − 1 D 2D + 1 2D Heisenberg scaling Δ = logN(FQτ/Ntp) D SQL t ∼ log r α 0 t ∼ r t ∼ rξ Forbidden FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Bound of quantum metrological enhancement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' In the regime of α > 2D + 1, a quantum many-body lattice is governed by a linear light cone (t ∼ r), resulting in that ∆ ≤ 1 − 1/D;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' while in the regime of α ≤ 2D + 1, “supersonic” information propagation (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' polynomial t ∼ rξ and logarithmic t ∼ log r light cones) is possible, which gives rise to that ∆ ≤ 3−α/D for α ∈ (2D, 2D+1] and ∆ ≤ 1 − logN(polylog(N)) (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' approaching the Heisenberg scaling in the limit of large system size) for α ∈ (D, 2D].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Supplementary Information) ∆ ≤ 1 − ξ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' (8) As one can see, as α → 2D and ξ → 0+, the measure- ment precision would approach the Heisenberg scaling (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' ∆ = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' While in the regime of α ∈ (D, 2D], the LR bounds give rise to a “logarithmic light cone” (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' t ∼ log R), or equivalently an exponentially growing speed of quantum information propagation [24, 48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Similarly, according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' (4), this would lead to the quantum metrological enhance- ment as (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 4 in Supplementary Information) ∆ ≤ 1 − logN polylog(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' (9) Note that logN polylog(N) < o(1) (namely, smaller than an arbitrarily small positive constant) for N → ∞, therefore the Heisenberg limit becomes asymptotically achievable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 2, we summarize the scaling behavior of these strong pre- cision limits of quantum metrology with respect to the system size for α > D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' For ultra long-range interacting systems with α ∈ [0, D], the notion of quasilocality is broken [49–51];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' in other words, the causal region defined by an effective light cone might disappear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' In this scenario, even faster information propagation and metrological state preparation are possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' In particular, we remark that the interaction regime of α = 0 offers very favorable systems to prepare many-body entangled metrological resource states, especially in experimental plat- forms of Bose-Einstein condensates [13, 38–40, 42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Design principles for quantum metrological systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='— Our result suggests that long-range interaction is favorable for achieving the quantum advantage of quantum metrology over the SQL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Below we present an illustrative example of the Ising 4 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='8 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='4 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='8 1 0 2 4 6 0 10 20 30 40 α 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='8 a FQ/N t Δf Δ b α FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Metrological enhancement by Ising chain with long-range interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' a, QFI growth with respect to the evolution time for dif- ferent values of α with N = 60 sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Starting from the coherent spin state along the x direction, we maximize the QFI at all times t by optimizing local interrogation operators, Ki = Sˆn, with Sˆn the spin-1/2 operator along the direction ˆn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' The circles mark the opti- mum of (FQ/tp) for tp > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' b, Metrological enhancing exponent {∆f = logN(FQ/N), ∆ = logN(FQτ/Ntp)} for different values of α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' We obtain each value of ∆ and ∆f by numerically fitting the quantities (FQ/tp) and FQ with respect to the system size N (Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 5 in Supplementary Information).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Here, the interrogation time is set as a unit (τ = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' chain (D = 1) with the Hamiltonian given by HIsing = 1 Nα � i 1 respectively to ensure system energy an extensive quantity [52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Despite the fact that all terms of the Ising Hamiltonian commute, rich genuine quan- tum features (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' spin squeezing [27], quantum magnetism [36] etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=') can occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 3a, we investigate in detail the growth dynamics of the QFI for different values of α, and find the maximal point where an optimal enhancing factor (FQ/tp) [cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' (6)] is obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' It is worth noting that the optimal metrological points are no more those maximizing the QFI when taking the state preparation time into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' As can be seen from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 3b, for long-range interaction, the metrological enhancing exponents ∆ are smaller than the ones (denoted as ∆f) without considering the required time for re- source state preparation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' solely determined by FQ/N), namely ∆ < ∆f ≡ logN(FQ/N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Nevertheless, it still re- sults in an apparent quantum advantage over the SQL (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' ∆ ≳ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='4) if α < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' In contrast, the SQL can not be surpassed for α ≳ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='4, since the maximal QFI would only scale approx- imately as FQ ∼ N (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' 5 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' S1 in Supplementary Information).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Our result also hints that the quantum advantage of quantum metrology can be achieved by exploiting higher- dimensional systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' For a larger dimension D, local infor- mation can propagate along more directions to spread across the entire lattice, resulting in the speed-up of QFI growth which is evidenced by the power exponent D of RL(t) [cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' (4)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' Given a power-law decaying exponent α, a larger D would change the shape of the effective light cone, and re- sult in an improved bound for the strong precision limit (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' An important example is the multipartite entanglement generation in quantum systems with U(1) symmetric dipo- lar interactions, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/vdFLT4oBgHgl3EQfjy_2/content/2301.12113v1.pdf'} +page_content=' HXX = − � iX 211) +(I)00 +C(A"TI. →XII) + +11 +plasma-water treatment time results in more formation of acidic radicals/species in water (17, +22, 25). Moreover, the PAW produced using CO2 plasma was considerably higher (82.14% +higher after 60 minutes of treatment) than PAW produced using air plasma. Hence, the +generated species in water when exposed to air plasma were more acidic compared to CO2 +plasma. Ma et al. (9) Subramanian et al. (1), El Shaer et al. (11), and Lu et al. (16) also showed +a decrease in pH of PAW with increasing plasma treatment with water. + +The oxidizing potential of PAW when produced using air and CO2 plasma is shown in +figure 4 (b). The oxidizing potential of PAW gives information regarding net combinations of +oxidizing and reducing species formed in water after plasma exposure(12, 23, 25). The +oxidation-reduction potential (ORP) of PAW prepared using air plasma was higher compared +to PAW prepared using CO2 plasma. This was due to the formation of a high concentration of +oxidizing species in PAW when produced using air plasma compared to CO2 plasma. For 60 +minutes of plasma treatment, the ORP of PAW prepared using air plasma was 27.1% higher +compared to CO2 plasma. The increase in ORP of PAW with increasing plasma-water +treatment is also shown in the work reported by Guo et al. (3), Xiang et al. (10), and Ma et al. +(9), etc. + +The rough estimation of conducting ions were measured by measuring total dissolved +solids (TDS) and electrical conductivity (EC). The TDS and EC give the information regarding +conducting ions formed in water due to plasma-water interaction. The observed TDS and EC +of PAW, when prepared using air and CO2 plasma are shown in figure 4 (c, d). Increasing +plasma treatment with water increased the TDS and EC of PAW for both the air and CO2 +plasma. The observed TDS and EC of PAW prepared using air plasma were substantially high +compared to CO2 plasma (937.0% and 987.3% higher after 60 minutes of treatment). Hence, +the concentration of inorganic ions formed in water after air plasma exposure was extremely +higher compared to CO2 plasma. The increase in EC with plasma treatment was also supported + + + +12 +by results of Subramanian et al. (1), Zhang et al. (37), and Sivachandiran et al. (15), and Lu et +al. (16), etc. + + +Figure 4. The variation in physicochemical properties of plasma activated water prepared using +air and CO2 plasma with plasma treatment time. (a) pH, (b) oxidation-reduction potential +(ORP), (c) total dissolved solids (TDS), and (d) electrical conductivity (EC). Statistically +significant (p < 0.05) difference between the group mean ± standard deviation (µ ± σ) is shown +by a different lowercase letter. +RONS concentration in plasma-activated water +The above-discussed variation in physicochemical properties of water after plasma treatment +occurs due to the formation of numerous reactive species in water (1, 3, 4, 6-8, 14, 20, 22). The +mechanism of formation of these reactive species in PAW is shown in equations (14-25) (1, 4, +12, 13, 16, 18, 22, 25). + +00 + +13 +Formation of reactive oxygen species (ROS) in plasma-activated water: +𝑂2(𝑔) → 2𝑂(𝑔) + + + + + + + + +(14) +𝑂2(𝑔) + 𝑂(𝑔) → 𝑂3(𝑔) +𝑎𝑞. +→ 𝑶𝟑(𝒂𝒒.) + + + + + +(15) +𝐻2𝑂(𝑔) → 𝐻·(𝑔) + 𝐻𝑂·(𝑔) +𝑎𝑞. +→ 𝑯+(𝒂𝒒.) + 𝒆−(𝒂𝒒.) + 𝐻𝑂·(𝑎𝑞.) + +(16) +2𝐻𝑂·(𝑎𝑞.) → 𝑯𝟐𝑶𝟐(𝒂𝒒. ) + + + + + + + +(17) +𝑯𝟐𝑶𝟐(𝒂𝒒.) + 𝑶𝟑(𝒂𝒒.) → 𝐻𝑂·(𝑎𝑞. ) + 𝐻𝑂2 +· (𝑎𝑞.) + 𝑂2(𝑎𝑞. ) + + +(18) +2𝐻𝑂2 +· (𝑎𝑞.) → 𝑯𝟐𝑶𝟐(𝒂𝒒.) + 𝑂2(𝑎𝑞.) + + + + + +(19) +Formation of reactive nitrogen species (RNS) in plasma-activated water: +𝑁2(𝑔) → 2𝑁(𝑔) + + + + + + + + +(20) +𝑁(𝑔) + 𝑥𝑂(𝑔) → 𝑁𝑂𝑥(𝑔) +𝑎𝑞. +→ 𝑁𝑂𝑥(𝑎𝑞. ) {𝑁𝑂(𝑎𝑞.), 𝑁𝑂2(𝑎𝑞. ), 𝑁𝑂3(𝑎𝑞.),𝑒𝑡𝑐.} (21) +2𝑁𝑂2 (𝑎𝑞.) + 𝐻2𝑂(𝑎𝑞. ) → 𝑵𝑶𝟐 +−(𝒂𝒒.) + 𝑵𝑶𝟑 +−(𝒂𝒒.) + 𝟐𝑯+(𝒂𝒒. ) {𝐻𝑁𝑂2(𝑎𝑞. ) + +𝐻𝑁𝑂3(𝑎𝑞.)} +(22) +𝑁𝑂(𝑎𝑞. ) + 𝑁𝑂2(𝑎𝑞.) + 𝐻2𝑂(𝑎𝑞.) → 𝟐𝑵𝑶𝟐 +−(𝒂𝒒.) + 𝟐𝑯+(𝒂𝒒.) {𝐻𝑁𝑂2(𝑎𝑞.)} (23) +𝑵𝑶𝟐 +−(𝒂𝒒.) + 𝑶𝟑(𝒂𝒒.) → 𝑵𝑶𝟑 +−(𝒂𝒒.) + 𝑂2(𝑎𝑞.) + + + + +(24) +𝑵𝑶𝟐 +−(𝒂𝒒.) + 𝑯𝟐𝑶𝟐(𝒂𝒒.) → 𝑵𝑶𝟑 +−(𝒂𝒒.) + 𝐻2𝑂(𝑎𝑞. ) + + + +(25) +Figure 5 showed the identified and measured concentration of RONS (reactive oxygen-nitrogen +species) present in PAW when prepared using air and CO2 plasma. Figure 5 (a, c, e, g) showed +the RONS such as NO2ˉ ions, NO3ˉ ions, H2O2, and dissolved O3 in PAW when prepared using +air plasma. The reactions involved in the formation of RONS in PAW (air) are given in +equations (14-25 (16)). Moreover, the reactive species formed in PAW when using CO2 plasma + + + +14 +are given as H2O2, dissolved O3, dissolved CO2, and CO32ˉ ions (equations (14-19, 26-27)) +(figure 5 (f, h) and figure 6). + +The concentration of NO3ˉ and NO2ˉ ions present in PAW prepared using air and CO2 +plasma is shown in figure 5 (a-d). A continuous increase in NO3ˉ and NO2ˉ ions concentration +with plasma treatment time observed in PAW prepared using air plasma (figure 5 (a, c)). The +observed maximum concentration of NO3ˉ and NO2ˉ ions in PAW (air) were given as 4.0 mg +L-1 and 401.5 mg L-1, respectively. The NO3ˉ and NO2ˉ ions form nitric and nitrous acid in +PAW (air) (equations (20-25)) (1, 6, 8, 12, 22). As nitric acid is a strong acid, therefore the +lowest pH value of PAW (air) was given as 2.8. The increasing concentration of NO2ˉ and +NO3ˉ ions with activation time was also reported by Subramanian et al. (1) and Xiang et al. +(10) in PAW prepared in an air atmosphere. However, the PAW (CO2) did not contain any +observable concentration of NO3ˉ and NO2ˉ ions as shown in figure 5 (b, d). As discussed in +equations (1-4, 20-23), the formation of RNS (reactive nitrogen species) in PAW required +excited nitrogen species (12, 18, 22, 25) that were not observed in emission spectra of CO2 +plasma (figure 3). Hence, the possible RNS present in PAW (CO2) such as (NO2ˉ and NO3ˉ +ions) were beyond the detection limit of the present investigation. +Moreover, the concentration of H2O2 present in PAW (CO2) was 316.7% higher than +PAW (air). This was due to no interference of NO2ˉ ions in H2O2 determination in PAW (CO2). +The NO2ˉ ions present in PAW (air) react with H2O2 to give more stable NO3ˉ ions (equation +25) (6, 18, 25). Therefore, interfere with the H2O2 determination in PAW (air). The interference +of NO2ˉ ions in H2O2 concentration and variation can be seen in figure 5 (e). Initially (t = 0 +minutes), no H2O2 was present in PAW (air), as the plasma treatment increased to 30 minutes, +a continuous increase in the H2O2 concentration was observed. Increasing plasma treatment +time to 45 minutes results in a decrease in H2O2 concentration due to the reaction of NO2ˉ ions +with H2O2 to give more stable NO3ˉ ions. Further increasing plasma treatment time to 60 + + + +15 +minutes results in H2O2 concentration enhancement. This showed saturation of NO2ˉ ions and +H2O2 reaction in PAW (air) and the unreacted H2O2 shown by enhanced H2O2 in PAW (air). +Similar behavior as H2O2 was observed in the concentration of dissolved O3 in PAW (air). +Since, NO2ˉ ions present in PAW (air) also reacts with dissolved O3 to give more stable NO3ˉ +ions by following equation (24). This rise and fall in H2O2 concentration in PAW (air) with +increasing plasma treatment time also was observed in work reported by Subramanian et al.(1) +and Sivachandiran et al. (15). + +However, this rise and fall in H2O2 and dissolved O3 concentration in PAW prepared +using CO2 plasma was not observed due to the absence of NO2ˉ ions (figure 5 (b, d, g, h)). As +no N2 emission peaks bands were observed in the CO2 plasma (figure 3) that confirms the +absence of nitrogen species in CO2 plasma. Hence, no interference of NO2ˉ ions in PAW (CO2) +results in a monotonous increase in H2O2 and dissolved O3 concentration with increasing +plasma treatment time with water (figure 5 (g, h)). + + + +16 + +Figure 5. The variation in reactive oxygen-nitrogen species (RONS) concentration of plasma- +activated water prepared using air and CO2 plasma with plasma treatment time. (a, b) NO3ˉ +ions, (c, d) NO2ˉ ions, (e, f) H2O2 concentration, and (g, h) Dissolved O3. Statistically +significant (p < 0.05) difference between the group mean ± standard deviation (µ ± σ) is shown +by a different lowercase letter. + +The variation in titratable acidity, dissolved CO2, and CO32ˉ ions with plasma treatment +time in PAW (CO2) is shown in figure 6. The excited carbon oxides (COx) and carbon oxide +ions (COx+), etc. observed in emission spectra of CO2 plasma (figure 3) when comes in contact +with water enhances the solubility of CO2 and formed carbonic acid (H2CO3), etc. in water +(equations (26-27)(38)). Due to which physicochemical properties of PAW (CO2) changed. +The acidic species concentration formed in PAW (CO2) was measured by measuring titratable +acidity. Increasing plasma treatment time with water continuously and significantly (p < 0.05) + +NO2 (mg/L) +uantofix +NO2 (mg/L) +N (Air) +PAW (CO2) +H,02 (mg/L) +H202(mg/L) +PAW (Air) +PAW (CO2) +Control +PAW (CO,) +Control +PAW(Air) + +17 +increases the titratable acidity, dissolved CO2, and CO32ˉ ions concentration. The uniform +increase in titratable acidity, dissolved CO2, and CO32ˉ ions concentration signifies continuous +production of reactive species in PAW (CO2) with increasing plasma-water treatment time. The +CO32ˉ ions exist in the form of carbonic acid in PAW (CO2). The dissolved CO2 and CO32ˉ ions +(carbonic acid) are weak acids due to which the pH of PAW (CO2) decreased. However, this +decreases in pH of PAW (CO2) significantly (p < 0.05) low compared to PAW (air). +Formation of carbonic acid in PAW: +𝐻 (𝑎𝑞.) + 𝐶𝑂2(𝑎𝑞.) → 𝐻𝑂𝐶𝑂(𝑎𝑞.) + + + + + +(26) +𝐻𝑂𝐶𝑂 (𝑎𝑞. ) + 𝑂𝐻(𝑎𝑞. ) → 𝑯𝟐𝑪𝑶𝟑(𝒂𝒒. ) + + + + +(27) + +Figure 6. (a) Titratable acidity and dissolved CO2, and (b) CO32ˉ ions concentration in plasma- +activated water produced using CO2 plasma. Statistically significant (p < 0.05) difference +between the group mean ± standard deviation (µ ± σ) is shown by a different lowercase letter. +Hence, the above results and discussion showed the higher discharge current filaments in CO2 +plasma compared to air plasma. Moreover, the emission spectrum of CO2 plasma is free from + +120 +(a) +a豆 +(b) +a +6. +500 +100 +5 +a +Titratable acidity (mmol/L) +400 +4 +b +80 +Dissolved CO, (mg/L) +TOq +300 +60 +2 +ci +200 +d +40 +1 +d' +e +100 + 20 +0 +口 +- -- - Titratable acidity +e +1 +- -o- - Dissolved CO, +.0 +0 - +0 +15 +30 +45 +60 +0 +15 +30 +45 +60 +Plasma treatment time (min) +Plasma treatment time (min) + +18 +nitrogen containing species. As a results, formation of reactive nitrogen species (RNS) is not +occurring in PAW (CO2). Hence, selective generation of reactive oxygen species (ROS) occurs +in PAW (CO2). Moreover, due to the use of CO2 gas plasma for PAW preparation. The carbonic +acid, dissolved CO2, CO32ˉ ions also occurs in PAW due to which pH of PAW (CO2) is +decreased. However, the pH of PAW (CO2) is significantly lower than PAW (air). +Conclusion +The present work compares the properties of PAW produced using air and CO2 plasma. The +acidity of PAW (air) is significantly higher than PAW (CO2). This is due to the dissolution of +strong acids (nitric acid) in PAW (air) compared to weak acids (carbonic acid) of PAW (CO2). +In addition, the oxidizing potential, total dissolved solids, and electrical conductivity of PAW +(air) are significantly higher than PAW (CO2). This is due to PAW (air) has high concentration +of strong ionic species in the form of HNO3 compared to weak H2CO3 species of PAW (CO2). +The PAW prepared using CO2 plasma does not contain any reactive nitrogen species. This is +due to the emission spectra of CO2 plasma not containing any N2 emission band peaks. Hence, +CO2 plasma-water interaction does not form any reactive nitrogen species in PAW (CO2). +Hence, selective production of reactive oxygen species can be achieved without the +interference of reactive nitrogen species. Therefore, the concentration of dissolved H2O2 in +PAW (CO2) is higher than PAW (air). In conclusion, selective production of reactive oxygen +species in plasma-activated water is possible by using CO2 as a plasma-forming gas. The +presence of reactive oxygen species in PAW (CO2) makes it a useful antimicrobial agent. +Moreover, it can also be used in numerous applications where conventional PAW could not be +used due to its low pH (such as low pH PAW could not be used for surface disinfection of +metal objects since it oxidizes its surface and damage it). +Acknowledgments + + + +19 +This work was supported by the Department of Atomic Energy (Government of India) doctrate +fellowship scheme (DDFS). +Data availability statement +The data that support the findings of this study are available upon reasonable request from the +authors. +Conflict of interests +The authors declare that there are no conflicts of interests. +Authors’ contributions +Both authors contributed to the study conception and design. Material preparation, data +collection, and analysis were performed by Vikas Rathore. The first draft of the manuscript +was written by Vikas Rathore, and both authors commented on previous versions of the +manuscript. Both authors read and approved the final manuscript. +ORCID iDs +Vikas Rathore https://orcid.org/0000-0001-6480-5009 +References +1. +Subramanian PG, Jain A, Shivapuji AM, Sundaresan NR, Dasappa S, Rao L. Plasma‐ +activated water from a dielectric barrier discharge plasma source for the selective treatment of +cancer cells. Plasma Processes Polymers. 2020;17(8):1900260. +2. +Rathore V, Tiwari BS, Nema SKJPC, Processing P. Treatment of pea seeds with plasma +activated water to enhance germination, plant growth, and plant composition. Plasma +Chemistry Plasma Processing. 2022;42(1):109-29. + + + +20 +3. +Guo J, Huang K, Wang X, Lyu C, Yang N, Li Y, et al. Inactivation of yeast on grapes +by plasma-activated water and its effects on quality attributes. 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Astronomy Astrophysics. 2021;646:A172. + + diff --git a/y9E4T4oBgHgl3EQfYwwf/content/tmp_files/load_file.txt b/y9E4T4oBgHgl3EQfYwwf/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..b1af8538a106ce22e892f76cc0320a9ecb0bb5d4 --- /dev/null +++ b/y9E4T4oBgHgl3EQfYwwf/content/tmp_files/load_file.txt @@ -0,0 +1,565 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf,len=564 +page_content='1 Title: Selective generation of reactive oxygen species in plasma activated water using CO2 plasma Authors Vikas Rathore1,2* and Sudhir Kumar Nema1,2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Atmospheric Plasma Division, Institute for Plasma Research (IPR), Gandhinagar, Gujarat 382428, India 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai 400094, India *Email: vikas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='rathore@ipr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='in Abstract In the present work, a process of a selective generation of reactive oxygen species (ROS) such as H2O2 and dissolved O3 in plasma-activated water (PAW) is discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' For selective ROS generation, pure CO2 was used as a plasma-forming gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The gases species present in plasma and properties of PAW are compared in details when CO2 and air are used as plasma forming gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The results reveal that PAW (CO2) has significantly higher pH, and low oxidizing potential and electrical conductivity compared to PAW (air).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The formed species in PAW (CO2) due to CO2 plasma-water interaction are dissolved O3, H2O2, dissolved CO2, and CO32ˉ ions, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' In addition, no detectable concentration of NO2ˉ and NO3ˉ ions is observed in PAW (CO2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' PAW (CO2) has a substantially higher concentration of H2O2 compared to PAW (air).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Moreover, increasing plasma treatment time with water significantly increases H2O2 and dissolved O3 concentration in PAW (CO2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' However, PAW (air) showed a rise and fall in H2O2 and dissolved 2 O3 concentration with time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' In conclusion, selective generation of ROS in PAW is possible using CO2 as plasma-forming gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Keywords: Plasma activated water, CO2 plasma, CO2 emission spectra, reactive oxygen- nitrogen species, Introduction The plasma-activated water (PAW) technology is one of the fastest growing novel technologies in cold plasma field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' This is due to its continuously evolving applications in the field of plasma medicine, plasma agriculture, plasma food science and technology, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' (1-11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' These applications of PAW are possible due to the presence of various stable reactive oxygen- nitrogen species (RONS) in it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' These RONS in PAW are formed as a resultant product of plasma-water interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Moreover, it brings a physicochemical change in PAW properties such as pH, oxidizing potential, and electrical conductivity, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' (4, 9-16) Different RONS have different significance in their applications (2, 4, 5, 17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Such as species like H2O2, dissolved O3, HO·, and ONOOˉ have applications in microbial inactivation, selective killing of cancer cells, enhancing the shelf life of various food products such as fruits, vegetables, meat, seafood, and dairy products, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' (1, 3-5, 8-11, 17, 18) Moreover, reactive nitrogen species can be used as a nitrogen replacement source for numerous agriculture applications (2, 7, 15, 19-21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The PAW produced due to plasma-water exposure contains both the reactive oxygen species (H2O2, dissolved O3, HO·, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') and reactive nitrogen species (NO2ˉ ions, NO3ˉ ions, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') (4, 13, 22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' This is due to conventionally used plasma forming gases during PAW production which contain oxygen and nitrogen molecules or ionization of surrounding air by noble gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The frequently used plasma-forming gases at atmospheric pressure during PAW production are air, nitrogen (N2), oxygen (O2), argon (Ar), Helium (He), and their mixture in 3 different compositions (4, 7, 9, 11, 13, 18, 23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Working with 100% O2 plasma at atmospheric pressure is not recommended.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Since, O2 is highly oxidizing and can ignite flammable material rapidly that can cause explosions at atmospheric pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The use of inert gases (Ar or He) for plasma production mainly discharges the atmospheric air resulting in the generation of various RONS during plasma-water exposure (23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Hence, the production of plasma-activated water with a selective generation of ROS (free from nitrogen species) at atmospheric pressure is still an open challenge to be overcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The presence of RNS forms nitrous and nitric acid (strong acid) in PAW due to which the pH of PAW decreased substantially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Therefore, PAW cannot be used in applications that do not prefer low pH solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Due to this applicability of PAW is restricted and also one of the main disadvantages of PAW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' As per the authors’ knowledge, no work has been reported that emphasizes the selective generation of reactive oxygen species (ROS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The ROS have applications in microbial and biofilm inactivation, medicine, food preservation, and enhancing seeds germination, etc (2-4, 8, 9, 24).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' This research gap tries to be fulfilled in present work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The conventionally used oxidizing and inert gases plasma formed nitrogen species in water as discussed above (4, 7, 9, 11, 13, 18, 23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Moreover, nitrogen free gases such as phosphine (PH3), hydrogen sulphide (H2S), arsine (AsH3) and sulphur dioxide (SO2), etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' have environmental hazards (highly toxic) at atmospheric pressure, hence not recommended.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Therefore, the present work uses CO2 as plasma forming gas for selective generation of reactive oxygen species in plasma-activated water.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Moreover, the PAW produced using CO2 plasma is also compared with PAW produced using air plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The comparison was performed based on plasma characterization, formation of plasma reactive species/radicals, and properties of PAW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Material and Methods Experimental Setup 4 The experimental schematic of characterization of air and CO2 plasma and production of plasma-activated water (PAW) is shown in figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The air and CO2 plasma were produced in a co-axial cylindrical pencil plasma jet (PPJ)(25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The PPJ setup based on the principle of dielectric barrier discharge and the schematic is shown in figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' In which the central ground electrode was made using a 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='6 mm tungsten rod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The high voltage electrode was made from copper in cylindrical form with an inner diameter of 6 mm in which dielectric quartz tube (outer diameter × inner diameter – 6 mm × 4 mm) was tightly fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The discharge gap between the dielectric surface and the ground electrode was 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='2 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' To measure the voltage drop across the PPJ setup a 1000x voltage probe (Tektronix P6015A) and a 100 MHz bandwidth, 2 Gs s-1 sampling rate, and a 4-CH oscilloscope (Tektronix TDS2014C) was used (26).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' A 10x (Tektronix TPP0201) voltage probe was used to measure the current and transported charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' This probe measured the voltage drop across the resistor (R - 30 Ω) and capacitor (C - 100 µF) connected in series with the ground as shown in figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The air and CO2 plasma emission spectra were measured by capturing the afterglow light photons using optical fiber and a spectrometer (Plasma and Vacuum Solution (PVS), model UVH-1) as shown in figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' For plasma-activated water production, 50 ml of ultrapure milli-Q water was taken in 600 ml of a glass beaker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' This water was treated with air and CO2 plasma as shown in figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The air and CO2 gas flow rate were controlled using a flow controller and the flow rate was fixed at 3 l min-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' To enhance the solubility of plasma produced reactive species in water and escalate the reaction between gases reactive species and water, a continuous stirring of water and cooling of water were performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' For water stirring, a mortarless magnetic stirrer was used and for cooling of water, ice-cooled water was placed in contact with a glass beaker in which PAW was kept during plasma-water interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' 5 Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Schematic of production of plasma activated water using CO2 and air plasma and these gases plasma electrical and optical emission characterization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Equipments used for measurement of physicochemical properties of PAW The physicochemical properties of PAW (air or CO2) such as pH, oxidation-reduction potential (ORP), total dissolved solids (TDS), and electrical conductivity (EC) were measured for PAW characterization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' A Hanna Instruments pH meter (HI98121), HM digital ORP meter (ORP- 200), HM digital TDS meter (AP-1), and Contech Instruments Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' EC meter (CC-01) were used to measure the pH, ORP, TDS, and EC of PAW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Measurement of Reactive Oxygen-Nitrogen Species Concentration The reactive oxygen-nitrogen species (RONS) form in PAW (air or CO2) due to air plasma or CO2 plasma water interaction was determined semi-quantitatively and quantitatively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Strip test and colorimetry test kits were used to determine the initial RONS concentration in PAW and plasma (VISOCOLOR alpha (MACHEREY-NAGEL item no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' 935065) nitrate (NO3ˉ) ions AAA WW Glass Beaker CO2 Ice water storage contaner Spectrometer 6 colorimetry test kit, dissolved O3 test kit (Hanna Instruments item no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' HI38054), H2O2 determination test strips (QUANTOFIX Peroxide 25, MACHEREY-NAGEL item no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' 91319), NO2ˉ ions determination test strips (QUANTOFIX Nitrite, MACHEREY-NAGEL item no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' 91311), gases O3 determination test strips (Ozone Test for Ozone in air, MACHEREY-NAGEL item no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' 90736)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The quantitative estimation of RONS concentration present in PAW was measured spectrophotometrically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The NO3ˉ ions concentration was measured using the ultraviolet screening method (27), and the standard curve of NO3ˉ ions was made using NaNO3 solution with molar attenuation coefficient 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='0602 (mg L-1)-1(25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' In acidic region, NO2ˉ ions present in the solution when react with the reaction mixture of N-(1-naphthyl) ethylenediamine dihydrochloride and sulfanilamide give reddish purple azo dye (λmax = 540 nm)(27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' This characterstic of NO2ˉ ions was utilize to determine its unknown concentration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The standard curve of NO2ˉ ions was made using NaNO2 solution with a molar attenuation coefficient of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='0009 (µg L-1)-1(25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The unknown concentration of H2O2 in PAW was determined spectrophotometrically using the titanium sulfate method (13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The standard curve of H2O2 was made of 30% H2O2 solution (molar attenuation coefficient 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='4857 mM-1(25)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The unknown concentration of dissolved O3 in PAW was determined using the indigo colorimetric method (27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The titratable acidity and dissolved CO2 concentration in PAW (CO2) were determined using the titration method(8, 28).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The titratable acidity of PAW (CO2) was determined using 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='1 M sodium hydroxide (NaOH) solution and a freshly prepared phenolphthalein indicator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' In addition, the dissolved CO2 concentration in PAW was determined using 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='02 N sodium carbonate (Na2CO3) solution and freshly prepared phenolphthalein as an indicator (28).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The dissolved carbonate ions (CO32ˉ) concentration in PAW (CO2) was determined using the UV screening method (29, 30) with CO32ˉ molar attenuation coefficient 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='0008 (mg L-1)-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' 7 Data analysis All the experimental were performed at least three times (n ≥ 3) in the present investigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The results were shown as µ ± σ (mean ± standard deviation (Error)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The statistically significant difference with a significant level of 95% (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='05) among the groups mean were calculated using one-way analysis of variance followed by a post-hoc test (Fischer Least Significant Difference (LSD)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Results and discussion Voltage current waveform The air and CO2 plasma voltage current waveform produced in dielectric barrier discharge (DBD) pencil plasma jet (PPJ) is shown in figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The air and CO2 plasma current waveform showed nanosecond (ns) current filaments peaks (~ 100 ns, shown in figure S1 of supplementary material) over each negative and positive current half cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The cluster of these nanosecond current filaments lies in the microsecond region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Therefore, these current discharges are known as filamentary DBD micro discharges (26).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The discharge current peaks observed in CO2 plasma were higher than air plasma for the same applied voltage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' This signifies the radicals and species produced in CO2 plasma had higher current carrying affinity compared to air plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Alongside, the other possible region is the generation of high concentration of plasma radicals and species in CO2 plasma compared to air plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Due to which high discharge current was observed in CO2 plasma for the same process parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The plasma discharge power consumed during the air and CO2 plasma generation was measured using voltage-transported charge Lissajous figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Initially, the energy consumed during discharge was calculated using the integral of voltage over the charge domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' For power calculation, a product of energy consumed with frequency (40 kHz) was performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' To 8 compare the properties of PAW produced using air and CO2 plasma, the energy and power kept in the range of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='0125 mJ to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='015 mJ and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='5 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='6 W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Voltage current waveform of (a) air and (b) CO2 plasma produced in pencil plasma jet Optical emission spectra of air and CO2 plasma The optical emission spectra of air and CO2 plasma in the afterglow region are shown in figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The overlay plot of air (solid line) and CO2 (dotted lines) plasma showed the deviation between the emission bands peaks lines of air and CO2 plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' These emission bands peaks lines are formed due to electronic transition radiative decay of the upper vibration state to the lower vibration state of ions or molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The emission spectrum of air plasma consists of strong emission band peaks of N2 second positive system (C 3Πu → B 3Πg) along with weak emission intensity band peaks of N2+ first negative system (B 2Σu+ → X 2Σg+)(31, 32).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The reactions associated with this transition are shown in equations (1-4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Moreover, the CO2 plasma afterglow region showed strong intensity emission band peaks of CO2+ first negative system (A 2Πg → X 2Πu).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Along with that weak intensity emission band peaks of CO+ (A 2Π 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='5 9 (a) Air (b) 4 4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='0 2 2 Voltage (kV) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='5 Current (mA) Voltage (kV) 3 Current (mA) 0 0 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='0 2 2 3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='5 4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='4 9 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='0 40 20 0 20 40 40 20 0 20 40 Time (μs) Time (μs) 9 → X 2Σ), CH (A 2Δ → X 2Π), CO (d 3Δ → a 3Π), and C2 (A 3Πg → X 3Πu) also observed in CO2 plasma afterglow region (33).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The formation of these upper state ions and molecules in the air and CO2 plasma region occurs due to the collision of gas (air or CO2) with high-energy electrons, photons, ions, and neutral particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' These collisions result in the excited/upper vibration state of the above molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The most common reactions involved in these collisions were excitation, ionization, and dissociation (33-36).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The details of air and CO2 emission band peaks lines observed in the air and CO2 plasma afterglow region are shown in Table S1 of supplementary material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' For air emission spectrum: N2 (X 1Σg+) + eˉ → N2 (C 3Πu) + eˉ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='(electron impact excitation) (1) N2 (C 3Πu) → N2 (B 3Πg) + hυ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='(radiative decay) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='(2) N2 (X 1Σg+) + eˉ → N2+ (B 2Σu+) + 2eˉ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='(electron impact ionization) (3) N2+ (B 2Σu+) → N2+ (X 1Σg+) + hυ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='(radiative decay) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='(4) For CO2 emission spectrum: CO2 (X 1Σ) + eˉ → CO2+ (A 2Πu) + 2eˉ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='(electron impact ionization) (5) CO2+ (A 2Πu) → CO2+ (X 2Πg) + hυ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='(radiative decay) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='(6) CO2 (X 1Σ) + eˉ → CO (d 3Δ) + O + 2eˉ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='(electron impact dissociation)(7) CO (d 3Δ) → CO (a 3Π) + hυ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='(radiative decay) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='(8) CO2 (X 1Σ) + eˉ → CO+ (A 2Π) + O + 2eˉ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='(electron impact dissociative ionization) (9) CO+ (A 2Π) → CO+ (X 2Σ) + hυ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='(radiative decay) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='(10) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='10 CO2 (X 1Σ) + eˉ → C + O2 + eˉ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='(electron impact dissociative ionization) (11) C + C → C2 (A 3Πg) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='(Recombination) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='(12) C2 (A 3Πg) → C2 (X 3Πu) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='(radiative decay) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='(13) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Air and CO2 plasma emission spectra recorded in afterglow region Physicochemical properties of plasma-activated water The plasma-activated water (PAW) produced using air and CO2 plasma is colorless in appearance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' However, PAW (CO2) and PAW (air) can be differentiated based on odor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' PAW (air) was odorless, but PAW (CO2) has a smoky and unpleasant odor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The physicochemical properties of PAW produced using air and CO2 plasma is shown in figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The pH of PAW produced using air and CO2 plasma showed a continuous decrease in its value with increasing plasma treatment time (figure 4 (a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' This signifies increasing CO CO* (A 3I → XII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') CO* (A TI-→X 2) CH (A 2△ →>X 211) (I)00 C(A"TI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' →XII) 11 plasma-water treatment time results in more formation of acidic radicals/species in water (17, 22, 25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Moreover, the PAW produced using CO2 plasma was considerably higher (82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='14% higher after 60 minutes of treatment) than PAW produced using air plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Hence, the generated species in water when exposed to air plasma were more acidic compared to CO2 plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Ma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' (9) Subramanian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' (1), El Shaer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' (11), and Lu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' (16) also showed a decrease in pH of PAW with increasing plasma treatment with water.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The oxidizing potential of PAW when produced using air and CO2 plasma is shown in figure 4 (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The oxidizing potential of PAW gives information regarding net combinations of oxidizing and reducing species formed in water after plasma exposure(12, 23, 25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The oxidation-reduction potential (ORP) of PAW prepared using air plasma was higher compared to PAW prepared using CO2 plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' This was due to the formation of a high concentration of oxidizing species in PAW when produced using air plasma compared to CO2 plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' For 60 minutes of plasma treatment, the ORP of PAW prepared using air plasma was 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='1% higher compared to CO2 plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The increase in ORP of PAW with increasing plasma-water treatment is also shown in the work reported by Guo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' (3), Xiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' (10), and Ma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' (9), etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The rough estimation of conducting ions were measured by measuring total dissolved solids (TDS) and electrical conductivity (EC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The TDS and EC give the information regarding conducting ions formed in water due to plasma-water interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The observed TDS and EC of PAW, when prepared using air and CO2 plasma are shown in figure 4 (c, d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Increasing plasma treatment with water increased the TDS and EC of PAW for both the air and CO2 plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The observed TDS and EC of PAW prepared using air plasma were substantially high compared to CO2 plasma (937.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='0% and 987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='3% higher after 60 minutes of treatment).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Hence, the concentration of inorganic ions formed in water after air plasma exposure was extremely higher compared to CO2 plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The increase in EC with plasma treatment was also supported 12 by results of Subramanian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' (1), Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' (37), and Sivachandiran et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' (15), and Lu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' (16), etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The variation in physicochemical properties of plasma activated water prepared using air and CO2 plasma with plasma treatment time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' (a) pH, (b) oxidation-reduction potential (ORP), (c) total dissolved solids (TDS), and (d) electrical conductivity (EC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Statistically significant (p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='05) difference between the group mean ± standard deviation (µ ± σ) is shown by a different lowercase letter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' RONS concentration in plasma-activated water The above-discussed variation in physicochemical properties of water after plasma treatment occurs due to the formation of numerous reactive species in water (1, 3, 4, 6-8, 14, 20, 22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The mechanism of formation of these reactive species in PAW is shown in equations (14-25) (1, 4, 12, 13, 16, 18, 22, 25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' 00 13 Formation of reactive oxygen species (ROS) in plasma-activated water: 𝑂2(𝑔) → 2𝑂(𝑔) (14) 𝑂2(𝑔) + 𝑂(𝑔) → 𝑂3(𝑔) 𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' → 𝑶𝟑(𝒂𝒒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') (15) 𝐻2𝑂(𝑔) → 𝐻·(𝑔) + 𝐻𝑂·(𝑔) 𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' → 𝑯+(𝒂𝒒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') + 𝒆−(𝒂𝒒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') + 𝐻𝑂·(𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') (16) 2𝐻𝑂·(𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') → 𝑯𝟐𝑶𝟐(𝒂𝒒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' ) (17) 𝑯𝟐𝑶𝟐(𝒂𝒒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') + 𝑶𝟑(𝒂𝒒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') → 𝐻𝑂·(𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' ) + 𝐻𝑂2 · (𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') + 𝑂2(𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' ) (18) 2𝐻𝑂2 · (𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') → 𝑯𝟐𝑶𝟐(𝒂𝒒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') + 𝑂2(𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') (19) Formation of reactive nitrogen species (RNS) in plasma-activated water: 𝑁2(𝑔) → 2𝑁(𝑔) (20) 𝑁(𝑔) + 𝑥𝑂(𝑔) → 𝑁𝑂𝑥(𝑔) 𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' → 𝑁𝑂𝑥(𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' ) {𝑁𝑂(𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' ), 𝑁𝑂2(𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' ), 𝑁𝑂3(𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='),𝑒𝑡𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='} (21) 2𝑁𝑂2 (𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') + 𝐻2𝑂(𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' ) → 𝑵𝑶𝟐 −(𝒂𝒒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') + 𝑵𝑶𝟑 −(𝒂𝒒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') + 𝟐𝑯+(𝒂𝒒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' ) {𝐻𝑁𝑂2(𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' ) + 𝐻𝑁𝑂3(𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=')} (22) 𝑁𝑂(𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' ) + 𝑁𝑂2(𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') + 𝐻2𝑂(𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') → 𝟐𝑵𝑶𝟐 −(𝒂𝒒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') + 𝟐𝑯+(𝒂𝒒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') {𝐻𝑁𝑂2(𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=')} (23) 𝑵𝑶𝟐 −(𝒂𝒒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') + 𝑶𝟑(𝒂𝒒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') → 𝑵𝑶𝟑 −(𝒂𝒒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') + 𝑂2(𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') (24) 𝑵𝑶𝟐 −(𝒂𝒒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') + 𝑯𝟐𝑶𝟐(𝒂𝒒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') → 𝑵𝑶𝟑 −(𝒂𝒒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') + 𝐻2𝑂(𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' ) (25) Figure 5 showed the identified and measured concentration of RONS (reactive oxygen-nitrogen species) present in PAW when prepared using air and CO2 plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Figure 5 (a, c, e, g) showed the RONS such as NO2ˉ ions, NO3ˉ ions, H2O2, and dissolved O3 in PAW when prepared using air plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The reactions involved in the formation of RONS in PAW (air) are given in equations (14-25 (16)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Moreover, the reactive species formed in PAW when using CO2 plasma 14 are given as H2O2, dissolved O3, dissolved CO2, and CO32ˉ ions (equations (14-19, 26-27)) (figure 5 (f, h) and figure 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The concentration of NO3ˉ and NO2ˉ ions present in PAW prepared using air and CO2 plasma is shown in figure 5 (a-d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' A continuous increase in NO3ˉ and NO2ˉ ions concentration with plasma treatment time observed in PAW prepared using air plasma (figure 5 (a, c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The observed maximum concentration of NO3ˉ and NO2ˉ ions in PAW (air) were given as 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='0 mg L-1 and 401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='5 mg L-1, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The NO3ˉ and NO2ˉ ions form nitric and nitrous acid in PAW (air) (equations (20-25)) (1, 6, 8, 12, 22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' As nitric acid is a strong acid, therefore the lowest pH value of PAW (air) was given as 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The increasing concentration of NO2ˉ and NO3ˉ ions with activation time was also reported by Subramanian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' (1) and Xiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' (10) in PAW prepared in an air atmosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' However, the PAW (CO2) did not contain any observable concentration of NO3ˉ and NO2ˉ ions as shown in figure 5 (b, d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' As discussed in equations (1-4, 20-23), the formation of RNS (reactive nitrogen species) in PAW required excited nitrogen species (12, 18, 22, 25) that were not observed in emission spectra of CO2 plasma (figure 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Hence, the possible RNS present in PAW (CO2) such as (NO2ˉ and NO3ˉ ions) were beyond the detection limit of the present investigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Moreover, the concentration of H2O2 present in PAW (CO2) was 316.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='7% higher than PAW (air).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' This was due to no interference of NO2ˉ ions in H2O2 determination in PAW (CO2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The NO2ˉ ions present in PAW (air) react with H2O2 to give more stable NO3ˉ ions (equation 25) (6, 18, 25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Therefore, interfere with the H2O2 determination in PAW (air).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The interference of NO2ˉ ions in H2O2 concentration and variation can be seen in figure 5 (e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Initially (t = 0 minutes), no H2O2 was present in PAW (air), as the plasma treatment increased to 30 minutes, a continuous increase in the H2O2 concentration was observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Increasing plasma treatment time to 45 minutes results in a decrease in H2O2 concentration due to the reaction of NO2ˉ ions with H2O2 to give more stable NO3ˉ ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Further increasing plasma treatment time to 60 15 minutes results in H2O2 concentration enhancement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' This showed saturation of NO2ˉ ions and H2O2 reaction in PAW (air) and the unreacted H2O2 shown by enhanced H2O2 in PAW (air).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Similar behavior as H2O2 was observed in the concentration of dissolved O3 in PAW (air).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Since, NO2ˉ ions present in PAW (air) also reacts with dissolved O3 to give more stable NO3ˉ ions by following equation (24).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' This rise and fall in H2O2 concentration in PAW (air) with increasing plasma treatment time also was observed in work reported by Subramanian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' (1) and Sivachandiran et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' (15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' However, this rise and fall in H2O2 and dissolved O3 concentration in PAW prepared using CO2 plasma was not observed due to the absence of NO2ˉ ions (figure 5 (b, d, g, h)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' As no N2 emission peaks bands were observed in the CO2 plasma (figure 3) that confirms the absence of nitrogen species in CO2 plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Hence, no interference of NO2ˉ ions in PAW (CO2) results in a monotonous increase in H2O2 and dissolved O3 concentration with increasing plasma treatment time with water (figure 5 (g, h)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' 16 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The variation in reactive oxygen-nitrogen species (RONS) concentration of plasma- activated water prepared using air and CO2 plasma with plasma treatment time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' (a, b) NO3ˉ ions, (c, d) NO2ˉ ions, (e, f) H2O2 concentration, and (g, h) Dissolved O3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Statistically significant (p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='05) difference between the group mean ± standard deviation (µ ± σ) is shown by a different lowercase letter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The variation in titratable acidity, dissolved CO2, and CO32ˉ ions with plasma treatment time in PAW (CO2) is shown in figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The excited carbon oxides (COx) and carbon oxide ions (COx+), etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' observed in emission spectra of CO2 plasma (figure 3) when comes in contact with water enhances the solubility of CO2 and formed carbonic acid (H2CO3), etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' in water (equations (26-27)(38)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Due to which physicochemical properties of PAW (CO2) changed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The acidic species concentration formed in PAW (CO2) was measured by measuring titratable acidity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Increasing plasma treatment time with water continuously and significantly (p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='05) NO2 (mg/L) uantofix NO2 (mg/L) N (Air) PAW (CO2) H,02 (mg/L) H202(mg/L) PAW (Air) PAW (CO2) Control PAW (CO,) Control PAW(Air) 17 increases the titratable acidity, dissolved CO2, and CO32ˉ ions concentration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The uniform increase in titratable acidity, dissolved CO2, and CO32ˉ ions concentration signifies continuous production of reactive species in PAW (CO2) with increasing plasma-water treatment time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The CO32ˉ ions exist in the form of carbonic acid in PAW (CO2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The dissolved CO2 and CO32ˉ ions (carbonic acid) are weak acids due to which the pH of PAW (CO2) decreased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' However, this decreases in pH of PAW (CO2) significantly (p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='05) low compared to PAW (air).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Formation of carbonic acid in PAW: 𝐻 (𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') + 𝐶𝑂2(𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') → 𝐻𝑂𝐶𝑂(𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=') (26) 𝐻𝑂𝐶𝑂 (𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' ) + 𝑂𝐻(𝑎𝑞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' ) → 𝑯𝟐𝑪𝑶𝟑(𝒂𝒒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' ) (27) Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' (a) Titratable acidity and dissolved CO2, and (b) CO32ˉ ions concentration in plasma- activated water produced using CO2 plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Statistically significant (p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='05) difference between the group mean ± standard deviation (µ ± σ) is shown by a different lowercase letter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Hence, the above results and discussion showed the higher discharge current filaments in CO2 plasma compared to air plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Moreover, the emission spectrum of CO2 plasma is free from 120 (a) a豆 (b) a 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=" 500 100 5 a Titratable acidity (mmol/L) 400 4 b 80 Dissolved CO, (mg/L) TOq 300 60 2 ci 200 d 40 1 d' e 100 20 0 口 Titratable acidity e 1 o Dissolved CO, ." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='0 0 0 15 30 45 60 0 15 30 45 60 Plasma treatment time (min) Plasma treatment time (min) 18 nitrogen containing species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' As a results, formation of reactive nitrogen species (RNS) is not occurring in PAW (CO2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Hence, selective generation of reactive oxygen species (ROS) occurs in PAW (CO2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Moreover, due to the use of CO2 gas plasma for PAW preparation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The carbonic acid, dissolved CO2, CO32ˉ ions also occurs in PAW due to which pH of PAW (CO2) is decreased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' However, the pH of PAW (CO2) is significantly lower than PAW (air).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Conclusion The present work compares the properties of PAW produced using air and CO2 plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The acidity of PAW (air) is significantly higher than PAW (CO2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' This is due to the dissolution of strong acids (nitric acid) in PAW (air) compared to weak acids (carbonic acid) of PAW (CO2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' In addition, the oxidizing potential, total dissolved solids, and electrical conductivity of PAW (air) are significantly higher than PAW (CO2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' This is due to PAW (air) has high concentration of strong ionic species in the form of HNO3 compared to weak H2CO3 species of PAW (CO2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The PAW prepared using CO2 plasma does not contain any reactive nitrogen species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' This is due to the emission spectra of CO2 plasma not containing any N2 emission band peaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Hence, CO2 plasma-water interaction does not form any reactive nitrogen species in PAW (CO2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Hence, selective production of reactive oxygen species can be achieved without the interference of reactive nitrogen species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Therefore, the concentration of dissolved H2O2 in PAW (CO2) is higher than PAW (air).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' In conclusion, selective production of reactive oxygen species in plasma-activated water is possible by using CO2 as a plasma-forming gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The presence of reactive oxygen species in PAW (CO2) makes it a useful antimicrobial agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Moreover, it can also be used in numerous applications where conventional PAW could not be used due to its low pH (such as low pH PAW could not be used for surface disinfection of metal objects since it oxidizes its surface and damage it).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Acknowledgments 19 This work was supported by the Department of Atomic Energy (Government of India) doctrate fellowship scheme (DDFS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Data availability statement The data that support the findings of this study are available upon reasonable request from the authors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Conflict of interests The authors declare that there are no conflicts of interests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Authors’ contributions Both authors contributed to the study conception and design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Material preparation, data collection, and analysis were performed by Vikas Rathore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' The first draft of the manuscript was written by Vikas Rathore, and both authors commented on previous versions of the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Both authors read and approved the final manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' ORCID iDs Vikas Rathore https://orcid.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content='41(3):871-902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' 22 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Rashid M, Rashid M, Reza M, Talukder MJPC, Processing P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Combined Effects of Air Plasma Seed Treatment and Foliar Application of Plasma Activated Water on Enhanced Paddy Plant Growth and Yield.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/y9E4T4oBgHgl3EQfYwwf/content/2301.05051v1.pdf'} +page_content=' Plasma Chemistry Plasma Processing.' metadata={'source': 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Germany +2Fraunhofer Institute of Optronics, System Technologies and Image Exploitation IOSB, Germany +3Fraunhofer Center for Machine Learning, Germany +chengzhi.wu@kit.edu +julius.pfrommer@iosb.fraunhofer.de +mingyuan.zhou@student.kit.edu +juergen.beyerer@iosb.fraunhofer.de +Abstract +We propose a combined generative and contrastive neural +architecture for learning latent representations of 3D volu- +metric shapes. The architecture uses two encoder branches +for voxel grids and multi-view images from the same under- +lying shape. The main idea is to combine a contrastive loss +between the resulting latent representations with an addi- +tional reconstruction loss. That helps to avoid collapsing the +latent representations as a trivial solution for minimizing the +contrastive loss. A novel switching scheme is used to cross- +train two encoders with a shared decoder. The switching +scheme also enables the stop gradient operation on a random +branch. Further classification experiments show that the la- +tent representations learned with our self-supervised method +integrate more useful information from the additional input +data implicitly, thus leading to better reconstruction and +classification performance. +1. Introduction +3D shapes can be represented in a range of different for- +mats. On the Euclidean side, they may be represented as +RGB-D images, multi-view images or volumetric data. On +the Non-Euclidean side, they may be represented as point +clouds or meshes. For computer vision tasks like classifi- +cation, segmentation, or even generative tasks like shape +reconstruction, the target 3D shape is usually converted into +a latent representation first. Before the rise of deep learning +[16], popular latent representations (or, 3D shape descriptors) +were Laplacian spectral eigenvectors [36], or heat kernel sig- +natures [38]. With neural networks, the latent representation +is usually the result of an encoder that reduces the 3D shape +to a vector representation with fixed dimensionality. +(a) General pipeline for contrastive learning from augmented data. +(b) Pipeline for the proposed generative-contrastive learning from +multi-modal input. +Figure 1: An illustration of (a) a general pipeline of con- +trastive learning methods and (b) our proposed generative +contrastive learning pipeline for 3D shapes. +When multi-modal input data is available, the question +arises how to use them jointly. For 3D learning tasks, take 3D +Euclidean data as an example, most state-of-the-art methods +in computer vision that deal with both image and voxel grid +input data either concatenate individual latent representations +for supervised tasks [22], or use only one of them on the +input and loss side separately [11, 40, 39, 45], or use them +jointly but with pre-training and finetuning [15]. We are +interested in seeking a better self-supervised way for learning +better latent representations for 3D volumetric shapes, with +the additional input from other modalities. +1 +arXiv:2301.04612v1 [cs.CV] 11 Jan 2023 + +Encoder +A +Aug image1 +Contrastive Loss +Input image +Encoder +B +Possible stop gradient +on fixed branch +Aug image2Reconstruction Loss +Encoder +A +Voxel grid +Contrastive Loss +Decoder +Input shape +Encoder +Voxel grid +B +Stop gradient +on random branch +Multi-view imagesApart from pretext tasks-based methods[14, 17], the other +two main self-supervised learning ways are generative-based +methods [1, 11] and contrastive-based methods [5, 18]. For +3D volumetric shapes, it is easy to implement a generative +model. But it is still an open question that how to do it in a +contrastive way, let alone the combination of these two. In a +recent review paper of self-supervised learning [28], the au- +thors argue that the only way of doing generative-contrastive +learning is to train an encoder-decoder to generate synthetic +samples and a discriminator to distinguish them from real +samples. We disagree with this argument. In their definition, +the discriminator is the contrastive part thus the model only +focuses on negative pairs. We think it is also possible to +use or only use positive pairs, e.g. in our case, using multi- +modalities from the same input shape for two branches. +Figure 1 shows the main idea of our proposed generative- +contrastive learning pipeline. Compared to the existing con- +trastive learning methods, our method shares some similari- +ties with them while some significant differences also exist. +Similarities are: (i) we both use a two-branches scheme to +encode two inputs that origin from the same ”raw data”; +(ii) after getting encoded latent representations, we both +compute a contrastive loss in the latent space; (iii) they use +positive pairs for training (optionally with additional nega- +tive pairs), we also use positive pairs. Differences are: (i) +they use different augmented data from the ”raw data”, while +we use different modalities from the ”raw data”; (ii) thus +our network architectures of encoder A and B are not identi- +cal, while theirs are identical mostly; (iii) we add a decoder +part and a reconstruction loss; (iv) they possibly have stop +gradient on one fixed branch, while we do stop gradient on +random branch with a switching scheme. +The main contributions of this paper are as follows: +• We propose a novel generative-contrastive learning +pipeline for 3D volumetric shapes, which makes the joint +training of encoders for multi-modal input data possible. +• With the switching scheme does the work of stopping +gradient on random branch, model collapse is avoided. +End-to-end training is also possible without the require- +ments of special pre-training. +• Better experimental results are achieved on both 3D shape +reconstruction and classification tasks with our proposed +model, compared to the results from the models which +learn only on single-modal data. +• Using the voxel encoder as a self-supervised pre-trained +feature extractor, we outperform 3D-GAN on the Model- +Net40 classification task with a much shorter latent vector +representations (128, compared to ca. 2.5 million dimen- +sions in 3D-GAN). +• The voxel encoder pre-trained on one single category still +performs surprisingly well as a feature extractor on the +full dataset with other categories during the testing. +2. Related Work +Contrastive learning: The work of contrastive learning +was pioneered by Yann LeCun’s group for face verification +[10]. This topic is getting more and more popular recently +since people find self-supervised learning are important for +feature extraction and we now have really mature deep learn- +ing techniques. SimCLR [5] proposes to use two identical +encoders for two branches, both positive pairs and negative +pairs are used. MoCo [7] stops the gradient for the second +branch, while using a momentum-based method to update +the parameters of its encoder. SwAV [2] proposes to use +a memory bank to get negative pairs out of the batch, the +contrastive loss in their case is computed after clustering. +For methods only use positive samples, BYOL [18] keeps +the idea of momentum updating from MoCo, but adds an ad- +ditional block in the first branch and only uses positive pairs. +SimSiam [8] reports an observation of competitive results +may still be achieved when modifying BYOL by making +two encoders identical. A review of most relevant methods +and their comparisons are given in [12]. +Learning on 3D shapes with Euclidean data: For su- +pervised tasks, VoxNet[30] is the pioneer to use 3D convo- +lutional network to learn features from volumetric data for +recognition. Its subsequent work of multi-level 3D CNN +[13] learns multi-scale spatial features by considering mul- +tiple resolutions of the voxel input. Qi et al. [32] propose +to use multi-resolution filtering in 3D for multi-view CNNs, +as well as using subvolume supervision for auxiliary train- +ing. FusionNet [22] fuses three networks together: two +VoxNets[30] and one MVCNN[37]. The three networks fuse +at the score layers where a linear combination of scores is +taken before the classification prediction. +For self-supervised tasks, ShapeNet [41] uses a reverse +VoxNet to reconstruct 3D volumetric shapes from latent rep- +resentations which are learned from depth maps. The T-L +network [15] combines a 3D autoencoder with an image re- +gressor to encode a unified vector representation given a 2D +image. Autoencoders have also been widely use for 3D shape +retrieval in other papers [44, 46]. Its variant, VAE, has been +used in a similar way for 3D shape learning [1]. View infor- +mation from images has also been widely investigated for 3D +shape reconstruction. Choy et al. [11] proposed a framework +named 3D-R2N2 to reconstruct 3D shapes from multi-view +images by leveraging the power of recurrent neural networks +[24]. [33] also uses a recurrent-based approach, but taking +depth images as input. Some other methods use view infor- +mation as auxiliary constraints [39, 45, 19]. Method uses +GAN for 3D volumetric shape generation has been proposed +in [40]. Some other latest works [31, 27] have also used +multi-modal input data for joint end-to-end training, but they +did not use a switching scheme. +We are aware that there are lots of other works applying +deep learning-based methods on other 3D Non-Euclidean +2 + +data formats, e.g. point clouds and meshes. But they are out +of the scope of this work and we would like to leave them +for future work. +3. Methodology +3.1. Generative-Contrastive Learning +Figure 1(b) shows the main idea of our proposed +generative-contrastive learning pipeline. Similar to most +existing contrastive learning methods, we use an architecture +with two encoder branches to compute a contrastive loss +between the latent representations from each branch. The +inputs to two branches are the voxel grid and the multi-view +images of an identical 3D shape. A generative decoder part +is added to compute the reconstruction loss. The decoder is +shared by two encoders and the two encoder branches are +co-trained with the help of a switching scheme. +For contrastive learning methods, mode collapse is a big +issue. Possible ways of dealing with it are adding additional +blocks for encoder A, or stop gradient for encoder B and +update its parameters in a momentum way slowly along with +the updated parameters in encoder A. In our case, encoder +A and B are already different network architectures thus the +momentum method can not be applied, but we still managed +to avoid model collapse successfully during the experiments. +We attribute this success to two things: the reconstruction +loss, and the switching scheme. The reconstruction loss has +a strong supervision over the representational capacity of +latent representations, while the switching scheme does the +work of stopping gradient on random branch. +To further improve the latent representations, Variational +Autoencoders (VAE) [26] are used instead of vanilla autoen- +coders. In a VAE, each input is mapped to a multivariate +normal distribution around a point in the latent space, which +makes a continuous latent space. A continuous latent space +makes the smooth transition of 3D shapes possible with la- +tent representations. The learned features are usually more +smooth and meaningful. +3.2. Switch Encoding +When dealing with multi-modal inputs, most state-of-the- +art methods just encode them separately into latent repre- +sentations and then perform concatenation. Unlike them, +we propose to use a switching scheme in the latent space to +jointly train both encoders with a shared decoder. During the +training, the switch is actuated for every training epoch with +a preset probability to randomly select the encoded output +from one encoder as the latent representation. This operation +of switching between encoders continues during the whole +end-to-end training. +The decoder is tasked to reconstruct the voxel represen- +tation of the 3D shape. Since the switched encoders are +trained concurrently for the same decoder, they are forced to +produce “mutually compatible” latent representations. The +different input modalities result in different features that nat- +urally emerge for the respective latent representation. For +example, a voxel-based encoder is much more likely to gen- +erate an “overall volume” feature (simply the number of +filled voxels) compared to a multi-view image encoder. By +the cross-training with switched encoding, useful features +for the latent representation can translate from one encoder +to the other via the shared decoder. This results in improved +latent representations also for the individual encoder when +just one input modality is used after the training. +3.3. Loss Functions +The SwitchVAE loss functions consists of three parts: a +reconstruction loss Lrecon, a KL divergence LKL between +latent representations and the normal prior distribution, and +a contrastive loss Lcontras between the latent representations +from the different input formats. The overall network is +parameterized by θ = (θvox, θimg, θd)⊤ for the voxel and +image encoder and the voxel decoder respectively. The train- +ing samples are denoted xα for the input α ∈ {img, vox}. +The switch value for α is randomly selected prior to ev- +ery training epoch. +The latent representations resulting +from the VAE encoders are (µα, σα) = eα(xα). +The +latent representation is sampled for the current training +epoch as zα ∼ N(µα, σα). The decoder part is shared +by both input modalities to reconstruct the voxel represen- +tation ˆxα = d(zα). Formally, the overall loss function +decomposes into three terms +Lθ(α, ximg, xvox) = +Lrecon(xvox, ˆxα) + λKLLKL(µα, σα) + +λcontrasLcontras(zimg, zvox) +(1) +with weights λKL and λcontras. +A modified Binary Cross Entropy (BCE) against the voxel +ground truth is used for the reconstruction loss. To improve +the training, modification has been made by the introduction +of a hyper-parameter γ that weights the relative importance +of false positives against false negatives. The reconstructed +voxels are indexed by k with value ˆxα +k ∈ [0, 1]. +Lrecon(xvox, ˆxα) = +� +k +� +− γ · xvox +k +· log(ˆxα +k) − +(1 − γ)(1 − xvox +k +) log(1 − ˆxα +k) +� +(2) +We set the hyperparameter γ = 0.8 during training for all of +the experiments conducted in Section 4. +In the training of VAE, the Kullback-Leibler (KL) diver- +gence is used between the actual distribution of latent vectors +and the N(0, I) Gaussian distribution. Note that the latent +representation has n dimensions. +LKL(µ, σ) = −1 +2 +n +� +i=1 +(1 + log(σ2 +i ) − µ2 +i − σ2 +i ) +(3) +3 + +Figure 2: The SwitchVAE architecture based on our pro- +posed generative-contrastive learning pipeline, with more +detail blocks illustrated. +In order to further force a close distance between the +latent representations learned from image and volumetric +data with the SwitchVAE model, a contrastive loss between +the encoders is proposed and used in the latent space during +the training phase. The contrastive loss is defined as the +Euclidean distance between the latent vectors from images +and volumetric data. +Lcontras(zimg, zvox) = ∥zimg − zvox∥2 +2 +(4) +Although in most other contrastive learning methods some +different contrastive losses has been used, e.g. InfoNCE +loss in SimCLR [5], we find that with latent representations +normalized, our method can already yield satisfying results +with a simple L2 Norm loss as the contrastive loss. +4. Experiments +We use the 3D-R2N2 and ModelNet 10/40 datasets for +our experiments. The 3D-R2N2 dataset [11] is a subset with +13 categories from the ShapeNet dataset [3]. It provides +good quality rendered multi-view images alongside a class +label and 32 × 32 × 32 voxel representations. We divide the +3D-R2N2 dataset into a training set of 29,599 samples and a +test set of 7406 samples. The ModelNet dataset [41] comes +in two variations with either 10 or 40 classes of shapes. The +ModelNet10 dataset contains 3991/908 training/test samples. +ModelNet40 contains 9843/2468 training/test samples. +For the SwitchVAE models, we use both a voxel and a +multi-view image encoder. The decoder always reconstructs +the voxel representation. During training for voxel test input, +the switch layer randomly selects either the voxel encoder +with a probability of 80%, or the multi-view image encoder +with a probability of 20%. +Concerning the other training parameters, we use a la- +tent dimension of 128 for all experiments. The network +parameters are trained by minimizing the loss function from +Equation 1 using the SGD optimizer with a momentum of +0.9 and Nesterov accelerated gradients [34]. The learning +rate is 2 × 10−4 with a decay of 0.96 per 10 epochs after +the first 50 epochs. The batch size is 32 for all experiments. +Training with multi-view image input uses 8 views for every +sample as it has been reported in [11] and its subsequent +works [42, 43] that the improvement from additional views +is negligible after the first 6-10 views. +4.1. Detailed Network Configuration +Figure 2 shows based on our proposed generative- +contrastive learning pipeline, how switched encoding is im- +plemented for a VAE with multi-view images and voxel +grids input. The encoder blocks of our SwitchVAE build on +the idea of volumetric convolutional networks [41] for the +voxel input, and 3D recurrent reconstruction neural networks +[11] for the multi-view images input. More detailed network +configurations are given as follows. +The image encoder of SwitchVAE learns the latent vector +from multi-view images, and it is composed of a view feature +embedding module and a view feature aggregator module. +The view feature embedding module is a ResNet18 [21] +whose weights are shared across all the views. The part with +pre-trained weights map a single view 137 × 137 × 3 RGB +image into 5 × 5 × 512 feature maps. We then flatten these +feature maps and add a fully connected layer, which outputs +a 1024 dimensional feature for a single view image. For a 3D +shape, 8 views of images are fed into the shared weights view +feature embedding module while training, which outputs a +8 × 1024 view features. +For the view feature aggregator module, we firstly tried a +max pooling as MVCNN [37], but it did not yield satisfying +results. Same for average pooling. To better aggregate +the multi-view image features, we finally use the Gated +Recurrent Unit (GRU) [9]. The view feature aggregator +outputs a 1024 dimensional feature after aggregating features +from all views. Then it is further fed into last fully connected +layers to generate the mean and the variance of the latent +vector. By using the reparametrization trick introduced in +[25], the image encoder finally outputs a 128 dimensional +sampled latent vector. +The voxel encoder is a 3D volumetric convolutional neu- +ral network. The encoder has 4 convolutional layer and two +fully connected layers. All convolutional layers use kernels +of size 3 × 3 × 3, their strides are {1, 2, 1, 2} and channel +numbers are {8, 16, 32, 64} respectively. All layers use the +exponential linear unit (eLu) as the activation function ex- +cept for the last fully connected layer. This layer maps an +shape of 32 × 32 × 32 voxels to a 343 dimensional feature. +The 343 dimensional feature is further fed into the last fully +connected layers to generate the mean and the variance of the +latent vector to finally produce a 128 dimensional sampled +latent vector. +The decoder of SwitchVAE mirrors the voxel encoder, +except that the last layer uses a sigmoid activation function. +4 + +Image Encoder +ResNet18 +leal +Switch +ResNet18 +View Feature +Latent Vector +Layer +Aggregator +variance +ResNet18 +Decoder +.atent Vector +Voxel Encoder +SwitchVAEInput/GT +Voxel VAE +SwitchVAE +(a) Reconstruction tests with voxel input. +Input (2/8 views) +GT +Image VAE +SwitchVAE +(b) Reconstruction tests with image input. +Figure 3: Some reconstruction results from different models with only voxel or multi-view images as the test input. +Test Input +Training Model +Reconstruction Metrics +IoU +Precision +Accuracy +Image +Image VAE +58.52% +68.21% +93.21% +SwitchVAE (λcontras = 0) +56.82% +67.72% +93.00% +SwitchVAE (λcontras = 1) +58.75% +68.50% +93.32% +Voxel +Voxel VAE +78.86% +82.80% +97.01% +SwitchVAE (λcontras = 0) +77.27% +80.04% +96.67% +SwitchVAE (λcontras = 1) +79.93% +84.68% +97.22% +Table 1: Reconstruction performance on the test set. Training and testing with the chair category from 3D-R2N2 dataset. +The decoder maps a 128 dimensional latent vector, which +was randomly sampled in encoder, to a 32 × 32 × 32 vol- +umetric reconstruction. It represents the predicted voxel +occupancy possibility of each voxel in the cube. +4.2. 3D Shape Reconstruction +We use Intersection-of-Union (IoU), precision, recall, +and accuracy (referred as average precision in [15]) as the +quantitative metrics for the reconstruction of 3D shapes. The +threshold at which a voxel is considered as filled is at 50%. +Similar to the last part, we show the results from only voxel +input training, only image input training, and both input +training with our SwitchVAE. +Table 1 shows that the reconstruction performance of +SwitchVAE is similar or slightly better to that of image/voxel +VAEs, and it focuses more on making every predicted occu- +pied voxel correct (higher precision score). This character- +istic may be more clearly observed in some reconstruction +results. Table 1 also shows that the contrastive loss term is +the key in our method. Figure 3 shows some qualitative re- +construction results from our SwitchVAE model that trained +on the chair category. Comparisons with the results from +the networks that only use one input format for training are +also presented. From the figure we can observe that Switch- +VAE takes more attention on not occupying original negative +voxels. This is quite obvious from the third row of Figure +3(b). Both Image VAE and SwitchVAE are not certain about +the leg number of the office chair is 4 or 5. The Image +VAE decides to merge them all together, while SwitchVAE +decides to only guess and occupy some voxels with small +sub-clusters in that area. +4.3. 3D Shape Classification +For the classification task, the networks are first trained +to perform reconstruction of the ground-truth voxel repre- +sentations. Then the encoder part of a trained network is +5 + +铺Training Dataset +Test Input +Training Model +Classification Accuracy +ModelNet40 +ModelNet10 +Chair Category +Multi-view images +Image VAE +75.28% +81.36% +SwitchVAE +77.07% +84.26% +Voxel data +Voxel VAE +80.19% +86.38% +SwitchVAE +80.60% +87.05% +ModelNet40 +Multi-view images +Image VAE +85.06% +88.62% +SwitchVAE +83.87% +89.96% +Voxel data +Voxel VAE +83.12% +87.95% +SwitchVAE +84.01% +90.07% +Table 2: Classification accuracy on the ModelNet40/ModelNet10 classification tasks with models trained with Image VAE, +Voxel VAE, and SwitchVAE on the chair category or on the full ModelNet40 dataset. +Supervision +Method +Data Modality +Classification Accuracy +ModelNet40 +ModelNet10 +Supervised +3D ShapNets [41] +Voxels +77.30% +85.30% +VoxNet [30] +Voxels +83.00% +92.00% +MVCNN [37] +Images +90.10% +- +FusionNets [22] +Images, Voxels +90.80% +93.11% +3D2SeqViews [20] +Images +93.40% +94.71% +VRN Ensemble [1] +Voxels +95.54% +97.14% +Self-supervised +LFD [4] +Images +75.50% +79.90% +T-L Network [15] +Images, Voxels +74.40% +- +VConv-DAE [35] +Voxels +75.50% +80.50% +3D GAN [40] +Voxels +83.30% +91.00% +SwitchVAE (trained on only chair category) +Images, Voxels +80.60% +87.05% +SwitchVAE (trained on ModelNet40 dataset) +Images, Voxels +84.01% +90.07% +Table 3: Classification accuracy on the ModelNet40/ModelNet10 dataset with different methods. Results from methods that +only used images and/or voxels are listed. Note that our latent representations are only of 128 dimensions. +used to produce latent representations of 128 dimensions as +input for classification. An SVM with RBF kernel and hyper- +parameter γ = 1/128 is trained on the latent representations +to perform classification. Same samples were used to train +the networks for latent representations and the SVM. The +evaluation of the SVM is performed with samples that were +neither used to train the networks nor the SVM. +Table 2 shows the impact of switched training on the +ModelNet 10/40 classification tasks. To make it more clear, +let’s take the voxel data testings as an example. During the +training phase, a voxel VAE only trains on the voxel train +set data, while a SwitchVAE trains on both the voxel train +set data and the correspondent multi-view images train set +data. During the testing phase, only the identical voxel test +set data is given to the trained voxel VAE model and the +trained SwitchVAE model. Latent representations of those +3D shapes (from voxel test set) obtained from the Switch- +VAE model always outperform that from the vanilla voxel +VAE in the ModelNet classification tasks. Note that no multi- +view images data of the test set is needed for SwitchVAE +during the testings. From Table 2, we can clearly observe +that under the condition of same training dataset and test +input, the results from SwitchVAE are better than the results +from the image VAE or the voxel VAE in most cases. Note +that they are even trained with a same number of epochs. +This means by using the data of other format in the training +phase, during the testing phase, the classification perfor- +mance has been improved compared to the models that only +use single format for the training. In conclusion, better latent +representations have been learned for 3D shapes by using +“data you don’t have” (i.e. data input formats that are not +used for the evaluation once the network is trained). +Table 3 lists the classification result in comparison to +other network architectures. Compared to most other unsu- +pervised learning method, we achieve better classification +performance. Comparing to 3D-GAN, we outperform it on +6 + +(a) Voxel VAE, +trained on ModelNet10 +(b) SwitchVAE (λcontras = 0), +trained on ModelNet10 +(c) SwitchVAE (λcontras = 1), +trained on ModelNet10 +(d) SwitchVAE (λcontras = 1), +trained on 3D-R2N2 dataset +Figure 4: t-SNE plots of the latent representations for Mod- +elNet10 shapes (10 categories) with (a) a vanilla voxel +VAE model trained on ModelNet10 dataset. (b) a Switch- +VAE model without contrastive loss trained on ModelNet10 +dataset. (c) a SwitchVAE model with contrastive loss trained +on ModelNet10 dataset. (d) a SwitchVAE model with con- +trastive loss trained on the full 3D-R2N2 dataset. Each color +represents one category. All latent representations used for +the plots use voxel data from the testing set as test input. +the ModelNet40 classification task and achieve competitive +performance on the ModelNet10 classification task. How- +ever, our method uses a much smaller latent vector of only +128 dimensions. 3D-GANs use all features maps in the last +three convolution layers, which makes the presentation for +each 3D shape a 2.5 million dimensional vector as input for +the classification. +t-SNE Visualization: In order to visualize the learned +latent representations, we use t-SNE [29] to map the latent +representations to a 2D plane. Figure 4 gives the visualiza- +tion results. we use ModelNet10 for most t-SNE visualiza- +tion experiments. Comparing Figure 4(a) and Figure 4(b), +we can observe that the switching scheme contributes to the +inter-category classification while makes the intra-category +clustering a bit fuzzy (all categories are a bit far from each +other, while each category itself is a bit less clustered). Com- +paring Figure 4(b) and Figure 4(c), we can observe that +adding the contrastive loss term to SwitchVAE helps to the +(a) Top Row: Trained on SwitchVAE, the ”chair arm” feature and +the “size” feature are entangled. Middle and Bottom Row: Trained +on Switch-BetaTCVAE with β = 5, the “chair arm” feature and +the “size” feature are more disentangled, changing one feature does +not impact the other one too much. +(b) Top Row: Trained on SwitchVAE, changing the “chair leg type” +feature also leads to the morphing of the top part. Bottom Row: +Trained on Switch-BetaTCVAE with β = 5, the top part stays more +fixed while changing the “chair leg type” feature. +Figure 5: Disentangling latent features with Beta-TCVAE. +intra-category clustering, making the performance of the +whole classification task mush better. Comparing Figure +4(c) and Figure 4(d), we can observe that with a larger train- +ing dataset, even better feature clustering results may be +achieved. The increased gaps between different categories +can be clearly observed. +4.4. Exploring Latent Representations +This subsection showcases some qualitative results to +give indication that SwitchVAE training results in a superior +latent representation that allows for better disentanglement +between categories, as well as between the salient features +of the 3D shapes in each category. +Latent space interpolation: Similar to as most 3D re- +construction papers, we also do the inter-class interpolation +with our trained models as shown in Figure 6. It can be ob- +served that our proposed method has the ability to do smooth +transition between two shapes, even if they are from different +categories. +Shape arithmetic: Another way to explore the learned +latent representations is to perform arithmetic operations in +the latent space whilst observing their effect on the recon- +structed geometry. We show some shape arithmetic results in +Figure 7 with a model trained on the full 3D-R2N2 dataset. +The model seems to capture the underline information and +is capable of generating meaningful combined shapes that +7 + +Figure 6: Shape interpolation between different categories. +(a) Shape arithmetic example with chair objects. +(b) Shape arithmetic example with table objects. +Figure 7: Shape arithmetic for chairs and tables. (a) Adding +chair arms to chair objects in the latent space. (b) Adding a +middle layer to table objects in the latent space. +do not occur as 3D shapes in the original dataset. +Feature disentanglement with VAE variations: One +good thing with VAE models is that the latent space learned +from it is more ”meaningful” comparing to that from GAN +models. By tuning the value in one specific latent dimension, +one can observe certain features on the output side changing +smoothly. However, for most features, they get entangled in +multiple latent dimensions with the vanilla VAE. It has been +reported that β-VAE [23] and β-TCVAE [6] can producing +better disentangled features in the latent space. We merge +it with our proposed method into SwitchBTCVAE. We train +our model with β = 5 on the chair category with a same +number of epochs as the other experiments shown in this +section. Although a small decrease on the reconstruction +performance metrics is observed, by investigating the learned +latent representations, we find that some features have been +better disentangled as shown in Figure 5. +5. Conclusion and Outlook +In this paper, we propose a generative-contrastive learn- +ing pipeline for learning better latent representations for +3D volumetric shapes, with the help of additional modal- +ity input. The switching scheme makes the joint training +for both encoders possible with competitive reconstruction +results. Classification experiments on ModelNet have also +been carried out to validate the effectiveness of the proposed +method. Improved classification results indicate that better +latent representations have been learned with our proposed +SwitchVAE architecture. +For future directions, other 3D data modalities, e.g., point +clouds and meshes may also be used. A new contrastive +loss may be designed and an optimal switching policy may +be studied. 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IEEE +International Conference on Security, Pattern Analysis, and +Cybernetics (SPAC), pages 279–284, 2014. +10 + diff --git a/ydE3T4oBgHgl3EQfmApc/content/tmp_files/load_file.txt b/ydE3T4oBgHgl3EQfmApc/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..f67bef76beaefcffb004f989743b5d9d1adc8963 --- /dev/null +++ b/ydE3T4oBgHgl3EQfmApc/content/tmp_files/load_file.txt @@ -0,0 +1,718 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf,len=717 +page_content='Generative-Contrastive Learning for Self-Supervised Latent Representations of 3D Shapes from Multi-Modal Euclidean Input Chengzhi Wu1, Julius Pfrommer2,3, Mingyuan Zhou1, and J¨urgen Beyerer2 1Institute for Anthropomatics and Robotics, Karlsruhe Institute of Technology, Germany 2Fraunhofer Institute of Optronics, System Technologies and Image Exploitation IOSB, Germany 3Fraunhofer Center for Machine Learning, Germany chengzhi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='wu@kit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='edu julius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='pfrommer@iosb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='fraunhofer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='de mingyuan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='zhou@student.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='kit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='edu juergen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='beyerer@iosb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='fraunhofer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='de Abstract We propose a combined generative and contrastive neural architecture for learning latent representations of 3D volu- metric shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The architecture uses two encoder branches for voxel grids and multi-view images from the same under- lying shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The main idea is to combine a contrastive loss between the resulting latent representations with an addi- tional reconstruction loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' That helps to avoid collapsing the latent representations as a trivial solution for minimizing the contrastive loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' A novel switching scheme is used to cross- train two encoders with a shared decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The switching scheme also enables the stop gradient operation on a random branch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Further classification experiments show that the la- tent representations learned with our self-supervised method integrate more useful information from the additional input data implicitly, thus leading to better reconstruction and classification performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Introduction 3D shapes can be represented in a range of different for- mats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' On the Euclidean side, they may be represented as RGB-D images, multi-view images or volumetric data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' On the Non-Euclidean side, they may be represented as point clouds or meshes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' For computer vision tasks like classifi- cation, segmentation, or even generative tasks like shape reconstruction, the target 3D shape is usually converted into a latent representation first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Before the rise of deep learning [16], popular latent representations (or, 3D shape descriptors) were Laplacian spectral eigenvectors [36], or heat kernel sig- natures [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' With neural networks, the latent representation is usually the result of an encoder that reduces the 3D shape to a vector representation with fixed dimensionality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' (a) General pipeline for contrastive learning from augmented data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' (b) Pipeline for the proposed generative-contrastive learning from multi-modal input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Figure 1: An illustration of (a) a general pipeline of con- trastive learning methods and (b) our proposed generative contrastive learning pipeline for 3D shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' When multi-modal input data is available, the question arises how to use them jointly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' For 3D learning tasks, take 3D Euclidean data as an example, most state-of-the-art methods in computer vision that deal with both image and voxel grid input data either concatenate individual latent representations for supervised tasks [22], or use only one of them on the input and loss side separately [11, 40, 39, 45], or use them jointly but with pre-training and finetuning [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' We are interested in seeking a better self-supervised way for learning better latent representations for 3D volumetric shapes, with the additional input from other modalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='04612v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='CV] 11 Jan 2023 Encoder A Aug image1 Contrastive Loss Input image Encoder B Possible stop gradient on fixed branch Aug image2Reconstruction Loss Encoder A Voxel grid Contrastive Loss Decoder Input shape Encoder Voxel grid B Stop gradient on random branch Multi-view imagesApart from pretext tasks-based methods[14, 17], the other two main self-supervised learning ways are generative-based methods [1, 11] and contrastive-based methods [5, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' For 3D volumetric shapes, it is easy to implement a generative model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' But it is still an open question that how to do it in a contrastive way, let alone the combination of these two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' In a recent review paper of self-supervised learning [28], the au- thors argue that the only way of doing generative-contrastive learning is to train an encoder-decoder to generate synthetic samples and a discriminator to distinguish them from real samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' We disagree with this argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' In their definition, the discriminator is the contrastive part thus the model only focuses on negative pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' We think it is also possible to use or only use positive pairs, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' in our case, using multi- modalities from the same input shape for two branches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Figure 1 shows the main idea of our proposed generative- contrastive learning pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Compared to the existing con- trastive learning methods, our method shares some similari- ties with them while some significant differences also exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Similarities are: (i) we both use a two-branches scheme to encode two inputs that origin from the same ”raw data”;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' (ii) after getting encoded latent representations, we both compute a contrastive loss in the latent space;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' (iii) they use positive pairs for training (optionally with additional nega- tive pairs), we also use positive pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Differences are: (i) they use different augmented data from the ”raw data”, while we use different modalities from the ”raw data”;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' (ii) thus our network architectures of encoder A and B are not identi- cal, while theirs are identical mostly;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' (iii) we add a decoder part and a reconstruction loss;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' (iv) they possibly have stop gradient on one fixed branch, while we do stop gradient on random branch with a switching scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The main contributions of this paper are as follows: We propose a novel generative-contrastive learning pipeline for 3D volumetric shapes, which makes the joint training of encoders for multi-modal input data possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' With the switching scheme does the work of stopping gradient on random branch, model collapse is avoided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' End-to-end training is also possible without the require- ments of special pre-training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Better experimental results are achieved on both 3D shape reconstruction and classification tasks with our proposed model, compared to the results from the models which learn only on single-modal data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Using the voxel encoder as a self-supervised pre-trained feature extractor, we outperform 3D-GAN on the Model- Net40 classification task with a much shorter latent vector representations (128, compared to ca.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='5 million dimen- sions in 3D-GAN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The voxel encoder pre-trained on one single category still performs surprisingly well as a feature extractor on the full dataset with other categories during the testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Related Work Contrastive learning: The work of contrastive learning was pioneered by Yann LeCun’s group for face verification [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' This topic is getting more and more popular recently since people find self-supervised learning are important for feature extraction and we now have really mature deep learn- ing techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' SimCLR [5] proposes to use two identical encoders for two branches, both positive pairs and negative pairs are used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' MoCo [7] stops the gradient for the second branch, while using a momentum-based method to update the parameters of its encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' SwAV [2] proposes to use a memory bank to get negative pairs out of the batch, the contrastive loss in their case is computed after clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' For methods only use positive samples, BYOL [18] keeps the idea of momentum updating from MoCo, but adds an ad- ditional block in the first branch and only uses positive pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' SimSiam [8] reports an observation of competitive results may still be achieved when modifying BYOL by making two encoders identical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' A review of most relevant methods and their comparisons are given in [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Learning on 3D shapes with Euclidean data: For su- pervised tasks, VoxNet[30] is the pioneer to use 3D convo- lutional network to learn features from volumetric data for recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Its subsequent work of multi-level 3D CNN [13] learns multi-scale spatial features by considering mul- tiple resolutions of the voxel input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Qi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' [32] propose to use multi-resolution filtering in 3D for multi-view CNNs, as well as using subvolume supervision for auxiliary train- ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' FusionNet [22] fuses three networks together: two VoxNets[30] and one MVCNN[37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The three networks fuse at the score layers where a linear combination of scores is taken before the classification prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' For self-supervised tasks, ShapeNet [41] uses a reverse VoxNet to reconstruct 3D volumetric shapes from latent rep- resentations which are learned from depth maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The T-L network [15] combines a 3D autoencoder with an image re- gressor to encode a unified vector representation given a 2D image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Autoencoders have also been widely use for 3D shape retrieval in other papers [44, 46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Its variant, VAE, has been used in a similar way for 3D shape learning [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' View infor- mation from images has also been widely investigated for 3D shape reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Choy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' [11] proposed a framework named 3D-R2N2 to reconstruct 3D shapes from multi-view images by leveraging the power of recurrent neural networks [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' [33] also uses a recurrent-based approach, but taking depth images as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Some other methods use view infor- mation as auxiliary constraints [39, 45, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Method uses GAN for 3D volumetric shape generation has been proposed in [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Some other latest works [31, 27] have also used multi-modal input data for joint end-to-end training, but they did not use a switching scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' We are aware that there are lots of other works applying deep learning-based methods on other 3D Non-Euclidean 2 data formats, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' point clouds and meshes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' But they are out of the scope of this work and we would like to leave them for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Methodology 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Generative-Contrastive Learning Figure 1(b) shows the main idea of our proposed generative-contrastive learning pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Similar to most existing contrastive learning methods, we use an architecture with two encoder branches to compute a contrastive loss between the latent representations from each branch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The inputs to two branches are the voxel grid and the multi-view images of an identical 3D shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' A generative decoder part is added to compute the reconstruction loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The decoder is shared by two encoders and the two encoder branches are co-trained with the help of a switching scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' For contrastive learning methods, mode collapse is a big issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Possible ways of dealing with it are adding additional blocks for encoder A, or stop gradient for encoder B and update its parameters in a momentum way slowly along with the updated parameters in encoder A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' In our case, encoder A and B are already different network architectures thus the momentum method can not be applied, but we still managed to avoid model collapse successfully during the experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' We attribute this success to two things: the reconstruction loss, and the switching scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The reconstruction loss has a strong supervision over the representational capacity of latent representations, while the switching scheme does the work of stopping gradient on random branch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' To further improve the latent representations, Variational Autoencoders (VAE) [26] are used instead of vanilla autoen- coders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' In a VAE, each input is mapped to a multivariate normal distribution around a point in the latent space, which makes a continuous latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' A continuous latent space makes the smooth transition of 3D shapes possible with la- tent representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The learned features are usually more smooth and meaningful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Switch Encoding When dealing with multi-modal inputs, most state-of-the- art methods just encode them separately into latent repre- sentations and then perform concatenation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Unlike them, we propose to use a switching scheme in the latent space to jointly train both encoders with a shared decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' During the training, the switch is actuated for every training epoch with a preset probability to randomly select the encoded output from one encoder as the latent representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' This operation of switching between encoders continues during the whole end-to-end training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The decoder is tasked to reconstruct the voxel represen- tation of the 3D shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Since the switched encoders are trained concurrently for the same decoder, they are forced to produce “mutually compatible” latent representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The different input modalities result in different features that nat- urally emerge for the respective latent representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' For example, a voxel-based encoder is much more likely to gen- erate an “overall volume” feature (simply the number of filled voxels) compared to a multi-view image encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' By the cross-training with switched encoding, useful features for the latent representation can translate from one encoder to the other via the shared decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' This results in improved latent representations also for the individual encoder when just one input modality is used after the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Loss Functions The SwitchVAE loss functions consists of three parts: a reconstruction loss Lrecon, a KL divergence LKL between latent representations and the normal prior distribution, and a contrastive loss Lcontras between the latent representations from the different input formats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The overall network is parameterized by θ = (θvox, θimg, θd)⊤ for the voxel and image encoder and the voxel decoder respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The train- ing samples are denoted xα for the input α ∈ {img, vox}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The switch value for α is randomly selected prior to ev- ery training epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The latent representations resulting from the VAE encoders are (µα, σα) = eα(xα).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The latent representation is sampled for the current training epoch as zα ∼ N(µα, σα).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The decoder part is shared by both input modalities to reconstruct the voxel represen- tation ˆxα = d(zα).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Formally, the overall loss function decomposes into three terms Lθ(α, ximg, xvox) = Lrecon(xvox, ˆxα) + λKLLKL(µα, σα) + λcontrasLcontras(zimg, zvox) (1) with weights λKL and λcontras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' A modified Binary Cross Entropy (BCE) against the voxel ground truth is used for the reconstruction loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' To improve the training, modification has been made by the introduction of a hyper-parameter γ that weights the relative importance of false positives against false negatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The reconstructed voxels are indexed by k with value ˆxα k ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Lrecon(xvox, ˆxα) = � k � − γ · xvox k log(ˆxα k) − (1 − γ)(1 − xvox k ) log(1 − ˆxα k) � (2) We set the hyperparameter γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='8 during training for all of the experiments conducted in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' In the training of VAE, the Kullback-Leibler (KL) diver- gence is used between the actual distribution of latent vectors and the N(0, I) Gaussian distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Note that the latent representation has n dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' LKL(µ, σ) = −1 2 n � i=1 (1 + log(σ2 i ) − µ2 i − σ2 i ) (3) 3 Figure 2: The SwitchVAE architecture based on our pro- posed generative-contrastive learning pipeline, with more detail blocks illustrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' In order to further force a close distance between the latent representations learned from image and volumetric data with the SwitchVAE model, a contrastive loss between the encoders is proposed and used in the latent space during the training phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The contrastive loss is defined as the Euclidean distance between the latent vectors from images and volumetric data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Lcontras(zimg, zvox) = ∥zimg − zvox∥2 2 (4) Although in most other contrastive learning methods some different contrastive losses has been used, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' InfoNCE loss in SimCLR [5], we find that with latent representations normalized, our method can already yield satisfying results with a simple L2 Norm loss as the contrastive loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Experiments We use the 3D-R2N2 and ModelNet 10/40 datasets for our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The 3D-R2N2 dataset [11] is a subset with 13 categories from the ShapeNet dataset [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' It provides good quality rendered multi-view images alongside a class label and 32 × 32 × 32 voxel representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' We divide the 3D-R2N2 dataset into a training set of 29,599 samples and a test set of 7406 samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The ModelNet dataset [41] comes in two variations with either 10 or 40 classes of shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The ModelNet10 dataset contains 3991/908 training/test samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' ModelNet40 contains 9843/2468 training/test samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' For the SwitchVAE models, we use both a voxel and a multi-view image encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The decoder always reconstructs the voxel representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' During training for voxel test input, the switch layer randomly selects either the voxel encoder with a probability of 80%, or the multi-view image encoder with a probability of 20%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Concerning the other training parameters, we use a la- tent dimension of 128 for all experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The network parameters are trained by minimizing the loss function from Equation 1 using the SGD optimizer with a momentum of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='9 and Nesterov accelerated gradients [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The learning rate is 2 × 10−4 with a decay of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='96 per 10 epochs after the first 50 epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The batch size is 32 for all experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Training with multi-view image input uses 8 views for every sample as it has been reported in [11] and its subsequent works [42, 43] that the improvement from additional views is negligible after the first 6-10 views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Detailed Network Configuration Figure 2 shows based on our proposed generative- contrastive learning pipeline, how switched encoding is im- plemented for a VAE with multi-view images and voxel grids input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The encoder blocks of our SwitchVAE build on the idea of volumetric convolutional networks [41] for the voxel input, and 3D recurrent reconstruction neural networks [11] for the multi-view images input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' More detailed network configurations are given as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The image encoder of SwitchVAE learns the latent vector from multi-view images, and it is composed of a view feature embedding module and a view feature aggregator module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The view feature embedding module is a ResNet18 [21] whose weights are shared across all the views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The part with pre-trained weights map a single view 137 × 137 × 3 RGB image into 5 × 5 × 512 feature maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' We then flatten these feature maps and add a fully connected layer, which outputs a 1024 dimensional feature for a single view image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' For a 3D shape, 8 views of images are fed into the shared weights view feature embedding module while training, which outputs a 8 × 1024 view features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' For the view feature aggregator module, we firstly tried a max pooling as MVCNN [37], but it did not yield satisfying results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Same for average pooling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' To better aggregate the multi-view image features, we finally use the Gated Recurrent Unit (GRU) [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The view feature aggregator outputs a 1024 dimensional feature after aggregating features from all views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Then it is further fed into last fully connected layers to generate the mean and the variance of the latent vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' By using the reparametrization trick introduced in [25], the image encoder finally outputs a 128 dimensional sampled latent vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The voxel encoder is a 3D volumetric convolutional neu- ral network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The encoder has 4 convolutional layer and two fully connected layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' All convolutional layers use kernels of size 3 × 3 × 3, their strides are {1, 2, 1, 2} and channel numbers are {8, 16, 32, 64} respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' All layers use the exponential linear unit (eLu) as the activation function ex- cept for the last fully connected layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' This layer maps an shape of 32 × 32 × 32 voxels to a 343 dimensional feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The 343 dimensional feature is further fed into the last fully connected layers to generate the mean and the variance of the latent vector to finally produce a 128 dimensional sampled latent vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The decoder of SwitchVAE mirrors the voxel encoder, except that the last layer uses a sigmoid activation function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' 4 Image Encoder ResNet18 leal Switch ResNet18 View Feature Latent Vector Layer Aggregator variance ResNet18 Decoder .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='atent Vector Voxel Encoder SwitchVAEInput/GT Voxel VAE SwitchVAE (a) Reconstruction tests with voxel input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Input (2/8 views) GT Image VAE SwitchVAE (b) Reconstruction tests with image input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Figure 3: Some reconstruction results from different models with only voxel or multi-view images as the test input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Test Input Training Model Reconstruction Metrics IoU Precision Accuracy Image Image VAE 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='52% 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='21% 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='21% SwitchVAE (λcontras = 0) 56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='82% 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='72% 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='00% SwitchVAE (λcontras = 1) 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='75% 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='50% 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='32% Voxel Voxel VAE 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='86% 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='80% 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='01% SwitchVAE (λcontras = 0) 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='27% 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='04% 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='67% SwitchVAE (λcontras = 1) 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='93% 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='68% 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='22% Table 1: Reconstruction performance on the test set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Training and testing with the chair category from 3D-R2N2 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The decoder maps a 128 dimensional latent vector, which was randomly sampled in encoder, to a 32 × 32 × 32 vol- umetric reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' It represents the predicted voxel occupancy possibility of each voxel in the cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' 3D Shape Reconstruction We use Intersection-of-Union (IoU), precision, recall, and accuracy (referred as average precision in [15]) as the quantitative metrics for the reconstruction of 3D shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The threshold at which a voxel is considered as filled is at 50%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Similar to the last part, we show the results from only voxel input training, only image input training, and both input training with our SwitchVAE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Table 1 shows that the reconstruction performance of SwitchVAE is similar or slightly better to that of image/voxel VAEs, and it focuses more on making every predicted occu- pied voxel correct (higher precision score).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' This character- istic may be more clearly observed in some reconstruction results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Table 1 also shows that the contrastive loss term is the key in our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Figure 3 shows some qualitative re- construction results from our SwitchVAE model that trained on the chair category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Comparisons with the results from the networks that only use one input format for training are also presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' From the figure we can observe that Switch- VAE takes more attention on not occupying original negative voxels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' This is quite obvious from the third row of Figure 3(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Both Image VAE and SwitchVAE are not certain about the leg number of the office chair is 4 or 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The Image VAE decides to merge them all together, while SwitchVAE decides to only guess and occupy some voxels with small sub-clusters in that area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' 3D Shape Classification For the classification task, the networks are first trained to perform reconstruction of the ground-truth voxel repre- sentations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Then the encoder part of a trained network is 5 铺Training Dataset Test Input Training Model Classification Accuracy ModelNet40 ModelNet10 Chair Category Multi-view images Image VAE 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='28% 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='36% SwitchVAE 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='07% 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='26% Voxel data Voxel VAE 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='19% 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='38% SwitchVAE 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='60% 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='05% ModelNet40 Multi-view images Image VAE 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='06% 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='62% SwitchVAE 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='87% 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='96% Voxel data Voxel VAE 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='12% 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='95% SwitchVAE 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='01% 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='07% Table 2: Classification accuracy on the ModelNet40/ModelNet10 classification tasks with models trained with Image VAE, Voxel VAE, and SwitchVAE on the chair category or on the full ModelNet40 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Supervision Method Data Modality Classification Accuracy ModelNet40 ModelNet10 Supervised 3D ShapNets [41] Voxels 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='30% 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='30% VoxNet [30] Voxels 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='00% 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='00% MVCNN [37] Images 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='10% FusionNets [22] Images, Voxels 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='80% 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='11% 3D2SeqViews [20] Images 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='40% 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='71% VRN Ensemble [1] Voxels 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='54% 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='14% Self-supervised LFD [4] Images 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='50% 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='90% T-L Network [15] Images, Voxels 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='40% VConv-DAE [35] Voxels 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='50% 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='50% 3D GAN [40] Voxels 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='30% 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='00% SwitchVAE (trained on only chair category) Images, Voxels 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='60% 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='05% SwitchVAE (trained on ModelNet40 dataset) Images, Voxels 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='01% 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='07% Table 3: Classification accuracy on the ModelNet40/ModelNet10 dataset with different methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Results from methods that only used images and/or voxels are listed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Note that our latent representations are only of 128 dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' used to produce latent representations of 128 dimensions as input for classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' An SVM with RBF kernel and hyper- parameter γ = 1/128 is trained on the latent representations to perform classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Same samples were used to train the networks for latent representations and the SVM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The evaluation of the SVM is performed with samples that were neither used to train the networks nor the SVM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Table 2 shows the impact of switched training on the ModelNet 10/40 classification tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' To make it more clear, let’s take the voxel data testings as an example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' During the training phase, a voxel VAE only trains on the voxel train set data, while a SwitchVAE trains on both the voxel train set data and the correspondent multi-view images train set data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' During the testing phase, only the identical voxel test set data is given to the trained voxel VAE model and the trained SwitchVAE model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Latent representations of those 3D shapes (from voxel test set) obtained from the Switch- VAE model always outperform that from the vanilla voxel VAE in the ModelNet classification tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Note that no multi- view images data of the test set is needed for SwitchVAE during the testings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' From Table 2, we can clearly observe that under the condition of same training dataset and test input, the results from SwitchVAE are better than the results from the image VAE or the voxel VAE in most cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Note that they are even trained with a same number of epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' This means by using the data of other format in the training phase, during the testing phase, the classification perfor- mance has been improved compared to the models that only use single format for the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' In conclusion, better latent representations have been learned for 3D shapes by using “data you don’t have” (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' data input formats that are not used for the evaluation once the network is trained).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Table 3 lists the classification result in comparison to other network architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Compared to most other unsu- pervised learning method, we achieve better classification performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Comparing to 3D-GAN, we outperform it on 6 (a) Voxel VAE, trained on ModelNet10 (b) SwitchVAE (λcontras = 0), trained on ModelNet10 (c) SwitchVAE (λcontras = 1), trained on ModelNet10 (d) SwitchVAE (λcontras = 1), trained on 3D-R2N2 dataset Figure 4: t-SNE plots of the latent representations for Mod- elNet10 shapes (10 categories) with (a) a vanilla voxel VAE model trained on ModelNet10 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' (b) a Switch- VAE model without contrastive loss trained on ModelNet10 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' (c) a SwitchVAE model with contrastive loss trained on ModelNet10 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' (d) a SwitchVAE model with con- trastive loss trained on the full 3D-R2N2 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Each color represents one category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' All latent representations used for the plots use voxel data from the testing set as test input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' the ModelNet40 classification task and achieve competitive performance on the ModelNet10 classification task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' How- ever, our method uses a much smaller latent vector of only 128 dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' 3D-GANs use all features maps in the last three convolution layers, which makes the presentation for each 3D shape a 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='5 million dimensional vector as input for the classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' t-SNE Visualization: In order to visualize the learned latent representations, we use t-SNE [29] to map the latent representations to a 2D plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Figure 4 gives the visualiza- tion results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' we use ModelNet10 for most t-SNE visualiza- tion experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Comparing Figure 4(a) and Figure 4(b), we can observe that the switching scheme contributes to the inter-category classification while makes the intra-category clustering a bit fuzzy (all categories are a bit far from each other, while each category itself is a bit less clustered).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Com- paring Figure 4(b) and Figure 4(c), we can observe that adding the contrastive loss term to SwitchVAE helps to the (a) Top Row: Trained on SwitchVAE, the ”chair arm” feature and the “size” feature are entangled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Middle and Bottom Row: Trained on Switch-BetaTCVAE with β = 5, the “chair arm” feature and the “size” feature are more disentangled, changing one feature does not impact the other one too much.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' (b) Top Row: Trained on SwitchVAE, changing the “chair leg type” feature also leads to the morphing of the top part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Bottom Row: Trained on Switch-BetaTCVAE with β = 5, the top part stays more fixed while changing the “chair leg type” feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Figure 5: Disentangling latent features with Beta-TCVAE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' intra-category clustering, making the performance of the whole classification task mush better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Comparing Figure 4(c) and Figure 4(d), we can observe that with a larger train- ing dataset, even better feature clustering results may be achieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The increased gaps between different categories can be clearly observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Exploring Latent Representations This subsection showcases some qualitative results to give indication that SwitchVAE training results in a superior latent representation that allows for better disentanglement between categories, as well as between the salient features of the 3D shapes in each category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Latent space interpolation: Similar to as most 3D re- construction papers, we also do the inter-class interpolation with our trained models as shown in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' It can be ob- served that our proposed method has the ability to do smooth transition between two shapes, even if they are from different categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Shape arithmetic: Another way to explore the learned latent representations is to perform arithmetic operations in the latent space whilst observing their effect on the recon- structed geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' We show some shape arithmetic results in Figure 7 with a model trained on the full 3D-R2N2 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The model seems to capture the underline information and is capable of generating meaningful combined shapes that 7 Figure 6: Shape interpolation between different categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' (a) Shape arithmetic example with chair objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' (b) Shape arithmetic example with table objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Figure 7: Shape arithmetic for chairs and tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' (a) Adding chair arms to chair objects in the latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' (b) Adding a middle layer to table objects in the latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' do not occur as 3D shapes in the original dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Feature disentanglement with VAE variations: One good thing with VAE models is that the latent space learned from it is more ”meaningful” comparing to that from GAN models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' By tuning the value in one specific latent dimension, one can observe certain features on the output side changing smoothly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' However, for most features, they get entangled in multiple latent dimensions with the vanilla VAE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' It has been reported that β-VAE [23] and β-TCVAE [6] can producing better disentangled features in the latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' We merge it with our proposed method into SwitchBTCVAE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' We train our model with β = 5 on the chair category with a same number of epochs as the other experiments shown in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Although a small decrease on the reconstruction performance metrics is observed, by investigating the learned latent representations, we find that some features have been better disentangled as shown in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Conclusion and Outlook In this paper, we propose a generative-contrastive learn- ing pipeline for learning better latent representations for 3D volumetric shapes, with the help of additional modal- ity input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' The switching scheme makes the joint training for both encoders possible with competitive reconstruction results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Classification experiments on ModelNet have also been carried out to validate the effectiveness of the proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' Improved classification results indicate that better latent representations have been learned with our proposed SwitchVAE architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' For future directions, other 3D data modalities, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=', point clouds and meshes may also be used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' A new contrastive loss may be designed and an optimal switching policy may be studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' More researches may be conducted to make the latent presentations more feature disentangled or more interpretable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' In our experiments, although an additional contrastive loss has been applied, we still observe large dis- tances between latent representations generated from the different input formats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydE3T4oBgHgl3EQfmApc/content/2301.04612v1.pdf'} +page_content=' An understanding how to force a close distance between representations without leading to a collapse from an increased contrastive loss would lead to more insight into contrastive learning itself.' metadata={'source': 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